title: Implementation of the Five Qubit Error Correction Benchmark

abstract:
  The smallest quantum code that can correct all one-qubit errors is based on
five qubits. We experimentally implemented the encoding, decoding and
error-correction quantum networks using nuclear magnetic resonance on a five
spin subsystem of labeled crotonic acid. The ability to correct each error was
verified by tomography of the process. The use of error-correction for
benchmarking quantum networks is discussed, and we infer that the fidelity
achieved in our experiment is sufficient for preserving entanglement.


title:
Formation and Dynamics of a Schr\"odinger-Cat State in Continuous
  Quantum Measurement

abstract:
  We consider the process of a single-spin measurement using magnetic resonance
force microscopy (MRFM) as an example of a truly continuous measurement in
quantum mechanics. This technique is also important for different applications,
including a measurement of a qubit state in quantum computation. The
measurement takes place through the interaction of a single spin with a
quasi-classical cantilever, modeled by a quantum oscillator in a coherent state
in a quasi-classical region of parameters. The entire system is treated
rigorously within the framework of the Schr\"odinger equation, without any
artificial assumptions. Computer simulations of the spin-cantilever dynamics,
where the spin is continuously rotated by means of cyclic adiabatic inversion,
show that the cantilever evolves into a Schr\"odinger-cat state: the
probability distribution for the cantilever position develops two asymmetric
peaks that quasi-periodically appear and vanish. For a many-spin system our
equations reduce to the classical equations of motion, and we accurately
describe conventional MRFM experiments involving cyclic adiabatic inversion of
the spin system. We surmise that the interaction of the cantilever with the
environment would lead to a collapse of the wave function; however, we show
that in such a case the spin does not jump into a spin eigenstate.


title: Cavity-damping-induced transitions in a driven atom-cavity system

abstract:
  We investigate the fluorescence spectrum of a two-level atom in a cavity when
the atom is driven by a classical field. We show that forbidden dipole
transitions in the Jaynes-Cummings Ladder structure are induced in the presence
of the cavity damping, which deteriorates the degree of otherwise perfect
destructive interference among the transition channels. With the larger cavity
decay, these transitions are more enhanced.


title: Zeno dynamics yields ordinary constraints

abstract:
  The dynamics of a quantum system undergoing frequent measurements (quantum
Zeno effect) is investigated. Using asymptotic analysis, the system is found to
evolve unitarily in a proper subspace of the total Hilbert space. For spatial
projections, the generator of the "Zeno dynamics" is the Hamiltonian with
Dirichlet boundary conditions.

categories: quant-ph cond-mat.mes-hall cond-mat.stat-mech math-ph math.MP physics.atom-ph


title: Non-adiabatic conditional geometric phase shift with NMR

abstract:
  Conditional geometric phase shift gate, which is fault tolerate to certain
errors due to its geometric property, is made by NMR technique recently under
adiabatic condition. By the adiabatic requirement, the result is inexact unless
the Hamiltonian changes extremely slowly in the process. However, in quantum
computation, everything has to be completed within the decoherence time. High
running speed of every gate in quantum computation is demanded because the
power of quantum computer can be exponentially proportional to the maximum
number of logic gate operation that can be taken sequentially within the
decoherence time. Adiabatic condition makes any fast conditional Berry
phase(cyclic adiabatic geometric phase) shift gate impossible. Here we show
that by using a new designed sequence of simple operations with an additional
vertical magnetic field, the conditional geometric phase shift can be done
non-adiabatically. Therefore geometric quantum computation can be done in the
same speed level of usual quantum computation.


title: Quantum effects after decoherence in a quenched phase transition

abstract:
  We study a quantum mechanical toy model that mimics some features of a
quenched phase transition. Both by virtue of a time-dependent Hamiltonian or by
changing the temperature of the bath we are able to show that even after
classicalization has been reached, the system may display quantum behaviour
again. We explain this behaviour in terms of simple non-linear analysis and
estimate relevant time scales that match the results of numerical simulations
of the master-equation. This opens new possibilities both in the study of
quantum effects in non-equilibrium phase transitions and in general
time-dependent problems where quantum effects may be relevant even after
decoherence has been completed.


title:
Continued fraction representation of quantum mechanical Green's
  operators

abstract:
  In this work we have presented a rather general and easy-to-apply method for
discrete Hilbert space representation of quantum mechanical Green's operators.
We have shown that if in some discrete Hilbert space basis representation the
Hamiltonian takes an infinite symmetric tridiagonal, i.e. Jacobi-matrix form
the corresponding Green's matrix can be calculated on the whole complex energy
plane by a continued fraction. The procedure necessitates only the analytic
calculation of the Hamiltonian matrix elements, which are used to construct the
coefficients of the continued fraction. This continued fraction representation
of the Green's operator was shown to be convergent for the bound state energy
region. The theory of analytic continuation of continued fractions was utilized
to extend the representation to the whole complex energy plane. The presented
method provides a simple, easily applicable and analytically correct recipe for
calculating discrete basis representation of Green's operators.


title: Individual consistency of 2-events quantum histories

abstract:
  We introduce a new notion of consistency for 2-events quantum histories,
based on the concept of mirror projection. Contrary to all notions of
consistency so far introduced, our consistency, named self-decoherence, is an
individual property, i.e., it can be attributed to every single sample of the
physical system. Furthermore, self-decoherence forbids contrary inferences.


title:
A Concentration/Purification Scheme for Two Partially Entangled Photon
  Pairs

abstract:
  An experimental scheme for concentrating entanglement in partially entangled
photon pairs is proposed. In this scheme, two separated parties obtain one
maximally entangled photon pair from previously shared two partially entangled
photon pairs by local operations and classical communication. A practical
realization of the proposed scheme is discussed, which uses imperfect photon
detectors and spontaneous parametric down-conversion as a photon source. This
scheme also works for purifying a class of mixed states.


title:
Efficient quantum key distribution scheme with nonmaximally entangled
  states

abstract:
  We propose an efficient quantum key distribution scheme based on
entanglement. The sender chooses pairs of photons in one of the two equivalent
nonmaximally entangled states randomly, and sends a sequence of photons from
each pair to the receiver. They choose from the various bases independently but
with substantially different probabilities, thus reducing the fraction of
discarded data, and a significant gain in efficiency is achieved. We then show
that such a refined data analysis guarantees the security of our scheme against
a biased eavesdropping strategy.


title: Quantum Zeno effects with "pulsed" and "continuous" measurements

abstract:
  The dynamics of a quantum system undergoing measurements is investigated.
Depending on the features of the interaction Hamiltonian, the decay can be
slowed (quantum Zeno effect) or accelerated (inverse quantum Zeno effect), by
changing the time interval between successive (pulsed) measurements or,
alternatively, by varying the "strength" of the (continuous) measurement.


title: A method for collective excitation of Bose-Einstein condensate

abstract:
  It is shown that by an appropriate modification of the trapping potential one
may create collective excitation in cold atom Bose-Einstein condensate. The
proposed method is complementary to earlier suggestions. It seems to be
feasible experimentally --- it requires only a proper change in time of the
potential in atomic traps, as realized in laboratories already.


title: Entanglement between motional states of a single trapped ion and light

abstract:
  We propose a generation method of Bell-type states involving light and the
vibrational motion of a single trapped ion. The trap itself is supposed to be
placed inside a high-$Q$ cavity sustaining a single mode, quantized
electromagnetic field. Entangled light-motional states may be readily generated
if a conditional measurement of the ion's internal electronic state is made
after an appropriate interaction time and a suitable preparation of the initial
state. We show that all four Bell states may be generated using different
motional sidebands (either blue or red), as well as adequate ionic relative
phases.


title: The Principles of Gauging

abstract:
  The aim of this paper is twofold: First, to present an examination of the
principles underlying gauge field theories. I shall argue that there are two
principles directly connected to the two well-known theorems of Emmy Noether
concerning global and local symmetries of the free matter-field Lagrangian, in
the following referred to as "conservation principle" and "gauge principle".
Since both these express nothing but certain symmetry features of the free
field theory, they are not sufficient to derive a true interaction coupling to
a new gauge field. For this purpose it is necessary to advocate a third, truly
empirical principle which may be understood as a generalization of the
equivalence principle. The second task of the paper is to deal with the
ontological question concerning the reality status of gauge potentials in the
light of the proposed logical structure of gauge theories. A nonlocal
interpretation of topological effects in gauge theories and, thus, the
non-reality of gauge potentials in accordance with the generalized equivalence
principle will be favoured.


title:
Comment on "Maximum likelihood reconstruction of CP maps",
  quant-ph/0009104

abstract:
  The treatment proposed by Sacchi quant-ph/0009104 does not represent correct
solution, since the necessary conditions on CP maps are not guaranteed.


title: Quantum cobwebs: Universal entangling of quantum states

abstract:
  Entangling an unknown qubit with one type of reference state is generally
impossible. However, entangling an unknown qubit with two types of reference
states is possible. To achieve this, we introduce a new class of states called
zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and
study their salient features. Using shared-ZSA state, local operation and
classical communication we give a protocol for creating multipartite entangled
states of an unknown quantum state with two types of reference states at remote
places. This provides a way of encoding an unknown pure qubit state into a
multiqubit entangled state. We quantify the amount of classical and quantum
resources required to create universal entangled states. This is possibly a
strongest form of quantum bit hiding with multiparties.


title:
New Tests of Macroscopic Local Realism using Continuous Variable
  Measurements

abstract:
  We show that quantum mechanics predicts an Einstein-Podolsky-Rosen paradox
(EPR), and also a contradiction with local hidden variable theories, for photon
number measurements which have limited resolving power, to the point of
imposing an uncertainty in the photon number result which is macroscopic in
absolute terms. We show how this can be interpreted as a failure of a new, very
strong premise, called macroscopic local realism. We link this premise to the
Schrodinger-cat paradox. Our proposed experiments ensure all fields incident on
each measurement apparatus are macroscopic. We show that an alternative
measurement scheme corresponds to balanced homodyne detection of quadrature
phase amplitudes. The implication is that where either EPR correlations or
failure of local realism is predicted for continuous variable (quadrature phase
amplitude) measurements, one can perform a modified experiment which would lead
to conclusions about the much stronger premise of macroscopic local realism.


title: Quantum state reconstruction of the single-photon Fock state

abstract:
  We have reconstructed the quantum state of optical pulses containing single
photons using the method of phase-randomized pulsed optical homodyne
tomography. The single-photon Fock state |1> was prepared using conditional
measurements on photon pairs born in the process of parametric down-conversion.
A probability distribution of the phase-averaged electric field amplitudes with
a strongly non-Gaussian shape is obtained with the total detection efficiency
of (55+-1)%. The angle-averaged Wigner function reconstructed from this
distribution shows a strong dip reaching classically impossible negative values
around the origin of the phase space.


title:
Proposal to test quantum mechanics against macroscopic realism using
  continuous variable entanglement: a definitive signature of a Schr\"odinger
  cat

abstract:
  In the Schr\"odinger-cat gedanken experiment a cat is in a quantum
superposition of two macroscopically distinct states, alive and dead.The
paradoxical interpretation of quantum mechanics is that the cat is not in one
state or the other, alive or dead, immediately prior to its measurement.
Because of this apparent defiance of macroscopic reality, quantum
superpositions of states macroscopically distinct have generated much interest.
Here we address the issue of proving a contradiction with macroscopic reality
objectively, through the testable predictions of quantum mechanics. We consider
the premises of macroscopic reality (that the ``cat'' is either ``dead'' or
``alive'', the measurement indicating which) and macroscopic locality (that
simultaneous measurements some distance away cannot induce the macroscopic
change, ``dead'' to ``alive'' and vice versa, to the ``cat''). The predictions
of quantum mechanics for certain states, generated using states exhibiting
continuous variable entanglement, are shown to be incompatible with the
predictions of all theories based on this dual premise. Our proof is along the
lines of Bell's theorem, but where all relevant measurements give
macroscopically distinct results.


title: Two-particle correlations via quasi-deterministic analyzer model

abstract:
  We introduce a quasi-deterministic eigenstate transition model of analyzers
in which the final eigenstate is selected by initial conditions. We combine
this analyzer model with causal spin coupling to calculate both proton-proton
and photon-photon correlations, one particle pair at a time. The calculated
correlations exceed the Bell limits and show excellent agreement with the
measured correlations of [M. Lamehi-Rachti and W. Mittig, Phys. Rev. D 14 (10),
2543 (1976)] and [ A. Aspect, P. Grangier and G. Rogers, Phys. Rev. Lett. 49 91
(1982)] respectively. We discuss why this model exceeds the Bell type limits.


title: A Lecture on Quantum Logic Gates

abstract:
  In this note we make a short review of constructions of n-repeated controlled
unitary gates in quantum logic gates.


title: Enhanced absorption Hanle effect on the Fg=F->Fe=F+1 closed transitions

abstract:
  We analyse the Hanle effect on a closed $F_g\to F_e=F_g+1$ transition. Two
configurations are examined, for linear- and circular-polarized laser
radiation, with the applied magnetic field collinear to the laser light
wavevector. We describe the peculiarities of the Hanle signal for
linearly-polarized laser excitation, characterized by narrow bright resonances
at low laser intensities. The mechanism behind this effect is identified, and
numerical solutions for the optical Bloch equations are presented for different
transitions.


title:
Mesoscopic superpositions of vibronic collective states of N trapped
  ions

abstract:
  We propose a scalable procedure to generate entangled superpositions of
motional coherent states and electronic states in N trapped ions. Beyond their
fundamental importance, these states may be of interest for quantum information
processing and may be used in experimental studies of decoherence.


title:
Universal quantum computation with spin-1/2 pairs and Heisenberg
  exchange

abstract:
  An efficient and intuitive framework for universal quantum computation is
presented that uses pairs of spin-1/2 particles to form logical qubits and a
single physical interaction, Heisenberg exchange, to produce all gate
operations. Only two Heisenberg gate operations are required to produce a
controlled pi-phase shift, compared to 19 for exchange-only proposals employing
three spins. Evolved from well-studied decoherence-free subspaces, this
architecture inherits immunity from collective decoherence mechanisms. The
simplicity and adaptability of this approach should make it attractive for
spin-based quantum computing architectures.


title: Prospects for a Quantum Dynamic Random Access Memory (Q-DRAM)

abstract:
  Compared to quantum logic gates, quantum memory has received far less
attention. Here, we explore the prognosis for a solid-state, scalable quantum
dynamic random access memory (Q-DRAM), where the qubits are encoded by the spin
orientations of single quantons in exchange-decoupled quantum dots. We address,
in particular, various possibilities for implementing refresh cycles.


title:
On the Coulomb Sturmian matrix elements of relativistic Coulomb Green's
  operators

abstract:
  The Hamiltonian of the radial Coulomb Klein-Gordon and second order Dirac
equations are shown to possess an infinite symmetric tridiagonal matrix
structure on the relativistic Coulomb Sturmian basis. This allows us to give an
analytic representation for the corresponding Coulomb Green's operators in
terms of continued fractions. The poles of the Green's matrix reproduce the
exact relativistic hydrogen spectrum.


title: Quantum information processing: A linear systems perspective

abstract:
  In this paper a system-oriented formalism of Quantum Information Processing
is presented. Its form resembles that of standard signal processing, although
further complexity is added in order to describe pure quantum-mechanical
effects and operations. Examples of the application of the formalism to quantum
time evolution and quantum measurement are given.


title: Quantum Information Theory - an Invitation

abstract:
  We give a non-technical introduction of the basic concepts of Quantum
Information Theory along the distinction between possible and impossible
machines. We then proceed to describe the mathematical framework of Quantum
Information Theory. The capacities of a quantum channel for classical and for
quantum information are defined in a unified scheme, and a mathematical
characterization of all teleportation and dense coding schemes is given.


title:
What the liar paradox can reveal about the quantum logical structure of
  our minds

abstract:
  In human consciousness perceptions are distinct or atomistic events despite
being perceived by an apparently undivided inner observer. This paper applies
both classical (Boolean) and quantum logic to analysis of the Liar paradox
which is taken as a typical example of a self-referential negation in the
perception space of an undivided observer. The conception of self-referential
paradoxes is a unique ability of the human mind still lacking an explanation on
the basis of logic. It will be shown that both classical and quantum logics
fail to resolve the paradox because of the particle-like (atomistic) nature of
physical events in the moments of perception. I suggest a physical mechanism
that can deal with our experience of self-referential paradox. Because it is
also shown that this cannot be achieved by any previously suggested classical
or quantum mechanical operation, the newly proposed mechanism provides a better
model than others for an important aspect of the structure of our minds.


title:
Ground state of antiferromagnetic ordering in fullerene $C_{60}$
  molecule

abstract:
  Theoretical study of mutual orientation of fullerene $C_{60}$ molecule atom
spins is presented in this work. Spin-spin interaction was described by
Habbard's model. Existence of antiferromagnetic sturcture of spin sub-system in
ground state is found.


title: Universal unitary gate for single-photon 2-qubit states

abstract:
  Upon entangling a spatial binary alternative of a photon with its
polarization, one can use single photons to study arbitrary 2-qubit states.
Sending the photon through a Mach-Zehnder interferometer, equipped with sets of
wave plates that change the polarization, amounts to performing a unitary
transformation on the 2-qubit state. We show that any desired unitary gate can
be realized by a judicious choice of the parameters of the set-up and discuss a
number of applications. They include the diagnosis of an unknown 2-qubit state,
an optical Grover search, and the realization of a thought experiment invented
by Vaidman, Aharonov, and Albert.


title: The mean king's problem: Spin 1

abstract:
  We show how one can ascertain the values of four mutually complementary
observables of a spin-1 degree of freedom.


title: Secure communication with single-photon two-qubit states

abstract:
  We propose a cryptographic scheme that is deterministic: Alice sends single
photons to Bob, and each and every photon detected supplies one key bit -- no
photon is wasted. This is in marked contrast to other schemes in which a random
process decides whether the next photon sent will contribute to the key or not.
The determinism is achieved by preparing the photons in two-qubit states,
rather than the one-qubit states used in conventional schemes. In particular,
we consider the realistic situation in which one qubit is the photon
polarization, the other a spatial alternative. Further, we show how one can
exploit the deterministic nature for direct secure communication, that is:
without the need for establishing a shared key first.


title: Casimir force between partially transmitting mirrors

abstract:
  The Casimir force can be understood as resulting from the radiation pressure
exerted by the vacuum fluctuations reflected by boundaries. We extend this
local formulation to the case of partially transmitting boundaries by
introducing reflectivity and transmittivity coefficients obeying conditions of
unitarity, causality and high frequency transparency. We show that the
divergences associated with the infiniteness of the vacuum energy do not appear
in this approach. We give explicit expressions for the Casimir force which hold
for any frequency dependent scattering and any temperature. The corresponding
expressions for the Casimir energy are interpreted in terms of phase shifts.
The known results are recovered at the limit of a perfect reflection.


title: Fluctuations and dissipation for a mirror in vacuum

abstract:
  A mirror in the vacuum is submitted to a radiation pressure exerted by
scattered fields. It is known that the resulting mean force is zero for a
motionless mirror, but not for a mirror moving with a non-uniform acceleration.
We show here that this force results from a motional modification of the field
scattering while being associated with the fluctuations of the radiation
pressure on a motionless mirror. We consider the case of a scalar field in a
two-dimensional spacetime and characterize the scattering upon the mirror by
frequency dependent transmissivity and reflectivity functions obeying
unitarity, causality and high frequency transparency conditions. We derive
causal expressions for dissipation and fluctuations and exhibit their relation
for any stationary input. We recover the known damping force at the limit of a
perfect mirror in vacuum. Finally, we interpret the force as a mechanical
signature of the squeezing effect associated with the mirror's motion.


title: Motional Casimir force

abstract:
  We study the situation where two point like mirrors are placed in the vacuum
state of a scalar field in a two-dimensional spacetime. Describing the
scattering upon the mirrors by transmittivity and reflectivity functions
obeying unitarity, causality and high frequency transparency conditions, we
compute the fluctuations of the Casimir forces exerted upon the two motionless
mirrors. We use the linear response theory to derive the motional forces
exerted upon one mirror when it moves or when the other one moves. We show that
these forces may be resonantly enhanced at the frequencies corresponding to the
cavity modes. We interpret them as the mechanical consequence of generation of
squeezed fields.


title:
Quantum State Tomography of Complex Multimode Fields using Array
  Detectors

abstract:
  We demonstrate that it is possible to use the balanced homodyning with array
detectors to measure the quantum state of correlated two-mode signal field. We
show the applicability of the method to fields with complex mode functions,
thus generalizing the work of Beck (Phys. Rev. Letts. 84, 5748 (2000)) in
several important ways. We further establish that, under suitable conditions,
array detector measurements from one of the two outputs is sufficient to
determine the quantum state of signals. We show the power of the method by
reconstructing a truncated Perelomov state which exhibits complicated structure
in the joint probability density for the quadratures.


title: Maximum-likelihood method in quantum estimation

abstract:
  The maximum-likelihood method for quantum estimation is reviewed and applied
to the reconstruction of density matrix of spin and radiation as well as to the
determination of several parameters of interest in quantum optics.


title:
Rapid and slow decoherence in conjunction with dissipation in a system
  of two-level atoms

abstract:
  We investigate the time evolution of a superposition of macroscopically
distinct quantum states in a system of two-level atoms interacting with a
thermal environment of photon modes. We show that the atomic coherent states
are robust against decoherence, therefore we call their superpositions atomic
Schr\"{o}dinger cat states. The initial fast regime of the time evolution is
associated with the process of decoherence, and it is directed towards the
statistical mixture of the constituent coherent states of the original state
for most of the initial conditions. However, certain superpositions, called
symmetric, exhibit exceptionally slow decoherence. By introducing a new
measure, we generalize the usual decoherence scheme regarding the evolution of
the state to account also for the symmetric case. To stress the fact that the
environment preserves symmetric superpositions much longer than the other
ones,we present Wigner function images of the decoherence of a suitably
oriented four component cat state.


title: Quasi Exactly Solvable NxN-Matrix Schroedinger Operators

abstract:
  New examples of matrix quasi exactly solvable Schroedinger operators are
constructed. One of them constitutes a matrix generalization of the quasi
exactly solvable anharmonic oscillator, the corresponding invariant vector
space is constructed explicitely. Also investigated are matrix generalizations
of the Lame equation.


title:
High efficiency entangled photon pair collection in type II parametric
  fluorescence

abstract:
  We report on a method for optimizing the collection of entangled photon pairs
in type-II parametric fluorescence. With this technique, we detected 360000
polarization-entangled photon pairs per second in the near-IR region in
single-mode optical fibers. The entanglement of the photon pairs was verified
by measuring polarization correlations in different bases of at least 96%.


title: Transient QED effects in absorbing dielectrics

abstract:
  The spontaneous emission rate of a radiating atom reaches its
time-independent equilibrium value after an initial transient regime. In this
paper we consider the associated relaxation effects of the spontaneous decay
rate of atoms in dispersive and absorbing dielectric media for atomic
transition frequencies near material resonances. A quantum mechanical
description of such media is furnished by a damped-polariton model, in which
absorption is taken into account through coupling to a bath. We show how all
field and matter operators in this theory can be expressed in terms of the bath
operators at an initial time. The consistency of these solutions for the field
and matter operators are found to depend on the validity of certain velocity
sum rules. The transient effects in the spontaneous decay rate are studied with
the help of several specific models for the dielectric constant, which are
shown to follow from the general theory by adopting particular forms of the
bath coupling constant.


title:
Classical and Quantum Action-Phase Variables for Time-Dependent
  Oscillators

abstract:
  For a time-dependent classical quadratic oscillator we introduce pairs of
real and complex invariants that are linear in position and momentum. Each pair
of invariants realize explicitly a canonical transformation from the phase
space to the invariant space, in which the action-phase variables are defined.
We find the action operator for the time-dependent oscillator via the
classical-quantum correspondence. Candidate phase operators conjugate to the
action operator are discussed, but no satisfactory ones are found.


title: 100 Years of the Quantum

abstract:
  As quantum theory celebrates its 100th birthday, spectacular successes are
mixed with outstanding puzzles and promises of new technologies. This article
reviews both the successes of quantum theory and the ongoing debate about its
consequences for issues ranging from quantum computation to consciousness,
parallel universes and the nature of physical reality. We argue that modern
experiments and the discovery of decoherence have have shifted prevailing
quantum interpretations away from wave function collapse towards unitary
physics, and discuss quantum processes in the framework of a tripartite
subject-object-environment decomposition. We conclude with some speculations on
the bigger picture and the search for a unified theory of quantum gravity.


title:
Normal ordering solution to quantum dissipation and its induced
  decoherence

abstract:
  We implement the normal ordering technique to study the quantum dissipation
of a single mode harmonic oscillator system. The dynamic evolution of the
system is investigated for a reasonable initial state by solving the
Schr\"{o}dinger equation directly through the normal ordering technique. The
decoherence process of the system for the cases $T=0K$ and $T\neq0K$ is
investigated as an application.


title: Quantum cryptography without a quantum channel

abstract:
  This paper has been withdrawn by the authors because the results obtained
have been reported earlier by other authors.


title: Causality, stability and passivity for a mirror in vacuum

abstract:
  The mean force exerted upon a perfect mirror moving in vacuum in a two
dimensional spacetime has the same expression as the radiation reaction force
computed in classical electron theory. It follows that unacceptable runaway
solutions are predicted. We show that this instability problem does not appear
when partially transmitting mirrors are studied. The mechanical impedance
describing the mirror coupled to vacuum radiation pressure is computed
explicitly; recoil is neglected. It is found to be a passive function, so that
stability is ensured. This is connected to the fact that no energy can be
extracted from the vacuum state.


title: Friction and inertia for a mirror in a thermal field

abstract:
  The force experienced by a mirror moving in vacuum vanishes in the case of
uniform velocity or uniform acceleration, as a consequence of spatial
symmetries of vacuum. These symmetries do not subsist in a thermal field. We
give a general expression of the corresponding viscosity coefficient valid at
any temperature and for any reflectivity function. We show that the computed
motional force also contains a non vanishing inertial term. The associated mass
correction goes to zero in the limiting cases of perfect reflection or of zero
temperature.


title: Inertia of Casimir energy

abstract:
  Moving mirrors are submitted to reaction forces by vacuum fields. The
motional force is known to vanish for a single mirror uniformly accelerating in
vacuum. We show that inertial forces (proportional to accelerations) arise in
the presence of a second scatterer, exhibiting properties expected for a
relative inertia: the mass corrections depend upon the distance between the
mirrors, and each mirror experiences a force proportional to the acceleration
of the other one. When the two mirrors move with the same acceleration, the
mass correction obtained for the cavity represents the contribution to inertia
of Casimir energy. Accounting for the fact that the cavity moves as a stressed
rigid body, it turns out that this contribution fits Einstein's law of inertia
of energy.


title: Driven Rydberg atoms reveal quartic level repulsion

abstract:
  The dynamics of Rydberg states of a hydrogen atom subject simultaneously to
uniform static electric field and two microwave fields with commensurate
frequencies is considered in the range of small fields amplitudes. In the
certain range of the parameters of the system the classical secular motion of
the electronic ellipse reveals chaotic behavior. Quantum mechanically, when the
fine structure of the atom is taken into account, the energy level statistics
obey predictions appropriate for the symplectic Gaussian random matrix
ensemble.


title: Violations of local realism with quNits up to N=16

abstract:
  Predictions for systems in entangled states cannot be described in local
realistic terms. However, after admixing some noise such a description is
possible. We show that for two quNits (quantum systems described by N
dimensional Hilbert spaces) in a maximally entangled state the minimal
admixture of noise increases monotonically with N. The results are a direct
extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418
(2000), where results for $N\leq 9$ were presented. The extension up to N=16 is
possible when one defines for each N a specially chosen set of observables. We
also present results concerning the critical detectors efficiency beyond which
a valid test of local realism for entangled quNits is possible.


title: Foundations of Probability and Physics, Round table

abstract:
  We present the summary of the general discussion on the probabilistic
foundations of quantum theory that took place during the round table at the
Int. Conf. "Foundations of Probability and Physics", V\"axj\"o, Sweden-2000. It
is possible to find at http://www.msi.vxu.se/aktuellt/konferens/Roundtable.html
continuation of this Round Table. You can send your contribution by Email to A.
Khr. (subject: Round Table).


title:
Relativistic precession of quantum elliptical states in the Coulomb
  potential

abstract:
  A special relativistic perturbation to non-relativistic quantum mechanics is
shown to lead to the special relativistic prediction for the rate of precession
for quantum states in the Coulomb potential. This behavior is shown using SO(4)
coherent states as examples. These states are localized on Kepler ellipses and
precess in the presence of a relativistic perturbation.


title: Bell's inequalities I: An explanation for their experimental violation

abstract:
  Derivations of two Bell's inequalities are given in a form appropriate to the
interpretation of experimental data for explicit determination of all the
correlations. They are arithmetic identities independent of statistical
reasoning and thus cannot be violated by data that meets the conditions for
their validity. Two experimentally performable procedures are described to meet
these conditions. Once such data are acquired, it follows that the measured
correlations cannot all equal a negative cosine of angular differences. The
relation between this finding and the predictions of quantum mechanics is
discussed in a companion paper.


title: Does Indeterminism Give Rise to an Intrinsic Time Arrow?

abstract:
  In any physical theory that admits true indeterminism, the thermodynamic
arrow of time can arise regardless of the system's initial conditions. Hence on
such theories time's arrow emerges out of the basic physical interactions. The
example of the GRW theory is studied in detail.


title:
Positive P simulations of spin squeezing in a two-component Bose
  condensate

abstract:
  The collisional interaction in a Bose condensate represents a non-linearity
which in analogy with non-linear optics gives rise to unique quantum features.
In this paper we apply a Monte Carlo method based on the positive P
pseudo-probability distribution from quantum optics to analyze the efficiency
of spin squeezing by collisions in a two-component condensate. The squeezing
can be controlled by choosing appropiate collision parameters or by
manipulating the motional states of the two components.


title: Constructing Qubits in Physical Systems

abstract:
  The notion of a qubit is ubiquitous in quantum information processing. In
spite of the simple abstract definition of qubits as two-state quantum systems,
identifying qubits in physical systems is often unexpectedly difficult. There
are an astonishing variety of ways in which qubits can emerge from devices.
What essential features are required for an implementation to properly
instantiate a qubit? We give three typical examples and propose an operational
characterization of qubits based on quantum observables and subsystems.


title:
Masses and fields in Microdynamics: a possible foundation for dynamic
  gravity

abstract:
  The quest for a complete theory of microphysics is probably near the top of
the agenda in fundamental physics today. We survey existing modifications of
quantum mechanics to assess their potential. In the following we present recent
results in microdynamics, focussing on dynamic charge. The theoretical model,
valid at all length scales, relates mass oscillations to static electric and
gravity fields. The same concept is used, with substantially lower frequencies,
to compute the intensity of gravity waves within the solar system. These waves,
in the range of kilohertz, can in principle be detected.


title:
Temporally stable coherent states in energy degenerate systems: The
  hydrogen atom

abstract:
  Klauder's recent generalization of the harmonic oscillator coherent states
[J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems,
requiring some additional structure if applied to systems with degeneracies.
The author suggests how this structure could be added, and applies the complete
method to the hydrogen atom problem. To illustrate how a certain degree of
freedom in the construction may be exercised, states are constructed which are
initially localized and evolve semi-classically, and whose long time evolution
exhibits "fractional revivals."


title: Generic entanglement generation, quantum statistics and complementarity

abstract:
  A general and an arbitrarily efficient scheme for entangling the spins (or
any spin-like degree of freedom) of two independent uncorrelated identical
particles by a combination of two particle interferometry and which way
detection is formulated. It is shown that the same setup could be used to
identify the quantum statistics of the incident particles from either the sign
or the magnitude of measured spin correlations. Our setup also exhibits a
curious complementarity between particle distinguishability and the amount of
generated entanglement.


title: Bell's inequalities II: logical loophole in their interpretation

abstract:
  Assumed data streams from a delayed choice gedanken experiment must satisfy a
Bell's identity independently of locality assumptions. The violation of Bell's
inequality by assumed correlations of identical form among these data streams
implies that they cannot all result from statistically equivalent variables of
a homogeneous process. This is consistent with both the requirements of
arithmetic and distinctions between commuting and noncommuting observables in
quantum mechanics. Neglect of these distinctions implies a logical loophole in
the conventional interpretation of Bell's inequalities.


title: Quantum Complex Henon-Heiles Potentials

abstract:
  Quantum-mechanical PT-symmetric theories associated with complex cubic
potentials such as V=x^2+y^2+igxy^2 and V=x^2+y^2+z^2+igxyz, where g is a real
parameter, are investigated. These theories appear to possess real, positive
spectra. Low-lying energy levels are calculated to very high order in
perturbation theory. The large-order behavior of the perturbation coefficients
is determined using multidimensional WKB tunneling techniques. This approach is
also applied to the complex Henon-Heiles potential V=x^2+y^2+ig(xy^2-x^3/3).


title: Entangled Nonorthogonal States and Their Decoherence Properties

abstract:
  This paper presents properties of the so-called quasi-Bell states: entangled
states written as superpositions of nonorthogonal states. It is shown that a
special class of those states, namely entangled coherent states, are more
robust against decoherence due to photon absorption than the standard bi-photon
Bell states.


title: Entanglement of transverse modes in a pendular cavity

abstract:
  We study the phenomena that arise in the transverse structure of
electromagnetic field impinging on a linear Fabry-Perot cavity with an
oscillating end mirror. We find quantum correlations among transverse modes
which can be considered as a signature of their entanglement.


title: Quantum Cryptography

abstract:
  Quantum cryptography could well be the first application of quantum mechanics
at the individual quanta level. The very fast progress in both theory and
experiments over the recent years are reviewed, with emphasis on open questions
and technological issues.


title: Decoherent Histories for Spacetime Domains

abstract:
  The decoherent histories approach is a natural medium in which to address
problems in quantum theory which involve time in a non-trivial way. This
article reviews the various attempts and difficulties involved in using the
decoherent histories approach to calculate the probability for crossing the
surface $x=0$ during a finite interval of time. The commonly encountered
difficulties in assigning crossing times arise here as difficulties in
satisfying the consistency (no-interference) condition. This can be overcome by
introducing an environment to produce decoherence, and probabilities exhibiting
the expected classical limit are obtained. The probabilities are, however,
dependent to some degree on the decohering environment. The results are
compared with a recently proposed irreversible detector model. A third method
is introduced, involving continuous quantum measurement theory. Some closely
related work on the interpretation of the wave function in quantum cosmology is
described.


title: Optimal Non-Universally Covariant Cloning

abstract:
  We consider non-universal cloning maps, namely cloning transformations which
are covariant under a proper subgroup G of the universal unitary group U(d),
where d is the dimension of the Hilbert space H of the system to be cloned. We
give a general method for optimizing cloning for any cost-function. Examples of
applications are given for the phase-covariant cloning (cloning of equatorial
qubits) and for the Weyl-Heisenberg group (cloning of "continuous variables").


abstract:
  Quantum cloning machines for equatorial qubits are studied. For the case of 1
to 2 phase-covariant quantum cloning machine, we present the networks
consisting of quantum gates to realize the quantum cloning transformations. The
copied equatorial qubits are shown to be separable by using Peres-Horodecki
criterion. The optimal 1 to M phase-covariant quantum cloning transformations
are given.


title: Mathematical Foundations of Holonomic Quantum Computer II

abstract:
  This is a sequel to the papers (quant-ph/9910063) and (quant-ph/0004102). The
aim of this paper is to give mathematical foundations to Holonomic Quantum
Computation (Computer) proposed by Zanardi and Rasetti (quant-ph/9904011) and
Pachos and Chountasis (quant-ph/9912093). In 2-qubit case we give an explicit
form to non-abelian Berry connection of quantum computational bundle which is
associated with Holonomic Quantum Computation, on some parameter space. We also
suggest a possibility that not only usual holonomy but also higher-dimensional
holonomies must be used to prove a universality of our Holonomic Quantum
Computation.


title:
Characterization of high finesse mirrors: loss, phase shifts and mode
  structure in an optical cavity

abstract:
  An extensive characterization of high finesse optical cavities used in cavity
QED experiments is described. Different techniques in the measurement of the
loss and phase shifts associated with the mirror coatings are discussed and
their agreement shown. Issues of cavity field mode structure supported by the
dielectric coatings are related to our effort to achieve the strongest possible
coupling between an atom and the cavity.


title: Quantum limits in interferometric measurements

abstract:
  Quantum noise limits the sensitivity of interferometric measurements. It is
generally admitted that it leads to an ultimate sensitivity, the ``standard
quantum limit''. Using a semi-classical analysis of quantum noise, we show that
a judicious use of squeezed states allows one in principle to push the
sensitivity beyond this limit. This general method could be applied to large
scale interferometers designed for gravitational wave detection.


title: Quantum Bit Commitment in a Noisy Channel

abstract:
  Under rather general assumptions about the properties of a noisy quantum
channel, a first quantum protocol is proposed which allows to implement the
secret bit commitment with the probability arbitrarily close to unity.


title:
Entanglement and Dynamic Stability of Nash Equilibria in a Symmetric
  Quantum Game

abstract:
  We study the evolutionary stability of Nash equilibria (NE) in a symmetric
quantum game played by the recently proposed scheme of applying `identity' and
`Pauli spin flip' operators on the initial state with classical probabilities.
We show that in this symmetric game dynamic stability of a NE can be changed
when the game changes its form, for example, from classical to quantum. It
happens even when the NE remains intact in both forms.


title: Probabilistic nonlocal gate operation via imperfect entanglement

abstract:
  Nonlocal gate operation is based on sharing an ancillary pair of qubits in
perfect entanglement. When the ancillary pair are partially entangled, the
efficiency of the gate operation drops. Using general transformations, we
devise probabilistic nonlocal gates, which perform the nonlocal operation
conclusively when the ancillary pair are only partially entangled. We show that
a controlled purification protocol can be implemented by the probabilistic
nonlocal operation.


title: "All versus nothing" inseparability for two observers

abstract:
  A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev.
Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-like
proof involving just two observers. On one hand, this new approach allows us to
derive an experimentally testable Bell inequality which is violated by quantum
mechanics. On the other hand, it leads to a new state-independent proof of the
Kochen-Specker theorem and provides a wider perspective on the relations
between the major proofs of no-hidden-variables.


title: Reducing the linewidth of an atom laser by feedback

abstract:
  A continuous atom laser will almost certainly have a linewidth dominated by
the effect of the atomic interaction energy, which turns fluctuations in the
condensate atom number into fluctuations in the condensate frequency. These
correlated fluctuations mean that information about the atom number could be
used to reduce the frequency fluctuations, by controlling a spatially uniform
potential. We show that feedback based on a physically reasonable quantum
non-demolition measurement of the atom number of the condensate in situ can
reduce the linewidth enormously.


title: Quantum Communication between N partners and Bell's inequalities

abstract:
  We consider a family of quantum communication protocols involving $N$
partners. We demonstrate the existence of a link between the security of these
protocols against individual attacks by the eavesdropper, and the violation of
some Bell's inequalities, generalizing the link that was noticed some years ago
for two-partners quantum cryptography. The arguments are independent of the
local hidden variable debate.


title: Visible compression of commuting mixed states

abstract:
  We analyze the problem of quantum data compression of commuting density
operators in the visible case. We show that the lower bound for the compression
factor given by the Levitin--Holevo function is reached by providing an
explicit protocol.


title:
Spontaneous Bremsstrahlung in Scattering of an Electron by a Nucleus in
  the Field of Two Light Waves

abstract:
  We theoretically investigate nonresonant spontaneous bremsstrahlung in the
scattering of an electron by a nucleus in the field of two linearly polarized
light waves propagating in the same direction in the general relativistic case.
It is demonstrated that there are two substantially different kinematic ranges:
the noninterference range, where the Bunkin-Fedorov quantum parameters serve as
multiphoton parameters,and the interference range, where interference effects
become significant, and quantum interference parameters play the role of
multiphoton parameters. We determine the cross sections of electron-nucleus
spontaneous bremsstrahlung in these kinematic ranges. It is demonstrated that
the partial cross section in the interference range with emission (absorption)
of photons at combination frequencies may considerably exceed the corresponding
cross section for any other geometry.


title:
A " quantum public key " based cryptographic scheme for continuous
  variables

abstract:
  By analogy to classical cryptography, we develop a "quantum public key" based
cryptographic scheme in which the two public and private keys consist in each
of two entangled beams of squeezed light. An analog message is encrypted by
modulating the phase of the beam sent in public. The knowledge of the degree of
non classical correlation between the beam quadratures measured in private and
in public allows only the receiver to decrypt the message. Finally, in a view
towards absolute security, we formally prove that any external intervention of
an eavesdropper makes him vulnerable to any subsequent detection.


title: Casimir Effect for a Dielectric Wedge

abstract:
  The Casimir effect is considered for a wedge with opening angle $\alpha $,
with perfectly conducting walls, when the interior region is filled with an
isotropic and nondispersive medium with permittivity $\epsilon $ and
permeability $\mu $. The electromagnetic energy-momentum tensor in the bulk is
calculated, together with the surface stress on the walls. A discussion is
given on the possibilities for measuring the influence of the medium, via the
Casimir-Polder force.


title: Quantum fluctuations of position of a mirror in vacuum

abstract:
  A mirror scattering vacuum fields is submitted to a quantum fluctuating
radiation pressure. It also experiences a motional force, related to force
fluctuations through fluctuation-dissipation relations. The resulting position
fluctuations of the coupled mirror are related to the dissipative part of the
mechanical admittance. We compute the time dependent position commutator, which
makes apparent the difference between the low-frequency and high-frequency
masses, and the anticommutator noise spectrum, which describes the ultimate
sensitivity in a length measurement using mirrors.


title: Quantum fluctuations of vacuum stress tensors and spacetime curvatures

abstract:
  We analyze the quantum fluctuations of vacuum stress tensors and spacetime
curvatures, using the framework of linear response theory which connects these
fluctuations to dissipation mechanisms arising when stress tensors and
spacetime metric are coupled. Vacuum fluctuations of spacetime curvatures are
shown to be a sum of two contributions at lowest orders; the first one
corresponds to vacuum gravitational waves and is restricted to light-like
wavevectors and vanishing Einstein curvature, while the second one arises from
gravity of vacuum stress tensors. From these fluctuations, we deduce noise
spectra for geodesic deviations registered by probe fields which determine
ultimate limits in length or time measurements. In particular, a relation
between noise spectra characterizing spacetime fluctuations and the number of
massless neutrino fields is obtained.


title: Classical information capacity of superdense coding

abstract:
  Classical communication through quantum channels may be enhanced by sharing
entanglement. Superdense coding allows the encoding, and transmission, of up to
two classical bits of information in a single qubit. In this paper, the maximum
classical channel capacity for states that are not maximally entangled is
derived. Particular schemes are then shown to attain this capacity, firstly for
pairs of qubits, and secondly for pairs of qutrits.


title:
Von Neumann's Formulation of Quantum Theory and the Role of Mind in
  Nature

abstract:
  Orthodox Copenhagen quantum theory renounces the quest to understand the
reality in which we are imbedded, and settles for practical rules that describe
connections between our observations. Many physicist have believed that this
renunciation of the attempt describe nature herself was premature, and John von
Neumann, in a major work, reformulated quantum theory as theory of the evolving
objective universe. In the course of his work he converted to a benefit what
had appeared to be a severe deficiency of the Copenhagen interpretation, namely
its introduction into physical theory of the human observers. He used this
subjective element of quantum theory to achieve a significant advance on the
main problem in philosophy, which is to understand the relationship between
mind and matter. That problem had been tied closely to physical theory by the
works of Newton and Descartes. The present work examines the major problems
that have appeared to block the development of von Neumann's theory into a
fully satisfactory theory of Nature, and proposes solutions to these problems.


title:
Quantum Data Compression of Ensembles of Mixed States with Commuting
  Density Operators

abstract:
  We provide a rate distortion interpretation of the problem of quantum data
compression of ensembles of mixed states with commuting density operators.
There are two versions of this problem. In the visible case the sequence of
states is available to the encoder and in the blind or hidden case the encoder
may access only a sequence of measurements. We find the exact optimal
compression rates for both the visible and hidden cases. Our analysis includes
the scenario in which asymptotic reconstruction is imperfect.


title: An Entangled Tale of Quantum Entanglement

abstract:
  This paper gives an overview from the perspective of Lie group theory of some
of the recent advances in the rapidly expanding research area of quantum
entanglement.
  This paper is a written version of the last of eight one hour lectures given
in the American Mathematical Society (AMS) Short Course on Quantum Computation
held in conjunction with the Annual Meeting of the AMS in Washington, DC, USA
in January 2000.
  More information about the AMS Short Course can be found at
http://www.csee.umbc.edu/~lomonaco/ams/Announce.html


title:
Quantum algebraic representation of localization and motion of a Dirac
  electron

abstract:
  Quantum algebraic observables representing localization in space-time of a
Dirac electron are defined. Inertial motion of the electron is represented in
the quantum algebra with electron mass acting as the generator of motion. Since
transformations to uniformly accelerated frames are naturally included in this
conformally invariant description, the quantum algebra is also able to deal
with uniformly accelerated motion.


title: Sub-wavelength lithography over extended areas

abstract:
  We demonstrate a systematic approach to sub-wavelength resolution
lithographic image formation on films covering areas larger than a wavelength
squared. For example, it is possible to make a lithographic pattern with a
feature size resolution of $\lambda/[2(N+1)]$ by using a particular $2
M$-photon, multi-mode entangled state, where $N < M$, and banks of birefringent
plates. By preparing a statistically mixed such a state one can form any pixel
pattern on a $(N+1) 2^{M-N} \times (N+1) 2^{M-N}$ pixel grid occupying a square
with a side of $L=2^{M-N-1}$ wavelengths. Hence, there is a trade-off between
the exposed area, the minimum lithographic feature size resolution, and the
number of photons used for the exposure. We also show that the proposed method
will work even under non-ideal conditions, albeit with somewhat poorer
performance.


title: Relaxation Method For Calculating Quantum Entanglement

abstract:
  In a previous paper, we showed how entanglement of formation can be defined
as a minimum of the quantum conditional mutual information (a.k.a. quantum
conditional information transmission). In classical information theory, the
Arimoto-Blahut method is one of the preferred methods for calculating extrema
of mutual information. In this paper, we present a new method, akin to the
Arimoto-Blahut method, for calculating entanglement of formation. We also
present several examples computed with a computer program called Causa Comun
that implements the ideas of this paper.


title: Linear in temperature correction to the Casimir force

abstract:
  We discuss the temperature correction to the Casimir force between nonideal
metallic bodies which caused disagreement in the literature. A general method
to find the troubling term is proposed that does not require a direct reference
to the Lifshitz formula. The linear in temperature correction is shown to
survive for nonideal metals. It is important for small separations between
bodies tested in the recent experiments.


title: Approximate integrals of motion and the quantum chaoticity problem

abstract:
  The problem of existence and constructing of integrals of motion in
stationary quantum mechanics and its connection with quantum chaoticity is
discussed. It is shown that the earlier suggested quantum chaoticity criterion
characterizes destruction of initial symmetry of regular system and of basis
quantum numbers under influence of perturbation. The convergent procedure
allowing to construct approximate integrals of motion in the form of
non-trivial combinations depending on operators $(q,p)$ is suggested.
Properties of the obtained integrals with complicated structure and the
consequences of their existence for system's dynamics are discussed. The method
is used for explicit construction and investigation of the approximate
integrals in Henon-Heiles problem.


title: Universal construction for the unsorted quantum search algorithms

abstract:
  The multiple-quantum operator algebra formalism has been exploited to
construct generally an unsorted quantum search algorithm. The exponential
propagator and its corresponding effective Hamiltonian are constructed
explicitly that describe in quantum mechanics the time evolution of a multi-
particle two-state quantum system from the initial state to the output of the
unsorted quantum search problem. The exponential propagator usually may not be
compatible with the mathematical structure and principle of the search problem
and hence is not a real quantum search network, but it can be further
decomposed into a product of a series of the oracle unitary operations such as
the selective phase-shift operations and the nonselective unitary operations
which can be expressed further as a sequence of elementary building blocks such
as one-qubit quantum gates and the two-qubit diagonal phase gates, resulting in
that the decomposed propagator is compatible with the mathematical structure
and principle of the search problem and thus, becomes a real quantum search
network. The decomposition for the propagator can be achieved with the help of
the operator algebra structure and symmetry of the effective Hamiltonian, and
the properties of the multiple-quantum operator algebra spaces, especially the
characteristic transformation behavior of the multiple-quantum operators under
the z-axis rotations. It has been shown that the computational complexity of
the search algorithm is dependent upon that of the numerical multidimensional
integration and hence it is believed that the search algorithm could solve
efficiently the unsorted search problem. An NMR device is also proposed to
solve efficiently the unsorted search problem in polynomial time.


title:
Law of Malus and Photon-Photon Correlations: A Quasi-Deterministic
  Analyzer Model

abstract:
  For polarization experiments involving photon counting we introduce a
quasi-deterministic eigenstate transition model of the analyzer process.
Distributions accumulated one photon at a time, provide a deterministic
explanation for the law of Malus. We combine this analyzer model with causal
polarization coupling to calculate photon-photon correlations, one photon pair
at a time. The calculated correlations exceed the Bell limits and show
excellent agreement with the measured correlations of [ A. Aspect, P. Grangier
and G. Rogers, Phys. Rev. Lett. 49 91 (1982)]. We discuss why this model
exceeds the Bell type limits.


title:
Temperature dependence of the Casimir force between real metals:
  problems and approach to their resolution

abstract:
  We investigate the Casimir force acting between real metals at nonzero
temperature. It is shown that the zero-frequency term of Lifshitz formula has
interpretation problem in the case of real metal described by Drude model. It
happens because the scattering theory underlying Lifshitz formula is not well
formulated when the dielectric permittivity takes account of dissipation. To
give the zeroth term of Lifshitz formula the definite meaning different
prescriptions were used recently by different authors with diversed results.
These results are shown to be improper and in disagreement with experiment and
the general physical requirements. We propose the new prescription which is a
generalization of Schwinger, DeRaad and Milton recipe formulated earlier for
ideal metals. On this base the detailed numerical and analytical computations
of the temperature Casimir force are performed in configuration of two plane
plates and a spherical lens (sphere) above a plate. The corrections due to
nonzero temperature and finite conductivity found in the paper are in agreement
with the limiting case of perfect metal and fit all experimental and
theoretical requirements. Among other facts, the previous results obtained in
frames of plasma model are confirmed. It appears they are the limiting case of
Drude model computations when the relaxation parameter goes to zero. The
comparison with the Casimir force acting between dielectric test bodies is
made.


title:
75 Years of the Wavefunction: Complex-Dynamical Extension of the
  Original Wave Realism and the Universal Schroedinger Equation

abstract:
  Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter
wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed,
at the beginning of 1926, the concept of wavefunction and wave equation for it.
Though endowed with a realistic undular interpretation by its father, the
wavefunction could not be considered as a real "matter wave" and has been
provided with only abstract, formally probabilistic interpretation. In this
paper we show how the resulting "mysteries" of usual theory are solved within
the unreduced, dynamically multivalued description of the underlying,
essentially nonlinear interaction process (quant-ph/9902015, quant-ph/9902016),
without artificial modification of the Schroedinger equation. The latter is
rigorously derived instead as universal expression of unreduced interaction
complexity. Causal, totally realistic wavefunction is obtained as a dynamically
probabilistic intermediate state of a simple system with interaction performing
dynamically discrete transitions between its localised, incompatible
"realisations" ("corpuscular" states). Causal wavefunction and Schroedinger
equation are then extended to arbitrary level of world dynamics. We outline
some applications of the obtained causal description, such as genuine quantum
chaos (quant-ph/9511034-36) and realistic quantum devices (physics/0211071),
and emphasize the basic difference of the proposed dynamically multivalued
theory from dynamically single-valued imitations of causality and complexity.
The causally complete wavefunction concept, representing the unified essence of
unreduced (multivalued) complex dynamics, provides a clear distinctive feature
of realistic science, absent in any its unitary imitation.


title: Understanding the production of dual BEC with sympathetic cooling

abstract:
  We show, both experimentally and theoretically, that sympathetic cooling of
$^{87}$Rb atoms in the $|F=2,m_F=2>$ state by evaporatively cooled atoms in the
$|F=1,m_F=-1>$ state can be precisely controlled to produce dual or single
condensate in either state. We also study the thermalization rate between two
species. Our model renders a quantitative account of the observed role of the
overlap between the two clouds and points out that sympathetic cooling becomes
inefficient when the masses are very different. Our calculation also yields an
analytical expression of the thermalization rate for a single species.


title: PT symmetric square well

abstract:
  In a PT symmetrically complexified square well, bound states are constructed
by the matching technique. Their energies prove real in a domain of weak
non-Hermiticity, and continuous in the Hermitian limit. At a sequence of
certain strong-Hermiticity thresholds, the lowest two energies merge and
disappear.


title: On Bohmian trajectories in two-particle interference devices

abstract:
  Claims have been made that, in two-particle interference experiments
involving bosons, Bohmian trajectories may entail observable consequences
incompatible with standard quantum mechanics. By general arguments and by an
examination of specific instances, we show that this is not the case.


title: Time and Space Bounds for Reversible Simulation

abstract:
  We prove a general upper bound on the tradeoff between time and space that
suffices for the reversible simulation of irreversible computation. Previously,
only simulations using exponential time or quadratic space were known.
  The tradeoff shows for the first time that we can simultaneously achieve
subexponential time and subquadratic space.
  The boundary values are the exponential time with hardly any extra space
required by the Lange-McKenzie-Tapp method and the ($\log 3$)th power time with
square space required by the Bennett method. We also give the first general
lower bound on the extra storage space required by general reversible
simulation. This lower bound is optimal in that it is achieved by some
reversible simulations.


title: The mean king's problem: Prime degrees of freedom

abstract:
  We show how one can ascertain the values of a complete set of mutually
complementary observables of a prime degree of freedom.


title: Rotational invariance and the Pauli exclusion principle

abstract:
  In this article, the rotational invariance of entangled quantum states is
investigated as a possible cause of the Pauli exclusion principle. First, it is
shown that a certain class of rotationally invariant states can only occur in
pairs. This will be referred to as the coupling principle. This in turn
suggests a natural classification of quantum systems into those containing
coupled states and those that do not. Surprisingly, it would seem that
Fermi-Dirac statistics follows as a consequence of this coupling while the
Bose-Einstein follows by breaking it. Finally, the experimental evidence to
justify the above classification will be discussed. Pacs: 3.65.Bz, 5.30 d,
12.40.Ee

categories: quant-ph cond-mat.stat-mech math-ph math.MP


title: Possibility of the tunneling time determination

abstract:
  We show that it is impossible to determine the time a tunneling particle
spends under the barrier. However, it is possible to determine the asymptotic
time, i.e., the time the particle spends in a large area including the barrier.
We propose a model of time measurements. The model provides a procedure for
calculation of the asymptotic tunneling and reflection times. The model also
demonstrates the impossibility of determination of the time the tunneling
particle spends under the barrier. Examples for delta-form and rectangular
barrier illustrate the obtained results.


title: Geometrisation of quantum formalism

abstract:
  We show that the Dirac equation can be rewritten as a relation describing the
fundamental symmetry group of special topological manifold corresponding to the
Dirac wave field. It leads to unification of the time-space and internal
symmetries within one symmetry group. We suppose that nonelectromagnetic
interactions appear within such approach as the deviations of the metrics from
the euclidian form. The expression for the long-range part of "effective"
nucleon-nucleon potential is derived using this assumption.


title:
Adapted-operator representations: Selective versus collective properties
  of quantum networks

abstract:
  Based on local unitary operators acting on a n-dimensional Hilbert-space, we
investigate selective and collective operator basis sets for N-particle quantum
networks. Selective cluster operators are used to derive the properties of
general cat-states for any n and N. Collective operators are conveniently used
to account for permutation symmetry: The respective Hilbert-space dimension is
then only polynomial in N and governed by strong selection rules. These
selection rules can be exploited for the design of decoherence-free subspaces
as well as for the implementation of efficient routes to entanglement if
suspended switching between states of different symmetry classes could be
realized.


title: Algebraic-statistical approach to quantum mechanics

abstract:
  It is proposed the scheme of quantum mechanics, in which a Hilbert space and
the linear operators are not primary elements of the theory. Instead of it
certain variant of the algebraic approach is considered. The elements of
noncommutative algebra (observables) and the nonlinear functionals on this
algebra (physical states) are used as the primary constituents. The functionals
associate with results of a particular measurement. It is suggested to consider
certain ensembles of the physical states as quantum states of the standart
quantum mechanics. It is shown that in such scheme the mathematical formalism
of the standart quantum mechanics can be reproduced completely.


title: Quantum Approach to a Derivation of the Second Law of Thermodynamics

abstract:
  We re-interprete the microcanonical conditions in the quantum domain as
constraints for the interaction of the "gas-subsystem" under consideration and
its environment ("container"). The time-average of a purity-measure is found to
equal the average over the respective path in Hilbert-space. We then show that
for typical (degenerate or non-degenerate) thermodynamical systems almost all
states within the allowed region of Hilbert-space have a local von
Neumann-entropy S close to the maximum and a purity P close to its minimum,
respectively. Typically thermodynamical systems should therefore obey the
second law.


title: A note on measurement

abstract:
  Grounded on the quantum measurement riddle, a general argument against the
universal validity of the superposition principle was recently put forward by
Bassi and Ghirardi. It is pointed out that this argument is valid only within
the realm of the philosophy of ``objectivistic realism'' which is not a
necessary part of the foundations of physics, and that recent developments
including decoherence theory do account for the appearance of macroscopic
objects without resorting to a break of the principle.


title: A quantum computing scheme for the Hamiltonian path problem

abstract:
  A quantum computing scheme that uses a single photon and multiple-slit
gratings is suggested for the Hamiltonian path problem on a simple graph G of N
vertices. The photon is input to an N-slit grating followed by an N x N matrix
of `processing units'. A unit consists of a delay line followed by a grating
with k slits (0 < k < N) whose outputs are directed to k units in the next row
in a manner determined by the adjacency matrix of G. There is a one-to-one
mapping between paths of length N-1 in the graph and physical paths through the
matrix. The photon's path is a superposition of all these physical paths. The
time taken by the photon along a physical path corresponding to a Hamiltonian
path in G is a fixed value equal to the sum of N distinct delays, and is
different from the time along any other path. The graph is Hamiltonian if any
one of N detectors placed in the output of the N units in row N detects the
photon at this fixed time.


title:
Identification of all Hardy-type correlations for two photons or
  particles with spin 1/2

abstract:
  By using an alternative, equivalent form of the CHSH inequality and making
extensive use of the experimentally testable property of physical locality we
determine the 64 different Bell-type inequalities (each one involving four
joint probabilities) into which Hardy's nonlocality theorem can be cast. This
allows one to identify all the two-qubit correlations which can exhibit
Hardy-type nonlocality.


title: What is Possible Without Disturbing Partially Known Quantum States?

abstract:
  Consider a situation in which a quantum system is secretly prepared in a
state chosen from the known set of states. We present a principle that gives a
definite distinction between the operations that preserve the states of the
system and those that disturb the states. The principle is derived by
alternately applying a fundamental property of classical signals and a
fundamental property of quantum ones. The principle can be cast into a simple
form by using a decomposition of the relevant Hilbert space, which is uniquely
determined by the set of possible states. The decomposition implies the
classification of the degrees of freedom of the system into three parts
depending on how they store the information on the initially chosen state: one
storing it classically, one storing it nonclassically, and the other one
storing no information. Then the principle states that the nonclassical part is
inaccessible and the classical part is read-only if we are to preserve the
state of the system. From this principle, many types of no-cloning,
no-broadcasting, and no-imprinting conditions can easily be derived in general
forms including mixed states. It also gives a unified view on how various
schemes of quantum cryptography work. The principle helps to derive optimum
amount of resources (bits, qubits, and ebits) required in data compression or
in quantum teleportation of mixed-state ensembles.


title:
Mimicking a Kerrlike medium in the dispersive regime of second-harmonic
  generation

abstract:
  We find an effective Hamiltonian describing the process of second-harmonic
generation in the far-off resonant limit. We show that the dynamics of the
fundamental mode is governed by a Kerrlike Hamiltonian. Some dynamical
consequences are examined.


title:
Einstein's quantum clocks and Poincare's classical clocks in special
  relativity

abstract:
  Einstein's reply to Weyl about the importance in General Relativity of the
identity of the sources of spectral lines is well know. We show that, already
in Special Relavitity, Einstein's definition of the unit of time from the
frequency of atomic emission is deeply incompatible with Poincare's classical
conception of time in his special relativity based on the duality "true
time-local time". By using Weisskopf's analysis of quantum nature of the
identity of atoms, we show that the concept of identity is implicit in
Einstein's principle of relativity. On the contrary, in Poincare's relativistic
logic, the use of the Lorentz transformations compensates the differences
(contraction of lengths and dilation of durations) that are real by principle.
The borderline "quantum-classical" passes therefore clearly between the two
conceptions of the clocks in special relativity.


title: Radiation trapping in coherent media

abstract:
  We show that the effective decay rate of Zeeman coherence, generated in a
Rb87 vapor by linearly polarized laser light, increases significantly with the
atomic density. We explain this phenomenon as the result of radiation trapping.
Our study shows that radiation trapping must be taken into account to fully
understand many electromagnetically induced transparency experiments with
optically thick media.


title: Quantum fingerprinting

abstract:
  Classical fingerprinting associates with each string a shorter string (its
fingerprint), such that, with high probability, any two distinct strings can be
distinguished by comparing their fingerprints alone. The fingerprints can be
exponentially smaller than the original strings if the parties preparing the
fingerprints share a random key, but not if they only have access to
uncorrelated random sources. In this paper we show that fingerprints consisting
of quantum information can be made exponentially smaller than the original
strings without any correlations or entanglement between the parties: we give a
scheme where the quantum fingerprints are exponentially shorter than the
original strings and we give a test that distinguishes any two unknown quantum
fingerprints with high probability. Our scheme implies an exponential
quantum/classical gap for the equality problem in the simultaneous message
passing model of communication complexity. We optimize several aspects of our
scheme.


title: Frequent observations accelerate decay: The anti-Zeno effect

abstract:
  The quantum Zeno effect (QZE) is the striking prediction that the decay of
any unstable quantum state can be inhibited by sufficiently frequent
observations (measurements). The consensus opinion has upheld the QZE as a
general feature of quantum mechanics, which should lead to the inhibition of
any decay. The claim of QZE generality hinges on the assumption that successive
observations can in principle be made at time intervals too short for the
system to change appreciably. However, this assumption and the generality of
the QZE have scarcely been investigated thus far. We have addressed these
issues by showing that (i) the QZE is principally unattainable in radiative or
radioactive decay, because the required measurement rates would cause the
system to disintegrate; (ii) decay acceleration by frequent measurements (the
anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE
is shown to be observable as the enhancement of tunneling rates (e.g., for
atoms trapped in ramped-up potentials or in current-swept Josephson junctions),
fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields)
and photon depolarization rates (in randomly modulated Pockels cells).


title: Measurement of time in nonrelativistic quantum and classical mechanics

abstract:
  Possible theoretical frameworks for measurement of (arrival) time in the
nonrelativistic quantum mechanics are reviewed. It is argued that the ambiguity
between indirect measurements by a suitably introduced time operator and direct
measurements by a physical clock particle has a counterpart in the
corresponding classical framework of measurement of the Newtonian time based on
the Hamiltonian mechanics.


title:
The physical meaning of phase and its importance for quantum
  teleportation

abstract:
  We argue that the two parties in a quantum teleportation protocol need to
share more resources than just an entangled state and a classical communication
channel. As the phase between orthogonal states has no physical meaning by
itself, a shared standard defining all relevant phases is necessary. We discuss
several physical implementations of qubits and the corresponding physical
meaning of phase.


title:
Generalizations of Kijowski's time-of-arrival distribution for
  interaction potentials

abstract:
  Several proposals for a time-of-arrival distribution of ensembles of
independent quantum particles subject to an external interaction potential are
compared making use of the ``crossing state'' concept. It is shown that only
one of them has the properties expected for a classical distribution in the
classical limit. The comparison is illustrated numerically with a collision of
a Gaussian wave packet with an opaque square barrier.


title: Interferometry with Entangled Atoms

abstract:
  A quantum gravity-gradiometer consists of two spatially separated ensembles
of atoms interrogated by pulses of a common laser beam. Laser pulses cause the
probability amplitudes of atomic ground-state hyperfine levels to interfere,
producing two motion-sensitive phase shifts which allow the measurement of the
average acceleration of each ensemble, and, via simple differencing, of the
acceleration gradient. Here I propose entangling the quantum states of the two
ensembles prior to the pulse sequence, and show that entanglement encodes their
relative acceleration in a single interference phase which can be measured
directly, with no need for differencing.


title:
Unified time analysis of photon and (nonrelativistic) particle
  Tunnelling, and the Superluminal group-velocity problem

abstract:
  A unified approach to the time analysis of tunnelling of nonrelativistic
particles is presented, in which Time is regarded as a quantum-mechanical
observable, canonically conjugated to Energy. The validity of the Hartman
effect (independence of the Tunnelling Time of the opaque barrier width, with
Superluminal group velocities as a consequence) is verified for ALL the known
expressions of the mean tunnelling time. Moreover, the analogy between particle
and photon tunnelling is suitably exploited. On the basis of such an analogy,
an explanation of some recent microwave and optics experimental results on
tunnelling times is proposed. Attention is devoted to some aspects of the
causality problem for particle and photon tunnelling.


title: Evolutionary quantum game

abstract:
  We present the first study of a dynamical quantum game. Each agent has a
`memory' of her performance over the previous m timesteps, and her strategy can
evolve in time. The game exhibits distinct regimes of optimality. For small m
the classical game performs better, while for intermediate m the relative
performance depends on whether the source of qubits is `corrupt'. For large m,
the quantum players dramatically outperform the classical players by `freezing'
the game into high-performing attractors in which evolution ceases.


title: Physical reality and the Complementarity Principle

abstract:
  Consideration of the von Neumann measurement process underlying interference
experiments shows that the uncertainty in the incoming wave, responsible for
its interference, translates during measurement into an uncertainty at the
measuring apparatus. However, subsequent measurement on the apparatus does not
reveal any new information about the interfering wave. This observation, in the
context of recent advances in quantum information, suggests an argument for an
information theoretic interpretation of quantum mechanics.


title:
Realization of Optimal Disentanglement by Teleportation via Separable
  Channel

abstract:
  We discuss here the best disentanglement processes of states of two two-level
systems which belong to (i) the universal set, (ii) the set in which the states
of one party lie on a single great circle of the Bloch sphere, and (iii) the
set in which the states of one party commute with each other, by teleporting
the states of one party (on which the disentangling machine is acting) through
three particular type of separable channels, each of which is a mixture of Bell
states. In the general scenario, by teleporting one party's state of an
arbitrary entangled state of two two-level parties through some mixture of Bell
states, we have shown that this entangled state can be made separable by using
a physically realizable map $\tilde{V}$, acting on one party's states, if
$\tilde{V} (I) = I, \tilde{V} ({\sigma}_j) = {\lambda}_j {\sigma}_j$, where
${\lambda}_j \ge 0$ (for $j = 1, 2, 3$), and ${\lambda}_1 + {\lambda}_2 +
{\lambda}_3 \le 1$.


title: Bipartite maximally entangled nonorthorgonal states

abstract:
  We give conditions under which general bipartite entangled nonorthogonal
states become maximally entangled states. By the conditions we construct a
large class of entangled nonorthogonal states with exact one ebit of
entanglement in both bipartite and multipartite systems. One remarkable
property is that the amount of entanglement in this class of states is
independent on the parameters involved in the states. Finally we discuss how to
generate the bipartite maximally entangled nonorthogonal states.


title: Decoherence of Atomic Gases in Largely Detuned Laser Fields

abstract:
  We study theoretically the decoherence of a gas of bosonic atoms induced by
the interaction with a largely detuned laser beam. It is shown that for a
standing laser beam decoherence coincides with the single-particle result. For
a running laser beam many-particle effects lead to significant modifications.


title:
Efficient loading and cooling in a dynamic optical evanescent-wave
  microtrap

abstract:
  We calculate the loading efficiency and cooling rates in a bichromatic
optical microtrap, where the optical potentials are generated by evanescent
waves of cavity fields at a dielectric-vacuum interface. The cavity modified
nonconservative dynamic light forces lead to efficient loading of the atoms as
well as cooling without the need for spontaneous emission. Steady-state
temperatures well below the trap depth, reaching the motional quantum regime,
yield very long capturing times for a neutral atom.


title:
Efficient quantum algorithms for some instances of the non-Abelian
  hidden subgroup problem

abstract:
  In this paper we show that certain special cases of the hidden subgroup
problem can be solved in polynomial time by a quantum algorithm. These special
cases involve finding hidden normal subgroups of solvable groups and
permutation groups, finding hidden subgroups of groups with small commutator
subgroup and of groups admitting an elementary Abelian normal 2-subgroup of
small index or with cyclic factor group.


title: A class of symmetric controlled quantum operations

abstract:
  Certain quantum gates, such as the controlled-NOT gate, are symmetric in
terms of the operation of the control system upon the target system and vice
versa. However, no operational criteria yet exist for establishing whether or
not a given quantum gate is symmetrical in this sense. We consider a
restricted, yet broad, class of two-party controlled gate operations for which
the gate transforms a reference state of the target into one of an orthogonal
set of states. We show that for this class of gates it is possible to establish
a simple necessary and sufficient condition for the gate operation to be
symmetric.


title: A Talk on Quantum Cryptography, or How Alice Outwits Eve

abstract:
  Alice and Bob wish to communicate without the archvillainess Eve
eavesdropping on their conversation. Alice, decides to take two college
courses, one in cryptography, the other in quantum mechanics. During the
courses, she discovers she can use what she has just learned to devise a
cryptographic communication system that automatically detects whether or not
Eve is up to her villainous eavesdropping. Some of the topics discussed are
Heisenberg's Uncertainty Principle, the Vernam cipher, the BB84 and B92
cryptographic protocols. The talk ends with a discussion of some of Eve's
possible eavesdropping strategies, opaque eavesdropping, translucent
eavesdropping, and translucent eavesdropping with entanglement.


title: Complete controllability of finite-level quantum systems

abstract:
  Complete controllability is a fundamental issue in the field of control of
quantum systems, not least because of its implications for dynamical
realizability of the kinematical bounds on the optimization of observables. In
this paper we investigate the question of complete controllability for
finite-level quantum systems subject to a single control field, for which the
interaction is of dipole form. Sufficient criteria for complete controllability
of a wide range of finite-level quantum systems are established and the
question of limits of complete controllability is addressed. Finally, the
results are applied to give a classification of complete controllability for
four-level systems.


title: Generalized Weyl-Wigner map and Vey quantum mechanics

abstract:
  The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics
directly from the standard operator formulation. The covariant generalization
of Moyal theory, also known as Vey quantum mechanics, was presented in the
literature many years ago. However, a derivation of the formalism directly from
standard operator quantum mechanics, clarifying the relation between the two
formulations is still missing. In this paper we present a covariant
generalization of the Weyl order prescription and of the Weyl-Wigner map and
use them to derive Vey quantum mechanics directly from the standard operator
formulation. The procedure displays some interesting features: it yields all
the key ingredients and provides a more straightforward interpretation of the
Vey theory including a direct implementation of unitary operator
transformations as phase space coordinate transformations in the Vey idiom.
These features are illustrated through a simple example.


title:
Continuous Time-Dependent Measurements: Quantum Anti-Zeno Paradox with
  Applications

abstract:
  We derive differential equations for the modified Feynman propagator and for
the density operator describing time-dependent measurements or histories
continuous in time. We obtain an exact series solution and discuss its
applications. Suppose the system is initially in a state with density operator
$\rho(0)$ and the projection operator $E(t) = U(t) E U^\dagger(t)$ is measured
continuously from $t = 0$ to $T$, where $E$ is a projector obeying $E\rho(0) E
= \rho(0)$ and $U(t)$ a unitary operator obeying $U(0) = 1$ and some smoothness
conditions in $t$. Then the probability of always finding $E(t) = 1$ from $t =
0$ to $T$ is unity. Generically $E(T) \neq E$ and the watched system is sure to
change its state, which is the anti-Zeno paradox noted by us recently. Our
results valid for projectors of arbitrary rank generalize those obtained by
Anandan and Aharonov for projectors of unit rank.


title: Quantum Template Matching

abstract:
  We consider the quantum analogue of the pattern matching problem, which
consists of classifying a given unknown system according to certain predefined
pattern classes. We address the problem of quantum template matching in which
each pattern class ${\cal C}_i$ is represented by a known quantum state $\hat
g_i$ called a template state, and our task is to find a template which
optimally matches a given unknown quantum state $\hat f$. We set up a precise
formulation of this problem in terms of the optimal strategy for an associated
quantum Bayesian inference problem. We then investigate various examples of
quantum template matching for qubit systems, considering the effect of allowing
a finite number of copies of the input state $\hat f$. We compare quantum
optimal matching strategies and semiclassical strategies and demonstrate an
entanglement assisted enhancement of performance in the general quantum optimal
strategy.


title: The Use of NMR for Solving the Problems of Quantum Computers

abstract:
  The analysis of papers on usage NMR in quantum computations is provided and
the probable direction of the future investigations are considered.


title:
Exact coherent states in one-dimensional quantum many-body systems with
  inverse-square interactions

abstract:
  For the models of $N$-body identical harmonic oscillators interacting through
potentials of homogeneous degree -2, the unitary operator that transforms a
system of time-dependent parameters into that of unit spring constant and unit
mass of different timescale is found. If the interactions can be written in
terms of the differences between positions of two particles, it is also shown
that the Schr\"{o}dinger equation is invariant under a unitary transformation.
These unitary relations can be used not only in finding coherent states from
the given stationary states in a system, but also in finding exact wave
functions of the Hamiltonian systems of time-dependent parameters from those of
time-independent Hamiltonian systems. Both operators are invariant under the
exchange of any pair of particles. The transformations are explicitly applied
for some of the Calogero-Sutherland models to find exact coherent states.


title:
Measurement of the degree of Polarization Entanglement Through Position
  Interference

abstract:
  We produce polarization entangled states with variable degree of entanglement
for twin photons. Entanglement in polarization is coupled to entanglement in
position that produces transverse coincidence interference fringes. We show
both theoretically and experimentally that, due to this coupling, we can use
the interference pattern to measure the polarization degree of entanglement.


title:
All multipartite Bell correlation inequalities for two dichotomic
  observables per site

abstract:
  We construct a set of 2^(2^n) independent Bell correlation inequalities for
n-partite systems with two dichotomic observables each, which is complete in
the sense that the inequalities are satisfied if and only if the correlations
considered allow a local classical model. All these inequalities can be
summarized in a single, albeit non-linear inequality. We show that quantum
correlations satisfy this condition provided the state has positive partial
transpose with respect to any grouping of the n systems into two subsystems. We
also provide an efficient algorithm for finding the maximal quantum mechanical
violation of each inequality, and show that the maximum is always attained for
the generalized GHZ state.


title: Teleportation with indistinguishable particles

abstract:
  We analyze in a critical way the mathematical treatment of a quantum
teleportation experiment performed with photon particles, showing that a
symmetrization operation over both the polarization and spatial degrees of
freedom of all the particles involved is necessary in order to reproduce
correctly the observed experimental data.


title: Comprehensive theory of the relative phase in atom-field interactions

abstract:
  We explore the role played by the quantum relative phase in a well-known
model of atom-field interaction, namely, the Dicke model. We introduce an
appropriate polar decomposition of the atom-field relative amplitudes that
leads to a truly Hermitian relative-phase operator, whose eigenstates correctly
describe the phase properties, as we demonstrate by studying the positive
operator-valued measure derived from it. We find the probability distribution
for this relative phase and, by resorting to a numerical procedure, we study
its time evolution.


title: Estimating the spectrum of a density operator

abstract:
  Given N quantum systems prepared according to the same density operator \rho,
we propose a measurement on the N-fold system which approximately yields the
spectrum of \rho. The projections of the proposed observable decompose the
Hilbert space according to the irreducible representations of the permutations
on N points, and are labeled by Young frames, whose relative row lengths
estimate the eigenvalues of \rho in decreasing order. We show convergence of
these estimates in the limit N\to\infty, and that the probability for errors
decreases exponentially with a rate we compute explicitly.


title: Photocount statistics of chaotic lasers

abstract:
  We derive the photocount statistics of the radiation emitted from a chaotic
laser resonator in the regime of single-mode lasing. Random spatial variations
of the resonator eigenfunctions lead to strong mode-to-mode fluctuations of the
laser emission. The distribution of the mean photocount over an ensemble of
modes changes qualitatively at the lasing transition, and displays up to three
peaks above the lasing threshold.


title:
Entangling capacity of global phases and implications for Deutsch-Jozsa
  algorithm

abstract:
  We investigate the creation of entanglement by the application of phases
whose value depends on the state of a collection of qubits. First we give the
necessary and sufficient conditions for a given set of phases to result in the
creation of entanglement in a state comprising of an arbitrary number of
qubits. Then we analyze the creation of entanglement between any two qubits in
three qubit pure and mixed states. We use our result to prove that entanglement
is necessary for Deutsch-Jozsa algorithm to have an exponential advantage over
its classical counterpart.


title: Geometric Phases and Quantum Computations

abstract:
  Calculation aspects of holonomic quantum computer (HQC) are considered.
Wilczek--Zee potential defining the set of quantum calculations for HQC is
explicitly evaluated. Principal possibility of realization of the logical gates
for this case is discussed.


title:
Operator method for solution of the Schr\"{o}dinger equation with the
  rational potential

abstract:
  The eigenvalue problem for one-dimensional Schr\"{o}dinger equation with the
rational potential is numerically solved by the operator method. We show that
the operator method, applied for solving the Schr\"{o}dinger equation with the
nonpolynomial structure of the Hamiltonian, becomes more efficient if a
nonunitary transformation of the Hamiltonian is used. We demonstrate on
numerous examples that this method can handle both perturbative and
nonperturbative regimes with very high accuracy and moderate computational
cost.