title: On Bell's Paradox

abstract:
  The correlations between the outcomes of pairs of spin component measurements
on particles in the singlet state exist and can be observed independently of
any a priori given frame of reference. We can even construct a frame of
reference that is based on these correlations. This observation-based frame of
reference is equivalent to the customary a priori given frame of reference of
the laboratory when describing real Bohm-Aharonov experiments.
  J.S. Bell has argued that local hidden parameter theories that reproduce the
predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning
leading to Bell's conclusion is physically meaningless if the frame of
reference that is based on spin component measurements is accepted as the
backdrop for Bohm-Aharonov experiments.
  The refutal of Bell's proof opens up for the construction of a viable hidden
parameter theory. A model of a spin h/2 particle in terms of a non-flat metric
of space-time is shown to allow the predictions of quantum mechanics in the
Bohm-Aharonov experiment to be reproduced, without introducing non-locality.


title: Spin-orbit pendulum in Dirac oscillator

abstract:
  The dynamics of wavepackets in a relativistic Dirac oscillator (DO) is
considered. A comparison to nonrelativistic spin-orbit pendulum effect is
discussed. Particular relativistic effects, like Zitterbewegung in spin motion,
are found in Dirac representation. This trembling motion disappears in
Foldy-Wouthuysen representation. A substantial difference between the dynamics
of wavepackets corresponding to circular and linear orbits of a particle is
obtained and discussed.


title:
Quantum Dot Cavity-QED in the Presence of Strong Electron-Phonon
  Interactions

abstract:
  A quantum dot strongly coupled to a single high finesse optical microcavity
mode constitutes a new fundamental system for quantum optics. Here, the effect
of exciton-phonon interactions on reversible quantum-dot cavity coupling is
analysed without making Born-Markov approximation. The analysis is based on
techniques that have been used to study the ``spin boson'' Hamiltonian.
Observability of vacuum-Rabi splitting depends on the strength and the
frequency dependence of the spectral density function characterizing the
interactions with phonons, both of which can be influenced by phonon
confinement.


title:
High efficiency Nondistortion Quantum Interrogation of atoms in quantum
  superpositions

abstract:
  We consider the nondistortion quantum interrogation (NQI) of an atom prepared
in a quantum superposition. By manipulating the polarization of the probe
photon and making connections to interaction free measurements of opaque
objects, we show that nondistortion interrogation of an atom in a quantum
superposition can be done with efficiency approaching unity. However, if any
component of the atom's superposition is completely transparent to the probe
wave function, a nondistortion interrogation of the atom is impossible.


title: NMR C-NOT gate through Aharanov-Anandan's phase shift

abstract:
  Recently, it is proposed to do quantum computation through the Berry's
phase(adiabatic cyclic geometric phase) shift with NMR (Jones et al, Nature,
403, 869(2000)). This geometric quantum gate is hopefully to be fault tolerant
to certain types of errors because of the geometric property of the Berry
phase. Here we give a scheme to realize the NMR C-NOT gate through
Aharonov-Anandan's phase(non-adiabatic cyclic phase) shift on the dynamic phase
free evolution loop.
  In our scheme, the gate is run non-adiabatically, thus it is less affected by
the decoherence. And, in the scheme we have chosen the the zero dynamic phase
time evolution loop in obtaining the gepmetric phase shift, we need not take
any extra operation to cancel the dynamic phase.


title: Electron State Entanglement at Double Ionization

abstract:
  Electron wave function entanglement and spin reconfiguration as source of
electron correlation are investigated. Properties of correlation function are
shown to have the best concordance with experimental data under supposition
that probability of change of electron state to triplet state is about 0.5 or
more.


title: Lossless quantum data compression and variable-length coding

abstract:
  In order to compress quantum messages without loss of information it is
necessary to allow the length of the encoded messages to vary. We develop a
general framework for variable-length quantum messages in close analogy to the
classical case and show that lossless compression is only possible if the
message to be compressed is known to the sender. The lossless compression of an
ensemble of messages is bounded from below by its von-Neumann entropy. We show
that it is possible to reduce the number of qbits passing through a quantum
channel even below the von-Neumann entropy by adding a classical side-channel.
We give an explicit communication protocol that realizes lossless and
instantaneous quantum data compression and apply it to a simple example. This
protocol can be used for both online quantum communication and storage of
quantum data.


title:
'Beyond quantum theory: a realist psycho-biological interpretation of
  reality' revisited

abstract:
  It is hypothesised, following Conrad et al. (1988)
(http://www.tcm.phy.cam.ac.uk/~bdj10/papers/urbino.html) that quantum physics
is not the ultimate theory of nature, but merely a theoretical account of the
phenomena manifested in nature under particular conditions. These phenomena
parallel cognitive phenomena in biosystems in a number of ways and are assumed
to arise from related mechanisms. Quantum and biological accounts are
complementary in the sense of Bohr and quantum accounts may be incomplete. In
particular, following ideas of Stapp, 'the observer' is a system that, while
lying outside the descriptive capacities of quantum mechanics, creates
observable phenomena such as wave function collapse through its probing
activities. Better understanding of such processes may pave the way to new
science.


title: Classical, quantum and total correlations

abstract:
  We discuss the problem of separating consistently the total correlations in a
bipartite quantum state into a quantum and a purely classical part. A measure
of classical correlations is proposed and its properties are explored.


title: Decoherence of quantum registers

abstract:
  The dynamical evolution of a quantum register of arbitrary length coupled to
an environment of arbitrary coherence length is predicted within a relevant
model of decoherence. The results are reported for quantum bits (qubits)
coupling individually to different environments (`independent decoherence') and
qubits interacting collectively with the same reservoir (`collective
decoherence'). In both cases, explicit decoherence functions are derived for
any number of qubits. The decay of the coherences of the register is shown to
strongly depend on the input states: we show that this sensitivity is a
characteristic of $both$ types of coupling (collective and independent) and not
only of the collective coupling, as has been reported previously. A non-trivial
behaviour ("recoherence") is found in the decay of the off-diagonal elements of
the reduced density matrix in the specific situation of independent
decoherence. Our results lead to the identification of decoherence-free states
in the collective decoherence limit. These states belong to subspaces of the
system's Hilbert space that do not get entangled with the environment, making
them ideal elements for the engineering of ``noiseless'' quantum codes. We also
discuss the relations between decoherence of the quantum register and
computational complexity based on the new dynamical results obtained for the
register density matrix.


title: A QES Band-Structure Problem in One Dimension

abstract:
  I show that the potential $$V(x,m) = \big [\frac{b^2}{4}-m(1-m)a(a+1) \big
]\frac{\sn^2 (x,m)}{\dn^2 (x,m)} -b(a+{1/2}) \frac{\cn (x,m)}{\dn^2 (x,m)}$$
constitutes a QES band-structure problem in one dimension. In particular, I
show that for any positive integral or half-integral $a$, $2a+1$ band edge
eigenvalues and eigenfunctions can be obtained analytically. In the limit of m
going to 0 or 1, I recover the well known results for the QES double
sine-Gordon or double sinh-Gordon equations respectively. As a by product, I
also obtain the boundstate eigenvalues and eigenfunctions of the potential
$$V(x) = \big [\frac{\beta^2}{4}-a(a+1) \big ] \sech^2 x +\beta(a+{1/2})\sech
x\tanh x$$ in case $a$ is any positive integer or half-integer.

categories: quant-ph cond-mat hep-th math-ph math.MP


title:
Representation of Joint Measurement in Quantum Mechanics. A Refutation
  of Quantum Teleportation

abstract:
  An inconsistency is pointed out within Quantum Mechanics as soon as
successive joint measurements are involved on entangled states. The resolution
of the inconsistency leads to a refutation of the use of entangled states as
eigenvectors. Hence, the concept of quantum teleportation, which is based on
the use of such entangled states--the Bell states--as eigenvectors, is
demonstrated to be irrelevant to Quantum Mechanics.


title: Quantum Digital Signatures

abstract:
  We present a quantum digital signature scheme whose security is based on
fundamental principles of quantum physics. It allows a sender (Alice) to sign a
message in such a way that the signature can be validated by a number of
different people, and all will agree either that the message came from Alice or
that it has been tampered with. To accomplish this task, each recipient of the
message must have a copy of Alice's "public key," which is a set of quantum
states whose exact identity is known only to Alice. Quantum public keys are
more difficult to deal with than classical public keys: for instance, only a
limited number of copies can be in circulation, or the scheme becomes insecure.
However, in exchange for this price, we achieve unconditionally secure digital
signatures. Sending an m-bit message uses up O(m) quantum bits for each
recipient of the public key. We briefly discuss how to securely distribute
quantum public keys, and show the signature scheme is absolutely secure using
one method of key distribution. The protocol provides a model for importing the
ideas of classical public key cryptography into the quantum world.


title:
Characteristic decay of the autocorrelation functions prescribed by the
  Aharonov-Bohm time operator

abstract:
  The wave functions, the autocorrelation functions of which decay faster than
$t^{-2}$, for both the one-dimensional free particle system and the
repulsive-potential system are examined. It is then shown that such wave
functions constitute a dense subset of $L^2 ({\bf R}^1)$, under several
conditions that are particularly satisfied by the square barrier potential
system. It implies that the faster than $t^{-2}$-decay character of the
autocorrelation function persists against the perturbation of potential. It is
also seen that the denseness of the above subset is guaranteed by that of the
domain of the Aharonov-Bohm time operator.


title: Four-photon Entanglement as Stochastic-signal Correlation

abstract:
  A fully classical model of a recent experiment exhibiting what is interpreted
as teleportation and four-photon entanglement is described. It is shown that
the reason that a classical model is possible, contrary to the current belief,
results ultimately from a misguided modification by Bohm of the EPR Gedanken
experiment. Finally, teleportation is reinterpreted as the passive filtration
of correlated but stochastic events in stead of the active transfer of either
material or information.


title:
A More General Quantum Searching Algorithm And the Precise Formula of
  the Amplitude and the Non-symmetric Effects of Different Rotating Angles

abstract:
  This paper presented two general quantum search algorithms. We derived the
iterated formulas and the simpler approximate formulas and the precise formula
for the amplitude in the desired state. A mathematical proof of Grover's
algorithm being optimal among the algorithms with arbitrary phase rotations was
given in this paper. This first reported the non-symmetric effects of different
rotating angles, and gave the first-order approximate phase condition when
rotating angles are different.


title: Are Number and Phase Complementary Observables?

abstract:
  We study various ways of characterising the quantum optical number and phase
as complementary observables.


title: Optimal quantum measurements for spin-1 and spin-3/2 particles

abstract:
  Positive operator valued measures (POVMs) are presented that allow an unknown
pure state of a spin-1 particle to be determined with optimal fidelity when 2
to 5 copies of that state are available. Optimal POVMs are also presented for a
spin-3/2 particle when 2 or 3 copies of the unknown state are available.
Although these POVMs are optimal they are not always minimal, indicating that
there is room for improvement.


title:
Controlled transfer of quantum amplitude via modulation of a potential
  barrier: numerical study in a model of SQUID

abstract:
  We numerically integrate the time-dependent Schrodinger equation in a
single-degree-of-freedom model of SQUID with a variable potential barrier
between the basis flux states. We find that linear superpositions of the basis
states, with relatively little residual excitation, can be formed by pulsed
modulations of the barrier, provided the pulse duration exceeds the period of
small oscillations of the flux. Two pulses applied in sequence exhibit strong
interference effects, which we propose to use for an experimental determination
of the decoherence time in SQUIDs.


title:
Notes on a Paulian Idea: Foundational, Historical, Anecdotal and
  Forward-Looking Thoughts on the Quantum

abstract:
  This document is the first installment of three in the Cerro Grande Fire
Series. It is a collection of letters written to various colleagues, most of
whom regularly circuit this archive, including Howard Barnum, Paul Benioff,
Charles Bennett, Herbert Bernstein, Doug Bilodeau, Gilles Brassard, Jeffrey
Bub, Carlton Caves, Gregory Comer, Robert Griffiths, Adrian Kent, Rolf
Landauer, Hideo Mabuchi, David Mermin, David Meyer, Michael Nielsen, Asher
Peres, John Preskill, Mary Beth Ruskai, Ruediger Schack, Abner Shimony, William
Wootters, Anton Zeilinger, and many others. The singular thread sewing all the
letters together is the quantum. Some of the pieces are my best efforts to date
to give substance to an evanescent thought I see rising from the field of
quantum information---I call it the Paulian idea. To the extent I have
communicated its misty shadow to my correspondents and seen a twinkle of
enthusiasm, it seemed worthwhile to expand the jury on this anniversary
occasion.


title: Opposite Arrows of Time Can Reconcile Relativity and Nonlocality

abstract:
  We present a quantum model for the motion of N point particles, implying
nonlocal (i.e., superluminal) influences of external fields on the
trajectories, that is nonetheless fully relativistic. In contrast to other
models that have been proposed, this one involves no additional space-time
structure as would be provided by a (possibly dynamical) foliation of
space-time. This is achieved through the interplay of opposite microcausal and
macrocausal (i.e., thermodynamic) arrows of time.


title: Polarization of Radiation in Multipole Jaynes-Cummings Model

abstract:
  We discuss the spatial properties of quantum radiation emitted by a multipole
transition in a single atom. The qualitative difference between the
representations of plane and spherical waves of photons is examined. In
particular, the spatial inhomogeneity of the zero-point oscillations of
multipole field is shown. We show that the vacuum noise of polarization is
concentrated in a certain vicinity of atoms where it strongly exceeds the level
predicted by the representation of the plane waves. A new general polarization
matrix is proposed. It is shown that the polarization and its vacuum noise
strongly depend on the distance from the source.


title: Information capacity formula of quantum optical channels

abstract:
  The applications of the general formulae of channel capacity developed in the
quantum information theory to evaluation of information transmission capacity
of optical channel are interesting subjects. In this review paper, we will
point out that the formulation based on only classical-quantum channel mapping
model may be inadequate when one takes into account a power constraint for
noisy channel. To define the power constraint well, we should explicitly
consider how quantum states are conveyed through a transmission channel. Basing
on such consideration, we calculate a capacity formula for an attenuated noisy
optical channel with genreral Gaussian state input; this gives certain progress
beyond the example in our former paper.


title: Symmetric photon-photon coupling by atoms with Zeeman-split sublevels

abstract:
  We propose a simple scheme for highly efficient nonlinear interaction between
two weak optical fields. The scheme is based on the attainment of
electromagnetically induced transparency simultaneously for both fields via
transitions between magnetically split F=1 atomic sublevels, in the presence of
two driving fields. Thereby, equal slow group velocities and symmetric
cross-coupling of the weak fields over long distances are achieved. By simply
tuning the fields, this scheme can either yield giant cross-phase modulation or
ultrasensitive two-photon switching.


title:
Some Exact Results for Mid-Band and Zero Band-Gap States of Associated
  Lame Potentials

abstract:
  Applying certain known theorems about one-dimensional periodic potentials, we
show that the energy spectrum of the associated Lam\'{e} potentials
$$a(a+1)m~{\rm sn}^2(x,m)+b(b+1)m~{\rm cn}^2(x,m)/{\rm dn}^2(x,m)$$ consists of
a finite number of bound bands followed by a continuum band when both $a$ and
$b$ take integer values. Further, if $a$ and $b$ are unequal integers, we show
that there must exist some zero band-gap states, i.e. doubly degenerate states
with the same number of nodes. More generally, in case $a$ and $b$ are not
integers, but either $a + b$ or $a - b$ is an integer ($a \ne b$), we again
show that several of the band-gaps vanish due to degeneracy of states with the
same number of nodes. Finally, when either $a$ or $b$ is an integer and the
other takes a half-integral value, we obtain exact analytic solutions for
several mid-band states.


title:
Orchestrating an NMR quantum computation: the N=3 Deutsch-Jozsa
  algorithm

abstract:
  A detailed description of the development of a three qubit NMR realization of
the Deutsch-Jozsa algorithm [Collins et.al., Phys. Rev. A 62, 022304 (2000)] is
provided. The theoretical and experimental techniques used for the reduction of
the algorithm's evolution steps into a sequence of NMR pulses are discussed at
length. This includes the description of general pulse sequence compilation
techniques, various schemes for indirectly coupled gate realizations,
experimental pulse parameterization techniques and bookkeeping methods for
pulse phases.


title: Finding a state in a haystack

abstract:
  We consider the problem to single out a particular state among $2^n$
orthogonal pure states. As it turns out, in general the optimal strategy is not
to measure the particles separately, but to consider joint properties of the
$n$-particle system. The required number of propositions is $n$. There exist
$2^n!$ equivalent operational procedures to do so. We enumerate some
configurations for three particles, in particular the
Greenberger-Horne-Zeilinger (GHZ)- and W-states, which are specific cases of a
unitary transformation For the GHZ-case, an explicit physical meaning of the
projection operators is discussed.


title:
Variational Sturmian Approximation: A nonperturbative method of solving
  time-independent Schr\"odinger equation

abstract:
  A variationally improved Sturmian approximation for solving time-independent
Schr\"odinger equation is developed. This approximation is used to obtain the
energy levels of a quartic anharmonic oscillator, a quartic potential, and a
Gaussian potential. The results are compared with those of the perturbation
theory, the WKB approximation, and the accurate numerical values.


title: An optical kaleidoscope using a single atom

abstract:
  A new method to track the motion of a single particle in the field of a
high-finesse optical resonator is described. It exploits near-degenerate
higher-order Gaussian cavity modes, whose symmetry is broken by the phase shift
on the light induced by the particle. Observation of the spatial intensity
distribution behind the cavity allows direct determination of the particle's
position with approximately wavelength accuracy. This is demonstrated by
generating a realistic atomic trajectory using a semiclassical simulation
including friction and diffusion and comparing it to the reconstructed path.
The path reconstruction itself requires no knowledge about the forces on the
particle.


title: The Time-Energy Uncertainty Relation

abstract:
  The time energy uncertainty relation has been a controversial issue since the
advent of quantum theory, with respect to appropriate formalisation, validity
and possible meanings. A comprehensive account of the development of this
subject up to the 1980s is provided by a combination of the reviews of Jammer
(1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are
concerned with different specific aspects of the subject. The purpose of this
chapter is to show that different types of time energy uncertainty relation can
indeed be deduced in specific contexts, but that there is no unique universal
relation that could stand on equal footing with the position-momentum
uncertainty relation. To this end, we will survey the various formulations of a
time energy uncertainty relation, with a brief assessment of their validity,
and along the way we will indicate some new developments that emerged since the
1990s.


title: Relativity of motion in quantum vacuum

abstract:
  The problem of relativity of motion in quantum vacuum is addressed by
considering a cavity moving in vacuum in a monodimensional space. The cavity is
an open system which emits photons when it oscillates in vacuum. Qualitatively
new effects like pulse shaping in the time domain and frequency conversion in
the spectrum may help to discrimate motion-induced radiation from potential
stray effects.


title: The Casimir force between metallic mirrors

abstract:
  In order to compare recent experimental results with theoretical predictions
we study the influence of finite conductivity of metals on the Casimir effect.
The correction to the Casimir force and energy due to imperfect reflection and
finite temperature are evaluated for plane metallic plates where the dielectric
functions of the metals are modeled by a plasma model. The results are compared
with the common approximation where conductivity and thermal corrections are
evaluated separately and simply multiplied.


title: Some Worlds of Quantum Theory

abstract:
  This paper assesses the Everettian approach to the measurement problem,
especially the version of that approach advocated by Simon Saunders and David
Wallace. I emphasise conceptual, indeed metaphysical, aspects rather than
technical ones; but I include an introductory exposition of decoherence. In
particular, I discuss whether -- as these authors maintain -- it is acceptable
to have no precise definition of 'branch' (in the Everettian kind of sense).


title: Quantum vacuum fluctuations

abstract:
  The existence of irreducible field fluctuations in vacuum is an important
prediction of quantum theory. These fluctuations have many observable
consequences, like the Casimir effect which is now measured with good accuracy
and agreement with theory, provided that the latter accounts for differences
between real experiments and the ideal situation considered by Casimir. But the
vacuum energy density calculated by adding field mode energies is much larger
than the density observed around us through gravitational phenomena. This
``vacuum catastrophe'' is one of the unsolved problems at the interface between
quantum theory on one hand, inertial and gravitational phenomena on the other
hand. It is however possible to put properly formulated questions in the
vicinity of this paradox. These questions are directly connected to observable
effects bearing upon the principle of relativity of motion in quantum vacuum.


title:
The Interpretation of Quantum-Mechanical Models with Non-Hermitian
  Hamiltonians and Real Spectra

abstract:
  We study the quantum-mechanical interpretation of models with non-Hermitian
Hamiltonians and real spectra. We set up a general framework for the analysis
of such systems in terms of Hermitian Hamiltonians defined in the usual Hilbert
space $L_2(-\infty,\infty)$. Special emphasis is put on the correct definition
of the algebra of physical observables. Within this scheme we consider various
examples, including the model recently introduced by Cannata et al. and the
model of Hatano and Nelson.


title: Long-Distance High-Fidelity Teleportation Using Singlet States

abstract:
  A quantum communication system is proposed that uses polarization-entangled
photons and trapped-atom quantum memories. This system is capable of
long-distance, high-fidelity teleportation, and long-duration quantum storage.


title:
Fibre bundle formulation of relativistic quantum mechanics. I.
  Time-dependent approach

abstract:
  We propose a new fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions.
  In the present first part of our investigation we consider the time-dependent
or Hamiltonian approach to bundle description of relativistic quantum
mechanics. In it the wavefunctions are replaced by (state) liftings of paths or
sections along paths of a suitably chosen vector bundle over space-time whose
(standard) fibre is the space of the wavefunctions. Now the quantum evolution
is described as a linear transportation (by means of the evolution transport
along paths in the space-time) of the state liftings/sections in the (total)
bundle space. The equations of these transportations turn to be the bundle
versions of the corresponding relativistic wave equations.


title: Entanglement, identical particles and the uncertainty principle

abstract:
  A new uncertainty relation (UR) is obtained for a system of N identical pure
entangled particles if we use symmetrized observables when deriving the
inequality. This new expression can be written in a form where we identify a
term which explicitly shows the quantum correlations among the particles that
constitute the system. For the particular cases of two and three particles,
making use of the Schwarz inequality, we obtain new lower bounds for the UR
that are different from the standard one.


title: Achievable rates for the Gaussian quantum channel

abstract:
  We study the properties of quantum stabilizer codes that embed a
finite-dimensional protected code space in an infinite-dimensional Hilbert
space. The stabilizer group of such a code is associated with a symplectically
integral lattice in the phase space of 2N canonical variables. From the
existence of symplectically integral lattices with suitable properties, we
infer a lower bound on the quantum capacity of the Gaussian quantum channel
that matches the one-shot coherent information optimized over Gaussian input
states.


title:
Linear representations of probabilistic transformations induced by
  context transitions

abstract:
  By using straightforward frequency arguments we classify transformations of
probabilities which can be generated by transition from one preparation
procedure (context) to another. There are three classes of transformations
corresponding to statistical deviations of different magnitudes: (a)
trigonometric; (b) hyperbolic; (c) hyper-trigonometric. It is shown that not
only quantum preparation procedures can have trigonometric probabilistic
behaviour. We propose generalizations of ${\bf C}$-linear space probabilistic
calculus to describe non quantum (trigonometric and hyperbolic) probabilistic
transformations. We also analyse superposition principle in this framework.


title: Quantum mutual entropy for two-level ion in a q-analog trap

abstract:
  Quantum mutual entropy is used as a measure of information content of ionic
state due to ion-laser interaction in a q-analog trap. The initial state of the
system is a Schrodinger cat state. It is found that the partial mutual entropy
is a good measure of the entanglement and purity of the ionic state at $t>0$.


title:
Experimental verification of the Heisenberg uncertainty principle for
  hot fullerene molecules

abstract:
  The Heisenberg uncertainty principle for material objects is an essential
corner stone of quantum mechanics and clearly visualizes the wave nature of
matter. Here we report a demonstration of the Heisenberg uncertainty principle
for the most massive, complex and hottest single object so far, the fullerene
molecule C70 at a temperature of 900 K. We find a good quantitative agreement
with the theoretical expectation: dx * dp = h, where dx is the width of the
restricting slit, dp is the momentum transfer required to deflect the fullerene
to the first interference minimum and h is Planck's quantum of action.


title:
Controlled entanglement of two field modes in a Cavity Quantum
  Electrodynamics experiment

abstract:
  Using a single circular Rydberg atom, we have prepared two modes of a
superconducting cavity in a maximally entangled state. The two modes share a
single photon. This entanglement is revealed by a second atom probing, after a
delay, the correlations between the two modes. This experiment opens
interesting perspectives for quantum information manipulation and fundamental
tests of quantum theory.


title: Coherent control of an atomic collision in a cavity

abstract:
  Following a recent proposal by S. B. Zheng and G. C. Guo (Phys. Rev. Lett.
85, 2392 (2000)), we report an experiment in which two Rydberg atoms crossing a
non-resonant cavity are entangled by coherent energy exchange. The process,
mediated by the virtual emission and absorption of a microwave photon, is
characterized by a collision mixing angle four orders of magnitude larger than
for atoms colliding in free space with the same impact parameter. The final
entangled state is controlled by adjusting the atom-cavity detuning. This
procedure, essentially insensitive to thermal fields and to photon decay, opens
promising perspectives for complex entanglement manipulations.


title: Superalgebras for the Penning Trap

abstract:
  The hamiltonian describing a single fermion in a Penning trap is shown to be
supersymmetric in certain cases. The supersymmetries of interest occur when the
ratio of the cyclotron frequency to the axial frequency is 3/2 and the particle
has anomalous magnetic moment 4/3 or 2/3. At these supersymmetric points, the
spectrum shows uniformly spaced crossed levels. The associated superalgebras
are su(2|1) and su(1|1). The phase space for this problem has an osp(2|6)
structure and contains all the degeneracy superalgebras.


title:
Self-consistent non-Markovian theory of a quantum state evolution for
  quantum information processing

abstract:
  It is shown that the operator sum representation for non-Markovian dynamics
and the Lindblad master equation in Markovian limit can be derived from a
formal solution to quantum Liouville equation for a qubit system in the
presence of decoherence processes self-consistently. Our formulation is the
first principle theory based on projection-operator formalism to obtain an
exact reduced density operator in time-convolutionless form starting from the
quantum Liouville equation for a noisy quantum computer. The advantage of our
approach is that it is general enough to describe a realistic quantum computer
in the presence of decoherence provided details of the Hamiltonians are known.


title:
Moebius Structure of the Spectral Space of Schroedinger Operators with
  Point Interaction

abstract:
  The Schroedinger operator with point interaction in one dimension has a U(2)
family of self-adjoint extensions. We study the spectrum of the operator and
show that (i) the spectrum is uniquely determined by the eigenvalues of the
matrix U belonging to U(2) that characterizes the extension, and that (ii) the
space of distinct spectra is given by the orbifold T^2/Z_2 which is a Moebius
strip with boundary. We employ a parametrization of U(2) that admits a direct
physical interpretation and furnishes a coherent framework to realize the
spectral duality and anholonomy recently found. This allows us to find that
(iii) physically distinct point interactions form a three-parameter quotient
space of the U(2) family.


title: General Polarization Matrix of Electromagnetic Radiation

abstract:
  A general form of the polarization matrix valid for any type of
electromagnetic radiation (plane waves, multipole radiation etc.) is defined in
terms of a certain bilinear form in the field-strength tensor. The quantum
counterpart is determined as an operator matrix with normal-ordered elements
with respect to the creation and annihilation operators. The zero-point
oscillations (ZPO) of polarization are defined via difference between the
anti-normal and normal ordered operator polarization matrices. It is shown that
ZPO of the multipole field are stronger than those described by the model of
plane waves and are concentrated in a certain neighborhood of a local source.


title: Dynamics of quantum systems

abstract:
  A relation between the eigenvalues of an effective Hamilton operator and the
poles of the $S$ matrix is derived which holds for isolated as well as for
overlapping resonance states. The system may be a many-particle quantum system
with two-body forces between the constituents or it may be a quantum billiard
without any two-body forces. Avoided crossings of discrete states as well as of
resonance states are traced back to the existence of branch points in the
complex plane. Under certain conditions, these branch points appear as double
poles of the $S$ matrix. They influence the dynamics of open as well as of
closed quantum systems. The dynamics of the two-level system is studied in
detail analytically as well as numerically.


title: Theory for the photon statistics of random lasers

abstract:
  A theory for the photon statistics of a random laser is presented. Noise is
described by Langevin operators, where both fluctuations of the electromagnetic
field and of the medium are included. The theory is valid for all lasers with
small outcoupling when the laser cavity is large compared to the wavelength of
the radiation. The theory is applied to a chaotic laser cavity with a small
opening. It is known that a large number of modes can be above threshold
simultaneously in such a cavity. It is shown the amount of fluctuations is
increased compared to the Poissonian value by an amount that depends on that
number.


title:
Quadrature-dependent Bogoliubov transformations and multiphoton squeezed
  states

abstract:
  We introduce a linear, canonical transformation of the fundamental
single--mode field operators $a$ and $a^{\dagger}$ that generalizes the linear
Bogoliubov transformation familiar in the construction of the harmonic
oscillator squeezed states. This generalization is obtained by adding to the
linear transformation a nonlinear function of any of the fundamental quadrature
operators $X_{1}$ and $X_{2}$, making the original Bogoliubov transformation
quadrature--dependent. Remarkably, the conditions of canonicity do not impose
any constraint on the form of the nonlinear function, and lead to a set of
nontrivial algebraic relations between the $c$--number coefficients of the
transformation. We examine in detail the structure and the properties of the
new quantum states defined as eigenvectors of the transformed annihilation
operator $b$. These eigenvectors define a class of multiphoton squeezed states.
The structure of the uncertainty products and of the quasiprobability
distributions in phase space shows that besides coherence properties, these
states exhibit a squeezing and a deformation (cooling) of the phase--space
trajectories, both of which strongly depend on the form of the nonlinear
function. The presence of the extra nonlinear term in the phase of the wave
functions has also relevant consequences on photon statistics and correlation
properties. The non quadratic structure of the associated Hamiltonians suggests
that these states be generated in connection with multiphoton processes in
media with higher nonlinearities.


title: Quantum Portfolios

abstract:
  Quantum computation holds promise for the solution of many intractable
problems. However, since many quantum algorithms are stochastic in nature they
can only find the solution of hard problems probabilistically. Thus the
efficiency of the algorithms has to be characterized both by the expected time
to completion {\it and} the associated variance. In order to minimize both the
running time and its uncertainty, we show that portfolios of quantum algorithms
analogous to those of finance can outperform single algorithms when applied to
the NP-complete problems such as 3-SAT.


title: Introducing Quantum Discord

abstract:
  Two classically identical expressions for the mutual information generally
differ when the two systems involved are quantum. We investigate this
difference -- quantum discord -- and show that it can be used as a criterion
for the classicality of the correlations. We also show that quantum discord can
be used for describing the selection of the preferred, effectively classical,
pointer states.


title: Quantum Switch for Continuous Variable Teleportation

abstract:
  A novel quantum switch for continuous variables teleportation is proposed.
Two pairs of EPR beams with identical frequency and constant phase relation are
composed on two beamsplitters to produce two pairs of conditional entangled
beams, two of which are sent to two sending stations(Alices) and others to two
receiving stations(bobs). The EPR entanglement initionally results from
two-mode quadrature squeezed state light. Converting the squeezed component of
one of EPR sources between amplitude and phase, the input quantum state at a
sender will be reproduced at two receivers in turn. The switching system
manipulated by squeezed state light might be developed as a practical quantum
switch device for the communication and teleportation of quantum information.


title: Pseudo-forces in quantum mechanics

abstract:
  Dynamical evolution is described as a parallel section on an infinite
dimensional Hilbert bundle over the base manifold of all frames of reference.
The parallel section is defined by an operator-valued connection whose
components are the generators of the relativity group acting on the base
manifold. In the case of Galilean transformations we show that the property
that the curvature for the fundamental connection must be zero is just the
Heisenberg equations of motion and the canonical commutation relation in
geometric language. We then consider linear and circular accelerating frames
and show that pseudo-forces must appear naturally in the Hamiltonian.


title: Thermal entanglement in three-qubit Heisenberg models

abstract:
  We study pairwise thermal entanglement in three-qubit Heisenberg models and
obtain analytic expressions for the concurrence. We find that thermal
entanglement is absent from both the antiferromagnetic $XXZ$ model, and the
ferromagnetic $XXZ$ model with anisotropy parameter $\Delta\ge 1$. Conditions
for the existence of thermal entanglement are discussed in detail, as is the
role of degeneracy and the effects of magnetic fields on thermal entanglement
and the quantum phase transition. Specifically, we find that the magnetic field
can induce entanglement in the antiferromagnetic $XXX$ model, but cannot induce
entanglement in the ferromagnetic $XXX$ model.


title: Improved semiclassical density matrix: taming caustics

abstract:
  We present a simple method to deal with caustics in the semiclassical
approximation to the thermal density matrix of a particle moving on the line.
For simplicity, only its diagonal elements are considered. The only ingredient
we require is the knowledge of the extrema of the Euclidean action. The
procedure makes use of complex trajectories, and is applied to the quartic
double-well potential.

categories: quant-ph cond-mat.stat-mech hep-ph hep-th


title: A Relation between Coherent States and Generalized Bell States

abstract:
  In the first half we show an interesting relation between coherent states and
the Bell states in the case of spin 1/2, which was suggested by Fivel. In the
latter half we treat generalized coherent states and try to generalize this
relation to get several generalized Bell states. Our method is based on a
geometry and our task may give a hint to open a deep relation between a
coherence and an entanglement.


title: Monte Carlo Simulation of Laser Diodes Sub-Poissonian Light Generation

abstract:
  When laser diodes are driven by high-impedance electrical sources the
variance of the number of photo-detection events counted over large time
durations is less than the average number of events (sub-Poissonian light). The
paper presents a Monte Carlo simulation that keeps track of each level
occupancy (0 or 1) in the conduction and valence bands, and of the number of
light quanta in the optical cavity. When there is good electron-lattice thermal
contact the electron and hole temperatures remain equal to that of the lattice.
In that case, elementary laser-diode noise theory results are accurately
reproduced by the simulation. But when the thermal contact is poor (or, almost
equivalently, at high power levels) new effects occur (spectral-hole burning,
temperature fluctuations, statistical fluctuations of the optical gain) that
are difficult to handle theoretically. Our numerical simulation shows that the
frequency domain over which the photo-current spectral density is below the
shot-noise level becomes narrower as the optical power increases.


title: Covariant localizations in the torus and the phase observables

abstract:
  We describe all the localization observables of a quantum particle in a
one-dimensional box in terms of sequences of unit vectors in a Hilbert space.
An alternative representation in terms of positive semidefinite complex
matrices is furnished and the commutative localizations are singled out. As a
consequence, we also get a vector sequence characterization of the covariant
phase observables.


title: Bell-inequality violation with "thermal" radiation

abstract:
  The model of a quantum-optical device for a conditional preparation of
entangled states from input mixed states is presented. It is demonstrated that
even thermal or pseudo-thermal radiation can be entangled in such a way, that
Bell-inequalities are violated.


title: Characteristic times in one dimensional scattering

abstract:
  This chapter reviews several quantities that have been proposed in scattering
theory to characterize the temporal aspects of one dimensional collisions: the
dwell time, the delay time, the decay time, and times characterizing transient
effects or the attainment of stationary conditions. Some aspects of tunnelling
times are also discussed.


title:
The critical perturbation parameter estimate for the transition from
  regularity to chaos in quantum systems

abstract:
  In this paper we continue to develop our approach to the chaoticity
properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity
criterion characterizes the initial symmetry breaking and the destruction of
the corresponding integrals of motion in a perturbed system, which causes the
system's chaotisation. Transition from regularity to chaos in quantum systems
occurs at a certain critical value of the perturbation parameter. In our
previous papers we had to diagonalize the perturbed system's Hamiltonian matrix
in order to estimate this parameter. In the present paper we demonstrate that
the critical perturbation parameter for the transition from regularity to chaos
can be estimated in the framework of the first order perturbation theory. The
values of thus obtained critical parameter are in good agreement with the
results of our previous precise calculations for Hennon-Heiles Hamiltonian and
diamagnetic Kepler problem.


title: Boole-Bell-type inequalities in Mathematica

abstract:
  Classical Pitowsky correlation polytopes are reviewed with particular
emphasis on the Minkowski-Weyl representation theorem. The inequalities
representing the faces of polytopes are Boole's ``conditions of possible
experience.'' Many of these inequalities have been discussed in the context of
Bell's inequalities. We introduce CddIF, a Mathematica package created as an
interface between Mathematica and the cdd program by Komei Fukuda, which
represents a highly efficient method to solve the hull problem for general
classical correlation polytopes.


title:
Observation of transient gain without population inversion in a
  laser-cooled rubidium lambda system

abstract:
  We have observed clear Rabi oscillations of a weak probe in a strongly driven
three-level lambda system in laser-cooled rubidium for the first time. When the
coupling field is non-adiabatically switched on using a Pockels cell, transient
probe gain without population inversion is obtained in the presence of
uncoupled absorptions. Our results are supported by three-state computations.


title: Forcing Discretization and Determination in Quantum History Theories

abstract:
  We present a formally deterministic representation for quantum history
theories where we obtain the probabilistic structure via a discrete contextual
variable: no continuous probabilities are as such involved at the primal level
-- we conceive as a history theory any theory that deals with sequential
quantum measurements but remains essentially a dichotomic propositional theory.
A major part of the paper consists of a concise survey of arXiv:
quant-ph/0008061 and quant-ph/0008062.


title:
The delta-function-kicked rotor: Momentum diffusion and the
  quantum-classical boundary

abstract:
  We investigate the quantum-classical transition in the delta-kicked rotor and
the attainment of the classical limit in terms of measurement-induced
state-localization. It is possible to study the transition by fixing the
environmentally induced disturbance at a sufficiently small value, and
examining the dynamics as the system is made more macroscopic. When the system
action is relatively small, the dynamics is quantum mechanical and when the
system action is sufficiently large there is a transition to classical
behavior. The dynamics of the rotor in the region of transition, characterized
by the late-time momentum diffusion coefficient, can be strikingly different
from both the purely quantum and classical results. Remarkably, the early time
diffusive behavior of the quantum system, even when different from its
classical counterpart, is stabilized by the continuous measurement process.
This shows that such measurements can succeed in extracting essentially quantum
effects. The transition regime studied in this paper is accessible in ongoing
experiments.


title:
From gauge transformations to topology computation in quantum lattice
  gas automata

abstract:
  The evolution of a quantum lattice gas automaton (LGA) for a single charged
particle is invariant under multiplication of the wave function by a global
phase. Requiring invariance under the corresponding local gauge transformations
determines the rule for minimal coupling to an arbitrary external
electromagnetic field. We develop the Aharonov-Bohm effect in the resulting
model into a constant time algorithm to distinguish a one dimensional periodic
lattice from one with boundaries; any classical deterministic LGA algorithm
distinguishing these two spatial topologies would have expected running time on
the order of the cardinality of the lattice.


title:
Remote state preparation in higher dimension and the parallelizable
  manifold $S^{n-1}$

abstract:
  This paper proves that the remote state preparation (RSP) scheme in real
Hilbert space can only be implemented when the dimension of the space is 2,4 or
8. This fact is shown to be related to the parallelazablity of the $n$-1
dimensional sphere $S^{n-1}$. When the dimension is 4 and 8 the generalized
scheme is explicitly presented. It is also shown that for a given state with
components having the same norm, RSP can be generalized to arbitrary dimension
case.


title: A search for a border between classical and quantum worlds

abstract:
  The effects of environmental decoherence on a mass center position of a
macroscopic body are studied using the linear quantum Boltzmann equation. The
border between the classical world and the quantum one is discussed and the
results are illustrated by the recent experiments od Zeilinger group involving
C_60 and C_70 fullerenes.


title: Normal forms and entanglement measures for multipartite quantum states

abstract:
  A general mathematical framework is presented to describe local equivalence
classes of multipartite quantum states under the action of local unitary and
local filtering operations. This yields multipartite generalizations of the
singular value decomposition. The analysis naturally leads to the introduction
of entanglement measures quantifying the multipartite entanglement (as
generalizations of the concurrence and the 3-tangle), and the optimal local
filtering operations maximizing these entanglement monotones are obtained.
Moreover a natural extension of the definition of GHZ-states to e.g. $2\times
2\times N$ systems is obtained.


title: Physical sectors of the confluent hypergeometric functions space

abstract:
  A relaxed factorization is used to obtain many of the properties obeyed by
the confluent hypergeometric functions. Their implications on the analytical
solutions of some interesting physical problems are also studied. It is quite
remarkable that, although these properties appear frequently in solving the
Schroedinger equation, it has been not clear the role they play in describing
the physical systems. The main objective of this communication is precisely to
throw some light on the subject.


title: Role of degenerate atomic levels in the entanglement and the decoherence

abstract:
  We studied the dispersive dissipation of denegerate-level atom interacting
with a single linearly-polarized mode field. It is found that the degeneracy of
the atomic level affects the dissipation bahavior of the system as well as the
subsystems. The degeneracy of the atomic level augment the periods of
entanglement and increase the degree of the maxima statistical mixture states.


title:
A Representation for Compound Quantum Systems as Individual Entities:
  Hard Acts of Creation and Hidden Correlations

abstract:
  We introduce an explicit definition for 'hidden correlations' on individual
entities in a compound system: when one individual entity is measured, this
induces a well-defined transition of the 'proper state' of the other individual
entities. We prove that every compound quantum system described in the tensor
product of a finite number of Hilbert spaces can be uniquely represented as a
collection of individual(ized) (peudo-)entities between which there exist such
hidden correlations. We investigate the significance of these hidden
correlation representations within the so-called
``creation-discovery-approach'' and in particular their compatibility with the
``hidden measurement formalism''. This leads us to the introduction of the
notions of 'soft' and 'hard' 'acts of creation' and to the observation that our
approach can be seen as a theory of (pseudo-)individuals when compared to the
standard quantum theory. (For a presentation of the ideas proposed in this
paper within a quantum logical setting, yielding a structural theorem for the
representation of a compound quantum system in terms of the Hilbert space
tensor product, we refer to quant-ph/0008054.)


title:
A (Classical) Representation for a Spin-S Entity as a compound system in
  R^3 consisting of 2S Individual Spin-1/2 Entities

abstract:
  We generalize the results of [B. Coecke, Helv. Phys. Acta 68, 396 (1995)] for
the representation of coherent states of a spin-1 entity to spin-S entities
with S>1 and to non-coherent spin states: through the introduction of 'hidden
correlations' (see quant-ph/0105093) we introduce a representation for a spin-S
entity as a compound system consisting of 2S 'individual' spin-1/2 entities,
each of them represented by a 'proper state', and such that we are able to
consider a measurement on the spin-S entity as a measurement on each of the
individual spin-1/2 entities. If the spin-S entity is in a maximal spin state,
the 2S individual spin-1/2 entities behave as a collection of indistinguishable
but separated entities. If not so, we have to introduce the same kind of hidden
correlations as required for a hidden correlation representation of a compound
quantum systems described by a symmetrical superposition. Moreover, by applying
the Majorana representation and Aerts' representation for a spin-1/2 entity,
this hidden correlation representation yields a classical mechanistic
representation of a spin-S entity in R^3.


title: Variational Perturbation Theory for the Ground-State Wave Function

abstract:
  We evaluate perturbatively the density matrix in the low-temperature limit
and thus the ground-state wave function of the anharmonic oscillator up to
second order in the coupling constant. We then employ Kleinert's variational
perturbation theory to determine the ground-state wave function for all
coupling strengths.


title: Quantum dense coding using three qubits

abstract:
  We consider a situation in which two parties, Alice and Bob, share a 3-qubit
system coupled in an initial maximally entangled, GHZ state. By manipulating
locally two of the qubits, Alice can prepare any one of the eight 3-qubit GHZ
states. Thus the sending of Alice's two qubits to Bob, entails 3 bits of
classical information which can be recovered by Bob by means of a measurement
distinguishing the eight (orthonormal) GHZ states. This contrasts with the
2-qubit case, in which Alice can prepare any of the four Bell states by acting
locally only on one of the qubits.


title:
The world according to quantum mechanics (or, the 18 errors of Henry P.
  Stapp)

abstract:
  Several errors in Stapp's interpretation of quantum mechanics and its
application to mental causation (Henry P. Stapp, "Quantum theory and the role
of mind in nature," e-Print quant-ph/0103043) are pointed out. An
interpretation of (standard) QM that avoids these errors is presented.


title: How many photons are needed to distinguish two transparencies?

abstract:
  We give a bound on the minimum number of photons that must be absorbed by any
quantum protocol to distinguish between two transparencies. We show how a
quantum Zeno method in which the angle of rotation is varied at each iteration
can attain this bound in certain situations.


title: Maximal entanglement of nonorthogonal states: classification

abstract:
  A necessary and sufficient condition for the maximal entanglement of
bipartite nonorthogonal pure states is found. The condition is applied to the
maximal entanglement of coherent states. Some new classes of maximally
entangled coherent states are explicited constructed; their limits give rise to
maximally entangled Bell-like states.


title:
Feasible Linear-optics Generation of Polarization-entangled Photons
  Assisted with Single-photon Quantum Non-demolition Measurement

abstract:
  We propose a feasible scheme to create $n$-party ($n\geq 2$)
polarization-entangled photon states in a controllable way. The scheme requires
only single-photon sources, single-photon quantum non-demolition measurement
(SP-QNDM) and simple linear optical elements, usually with high perfections.
The SP-QNDM acts as a non-destructive projection measurement onto the wanted
entangled states and filters out the unwanted terms. Our scheme in fact
realizes entanglement of non-interacting photons; the interaction occurs only
implicitly in the optical elements and SP-QNDM. We also briefly consider
purification of mixed single-photon states within our scheme.


title: The Two-State Vector Formalism of Qauntum Mechanics: an Updated Review

abstract:
  In this paper we present the two-state vector formalism of quantum mechanics.
It is a time-symmetrized approach to standard quantum theory particularly
helpful for the analysis of experiments performed on pre- and post-selected
ensembles. Several peculiar effects which naturally arise in this approach are
considered. In particular, the concept of ``weak measurements'' (standard
measurements with weakening of the interaction) is discussed in depth revealing
a very unusual but consistent picture. Also, a design of a gedanken experiment
which implements a kind of quantum ``time machine'' is described. The issue of
time-symmetry in the context of the two-state vector formalism is clarified.


title: Quantum Computing with Quantum Dots on Linear Supports

abstract:
  Motivated by the recently demonstrated ability to attach quantum dots to
polymers at well defined locations, we propose a condensed phase analog of the
ion trap quantum computer: a scheme for quantum computation using chemically
assembled semiconductor nanocrystals attached to a linear support. The linear
support is either a molecular string (e.g., DNA) or a nanoscale rod. The phonon
modes of the linear support are used as a quantum information bus between the
dots. Our scheme offers greater flexibiliy in optimizing material parameters
than the ion trap method but has additional complications. We discuss the
relevant physical parameters, provide a detailed feasibility study, and suggest
materials for which quantum computation may be possible with this approach. We
find that Si is a potentially promising quantum dot material, already allowing
5-10 qubits quantum computer to operate with an error threshold of 10^-3.


title: Gravity Induced New Topological Phase in Optics

abstract:
  It is shown that both classical and quantum light can acquire a topological
phase shift induced by classical gravity, and the latter is detectable in a
laboratory-scale experiment.


title: A uniqueness theorem for entanglement measures

abstract:
  We obtain a mathematically simple characterization of all functionals
coinciding with the von Neumann reduced entropy on pure states based on the
Khinchin-Faddeev axiomatization of Shannon entropy and give a physical
interpretation of the axioms in terms of entanglement.


title:
Long-distance quantum communication with atomic ensembles and linear
  optics

abstract:
  Quantum communication holds a promise for absolutely secure transmission of
secret messages and faithful transfer of unknown quantum states. Photonic
channels appear to be very attractive for physical implementation of quantum
communication. However, due to losses and decoherence in the channel, the
communication fidelity decreases exponentially with the channel length. We
describe a scheme that allows to implement robust quantum communication over
long lossy channels. The scheme involves laser manipulation of atomic
ensembles, beam splitters, and single-photon detectors with moderate
efficiencies, and therefore well fits the status of the current experimental
technology. We show that the communication efficiency scale polynomially with
the channel length thereby facilitating scalability to very long distances.


title:
The Description of Joint Quantum Entities and the Formulation of a
  Paradox

abstract:
  We formulate a paradox in relation to the description of a joint entity
consisting of two subentities by standard quantum mechanics. We put forward a
proposal for a possible solution, entailing the interpretation of density
states as pure states. We explain where the inspiration for this proposal comes
from and how its validity can be tested experimentally. We discuss the
consequences on quantum axiomatics of the proposal.


title: Quantum axiomatics and a theorem of M.P. Soler

abstract:
  Three of the traditional quantum axioms (orthocomplementation,
orthomodularity and the covering law) show incompatibilities with two products
introduced by Aerts for the description of joint entities. Inspired by Soler's
theorem and Holland's AUG axiom, we propose a property of 'plane transitivity',
which also characterizes classical Hilbert spaces among infinite dimensional
orthomodular spaces, as a possible partial substitute for the 'defective'
axioms.


title:
State property systems and closure spaces: a study of categorical
  equivalence

abstract:
  We show that the natural mathematical structure to describe a physical entity
by means of its states and its properties within the Geneva-Brussels approach
is that of a state property system. We prove that the category of state
property systems (and morphisms), SP, is equivalent to the category of closure
spaces (and continuous maps), Cls. We show the equivalence of the 'state
determination axiom' for state property systems with the 'T0 separation axiom'
for closure spaces. We also prove that the category SP0 of state determined
state property systems is equivalent to the category L0 of based complete
lattices. In this sense the equivalence of SP and Cls generalizes the
equivalence of Cls0 and L0, proven in Erne 1984.


title:
Foundations of quantum physics: a general realistic and operational
  approach

abstract:
  We present a general formalism with the aim of describing the situation of an
entity, how it is, how it reacts to experiments, how we can make statistics
with it, and how it changes under the influence of the rest of the universe.
Therefore we base our formalism on the following basic notions: (1) the states
of the entity; they describe the modes of being of the entity, (2) the
experiments that can be performed on the entity; they describe how we act upon
and collect knowledge about the entity, (3) the probabilities; they describe
our repeated experiments and the statistics of these repeated experiments, (4)
the symmetries; they describe the interactions of the entity with the external
world without being experimented upon. Starting from these basic notions we
formulate the necessary derived notions: mixed states, mixed experiments and
events, an eigen closure structure describing the properties of the entity, an
ortho closure structure introducing an orthocomplementation, outcome
determination, experiment determination, state determination and atomicity
giving rise to some of the topological separation axioms for the closures. We
define the notion of sub entity in a general way and identify the morphisms of
our structure. We study specific examples in detail in the light of this
formalism: a classical deterministic entity and a quantum entity described by
the standard quantum mechanical formalism. We present a possible solution to
the problem of the description of sub entities within the standard quantum
mechanical procedure using the tensor product of the Hilbert spaces, by
introducing a new completed quantum mechanics in Hilbert space, were new 'pure'
states are introduced, not represented by rays of the Hilbert space.


title: Mesoscopic interference

abstract:
  We analyze a double-slit experiment when the interfering particle is
"mesoscopic" and one endeavors to obtain Welcher Weg information by shining
light on it. We derive a compact expression for the visibility of the
interference pattern: coherence depends on both the spatial and temporal
features of the wave function during its travel to the screen. We set a bound
on the temperature of the mesoscopic particle in order that its quantum
mechanical coherence be maintained.


title: Entanglement degradation in continuous-variable quantum teleportation

abstract:
  The influence of losses in the transmission of continuous-variable entangled
light through linear devices such as optical fibers is studied, with special
emphasis on Gaussian states. Upper bounds on entanglement and the distance to
the set of separable Gaussian states are calculated. Compared with the distance
measure, the bounds can substantially overestimate the entanglement and thus do
not show the drastic decrease of entanglement with increasing mean photon
number, as does the distance measure. In particular, it shows that losses give
rise to entanglement saturation, which principally limits the amount of
information that can be transferred quantum mechanically in continuous-variable
teleportation. Even for an initially infinitely squeezed two-mode squeezed
vacuum, high-fidelity teleportation is only possible over distances that are
much smaller than the absorption lengths.


title: On Koopman-von Neumann Waves

abstract:
  In this paper we study the classical Hilbert space introduced by Koopman and
von Neumann in their operatorial formulation of classical mechanics. In
particular we show that the states of this Hilbert space do not spread,
differently than what happens in quantum mechanics. The role of the phases
associated to these classical "wave functions" is analyzed in details. In this
framework we also perform the analog of the two-slit experiment and compare it
with the quantum case.


title: Minimal Coupling in Koopman-von Neumann Theory

abstract:
  Classical mechanics (CM), like quantum mechanics (QM), can have an
operatorial formulation. This was pioneered by Koopman and von Neumann (KvN) in
the 30's. They basically formalized, via the introduction of a classical
Hilbert space, earlier work of Liouville who had shown that the classical time
evolution can take place via an operator, nowadays known as the Liouville
operator. In this paper we study how to perform the coupling of a point
particle to a gauge field in the KvN version of CM. So we basically implement
at the classical operatorial level the analog of the minimal coupling of QM. We
show that, differently than in QM, not only the momenta but also other
variables have to be coupled to the gauge field. We also analyze in details how
the gauge invariance manifests itself in the Hilbert space of KvN and indicate
the differences with QM. As an application of the KvN method we study the
Landau problem proving that there are many more degeneracies at the classical
operatorial level than at the quantum one. As a second example we go through
the Aharonov-Bohm phenomenon showing that, at the quantum level, this
phenomenon manifests its effects on the spectrum of the quantum Hamiltonian
while at the classical level there is no effect whatsoever on the spectrum of
the Liouville operator.


title:
Optimal Summation and Integration by Deterministic, Randomized, and
  Quantum Algorithms

abstract:
  We survey old and new results about optimal algorithms for summation of
finite sequences and for integration of functions from Hoelder or Sobolev
spaces. First we discuss optimal deterministic and randomized algorithms. Then
we add a new aspect, which has not been covered before on conferences about
(quasi-) Monte Carlo methods: quantum computation. We give a short introduction
into this setting and present recent results of the authors on optimal quantum
algorithms for summation and integration. We discuss comparisons between the
three settings. The most interesting case for Monte Carlo and quantum
integration is that of moderate smoothness k and large dimension d which, in
fact, occurs in a number of important applied problems. In that case the
deterministic exponent is negligible, so the n^{-1/2} Monte Carlo and the
n^{-1} quantum speedup essentially constitute the entire convergence rate. We
observe that -- there is an exponential speed-up of quantum algorithms over
deterministic (classical) algorithms, if k/d tends to zero; -- there is a
(roughly) quadratic speed-up of quantum algorithms over randomized classical
algorithms, if k/d is small.


title:
Dynamical description of quantum computing: generic nonlocality of
  quantum noise

abstract:
  We develop dynamical non-Markovian description of quantum computing in weak
coupling limit, in lowest order approximation. We show that long range memory
of quantum reservoir produces strong interrelation between structure of noise
and quantum algorithm, implying nonlocal attacks of noise. We then argue that
the quantum error correction method fails to protect quantum computation
against electromagnetic or phonon vacuum which exhibit $1/t^4$ memory. This
shows that the implicit assumption of quantum error correction theory --
independence of noise and self-dynamics -- fails in long time regimes. We also
use our approach to present {\it pure} decoherence and decoherence accompanied
by dissipation in terms of spectral density of reservoir. The so-called {\it
dynamical decoupling} method is discussed in this context. Finally, we propose
{\it minimal decoherence model}, in which the only source of decoherence is
vacuum. We optimize fidelity of quantum information processing under the
trade-off between speed of gate and strength of decoherence.


title: Quantum Summation with an Application to Integration

abstract:
  We study summation of sequences and integration in the quantum model of
computation. We develop quantum algorithms for computing the mean of sequences
which satisfy a p-summability condition and for integration of functions from
Lebesgue spaces L_p([0,1]^d) and analyze their convergence rates. We also prove
lower bounds which show that the proposed algorithms are, in many cases,
optimal within the setting of quantum computing. This extends recent results of
Brassard, Hoyer, Mosca, and Tapp (2000) on computing the mean for bounded
sequences and complements results of Novak (2001) on integration of functions
from Hoelder classes.


title: From Classical State-Swapping to Quantum Teleportation

abstract:
  The quantum teleportation protocol is extracted directly out of a standard
classical circuit that exchanges the states of two qubits using only
controlled-NOT gates. This construction of teleportation from a classically
transparent circuit generalizes straightforwardly to d-state systems.


title: Quantum radiation at finite temperature

abstract:
  We investigate the phenomenon of quantum radiation - i.e. the conversion of
(virtual) quantum fluctuations into (real) particles induced by dynamical
external conditions - for an initial thermal equilibrium state. For a
resonantly vibrating cavity a rather strong enhancement of the number of
generated particles (the dynamical Casimir effect) at finite temperatures is
observed. Furthermore we derive the temperature corrections to the energy
radiated by a single moving mirror and an oscillating bubble within a
dielectric medium as well as the number of created particles within the
Friedmann-Robertson-Walker universe. Possible implications and the relevance
for experimental tests are addressed. PACS: 42.50.Lc, 03.70.+k, 11.10.Ef,
11.10.Wx.


title: Designing optimum CP maps for quantum teleportation

abstract:
  We study general teleportation scheme with an arbitrary state of the pair of
particles (2 and 3) shared by Alice and Bob, and arbitrary measurements on the
input particle 1 and one of the members (2) of the pair on Alice's side. We
find an efficient iterative algorithm for identifying optimum local operations
on Bob's side. In particular we find that simple unitary transformations on his
side are not always optimal even if particles 2 and 3 are perfectly entangled.
We describe the most interesting protocols in the language of extremal
completely-positive maps.


title: Spin-Space Entanglement Transfer and Quantum Statistics

abstract:
  Both the topics of entanglement and particle statistics have aroused enormous
research interest since the advent of quantum mechanics. Using two pairs of
entangled particles we show that indistinguishability enforces a transfer of
entanglement from the internal to the spatial degrees of freedom without any
interaction between these degrees of freedom. Moreover, sub-ensembles selected
by local measurements of the path will in general have different amounts of
entanglement in the internal degrees of freedom depending on the statistics
(either fermionic or bosonic) of the particles involved.


title:
Proof of security of quantum key distribution with two-way classical
  communications

abstract:
  Shor and Preskill have provided a simple proof of security of the standard
quantum key distribution scheme by Bennett and Brassard (BB84) by demonstrating
a connection between key distribution and entanglement purification protocols
with one-way communications. Here we provide proofs of security of standard
quantum key distribution schemes, BB84 and the six-state scheme, against the
most general attack, by using the techniques of *two*-way entanglement
purification. We demonstrate clearly the advantage of classical post-processing
with two-way classical communications over classical post-processing with only
one-way classical communications in QKD. This is done by the explicit
construction of a new protocol for (the error correction/detection and privacy
amplification of) BB84 that can tolerate a bit error rate of up to 18.9%, which
is higher than what any BB84 scheme with only one-way classical communications
can possibly tolerate. Moreover, we demonstrate the advantage of the six-state
scheme over BB84 by showing that the six-state scheme can strictly tolerate a
higher bit error rate than BB84. In particular, our six-state protocol can
tolerate a bit error rate of 26.4%, which is higher than the upper bound of 25%
bit error rate for any secure BB84 protocol. Consequently, our protocols may
allow higher key generation rate and remain secure over longer distances than
previous protocols. Our investigation suggests that two-way entanglement
purification is a useful tool in the study of advantage distillation, error
correction, and privacy amplification protocols.


title:
High order quantum decoherence via multi-particle amplitude for boson
  system

abstract:
  In this paper we depict the high order quantum coherence of a boson system by
using the multi-particle wave amplitude, whose norm square is just the high
order correlation function. This multi-time amplitude can be shown to be a
superposition of several "multi-particle paths". When the environment or a
apparatus entangles with them to form a generalized "which-way" measurement for
many particle system, the quantum decoherence happens in the high order case
dynamically. An explicit illustration is also given with an intracavity system
of two modes interacting with a moving mirror.


title:
Scheme for the preparation of the multi-particle entanglement in cavity
  QED

abstract:
  Here we present a quantum electrodynamics (QED) model involving a
large-detuned single-mode cavity field and $n$ identical two-level atoms. One
of its applications for the preparation of the multi-particle states is
analyzed. In addition to the Greenberger-Horne-Zeilinger (GHZ) state, the W
class states can also be generated in this scheme. The further analysis for the
experiment of the model of $n=2$ case is also presented by considering the
possible three-atom collision.


title: Extremal equation for optimal completely-positive maps

abstract:
  We derive an extremal equation for optimal completely-positive map which most
closely approximates a given transformation between pure quantum states.
Moreover, we also obtain an upper bound on the maximal mean fidelity that can
be attained by the optimal approximate transformation. The developed formalism
is applied to universal-NOT gate, quantum cloning machines, quantum entanglers,
and qubit theta-shifter.


title: A Measure of Stregth of an Unextendible Product Basis

abstract:
  A notion of strength of an unextendible product basis is introduced and a
quantitative measure for it is suggested with a view to providing an indirect
measure for the bound entanglement of formation of the bound entangled mixed
state associated with an unextendible product basis.


title:
The hidden measurement formalism: what can be explained and where
  quantum paradoxes remain

abstract:
  In the hidden measurement formalism that we develop in Brussels we explain
the quantum structure as due to the presence of two effects, (a) a real change
of state of the system under influence of the measurement and, (b) a lack of
knowledge about a deeper deterministic reality of the measurement process. We
show that the presence of these two effects leads to the major part of the
quantum mechanical structure of a theory where the measurements contain the two
mentioned effects. We present a quantum machine, where we can illustrate in a
simple way how the quantum structure arises as a consequence of the two
effects. We introduce a parameter 'epsilon' that measures the amount of the
lack of knowledge on the measurement process, and by varying this parameter, we
describe a continuous evolution from a quantum structure (maximal lack of
knowledge) to a classical structure (zero lack of knowledge). We show that for
intermediate values of epsilon we find a new type of structure that is neither
quantum nor classical. We analyze the quantum paradoxes and show that they can
be divided into two groups: (1) The group (measurement problem and Schrodingers
cat paradox) where the paradoxical aspects arise mainly from the application of
standard quantum theory as a general theory (e.g. also describing the
measurement apparatus). This type of paradox disappears in the hidden
measurement formalism. (2) A second group collecting the paradoxes connected to
the effect of non-locality (the Einstein-Podolsky-Rosen paradox and the
violation of Bell inequalities). We show that these paradoxes are internally
resolved because the effect of non-locality turns out to be a fundamental
property of the hidden measurement formalism itself.


title: Decoherence, einselection, and the quantum origins of the classical

abstract:
  Decoherence is caused by the interaction with the environment. Environment
monitors certain observables of the system, destroying interference between the
pointer states corresponding to their eigenvalues. This leads to
environment-induced superselection or einselection, a quantum process
associated with selective loss of information. Einselected pointer states are
stable. They can retain correlations with the rest of the Universe in spite of
the environment. Einselection enforces classicality by imposing an effective
ban on the vast majority of the Hilbert space, eliminating especially the
flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase
space emerges from the quantum Hilbert space in the appropriate macroscopic
limit: Combination of einselection with dynamics leads to the idealizations of
a point and of a classical trajectory. In measurements, einselection replaces
quantum entanglement between the apparatus and the measured system with the
classical correlation.


title: A double slit and a position-momentum EPR correlation

abstract:
  This paper has been withdrawn by the author, due to the fact that a similar
paper (quant-ph/9904075) has been published.


title: Non-classical behavior of atoms in an interferometer

abstract:
  We have studied the properties of the non-classical behavior of atoms in a
double-slit interferometer. An indication of this behavior for metastable
helium was reported by Kurtsiefer, Pfau and Mlynek [Nature 386, 150 (1997)]
showing distinctive negative values of the Wigner function, which was
reconstructed from the measured diffraction data. Our approach to explain this
non-classical behavior is based on the de Broglie-Bohm-Vigier-Selleri
understanding of the wave-particle duality and compatible statistical
interpretation of the atomic wave function. It follows from the results that
the atomic motion is non-classical because it does not obey the laws of
classical mechanics. However, there is no evidence that this atomic behavior
violates the classical probability law of the addition of probabilities.


title: Testing Hall-Post Inequalities With Exactly Solvable N-Body Problems

abstract:
  The Hall--Post inequalities provide lower bounds on $N$-body energies in
terms of $N'$-body energies with $N'<N$. They are rewritten and generalized to
be tested with exactly-solvable models of Calogero-Sutherland type in one and
higher dimensions. The bound for $N$ spinless fermions in one dimension is
better saturated at large coupling than for noninteracting fermions in an
oscillator


title:
Synthesis and characterization of entangled mesoscopic superpositions
  for a trapped electron

abstract:
  We propose a scheme for the generation and reconstruction of entangled states
between the internal and external (motional) degrees of freedom of a trapped
electron. Such states also exhibit quantum coherence at a mesoscopic level.


title:
Experimental violation of a spin-1 Bell inequality using
  maximally-entangled four-photon states

abstract:
  We demonstrate the first experimental violation of a spin-1 Bell inequality.
The spin-1 inequality is a calculation based on the Clauser, Horne, Shimony and
Holt formalism. For entangled spin-1 particles the maximum quantum mechanical
prediction is 2.552 as opposed to a maximum of 2, predicted using local hidden
variables. We obtained an experimental value of 2.27 $\pm 0.02$ using the
four-photon state generated by pulsed, type-II, stimulated parametric
down-conversion. This is a violation of the spin-1 Bell inequality by more than
13 standard deviations.


title: A Quantum Full Adder for a Scalable Nuclear Spin Quantum Computer

abstract:
  We demonstrate a strategy for implementation a quantum full adder in a spin
chain quantum computer. As an example, we simulate a quantum full adder in a
chain containing 201 spins. Our simulations also demonstrate how one can
minimize errors generated by non-resonant effects.


title: Multivariable functions approximation using a single quantum neuron

abstract:
  We describe a model element able to perform universal stochastic
approximations of continuous multivariable functions in both neuron-like and
quantum form. The implementation of this model in the form of a multi-barrier,
multiple-slit system is proposed and it is demonstrated that this single
neuron-like model is able to perform the XOR function unrealizable with single
classical neuron. For the simplified waveguide variant of this model it is
proved for different interfering quantum alternatives with no correlated
adjustable parameters, that the system can approximate any continuous function
of many variables. This theorem is applied to the 2-input quantum neural model
based on the use of the schemes developed for controlled nonlinear multiphoton
absorption of light by quantum systems. The relation between the field of
quantum neural computing and quantum control is discussed.


title:
Improving the Efficiency of an Ideal Heat Engine: The Quantum
  Afterburner

abstract:
  By using a laser and maser in tandem, it is possible to obtain laser action
in the hot exhaust gases involved in heat engine operation. Such a "quantum
afterburner" involves the internal quantum states of working gas atoms or
molecules as well as the techniques of cavity quantum electrodynamics and is
therefore in the domain of quantum thermodynamics. As an example, it is shown
that Otto cycle engine performance can be improved beyond that of the "ideal"
Otto heat engine.


title: Delayed-choice measurement and temporal nonlocality

abstract:
  We study for a composite quantum system with a quantum Turing architecture
the temporal non-locality of quantum mechanics by using the temporal Bell
inequality, which will be derived for a discretized network dynamics by
identifying the subsystem indices with (discrete) parameter time. However, the
direct ``observation'' of the quantum system will lead to no violation of the
temporal Bell inequality and to consistent histories of any subsystem. Its
violation can be demonstrated, though, for a delayed-choice measurement.


title: Limits to squeezing in the degenerate OPO

abstract:
  We develop a systematic theory of quantum fluctuations in the driven
parametric oscillator (OPO), including the region near threshold. This allows
us to treat the limits imposed by nonlinearities to quantum squeezing and noise
reduction, in this non-equilibrium quantum phase-transition. In particular, we
compute the squeezing spectrum near threshold, and calculate the optimum value.
We find that the optimal noise reduction occurs at different driving fields,
depending on the ratio of damping rates. The largest spectral noise reductions
are predicted to occur with a very high-Q second-harmonic cavity. Our analytic
results agree well with stochastic numerical simulations. We also compare the
results obtained in the positive-P representation, as a fully quantum
mechanical calculation, with the truncated Wigner phase space equation, also
known as semiclassical theory.


title: Real measurements and Quantum Zeno effect

abstract:
  In 1977, Mishra and Sudarshan showed that an unstable particle would never be
found decayed while it was continuously observed. They called this effect the
quantum Zeno effect (or paradox). Later it was realized that the frequent
measurements could also accelerate the decay (quantum anti-Zeno effect). In
this paper we investigate the quantum Zeno effect using the definite model of
the measurement. We take into account the finite duration and the finite
accuracy of the measurement. A general equation for the jump probability during
the measurement is derived. We find that the measurements can cause inhibition
(quantum Zeno effect) or acceleration (quantum anti-Zeno effect) of the
evolution, depending on the strength of the interaction with the measuring
device and on the properties of the system. However, the evolution cannot be
fully stopped.


title: Discrimination between nonorthogonal two-photon polarization states

abstract:
  It is shown that generalized measurements, required for optimally
discriminating between nonorthogonal joint polarization states of two
indistinguishable photons, can be realized with the help of
polarization-dependent two-photon absorption and by means of sum-frequency
generation. Optimization schemes are investigated with respect to minimizing
the error probability in inferring the states, as well as with respect to
maximizing the probability of success for unambiguous discrimination. Moreover,
an implementation of error-minimizing discrimination between N symmetric
single-photon states is studied. The latter can be used to extract information
from the inconclusive results occurring in unambiguous discrimination between
three symmetric two-photon polarization states.


title: Theory of nonlinear Landau-Zener tunneling

abstract:
  A nonlinear Landau-Zener model was proposed recently to describe, among a
number of applications, the nonadiabatic transition of a Bose-Einstein
condensate between Bloch bands. Numerical analysis revealed a striking
phenomenon that tunneling occurs even in the adiabatic limit as the nonlinear
parameter $C$ is above a critical value equal to the gap $V$ of avoided
crossing of the two levels. In this paper, we present analytical results that
give quantitative account of the breakdown of adiabaticity by mapping this
quantum nonlinear model into a classical Josephson Hamiltonian. In the critical
region, we find a power-law scaling of the nonadiabatic transition probability
as a function of $C/V-1$ and $\alpha $, the crossing rate of the energy levels.
In the subcritical regime, the transition probability still follows an
exponential law but with the exponent changed by the nonlinear effect. For
$C/V>>1$, we find a near unit probability for the transition between the
adiabatic levels for all values of the crossing rate.


title:
Strictly contractive quantum channels and physically realizable quantum
  computers

abstract:
  We study the robustness of quantum computers under the influence of errors
modelled by strictly contractive channels. A channel $T$ is defined to be
strictly contractive if, for any pair of density operators $\rho,\sigma$ in its
domain, $\| T\rho - T\sigma \|_1 \le k \| \rho-\sigma \|_1$ for some $0 \le k <
1$ (here $\| \cdot \|_1$ denotes the trace norm). In other words, strictly
contractive channels render the states of the computer less distinguishable in
the sense of quantum detection theory. Starting from the premise that all
experimental procedures can be carried out with finite precision, we argue that
there exists a physically meaningful connection between strictly contractive
channels and errors in physically realizable quantum computers. We show that,
in the absence of error correction, sensitivity of quantum memories and
computers to strictly contractive errors grows exponentially with storage time
and computation time respectively, and depends only on the constant $k$ and the
measurement precision. We prove that strict contractivity rules out the
possibility of perfect error correction, and give an argument that approximate
error correction, which covers previous work on fault-tolerant quantum
computation as a special case, is possible.


title: A Convergent Iterative Solution of the Quantum Double-well Potential

abstract:
  We present a new convergent iterative solution for the two lowest quantum
wave functions $\psi_{ev}$ and $\psi_{od}$ of the Hamiltonian with a quartic
double well potential $V$ in one dimension. By starting from a trial function,
which is by itself the exact lowest even or odd eigenstate of a different
Hamiltonian with a modified potential $V+\delta V$, we construct the Green's
function for the modified potential. The true wave functions, $\psi_{ev}$ or
$\psi_{od}$, then satisfies a linear inhomogeneous integral equation, in which
the inhomogeneous term is the trial function, and the kernel is the product of
the Green's function times the sum of $\delta V$, the potential difference, and
the corresponding energy shift. By iterating this equation we obtain successive
approximations to the true wave function; furthermore, the approximate energy
shift is also adjusted at each iteration so that the approximate wave function
is well behaved everywhere. We are able to prove that this iterative procedure
converges for both the energy and the wave function at all $x$.


title: Quantum algebraic symmetries in atomic clusters, molecules and nuclei

abstract:
  Quantum algebras (also called quantum groups) are deformed versions of the
usual Lie algebras, to which they reduce when the deformation parameter q is
set equal to unity. From the mathematical point of view they are Hopf algebras.
Their use in physics became popular with the introduction of the q-deformed
harmonic oscillator as a tool for providing a boson realization of the quantum
algebra SUq(2), although similar mathematical structures had already been
known. Initially used for solving the quantum Yang-Baxter equation, quantum
algebras have subsequently found applications in several branches of physics,
as, for example, in the description of spin chains, squeezed states, hydrogen
atom and hydrogen-like spectra, rotational and vibrational nuclear and
molecular spectra, and in conformal field theories. By now much work has been
done on the q-deformed oscillator and its relativistic extensions, and several
kinds of generalized deformed oscillators and SU(2) algebras have been
introduced. Here we shall confine ourselves to a list of applications of
quantum algebras in nuclear structure physics and in molecular physics and, in
addition, a recent application of quantum algebraic techniques to the structure
of atomic clusters will be discussed in more detail.

categories: quant-ph math-ph math.MP nucl-th physics.chem-ph


title: Spin squeezing of atoms by Rydberg blockade

abstract:
  We show that the interaction between Rydberg atomic states can provide
continuous spin squeezing of atoms with two ground states. The interaction
prevents the simultaneous excitation of more than a single atom in the sample
to the Rydberg state, and we propose to utilize this blockade effect to realize
an effective collective spin hamiltonian J_x^2-J_y^2. With this hamiltonian the
quantum mechanical uncertainty of the spin variable J_x+J_y can be reduced
significantly.


title:
Complete solution of the Schr\"odinger equation for the time-dependent
  linear potential

abstract:
  The complete solutions of the Schr\"odinger equation for a particle with
time-dependent mass moving in a time-dependent linear potential are presented.
One solution is based on the wave function of the plane wave, and the other is
with the form of the Airy function. A comparison is made between the present
solution and former ones to show the completeness of the present solution.


title: Relational Reality in Relativistic Quantum Mechanics

abstract:
  Up to now it has been impossible to find a realistic interpretation for the
reduction process in relativistic quantum mechanics. The basic problem is the
dependence of the states on the frame within which collapse takes place. A
suitable use of the causal structure of the devices involved in the measurement
process allows us to introduce a covariant notion for the collapse of quantum
states.


title:
Non-thermal nuclear magnetic resonance quantum computing using
  hyperpolarized Xenon

abstract:
  Current experiments in liquid-state nuclear magnetic resonance quantum
computing are limited by low initial polarization. To address this problem, we
have investigated the use of optical pumping techniques to enhance the
polarization of a 2-qubit NMR quantum computer (13C and 1H in 13CHCl3). To
efficiently use the increased polarization, we have generalized the procedure
for effective pure state preparation. With this new, more flexible scheme, an
effective pure state was prepared with polarization-enhancement of a factor of
10 compared to the thermal state. An implementation of Grover's quantum search
algorithm was demonstrated using this new technique.


title:
Generation of bright squeezed light at 1.06 $\mu m$ using cascaded
  non-linearities in a triply resonant c.w. PPLN OPO

abstract:
  We have used an ultra-low threshold continuous-wave Optical Parametric
Oscillator (OPO) to reduce the quantum fluctuations of the reflected pump beam
below the shot noise limit. The OPO consisted of a triply resonant cavity
containing a Periodically-Poled Lithium Niobate crystal pumped by a Nd:YAG
laser and giving signal and idler wavelengths close to 2.12 microns and a
threshold as low as 300 microwatts. We detected the quantum fluctuations of the
pump beam reflected by the OPO using a slightly modified homodyne detection
technique. The measured noise reduction was 30 % (inferred noise reduction at
the output of the OPO 38 %).


title: Quantum computer inverting time arrow for macroscopic systems

abstract:
  A legend tells that once Loschmidt asked Boltzmann on what happens to his
statistical theory if one inverts the velocities of all particles, so that, due
to the reversibility of Newton's equations, they return from the equilibrium to
a nonequilibrium initial state. Boltzmann only replied ``then go and invert
them''. This problem of the relationship between the microscopic and
macroscopic descriptions of the physical world and time-reversibility has been
hotly debated from the XIXth century up to nowadays. At present, no modern
computer is able to perform Boltzmann's demand for a macroscopic number of
particles. In addition, dynamical chaos implies exponential growth of any
imprecision in the inversion that leads to practical irreversibility. Here we
show that a quantum computer composed of a few tens of qubits, and operating
even with moderate precision, can perform Boltzmann's demand for a macroscopic
number of classical particles. Thus, even in the regime of dynamical chaos, a
realistic quantum computer allows to rebuild a specific initial distribution
from a macroscopic state given by thermodynamic laws.


title: Doppler cooling of a Coulomb crystal

abstract:
  We study theoretically Doppler laser-cooling of a cluster of 2-level atoms
confined in a linear ion trap. Using several consecutive steps of averaging we
derive, from the full quantum mechanical master equation, an equation for the
total mechanical energy of the one dimensional crystal, defined on a
coarse-grained energy scale whose grid size is smaller than the linewidth of
the electronic transition. This equation describes the cooling dynamics for an
arbitrary number of ions and in the quantum regime. We discuss the validity of
the ergodic assumption (i.e. that the phase space distribution is only a
function of energy). From our equation we derive the semiclassical limit (i.e.
when the mechanical motion can be treated classically) and the Lamb-Dicke limit
(i.e. when the size of the mechanical wave function is much smaller than the
laser wavelength). We find a Fokker-Planck equation for the total mechanical
energy of the system, whose solution is in agreement with previous analytical
calculations which were based on different assumptions and valid only in their
specific regimes. Finally, in the classical limit we derive an analytic
expression for the average coupling, by light scattering, between motional
states at different energies.


title:
Lower bound for the quantum capacity of a discrete memoryless quantum
  channel

abstract:
  We generalize the random coding argument of stabilizer codes and derive a
lower bound on the quantum capacity of an arbitrary discrete memoryless quantum
channel. For the depolarizing channel, our lower bound coincides with that
obtained by Bennett et al. We also slightly improve the quantum
Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue
of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof
is restricted to the binary quantum channels, but its extension of to l-adic
channels is straightforward.


title:
An implementation of the polynomial Lie algebra methods for solving a
  class of nonlinear models in quantum optics

abstract:
  We develop some calculation schemes to determine dynamics of a wide class of
integrable quantum-optical models using their symmetry adapted reformulation in
terms of polynomial Lie algebras $su_{pd}(2)$. These schemes, based on
"diagonal" representations of model evolution operators (via diagonalizing
Hamiltonians with the help of the $su_{pd}(2)$ defining relations), are
implemented in the form adapted for numerical calculations. Their efficiency is
demonstrated on the example of the second-harmonic-generation model.