title:
Exact gate-sequences for universal quantum computation using the
  XY-interaction alone

abstract:
  In a previous publication [1] we showed that it is possible to implement
universal quantum computation with the anisotropic XY-Heisenberg exchange
acting as a single interaction. To achieve this we used encodings of the states
of the computation into a larger Hilbert space. This proof is non-
constructive, however, and did not explicitly give the trade-offs in time that
are required to implement encoded single qubit operations and encoded two-qubit
gates. Here we explicitly give the gate-sequences needed to simulate these
operations on encoded qubits and qutrits (three-level systems) and analyze the
trade-offs involved. We also propose a possible layout for the qubits in a
triangular arrangement.


title: Purification and correlated measurements of bipartite mixed states

abstract:
  We prove that all purifications of a non-factorable state (i.e., the state
which cannot be expressed in a form $\rho_{AB}=\rho_A\otimes\rho_B$) are
entangled. We also show that for any bipartite state there exists a pair of
measurements which are correlated on this state if and only if the state is
non-factorable.


title: Aspects of Two-Level Systems under External Time Dependent Fields

abstract:
  The dynamics of two-level systems in time-dependent backgrounds is under
consideration. We present some new exact solutions in special backgrounds
decaying in time. On the other hand, following ideas of Feynman, Vernon and
Hellwarth, we discuss in detail the possibility to reduce the quantum dynamics
to a classical Hamiltonian system. This, in particular, opens the possibility
to directly apply powerful methods of classical mechanics (e.g. KAM methods) to
study the quantum system. Following such an approach, we draw conclusions of
relevance for ``quantum chaos'' when the external background is periodic or
quasi-periodic in time.

categories: quant-ph hep-th math-ph math.MP physics.optics


title: Quantum fast Fourier transform using multilevel atoms

abstract:
  We propose an implementation of the quantum fast Fourier transform algorithm
in an entangled system of multilevel atoms. The Fourier transform occurs
naturally in the unitary time evolution of energy eigenstates and is used to
define an alternate wave-packet basis for quantum information in the atom. A
change of basis from energy levels to wave packets amounts to a discrete
quantum Fourier transform within each atom. The algorithm then reduces to a
series of conditional phase transforms between two entangled atoms in mixed
energy and wave-packet bases. We show how to implement such transforms using
wave-packet control of the internal states of the ions in the linear ion-trap
scheme for quantum computing.


title:
Continuous variable teleportation of single photon states (Proceedings
  version)

abstract:
  We investigate the changes to a single photon state caused by the non-maximal
entanglement in continuous variable quantum teleportation. It is shown that the
teleportation measurement introduces field coherence in the output.


title: Classical entanglement

abstract:
  Classical systems can be entangled. Entanglement is defined by coincidence
correlations. Quantum entanglement experiments can be mimicked by a mechanical
system with a single conserved variable and 77.8% conditional efficiency.
Experiments are replicated for four particle entanglement swapping and GHZ
entanglement.


title: Comment on "The Quantum State of a Propagating Laser Field"

abstract:
  We comment on the theoretical quantum state of a propagating laser field
proposed by van Enk and Fuchs [quant-ph/0104036, quant-ph/0111157] and clarify
that the multimode description of the propagating laser field does not modify
our analysis of continuous variable quantum teleportation [quant-ph/0103147].
Furthermore we point out that the ``complete measurements'' discussed by van
Enk and Fuchs have not been achieved by existing technology and may not be
possible even in principle.


title:
Quantum Mechanics and Stochastic Mechanics for compatible observables at
  different times

abstract:
  Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum
Mechanics in presence of non-interacting subsystems. In both cases, it is shown
that correlations at different times of compatible position observables on
stationary states agree with Quantum Mechanics only in the case of product wave
functions. By appropriate Bell-like inequalities it is shown that no classical
theory, in particular no stochastic process, can reproduce the quantum
mechanical correlations of position variables of non interacting systems at
different times.


title: Entanglement swapping between multi-qudit systems

abstract:
  We generalize the entanglement swapping scheme originally proposed for two
pairs of qubits to an arbitrary number $q$ of systems composed from an
arbitrary number $m_j$ of qudits. Each of the system is supposed to be prepared
in a maximally entangled state of $m_j$ qudits, while different systems are not
correlated at all. We show that when a set $\sum_{j=1}^q a_j$ particles (from
each of the $q$ systems $a_j$ particles are measured) are subjected to a
generalized Bell-type measurement, the resulting set of $\sum_{j=1}^q
(m_j-a_j)$ particles will collapse into a maximally entangled state.


title: Open n-Qubit System as a Quantum Computer with Four-Valued Logic

abstract:
  In this paper we generalize the usual model of quantum computer to a model in
which the state is an operator of density matrix and the gates are general
superoperators (quantum operations), not necessarily unitary. A mixed state
(operator of density matrix) of n two-level quantum system (open or closed
n-qubit system) is considered as an element of $4^{n}$-dimensional operator
Hilbert space (Liouville space). It allows to use quantum computer (circuit)
model with 4-valued logic. The gates of this model are general superoperators
which act on n-ququats state. Ququat is quantum state in a 4-dimensional
(operator) Hilbert space. Unitary two-valued logic gates and quantum operations
for n-qubit open system are considered as four-valued logic gates acting on
n-ququats. We discuss properties of quantum 4-valued logic gates. In the paper
we study universality for quantum four-valued logic gates.


title: Specification of statistical description in quantum mechanics

abstract:
  It is shown that the statistical conception of quantum mechanics is dynamical
but not probabilistic, i.e. the statistical description in quantum mechanics is
founded on dynamics. A use of the probability theory, when it takes place, is
auxiliary. Attention is drawn to the fact that in the quantum mechanics there
are two different objects: an individual object to be statistically described
and a statistical average object, which is a result of the statistical
description. Identification of the two different objects (a use of the same
term for both) is an origin of many known quantum mechanics paradoxes.


title:
Universal Quantum Gates for Single Cooper Pair Box Based Quantum
  Computing

abstract:
  We describe a method for achieving arbitrary 1-qubit gates and controlled-NOT
gates within the context of the Single Cooper Pair Box (SCB) approach to
quantum computing. Such gates are sufficient to support universal quantum
computation. Quantum gate operations are achieved by applying sequences of
voltages and magnetic fluxes to single qubits or pairs of qubits. Neither the
temporal duration, nor the starting time, of a gate operation is used as a
control parameter. As a result, the quantum gates have a constant and known
duration, and depend upon standard control parameter sequences regardless of
when the gate operation begins. This simplifies the integration of quantum
gates into parallel, synchronous, quantum circuits. In addition, we demonstrate
the ability to fabricate such gates, and large-scale quantum circuits, using
current e-beam lithography technology. These features make the SCB-based scheme
a credible contender for practical quantum computer hardware.


title: Dynamics of Josephson junction systems in the computational subspace

abstract:
  The quantum dynamics of the Josephson junction system in the computational
subspace is investigated. A scheme for the controlled not operation is given
for two capasitively coupled SQUIDs. In this system, there is no systematic
error for the two qubit operation. For the inductively coupled SQUIDs, the
effective Hamiltonian causes systematic errors in the computational subspace
for the two qubit operation. Using the purterbation theory, we construct a more
precise effective Hamiltonian. This new effective Hamiltonian reduces the
systematic error to the level much lower than the threshold of the fault
resilent quantum computation.


title:
Dynamical effects of a one-dimensional multibarrier potential of finite
  range

abstract:
  We discuss the properties of a large number N of one-dimensional (bounded)
locally periodic potential barriers in a finite interval. We show that the
transmission coefficient, the scattering cross section $\sigma$, and the
resonances of $\sigma$ depend sensitively upon the ratio of the total spacing
to the total barrier width. We also show that a time dependent wave packet
passing through the system of potential barriers rapidly spreads and deforms, a
criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum
by imposing (large) periodic boundary conditions we find a Wigner type
distribution. We investigate also the S-matrix poles; many resonances occur for
certain values of the relative spacing between the barriers in the potential.


title: Generalizations of Heisenberg uncertainty relation

abstract:
  A survey on the generalizations of Heisenberg uncertainty relation and a
general scheme for their entangled extensions to several states and observables
is presented. The scheme is illustrated on the examples of one and two states
and canonical quantum observables, and spin and quasi-spin components. Several
new uncertainty relations are displayed.
  PACS 0365H, 4250D, 0220.


title:
Tripartite Entanglement in a Bose Condensate by Stimulated Bragg
  Scattering

abstract:
  We show that it is possible to entangle three different many-particle states
by Bragg spectroscopy with nonclassical light in a Bose condensate of weakly
interacting atomic gases. Among these three states, two are of atoms
corresponding to two opposite momentum side-modes of the condensate; and the
other is of single-mode photons of the output probe beam. We demonstrate strong
dependence of the multiparticle entanglement on the quantum statistics of the
probe light. We present detailed results on entanglement keeping in view of the
possible experimental situation.


title: A random matrix approach to decoherence

abstract:
  In order to analyze the effect of chaos or order on the rate of decoherence
in a subsystem, we aim to distinguish effects of the two types of dynamics by
choosing initial states as random product states from two factor spaces
representing two subsystems. We introduce a random matrix model that permits to
vary the coupling strength between the subsystems. The case of strong coupling
is analyzed in detail, and we find no significant differences except for very
low-dimensional spaces.


title:
Implementation of quantum gates and preparation of entangled states in
  cavity QED with cold trapped ions

abstract:
  We propose a scheme to perform basic gates of quantum computing and prepare
entangled states in a system with cold trapped ions located in a single mode
optical cavity. General quantum computing can be made with both motional state
of the trapped ion and cavity state being qubits. We can also generate
different kinds of entangled states in such a system without state reduction,
and can transfer quantum states from the ion in one trap to the ion in another
trap. Experimental requirement for achieving our scheme is discussed.


title: Darboux's Theorem and Quantisation

abstract:
  It has been established that endowing classical phase space with a Riemannian
metric is sufficient for describing quantum mechanics. In this letter we argue
that, while sufficient, the above condition is certainly not necessary in
passing from classical to quantum mechanics. Instead, our approach to quantum
mechanics is modelled on a statement that closely resembles Darboux's theorem
for symplectic manifolds.


title: Alpha and Electro-weak Coupling

abstract:
  It is shown that the fine structure constant alpha has the same value that
"characterises" a relation, denoted by alpha_137(29*137), between a
representation of the cyclic group of order 29*137 and the induced
representation for the cyclic subgroup of order 137. The value of this
characteristic is alpha_137(29*137) = 0.007297352532... . The complementary
characteristic alpha_29(29*137)=0.034280626357... for the cyclic subgroup of
order 29 is shown to represent the gauge theory electro-weak coupling quantity
g^2/(4 pi). Kinematic aspects of the representation geometry are discussed and
a generalized version of the Weinberg electro-weak mixing angle is introduced.


title: The power of entangled quantum channels

abstract:
  All communication channels are at bottom quantum mechanical. Quantum
mechanics contributes both obstacles to communication in the form of noise, and
opportunities in the use of intrinsically quantum representations for
information. This paper investigates the trade-off between power and
communication rate for coupled quantum channels. By exploiting quantum
correlations such as entanglement, coupled quantum channels can communicate at
a potentially higher rate than unentangled quantum channels given the same
power. In particular, given the same overall power, M coupled, entangled
quantum channels can send M bits in the same time it takes a single channel to
send a single bit, and in the same time it takes M unentangled channels to send
$\sqrt M$ bits.


title: A General SU(2) Formulation for Quantum Searching with Certainty

abstract:
  A general quantum search algorithm with arbitrary unitary transformations and
an arbitrary initial state is considered in this work. To serach a marked state
with certainty, we have derived, using an SU(2) representation: (1) the
matching condition relating the phase rotations in the algorithm, (2) a concise
formula for evaluating the required number of iterations for the search, and
(3) the final state after the search, with a phase angle in its amplitude of
unity modulus. Moreover, the optimal choices and modifications of the phase
angles in the Grover kernel is also studied.


title: Continuous variable quantum cloning via the Cavity QED with trapped ions

abstract:
  We present a feasible scheme to use trapped ions Cavity QED system to
implement optimal $1\to N$ cloning machine of coherent state. In present
scheme, as the ouput of the clone machine, the copies of the cavity mode emerge
at the vibrational modes and cavity modes is acted as the ancilla mode in the
implementation of the cloning. We further show that such system can be used to
generated multimodes quantum state, which can realize optimum symmetric $1\to
N$ telecloning of coherent state of distant cavity.


title: Probability Models and Ultralogics

abstract:
  In this paper, we show how nonstandard consequence operators, ultralogics,
can generate the general informational content displayed by probability models.
In particular, a probability model that predicts that a specific single event
will occur and those models that predict that a specific distribution of events
will occur.


title:
The Einstein-Podolsky-Rosen Paradox and Entanglement 1: Signatures of
  EPR correlations for continuous variables

abstract:
  A generalization of the 1935 Einstein-Podolsky-Rosen (EPR) argument for
measurements with continuous variable outcomes is presented to establish
criteria for the demonstration of the EPR paradox, for situations where the
correlation between spatially separated subsystems is not perfect. Two types of
criteria for EPR correlations are determined. The first type are based on
measurements of the variances of conditional probability distributions and are
necessary to reflect directly the situation of the original EPR paradox. The
second weaker set of EPR criteria are based on the proven failure of
(Bell-type) local realistic theories which could be consistent with a local
quantum description for each subsystem. The relationship with criteria
sufficient to prove entanglement is established, to show that any demonstration
of EPR correlations will also signify entanglement. It is also shown how a
demonstration of entanglement between two spatially separated subsystems, if
not able to interpreted as a violation of a Bell-type inequality, may be
interpreted as a demonstration of the EPR correlations. In particular it is
explained how the experimental observation of two-mode squeezing using
spatially separated detectors will signify not only entanglement but EPR
correlations defined in a general sense.


title:
The Einstein-Podolsky-Rosen Paradox and Entanglement 2: Application to
  Proof of Security for Continuous Variable Quantum Cryptography

abstract:
  In a previous paper certain measurable criteria have been derived, that are
sufficient to demonstrate the existence of Einstein-Podolsky-Rosen (EPR)
correlations for measurements with continuous variable outcomes. Here it is
shown how such EPR criteria, which do not demand perfect EPR correlations, can
be used to prove the extent of security for continuous variable quantum
cryptographic schemes (in analogy to that proposed by Ekert) where Alice and
Bob hope to construct a secure sequence of values from measurements performed
on continuous-variable EPR-correlated fields sent from a distant source. It is
proven that the demonstration of the EPR criterion on Alice's and Bob's joint
statistics compels a necessary loss in the ability to infer the results shared
by Alice and Bob, by measurements performed on any third channel potentially
representing an eavesdropper (Eve). This result makes no assumption about the
nature of the quantum source of the fields transmitted to Alice and Bob, except
that the EPR correlations are observed at the final detector locations. In this
way a means is provided to establish security in the presence of some loss and
less than optimal correlation, and against any eavesdropping strategy employed
by Eve prior to detection of the fields by Alice and Bob.


title:
Polynomial Lie algebra methods in solving the second-harmonic generation
  model: some exact and approximate calculations

abstract:
  We compare exact and SU(2)-cluster approximate calculation schemes to
determine dynamics of the second-harmonic generation model using its
reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related
spectral representations of the model evolution operator realized in
algorithmic forms. It enabled us to implement computer experiments exhibiting a
satisfactory accuracy of the cluster approximations in a large range of
characteristic model parameters.


title: Cold Trapped Ions as Quantum Information Processors

abstract:
  In this tutorial we review physical implementation of quantum computing using
a system of cold trapped ions. We discuss systematically all the aspects for
making the implementation possible. Firstly, we go through the loading and
confining of atomic ions in the linear Paul trap, then we describe the
collective vibrational motion of trapped ions. Further, we discuss interactions
of the ions with a laser beam. We treat the interactions in the travelling-wave
and standing-wave configuration for dipole and quadrupole transitions. We
review different types of laser cooling techniques associated with trapped
ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke
limit, sympathetic cooling and laser cooling using electromagnetically induced
transparency. After that we discuss the problem of state detection using the
electron shelving method. Then quantum gates are described. We introduce
single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT
gates. We also comment on more advanced multi-qubit logic gates. We describe
how quantum logic networks may be used for the synthesis of arbitrary pure
quantum states. Finally, we discuss the speed of quantum gates and we also give
some numerical estimations for them. A discussion of dynamics on off-resonant
transitions associated with a qualitative estimation of the weak coupling
regime and of the Lamb-Dicke regime is included in Appendix.


title: Entanglement in the Dicke model

abstract:
  We show how an ion trap, configured for the coherent manipulation of external
and internal quantum states, can be used to simulate the irreversible dynamics
of a collective angular momentum model known as the Dicke model. In the special
case of two ions, we show that entanglement is created in the coherently driven
steady state with linear driving. For the case of more than two ions we
calculate the entanglement between two ions in the steady state of the Dicke
model by tracing over all the other ions. The entanglement in the steady state
is a maximum for the parameter values corresponding roughly to a bifurcation of
a fixed point in the corresponding semiclassical dynamics. We conjecture that
this is a general mechanism for entanglement creation in driven dissipative
quantum systems.


title: Finite Renormalization ll

abstract:
  This paper is an updated version of the paper of similar title published in
September 1998 {21} modified to take into account recent experimental results
and recommendations from CODATA {19} and also to incorporate a correction. The
original abstract follows and is still valid. A 1960's suggestion by R. P.
Feynman, concerning the possibility of carrying out a "finite" renormalization
procedure in quantum electrodynamics, is here implemented using a newly
discovered "formula" for alpha, the fine structure constant.


title: A proposal of quantum logic gates using cold trapped ions in a cavity

abstract:
  We propose a scheme for implementation of logical gates in a trapped ion
inside a high-Q cavity. The ion is simultaneously interacting with a
(classical) laser field as well as with the (quantized) cavity field. We
demonstrate that simply by tuning the ionic internal levels with the
frequencies of the fields, it is possible to construct a controlled-NOT gate in
a three step procedure, having the ion's internal as well as motional levels as
qubits. The cavity field is used as an auxiliary qubit and basically remains in
the vacuum state.


title:
Suppression of decoherence in quantum registers by entanglement with a
  nonequilibrium environment

abstract:
  It is shown that a nonequilibrium environment can be instrumental in
suppressing decoherence between distinct decoherence free subspaces in quantum
registers. The effect is found in the framework of exact coherent-product
solutions for model registers decohering in a bath of degenerate harmonic
modes, through couplings linear in bath coordinates. These solutions represent
a natural nonequilibrium extension of the standard solution for a decoupled
initial register state and a thermal environment. Under appropriate conditions,
the corresponding reduced register distribution can propagate in an unperturbed
manner, even in the presence of entanglement between states belonging to
distinct decoherence free subspaces, and despite persistent bath entanglement.
As a byproduct, we also obtain a refined picture of coherence dynamics under
bang-bang decoherence control. In particular, it is shown that each
radio-frequency pulse in a typical bang-bang cycle induces a revival of
coherence, and that these revivals are exploited in a natural way by the
time-symmetrized version of the bang-bang protocol.


title:
Maximal-entropy-production-rate nonlinear quantum dynamics compatible
  with second law, reciprocity, fluctuation-dissipation, and time-energy
  uncertainty relations

abstract:
  In view of the recent quest for well-behaved nonlinear extensions of the
traditional Schroedinger-von Neumann unitary dynamics that could provide
fundamental explanations of recent experimental evidence of loss of quantum
coherence at the microscopic level, in this paper, together with a review of
the general features of the nonlinear quantum (thermo)dynamics I proposed in a
series of papers [see references in G.P. Beretta, Found.Phys. 17, 365 (1987)],
I show its exact equivalence with the maximal-entropy-production
variational-principle formulation recently derived in S.
Gheorghiu-Svirschevski, Phys.Rev. A 63, 022105 (2001). In addition, based on
the formalism of general interest I developed for the analysis of composite
systems, I show how the variational derivation can be extended to the case of a
composite system to obtain the general form of my equation of motion, that
turns out to be consistent with the demanding requirements of strong
separability. Moreover, I propose a new intriguing fundamental ansatz: that the
time evolution along the direction of steepest entropy ascent unfolds at the
fastest rate compatible with the time-energy Heisenberg uncertainty relation.
This ansatz provides a possible well-behaved general closure of the nonlinear
dynamics, compatible with the nontrivial requirements of strong separability,
and with no need of new physical constants. In any case, the time-energy
uncertainty relation provides lower bounds to the internal-relaxation-time
functionals and, therefore, upper bounds to the rate of entropy production.


title: Stochastic Simulation of The Three Dimensional Quantum Vacuum

abstract:
  A complete solution to the long standing problem of basing Schroedinger
quantum theory on standard stochastic theory is given. The solution covers all
"single" particle three-dimensional Schroedinger theory linear or nonlinear and
with any external potential present. The system is classical, set in a
six-dimensional space and involves vacuum polarization as the background
process. Basic vacuum polarization energy characterised oscillators are
identified and then in assemblies are analysed in terms of energy occurrence
frequencies. The orbits of polarization monopoles are given and shown to be
elliptical on subspaces surfaces. The basic process takes place at the speed of
light and is of a statistical "zitterbewegung" character. The orthodox quantum
probability density bilinear quadratic form is derived from angular momentum
consideration within the system which is shown to be a generalisation of the
usual quantum structure. Two statistical assemblies are identified, a linear
one associated with superposition of eigenfunctions and a quadratic one
associated with interactions between eigenstates. It is suggested that this
two-tier probabilistic system will remove some possible paradoxes that plague
the orthodox thoory. The relation of vacuum polarization in this work with its
occurrence in other physical contexts and a connection with "spin" is
discussed.


title: A Quantum Coupling Conjecture

abstract:
  Following the successful prediction of an exact value for the fine structure
constant later confirmed to differ numerically from the centre value of the
latest experimental recommended CODATA range by 10^{-12}, further analysis and
predictions of exact values for two other quantum coupling constants, the
strong and the electroweak, are given. The method employed to obtain these
theoretical values depends on the conjecture that measured values of a
fundamental set of quantum coupling constants approximate to exact values that
can be found in a specific set C_Q of numerical values which has a countable
number of elements. The letter C and its subscript Q stand for coupling and
quantum respectively. A full definition of this set are given in the body of
this paper. Questions of how this conjecture might be validated from the
theoretical and measurement point of view and the identification of those
elements of C_Q which have values of definite physical significance constitute
the subject matter of this paper.


title: Statistical Origin of Quantum Mechanics

abstract:
  The one particle quantum mechanics is considered in the frame of a N-body
classical kinetics in the phase space. Within this framework, the scenario of a
subquantum structure for the quantum particle, emerges naturally, providing an
ontological support to the orthodox quantum mechanics. This approach to quantum
mechanics, constitutes a deductive and direct method which, in a
self-consistent scheme of a classical kinetics, allows us: i) to obtain the
probabilistic nature of the quantum description and to interpret the wave
function $\psi$ according to the Copenhagen school; ii) to derive the quantum
potential and then the Schr\"odinger equation; iii) to calculate the values of
the physical observables as mean values of the associated quantum operators;
iv) to obtain the Heisenberg uncertainty principle.

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


title: Entanglement Swapping of Generalized Cat States and Secret Sharing

abstract:
  We introduce generalized cat states for d-level systems and obtain concise
formulas for their entanglement swapping with generalized Bell states. We then
use this to provide both a generalization to the d-level case and a transparent
proof of validity for an already proposed protocol of secret sharing based on
entanglement swapping


title:
Optimal unambiguous discrimination between subsets of non-orthogonal
  quantum states

abstract:
  It is known that unambiguous discrimination among non-orthogonal but linearly
independent quantum states is possible with a certain probability of success.
Here, we consider a variant of that problem. Instead of discriminating among
all of the different states, we shall only discriminate between two subsets of
them. In particular, for the case of three non-orthogonal states, we show that
the optimal strategy to distinguish between a set containing one of the states
from the set containing the other two has a higher success rate than if we wish
to discriminate among all three states. Somewhat surprisingly, for unambiguous
discrimination the subsets need not be linearly independent. A fully analytical
solution is presented, and we also show how to construct generalized
interferometers (multiports) that provide an optical implementation of the
optimal strategy.


title: Non-Newtonian Mechanics

abstract:
  The classical motion of spinning particles can be described without employing
Grassmann variables or Clifford algebras, but simply by generalizing the usual
spinless theory. We only assume the invariance with respect to the Poincare'
group; and only requiring the conservation of the linear and angular momenta we
derive the zitterbewegung: namely the decomposition of the 4-velocity in the
newtonian constant term p/m and in a non-newtonian time-oscillating spacelike
term. Consequently, free classical particles do not obey, in general, the
Principle of Inertia. Superluminal motions are also allowed, without violating
Special Relativity, provided that the energy-momentum moves along the worldline
of the center-of-mass. Moreover, a non-linear, non-constant relation holds
between the time durations measured in different reference frames. Newtonian
Mechanics is re-obtained as a particular case of the present theory: namely for
spinless systems with no zitterbewegung. Introducing a Lagrangian containing
also derivatives of the 4-velocity we get a new equation of the motion,
actually a generalization of the Newton Law a=F/m. Requiring the rotational
symmetry and the reparametrization invariance we derive the classical spin
vector and the conserved scalar Hamiltonian, respectively. We derive also the
classical Dirac spin and analyze the general solution of the Eulero-Lagrange
equation for Dirac particles. The interesting case of spinning systems with
zero intrinsic angular momentum is also studied.


title: Quantum oscillations without quantum coherence

abstract:
  We study numerically the damping of quantum oscillations and the increase of
entropy with time in model spin systems decohered by a spin bath. In some
experimentally relevant cases, the oscillations of considerable amplitude can
persist long after the entropy has saturated near its maximum, i.e. when the
system has been decohered almost completely. Therefore, the pointer states of
the system demonstrate non-trivial dynamics. The oscillations exhibit slow
power-law decay, rather than exponential or Gaussian, and may be observable in
experiments.


title:
Combined encoding and decoupling solution to problems of decoherence and
  design in solid-state quantum computing

abstract:
  Proposals for scalable quantum computing devices suffer not only from
decoherence due to the interaction with their environment, but also from severe
engineering constraints. Here we introduce a practical solution to these major
concerns, addressing solid state proposals in particular. Decoherence is first
reduced by encoding a logical qubit into two qubits, then completely eliminated
by an efficient set of decoupling pulse sequences. The same encoding removes
the need for single-qubit operations, that pose a difficult design constraint.
We further show how the dominant decoherence processes can be identified
empirically, in order to optimize the decoupling pulses.


title: A Refinement of Shor's Algorithm

abstract:
  A refinement of Shor's Algorithm for determining order is introduced, which
determines a divisor of the order after any one run of a quantum computer with
almost absolute certainty. The information garnered from each run is
accumulated to determine the order, and for any k greater than 1, there is a
guaranteed minimum positive probability that the order will be determined after
at most k runs. The probability of determination of the order after at most k
runs exponentially approaches a value negligibly less than one, so that the
accumulated information determines the order with almost absolute certainty.
The probability of determining the order after at most two runs is more than
60%, and the probability of determining the order after at most four runs is
more than 90%.


title: Fluctuations of the Retarded Van der Waals Force

abstract:
  The retarded Van der Waals force between a polarizable particle and a
perfectly conducting plate is re-examined. The expression for this force given
by Casimir and Polder represents a mean force, but there are large fluctuations
around this mean value on short time scales which are of the same order of
magnitude as the mean force itself. However, these fluctuations occur on time
scales which are typically of the order of the light travel time between the
atom and the plate. As a consequence, they will not be observed in an
experiment which measures the force averaged over a much longer time. In the
large time limit, the magnitude of the mean squared velocity of a test particle
due to this fluctuating Van der Waals force approaches a constant, and is
similar to a Brownian motion of a test particle in an thermal bath with an
effective temperature. However the fluctuations are not isotropic in this case,
and the shift in the mean square velocity components can even be negative. We
interpret this negative shift to correspond to a reduction in the velocity
spread of a wavepacket. The force fluctuations discussed in this paper are
special case of the more general problem of stress tensor fluctuations. These
are of interest in a variety of areas fo physics, including gravity theory.
Thus the effects of Van der Waals force fluctuations serve as a useful model
for better understanding quantum effects in gravity theory.


title: Quantum computation with trapped ions in strongly detuned optical cavity

abstract:
  We propose a scheme to implement quantum phase gate for two $\Lambda$ ions
trapped in optical cavity. It is shown that quantum phase gate can be
implemented by applying a laser addressing to a single ions in strongly detuned
optical cavity. We further demonstrate that geometric quantum phase gate can be
implemented by introducing a auxiliary ground state.


title:
Temporal Oscillations of Nonlinear Faraday Rotation in Coherently Driven
  Media

abstract:
  New phenomenon of temporal oscillations of nonlinear Faraday rotation in a
driven four-level system is predicted. We show that in this system with one
upper level, under the conditions of electromagnetically induced transparency
created by a strong coupling field, the polarization rotation of weak probe
light exhibits slowly damped oscillations with a frequency proportional to the
strength of an applied magnetic field. This opens up an alternate way to
sensitive magnetometric measurements. Applications in low-light nonlinear
optics such as photon entanglement are feasible.


title: Stoppage of Light Made Flexible by an Additional Control Field

abstract:
  We show how the application of a coupling field connecting the two lower
metastable states of a Lambda system facilitates stoppage of light in a coheren
tly driven Doppler broadened atomic medium via electromagnetic induced
transparency


title: Sensitivity of Quantum Motion for Classically Chaotic Systems

abstract:
  We discuss the behavior of fidelity for a classically chaotic quantum system
in the metallic regime. We show the existence of a critical value of the
perturbation below which the exponential decay of fidelity is determined by the
width of the Breit-Wigner distribution and above which the quantum decay
follows the classical one which is ruled by the Lyapunov exponent. The
independence of the decay {\it rate} from the perturbation strength derives
from the similarity of the quantum and classical relaxation process inside the
Heisenberg time scale.


title:
Bogoliubov transformations and exact isolated solutions for simple
  non-adiabatic Hamiltonians

abstract:
  We present a new method for finding isolated exact solutions of a class of
non-adiabatic Hamiltonians of relevance to quantum optics and allied areas.
Central to our approach is the use of Bogoliubov transformations of the bosonic
fields in the models. We demonstrate the simplicity and efficiency of this
method by applying it to the Rabi Hamiltonian.


title:
Continuous-variable Werner state: separability, nonlocality, squeezing
  and teleportation

abstract:
  We investigate the separability, nonlocality and squeezing of
continuous-variable analogue of the Werner state: a mixture of pure two-mode
squeezed vacuum state with local thermal radiations. Utilizing this Werner
state, coherent-state teleportation in Braunstein-Kimble setup is discussed.


title:
A generalization of the Fenyes-Nelson stochastic model of quantum
  mechanics

abstract:
  It is shown that the stochastic model of Fenyes and Nelson can be generalized
in such a way that the diffusion constant of the Markov theory becomes a free
parameter. This extra freedom allows one to identify quantum mechanics with a
class of Markov processes with diffusion constants varying from zero to
infinity.


title:
On the quantification of entanglement in infinite-dimensional quantum
  systems

abstract:
  We investigate entanglement measures in the infinite-dimensional regime.
First, we discuss the peculiarities that may occur if the Hilbert space of a
bi-partite system is infinite-dimensional, most notably the fact that the set
of states with infinite entropy of entanglement is trace-norm dense in state
space, implying that in any neighborhood of every product state there lies an
arbitrarily strongly entangled state. The starting point for a clarification of
this counterintuitive property is the observation that if one imposes the
natural and physically reasonable constraint that the mean energy is bounded
from above, then the entropy of entanglement becomes a trace-norm continuous
functional. The considerations will then be extended to the asymptotic limit,
and we will prove some asymptotic continuity properties. We proceed by
investigating the entanglement of formation and the relative entropy of
entanglement in the infinite-dimensional setting. Finally, we show that the set
of entangled states is still trace-norm dense in state space, even under the
constraint of a finite mean energy.


title: Demonstration of the Complementarity of One- and Two-Photon Interference

abstract:
  The visibilities of second-order (single-photon) and fourth-order
(two-photon) interference have been observed in a Young's double-slit
experiment using light generated by spontaneous parametric down-conversion and
a photon-counting intensified CCD camera. Coherence and entanglement underlie
one-and two-photon interference, respectively. As the effective source size is
increased, coherence is diminished while entanglement is enhanced, so that the
visibility of single-photon interference decreases while that of two-photon
interference increases. This is the first experimental demonstration of the
complementarity between single- and two-photon interference (coherence and
entanglement) in the spatial domain.


title: A Balanced Truncation Primer

abstract:
  Balanced truncation, a technique from robust control theory, is a systematic
method for producing simple approximate models of complex linear systems. This
technique may have significant applications in physics, particularly in the
study of large classical and quantum systems. These notes summarize the
concepts and results necessary to apply balanced truncation.


title: On the physical meaning of the EPR--chameleon experiment

abstract:
  The physical meaning of the EPR--chameleon experiment proposed in
AcRe00b,AcRe01a, in which the EPR correlations are reproduced by local,
independent, deterministic choices is re-examined. In addition we extend the
mathematical model of AcRe00b,AcRe01a by showing that the dynamics considered
there is effectively the reduced dynamics of a fully reversible evolution. We
also propose a new protocol, more directly corresponding to real experiments,
in which the local computers only send back to the central one the results of
the evaluation of $\pm1$--valued functions. The program to run the experiment
is available from the WEB-page: http://volterra.mat.uniroma2.it.


title: Range Theorems for Quantum Probability and Entanglement

abstract:
  We consider the set of all matrices of the form $p_{ij}=tr[W(E_{i}\otimes
F_{j})]$ where $E_{i}$, $F_{j}$ are projections on a Hilbert space $H$, and $W$
is some state on $H\otimes H$. We derive the basic properties of this set,
compare it with the classical range of probability, and note how its properties
may be related to geometric measures of entanglement.


title:
Geometrical Aspects of Lie Groups Representations and Their Optical
  Applications

abstract:
  In this paper we present a new procedure to obtain unitary and irreducible
representations of Lie groups starting from the cotangent bundle of the group
(the cotangent group). We discuss some applications of the construction in
quantum-optics problems.


title: Quantum field theory and dense measurement

abstract:
  We show, using quantum field theory, that performing a large number of
identical repetitions of the same measurement does not only preserve the
initial state of the wave function (the Zeno effect), but also produces
additional physical effects. We first demonstrate that a Zeno type effect can
emerges also in the framework of quantum field theory, that is, as a quantum
field phenomenon. We also derive a Zeno type effect from quantum field theory
for the general case in which the initial and final states are different. The
basic physical entities dealt with in this work are not the conventional
once-perfomed physical processes, but their $n$ times repetition where $n$
tends to infinity. We show that the presence of these repetitions entails the
presence of additional excited state energies, and the absence of them entails
the absence of these excited energies. We also show that in the presence of
these repetitions the Schroedinger equation may be derived from the functional
generalization of quantum mechanics.


title:
A simple way to detect the state transition caused by the nondiagonal
  abelian Berry phase

abstract:
  In a nondegenerate syste, the abelian Berry's phase will never cause
transitions among the Hamiltonian's eigenstate. However, in a degenerate
syatem, it is well known that the state transition can be caused by the
non-abelian Berry phase. Actually, in a such a system, the phase factor is not
always nonabelian. Even in the case that the phase is a nondiagonal matrix, it
still can be an abelian phase and can cause the state transitions. We then
propose a simple scheme to detect such an effect of the Berry phase to the
degenerate states by using the optical entangled pair state. In this scheme, we
need not control any external parameters during the quantum state evolution.


title: Vacuum Squeezing in Atomic Media via Self-Rotation

abstract:
  When linearly polarized light propagates through a medium in which
elliptically polarized light would undergo self-rotation, squeezed vacuum can
appear in the orthogonal polarization. A simple relationship between
self-rotation and the degree of vacuum squeezing is developed. Taking into
account absorption, we find the optimum conditions for squeezing in any medium
that can produce self-rotation. We then find analytic expressions for the
amount of vacuum squeezing produced by an atomic vapor when light is
near-resonant with a transition between various low-angular-momentum states.
Finally, we consider a gas of multi-level Rb atoms, and analyze squeezing for
light tuned near the D-lines under realistic conditions.


title: Universal Quantum Estimator

abstract:
  We present a simple device based on the controlled-SWAP gate that performs
quantum state tomography. It can also be used to determine maximum and minimum
eigenvalues, expectation values of arbitrary observables, purity estimation as
well as characterizing quantum channels. The advantage of this scheme is that
the architecture is fixed and the task performed is determined by the input
data.


title: A Thermodynamical Approach to Quantifying Quantum Correlations

abstract:
  We consider the amount of work which can be extracted from a heat bath using
a bipartite state shared by two parties. In general it is less then the amount
of work extractable when one party is in possession of the entire state. We
derive bounds for this "work deficit" and calculate it explicitly for a number
of different cases. For pure states the work deficit is exactly equal to the
distillable entanglement of the state, and this is also achievable for
maximally correlated states. In these cases a form of complementarity exists
between physical work which can be extracted and distillable entanglement. The
work deficit is a good measure of the quantum correlations in a state and
provides a new paradigm for understanding quantum non-locality.


title:
Information and Distinguishability of Ensembles of Identical Quantum
  States

abstract:
  We consider a fixed quantum measurement performed over $n$ identical copies
of quantum states. Using a rigorous notion of distinguishability We consider a
fixed quantum measurement performed over $n$ identical copies of quantum
states. Using a rigorous notion of distinguishability based on Shannon's 12th
theorem, we show that in the case of a single qubit the number of
distinguishable states is
$W(\alpha_1,\alpha_2,n)=|\alpha_1-\alpha_2|\sqrt{\frac{2n}{\pi e}}$, where
$(\alpha_1,\alpha_2)$ is the angle interval from which the states are chosen.
In the general case of an $N$-dimensional Hilbert space and an area $\Omega$ of
the domain on the unit sphere from which the states are chosen, the number of
distinguishable states is $W(N,n,\Omega)=\Omega(\frac{2n}{\pi
e})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in
Cartesian coordinates.based on Shannon's 12th theorem, we show that in the case
of a single qubit the number of distinguishable states is
$W(\alpha_1,\alpha_2,n)=|\alpha_1-\alpha_2|\sqrt{\frac{2n}{\pi e}}$, where
$(\alpha_1,\alpha_2)$ is the angle interval from which the states are chosen.
In the general case of an $N$-dimensional Hilbert space and an area $\Omega$ of
the domain on the unit sphere from which the states are chosen, the number of
distinguishable states is $W(N,n,\Omega)=\Omega(\frac{2n}{\pi
e})^{\frac{N-1}{2}}$. The optimal distribution is uniform over the domain in
Cartesian coordinates.


title: Stochastic quantization of the linearized gravitational field

abstract:
  Stochastic field equations for linearized gravity are presented. The theory
is compared with the usual quantum field theory and questions of Lorentz
covariance are discussed. The classical radiation approximation is also
presented.


title:
Probability and Nonlocality in Many Minds Interpretations of Quantum
  Mechanics

abstract:
  We argue that a certain type of many minds (and many worlds) interpretations
of quantum mechanics due to Lockwood (and Deutsch) do not provide a coherent
interpretation of the quantum mechanical probabilistic algorithm. By contrast,
in Albert and Loewer's version of the many minds interpretation there is a
coherent interpretation of the quantum mechanical probabilities. We consider
Albert and Loewer's probability interpretation in the context of Bell-type and
GHZ-type states and argue that it exhibits a certain form of nonlocality which
is, however, much weaker than Bell's nonlocality.


title: Interference of spontaneously emitted photons

abstract:
  We discuss an experimental setup where two laser-driven atoms spontaneously
emit photons and every photon causes a ``click'' at a point on a screen. By
deriving the probability density for an emission into a certain direction from
basic quantum mechanical principles we predict a spatial interference pattern.
Similarities and differences with the classical double-slit experiment are
discussed.


title: Quantum cryptographic ranging

abstract:
  We present a system to measure the distance between two parties that allows
only trusted people to access the result. The security of the protocol is
guaranteed by the complementarity principle in quantum mechanics. The protocol
can be realized with available technology, at least as a proof of principle
experiment.


title: Liouville invariance in quantum and classical mechanics

abstract:
  The density-matrix and Heisenberg formulations of quantum mechanics
follow--for unitary evolution--directy from the Schr"odinger equation.
Nevertheless, the symmetries of the corresponding evolution operator, the
Liouvillian L=i[.,H], need not be limited to those of the Hamiltonian H. This
is due to L only involving eigenenergy_differences_, which can be degenerate
even if the energies themselves are not. Remarkably, this possibility has
rarely been mentioned in the literature, and never pursued more generally. We
consider an example involving mesoscopic Josephson devices, but the analysis
only assumes familiarity with basic quantum mechanics. Subsequently, such
_L-symmetries_ are shown to occur more widely, in particular also in classical
mechanics. The symmetry's relevance to dissipative systems and
quantum-information processing is briefly discussed.


title: Space-Time and Probability

abstract:
  Special relativity is most naturally formulated as a theory of space-time
geometry, but within the space-time framework probability apears to be at best
an epistemic notion - a matter of what can be known, not of the status of
events in themselves. However, a non-epistemic account of probability can be
given in Minkowski space-time, in terms of the Everett interpretation. We work
throughout in the consistent histories formalism, first in tems of a single
history, and then using many


title: Role of interference and entanglement in quantum neural processing

abstract:
  The role of interference and entanglement in quantum neural processing is
discussed. It is argued that on contrast to the quantum computing the problem
of the use of exponential resources as the payment for the absense of
entanglement does not exist for quantum neural processing. This is because of
corresponding systems, as any modern classical artificial neural systems, do
not realize functions precisely, but approximate them by training on small sets
of examples. It can permit to implement quantum neural systems optically,
because in this case there is no need in exponential resources of optical
devices (beam-splitters etc.). On the other hand, the role of entanglement in
quantum neural processing is still very important, because it actually
associates qubit states: this is necessary feature of quantum neural memory
models.


title:
Geometric quantization of completely integrable Hamiltonian systems in
  the action-angle variables

abstract:
  We provide geometric quantization of a completely integrable Hamiltonian
system in the action-angle variables around an invariant torus with respect to
polarization spanned by almost-Hamiltonian vector fields of angle variables.
The associated quantum algebra consists of functions affine in action
coordinates. We obtain a set of its nonequivalent representations in the
separable pre-Hilbert space of smooth complex functions on the torus where
action operators and a Hamiltonian are diagonal and have countable spectra.


title: Sympathetic Cooling of Trapped Cd+ Isotopes

abstract:
  We sympathetically cool a trapped 112Cd+ ion by directly Doppler-cooling a
114Cd+ ion in the same trap. This is the first demonstration of optically
addressing a single trapped ion being sympathetically cooled by a different
species ion. Notably, the experiment uses a single laser source, and does not
require strong focusing. This paves the way toward reducing decoherence in an
ion trap quantum computer based on Cd+ isotopes.


title:
Intense laser interacting with a two level atom: WKB expressions for
  dipole transitions and population inversion

abstract:
  In a previous paper, we have already considered the system composed by a two
level atom interacting with a coherent external electromagnetic field. No
application whatsoever has been made of the rotating wave approximation. Being
specially interested in the problem of higher harmonic generations for the case
of very intense laser fields, we have developed in this letter a much more
efficient way to obtain these solutions as well as to carry out some
calculations in a range in which the parameters take extreme values. Also the
formalism allows us now to provide analytic expressions in the WKB regime for
the electric dipole moment and the population inversion. The spectrum can be
decomposed in periodic and non-periodic contributions. Only the latter depends
upon the Floquet exponent and can be responsible of the main complexities of
the observed Rabi revivals and the hyper-Raman shift.


title:
Quantum lower bounds for the collision and the element distinctness
  problems

abstract:
  Given a function f as an oracle, the collision problem is to find two
distinct inputs i and j such that f(i)=f(j), under the promise that such inputs
exist. Since the security of many fundamental cryptographic primitives depends
on the hardness of finding collisions, quantum lower bounds for the collision
problem would provide evidence for the existence of cryptographic primitives
that are immune to quantum cryptanalysis.
  In this paper, we prove that any quantum algorithm for finding a collision in
an r-to-one function must evaluate the function Omega((n/r)^{1/3}) times, where
n is the size of the domain and r|n. This improves the previous best lower
bound of Omega((n/r)^{1/5}) evaluations due to Aaronson [quant-ph/0111102], and
is tight up to a constant factor.
  Our result also implies a quantum lower bound of Omega(n^{2/3}) queries to
the inputs for the element distinctness problem, which is to determine whether
or not the given n real numbers are distinct. The previous best lower bound is
Omega(sqrt{n}} queries in the black-box model; and Omega(sqrt{n}log{n})
comparisons in the comparisons-only model, due to H{\o}yer, Neerbek, and Shi
[ICALP'01, quant-ph/0102078].


title: Coins, Quantum Measurements, and Turing's Barrier

abstract:
  Is there any hope for quantum computing to challenge the Turing barrier, i.e.
to solve an undecidable problem, to compute an uncomputable function? According
to Feynman's '82 argument, the answer is {\it negative}. This paper re-opens
the case: we will discuss solutions to a few simple problems which suggest that
{\it quantum computing is {\it theoretically} capable of computing uncomputable
functions}. In this paper a mathematical quantum "device" (with sensitivity
$\epsilon$) is constructed to solve the Halting Problem. The "device" works on
a randomly chosen test-vector for $T$ units of time. If the "device" produces a
click, then the program halts. If it does not produce a click, then either the
program does not halt or the test-vector has been chosen from an {\it
undistinguishable set of vectors} ${\IF}_{\epsilon, T}$. The last case is not
dangerous as our main result proves: {\it the Wiener measure of}
${\IF}_{\epsilon, T}$ {\it constructively tends to zero when} $T$ {\it tends to
infinity}. The "device", working in time $T$, appropriately computed, will
determine with a pre-established precision whether an arbitrary program halts
or not. {\it Building the "halting machine" is mathematically possible.}


title: Linear Optical CNOT Gate in the Coincidence Basis

abstract:
  We describe the operation and tolerances of a non-deterministic, coincidence
basis, quantum CNOT gate for photonic qubits. It is constructed solely from
linear optical elements and requires only a two-photon source for its
demonstration.


title: The Wave Theory of the Field

abstract:
  As a substitute for the current hypothesis of space-time continuity, we show
the nature and the characteristics of a Schild's discrete space-time. With the
wave perturbations of its metrical structure we formulate the working
hypothesis that all subatomic particles are elementary sources of spherical
waves constituting on the whole the mass fields, the electromagnetic and the
nuclear field we attribute to the particles. The explicative effectiveness of
the new wave unification between quantum mechanics and general relativity is
shown by a wave interpretation of three experimental phenomena that lie
different physics: astrophysics, optics and quantum physics. A further use of
wave Compton effect leads us to discover a mechanism of wave resonance which is
able to verify the possible existence of a source of elementary waves that
shows a wave model of electron and all the particles. The wave nature of masses
and the generalized effect of a Relative Symmetry Principle leads us to
consider the inertia as a local consequence of the wave structure of bodies.
The same changeable wave model used for explaining inertia it is also valid to
show a quantized gravitational interaction and the wave nature of gravity.


title: Introduction to Coherent States and Quantum Information Theory

abstract:
  The purpose of this paper is to introduce several basic theorems of coherent
states and generalized coherent states based on Lie algebras su(2) and su(1,1),
and to give some applications of them to quantum information theory for
graduate students or non--experts who are interested in both Geometry and
Quantum Information Theory. In the first half we make a general review of
coherent states and generalized coherent states based on Lie algebras su(2) and
su(1,1) from the geometric point of view and, in particular, prove that each
resolution of unity can be obtained by the curvature form of some bundle on the
parameter space. In the latter half we apply a method of generalized coherent
states to some important topics in Quantum Information Theory, in particular,
swap of coherent states and cloning of coherent ones. We construct the swap
operator of coherent states by making use of a generalized coherent operator
based on su(2) and show an "imperfect cloning" of coherent states, and moreover
present some related problems. In conclusion we state our dream, namely, a
construction of {\bf Geometric Quantum Information Theory}.


title:
Anderson's absolute objects and constant timelike vector hidden in Dirac
  matrices

abstract:
  Anderson's theorem asserting, that symmetry of dynamic equations written in
the relativisitically covariant form is determined by symmetry of its absolute
objects, is applied to the free Dirac equation. Dirac matrices are the only
absolute objects of the Dirac equation. There are two ways of the Dirac
matrices transformation: (1) Dirac matrices form a 4-vector and wave function
is a scalar, (2) Dirac matrices are scalars and the wave function is a spinor.
In the first case the Dirac equation is nonrelativistic, in the second one it
is relativistic. Transforming Dirac equation to another scalar-vector
variables, one shows that the first way of transformation is valid, and the
Dirac equation is not relativistic


title: Destruction of states in quantum mechanics

abstract:
  A description of destruction of states on the grounds of quantum mechanics
rather than quantum field theory is proposed. Several kinds of maps called
supertraces are defined and used to describe the destruction procedure. The
introduced algorithm can be treated as a supplement to the von Neumann-Lueders
measurement. The discussed formalism may be helpful in a description of EPR
type experiments and in quantum information theory.


title:
Delay-dependent amplification of a probe pulse via stimulated Rayleigh
  scattering

abstract:
  Stimulated Rayleigh scattering of pump and probe light pulses of close
carrier frequencies is considered. A nonzero time delay between the two pulses
is shown to give rise to amplification of the delayed (probe) pulse accompanied
by attenuation of the pump, both on resonance and off resonance. In either
case, phase-matching effects are shown to provide a sufficiently large gain,
which can exceed significantly direct one-photon-absorption losses.


title: Cloning of symmetric d-level photonic states in physical systems

abstract:
  Optimal procedures play an important role in quantum information. It turns
out that some naturally occurring processes like emission of light from an atom
can realize optimal transformations. Here we study how arbitrary symmetric
states of a number of d-level systems can be cloned using a multilevel atomic
system. It is shown that optimality is always ensured even though the output
number of systems is probabilistic.


title:
Why Decoherence has not Solved the Measurement Problem: A Response to P.
  W. Anderson

abstract:
  We discuss why, contrary to claims recently made by P. W. Anderson,
decoherence has not solved the quantum measurement problem.


title: Clebsch-Gordan coefficients and the binomial distribution

abstract:
  A class of Clebsch-Gordan coefficients are derived from the properties of
conditional probability using the binomial distribution. In particular, in the
case of $l=l_1+l_2$ it is shown that $$[<l_1/2-k_1, l_2/2-k_2|l/2,
k=k_1+k_2]>^2 =\frac{(\begin{array}{c} l_1 k_1\end{array}) (\begin{array}{c}l_2
k_2\end{array})}{(\begin{array}{c}l k \end{array})}$$


title: An entanglement monotone derived from Grover's algorithm

abstract:
  This paper demonstrates that how well a state performs as an input to
Grover's search algorithm depends critically upon the entanglement present in
that state; the more entanglement, the less well the algorithm performs. More
precisely, suppose we take a pure state input, and prior to running the
algorithm apply local unitary operations to each qubit in order to maximize the
probability P_max that the search algorithm succeeds. We prove that, for pure
states, P_max is an entanglement monotone, in the sense that P_max can never be
decreased by local operations and classical communication.


title: Spectra of regular quantum graphs

abstract:
  We consider a class of simple quasi one-dimensional classically
non-integrable systems which capture the essence of the periodic orbit
structure of general hyperbolic nonintegrable dynamical systems. Their behavior
is simple enough to allow a detailed investigation of both classical and
quantum regimes. Despite their classical chaoticity, these systems exhibit a
``nonintegrable analog'' of the Einstein-Brillouin-Keller quantization formula
which provides their spectra explicitly, state by state, by means of convergent
periodic orbit expansions.


title:
The origin of the algebra of quantum operators in the stochastic
  formulation of quantum mechanics

abstract:
  The origin of the algebra of the non-commuting operators of quantum mechanics
is explained in the general Fenyes-Nelson stochastic models in which the
diffusion constant is a free parameter. This is achieved by continuing the
diffusion constant to imaginary values, a continuation which destroys the
physical interpretation, but does not affect experimental predictions. This
continuation leads to great mathematical simplification in the stochastic
theory, and to an understanding of the entire mathematical formalism of quantum
mechanics. It is more than a formal construction because the diffusion
parameter is not an observable in these theories.


title: Multiple return times in the quantum baker map

abstract:
  For chaotic classical systems, the distribution of return times to a small
region of phase space is universal. We propose a simple tool to investigate
multiple returns in quantum systems. Numerical evidence for the baker map and
kicked top points, also in the quantum case, at a universal distribution.


title: Entanglement Creation Using Quantum Interrogation

abstract:
  We present some applications of high efficiency quantum interrogation
("interaction free measurement") for the creation of entangled states of
separate atoms and of separate photons. The quantum interrogation of a quantum
object in a superposition of object-in and object-out leaves the object and
probe in an entangled state. The probe can then be further entangled with other
objects in subsequent quantum interrogations. By then projecting out those
cases were the probe is left in a particular final state, the quantum objects
can themselves be left in various entangled states. In this way we show how to
generate two-, three-, and higher qubit entanglement between atoms and between
photons. The effect of finite efficiency for the quantum interrogation is
delineated for the various schemes.


title: Violation of Bell's inequalities implies distillability for N qubits

abstract:
  We consider quantum systems composed of $N$ qubits, and the family of all
Bell's correlation inequalities for two two-valued measurements per site. We
show that if a $N$-qubit state $\rho$ violates any of these inequalities, then
it is at least bipartite distillable. Indeed there exists a link between the
amount of Bell's inequality violation and the degree of distillability. Thus,
we strengthen the interpretation of Bell's inequalities as detectors of useful
entanglement.


title:
Lower Bounds on the Quantum Capacity and Highest Error Exponent of
  General Memoryless Channels

abstract:
  Tradeoffs between the information rate and fidelity of quantum
error-correcting codes are discussed. Quantum channels to be considered are
those subject to independent errors and modeled as tensor products of copies of
a general completely positive linear map, where the dimension of the underlying
Hilbert space is a prime number. On such a quantum channel, the highest
fidelity of a quantum error-correcting code of length $n$ and rate R is proven
to be lower bounded by 1 - \exp [-n E(R) + o(n)] for some function E(R). The
E(R) is positive below some threshold R', which implies R' is a lower bound on
the quantum capacity. The result of this work applies to general discrete
memoryless channels, including channel models derived from a physical law of
time evolution, or from master equations.


title: Scattering of heavy charged particles on hydrogen atoms

abstract:
  The low energy scattering of heavy positively charged particles on hydrogen
atoms (H) are investigated by solving the Faddeev equations in configuration
space. A resonant value of the pH scattering length, $a=750\pm 5$ a.u., in the
pp antisymmetric state was found. This large value indicates the existence of a
first excited state with a binding energy B=1.14$\times10^{-9}$ a.u. below the
H ground state. Several resonances for non zero angular momenta states are
predicted.

categories: quant-ph physics.atom-ph physics.chem-ph physics.comp-ph


title: Information and Computation: Classical and Quantum Aspects

abstract:
  Quantum theory has found a new field of applications in the realm of
information and computation during the recent years. This paper reviews how
quantum physics allows information coding in classically unexpected and subtle
nonlocal ways, as well as information processing with an efficiency largely
surpassing that of the present and foreseeable classical computers. Some
outstanding aspects of classical and quantum information theory will be
addressed here. Quantum teleportation, dense coding, and quantum cryptography
are discussed as a few samples of the impact of quanta in the transmission of
information. Quantum logic gates and quantum algorithms are also discussed as
instances of the improvement in information processing by a quantum computer.
We provide finally some examples of current experimental realizations for
quantum computers and future prospects.


title: Approximate quantum error correction

abstract:
  The errors that arise in a quantum channel can be corrected perfectly if and
only if the channel does not decrease the coherent information of the input
state. We show that, if the loss of coherent information is small, then
approximate error correction is possible.


title: Quantum Shift Register

abstract:
  We consider a quantum circuit in which shift and rotation operations on
qubits are performed by swap gates and controlled swap gates. These operations
can be useful for quantum computers performing elementary arithmetic operations
such as multiplication and a bit-wise comparison of qubits.


title:
Generalized Hartree Method: A Novel Non-perturbative Scheme for
  Interacting Quantum systems

abstract:
  A self-consistent, non-perturbative scheme of approximation is proposed for
arbitrary interacting quantum systems by generalization of the Hartree
method.The scheme consists in approximating the original interaction term
$\lambda H_I$ by a suitable 'potential' $\lambda V(\phi)$ which satisfies the
following two requirements: (i) the 'Hartree Hamiltonian' $H_o$ generated by
$V(\phi)$ is exactly solvable i.e, the eigen states $|n>$ and the eigenvalues
$E_n$ are known and (ii) the 'quantum averages' of the two are equal, i.e. $<
n|H_I|n>$ = $<n|V(\phi)|n>$ for arbitrary $'n '$. The leading-order results for
$|n>$ and $E_n$, which are already accurate, can be systematically improved
further by the development of a 'Hartree-improved perturbation theory' (HIPT)
with $H_o$ as the unperturbed part and the modified interaction:$\lambda
H^{\prime} \equiv \lambda (H_I-V)$ as the perturbation. The HIPT is assured of
rapid convergence because of the 'Hartree condtion' : $<n| H'| n> = 0$. This is
in contrast to the naive perturbation theory developed with the original
interaction term $\lambda H_I$ chosen as the perturbation, which diverges even
for infinitesimal $\lambda$ ! The structure of the Hartree vacuum is shown to
be highly non-trivial. Application of the method to the anharmonic-and
double-well quartic-oscillators, anharmonic- sextic and octic- oscillators
leads to very accurate results for the energy levels. In case of $\lambda
\phi^{4}$ quantum field theory, the method reproduces, in the leading order,
the results of Gaussian approximation, which can be improved further by the
HIPT. We study the vacuum structure, renormalisation and stability of the
theory in GHA.


title:
Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark
  description

abstract:
  This papers presents a formalism describing the dynamics of a quantum
particle in a one-dimensional tilted time-dependent lattice. The description
uses the Wannier-Stark states, which are localized in each site of the lattice
and provides a simple framework leading to fully-analytical developments.
Particular attention is devoted to the case of a time-dependent potential,
which results in a rich variety of quantum coherent dynamics is found.


title: Alternative commutation relations, star products and tomography

abstract:
  Invertible maps from operators of quantum obvservables onto functions of
c-number arguments and their associative products are first assessed. Different
types of maps like Weyl-Wigner-Stratonovich map and s-ordered quasidistribution
are discussed. The recently introduced symplectic tomography map of observables
(tomograms) related to the Heisenberg-Weyl group is shown to belong to the
standard framework of the maps from quantum observables onto the c-number
functions. The star-product for symbols of the quantum-observable for each one
of the maps (including the tomographic map) and explicit relations among
different star-products are obtained. Deformations of the Moyal star-product
and alternative commutation relations are also considered.


title: Quantum Clock Synchronization: a Multi-Party Protocol

abstract:
  We present a multi-party quantum clock synchronization protocol that utilizes
shared prior entanglement and broadcast of classical information to synchronize
spatially separated clocks. Notably, it is necessary only for any one party to
publish classical information. Consequently, the efficacy of the method is
independent of the relative location of the parties. The suggested protocol is
robust and does not require precise sequencing of procedural steps.


title: Tomographic map within the framework of star-product quantization

abstract:
  Tomograms introduced for the description of quantum states in terms of
probability distributions are shown to be related to a standard star-product
quantization with appropriate kernels. Examples of symplectic tomograms and
spin tomograms are presented.


title: Mesoscopic molecular ions in Bose-Einstein condensates

abstract:
  We study the possible formation of large (mesoscopic) molecular ions in an
ultracold degenerate bosonic gas doped with charged particles (ions). We show
that the polarization potentials produced by the ionic impurities are capable
of capturing hundreds of atoms into loosely bound states. We describe the
spontaneous formation of these hollow molecular ions via phonon emission and
suggest an optical technique for coherent stimulated transitions of free atoms
into a specific bound state. These results open up new interesting
possibilities for manipulating tightly confined ensembles.


title: Momentum in stochastic quantum mechanics

abstract:
  Momentum is analyzed as a random variable in stochastic quantum mechanics.
Arbitrary potential energy functions are considered. The oscillator is
presented as an example.


title:
Inequivalence of pure state ensembles for open quantum systems: the
  preferred ensembles are those that are physically realizable

abstract:
  An open quantum system in steady state $\hat\rho_{ss}$ can be represented by
a weighted ensemble of pure states $\hat\rho_{ss}=\sum_{k}\wp_{k}\ket{\psi_k}
\bra{\psi_k}$ in infinitely many ways. A physically realizable (PR) ensemble is
one for which some continuous measurement of the environment will collapse the
system into a pure state $\ket{\psi(t)}$, stochastically evolving such that the
proportion of time for which $\ket{\psi(t)} = \ket{\psi_{k}}$ equals $\wp_{k}$.
Some, but not all, ensembles are PR. This constitutes the preferred ensemble
fact, with the PR ensembles being the preferred ensembles. We present the
necessary and sufficient conditions for a given ensemble to be PR, and
illustrate the method by showing that the coherent state ensemble is not PR for
an atom laser.


title:
Weak Values, Quantum Trajectories, and the Stony-Brook Cavity QED
  experiment

abstract:
  Weak values as introduced by Aharonov, Albert and Vaidman (AAV) are ensemble
average values for the results of weak measurements. They are interesting when
the ensemble is preselected on a particular initial state and postselected on a
particular final measurement result. I show that weak values arise naturally in
quantum optics, as weak measurements occur whenever an open system is monitored
(as by a photodetector). I use quantum trajectory theory to derive a
generalization of AAV's formula to include (a) mixed initial conditions, (b)
nonunitary evolution, (c) a generalized (non-projective) final measurement, and
(d) a non-back-action-evading weak measurement. I apply this theory to the
recent Stony-Brook cavity QED experiment demonstrating wave-particle duality
[G.T. Foster, L.A. Orozco, H.M. Castro-Beltran, and H.J. Carmichael, Phys. Rev.
Lett. {85}, 3149 (2000)]. I show that the ``fractional'' correlation function
measured in that experiment can be recast as a weak value in a form as simple
as that introduced by AAV.


title: A Raman approach to quantum logic in Calcium-like ions

abstract:
  We consider the feasibility of performing quantum logic operations based on
stimulated Raman transitions in trapped Calcium ions. This technique avoids
many of the technical difficulties involved with laser stabilisation, and only
three laser wavelengths are required, none of which need have particularly
stringent requirements on their bandwidths. The possible problems with
experimental realisations are discussed in detail.


title: Some Points On Casimir Forces

abstract:
  Casimir forces of massive fermionic Dirac fields are calculated for parallel
plates geometry in spatial space with dimension d and imposing bag model
boundary conditions.It is shown that in the range of ma>>1 where m is mass of
fields quanta and a is the separation distance of the plates,it is equal to
massive bosonic fields Casimir force for each degree of freedom.We argue this
equality exists for any massive anyonic field in two-dimensional spatial
space.Also the ratio of massless fermionic field Casimir force to its bosonic
correspondent in d-dimentional spatial space is $(1-1/2^d)$.


title:
Quantum mechanics without spacetime - a possible case for noncommutative
  differential geometry?

abstract:
  The rules of quantum mechanics require a time coordinate for their
formulation. However, a notion of time is in general possible only when a
classical spacetime geometry exists. Such a geometry is itself produced by
classical matter sources. Thus it could be said that the currently known
formulation of quantum mechanics pre-assumes the presence of classical matter
fields. A more fundamental formulation of quantum mechanics should exist, which
avoids having to use a notion of time. In this paper we discuss as to how such
a fundamental formulation could be constructed for single particle,
non-relativistic quantum mechanics. We argue that there is an underlying
non-linear theory of quantum gravity, to which both standard quantum mechanics
and classical general relativity are approximations. The timeless formulation
of quantum mechanics follows from the underlying theory when the mass of the
particle is much smaller than Planck mass. On the other hand, when the
particle's mass is much larger than Planck mass, spacetime emerges and the
underlying theory should reduce to classical mechanics and general relativity.
We also suggest that noncommutative differential geometry is a possible
candidate for describing this underlying theory.


title: Quantum Bit Commitment can be Unconditionally Secure

abstract:
  It is generally believed that unconditionally secure quantum bit commitment
(QBC) is proven impossible by a "no-go theorem". We point out that the theorem
only establishes the existence of a cheating unitary transformation in any QBC
scheme secure against the receiver, but this fact alone is not sufficient to
rule out unconditionally secure QBC as a matter of principle, because there
exists no proof that the cheating unitary transformation must be known to the
cheater in all possible cases. In this work, we show how to circumvent the
"no-go theorem" and prove that unconditionally secure QBC is in fact possible.


title: Momentum kicks due to quantum localization

abstract:
  The momentum changes caused by position measurements are a central feature of
wave-particle duality. Here we investigate two cases - localization by a single
slit, and which-way detection in the double-slit interference experiment - and
examine in detail the associated momentum changes. Particular attention is
given to the transfer of momentum between particle and detector, and the recoil
of the measuring device. We find that single-slit diffraction relies on a form
of `interaction-free' scattering, and that an ideal which-way measurement can
be made without any back-reaction on the detector.


title:
Relativistic Wigner Function, Charge Variable and Structure of Position
  Operator

abstract:
  The relativistic phase-space representation by means of the usual position
and momentum operators for a class of observables with Weyl symbols independent
of charge variable (i.e. with any combination of position and momentum) is
proposed. The dynamical equation coincides with its analogue in the non-local
theory (generalization of the Newton-Wigner position operator approach) under
conditions when particles creation is impossible. Differences reveal themselves
in specific constraints on possible initial conditions.


title:
Classical and Quantum-like approaches to Charged-Particle Fluids in a
  Quadrupole

abstract:
  A classical description of the dynamics of a dissipative charged-particle
fluid in a quadrupole-like device is developed. It is shown that the set of the
classical fluid equations contains the same information as a complex function
satisfying a Schrodinger-like equation in which Planck's constant is replaced
by the time-varying emittance, which is related to the time-varying temperature
of the fluid. The squared modulus and the gradient of the phase of this complex
function are proportional to the fluid density and to the current velocity,
respectively. Within this framework, the dynamics of an electron bunch in a
storage ring in the presence of radiation damping and quantum-excitation is
recovered. Furthermore, both standard and generalized (including dissipation)
coherent states that may be associated with the classical particle fluids are
fully described in terms of the above formalism.


title: Optimal conversion of non--local unitary operations

abstract:
  We study when a non--local unitary operation acting on two $d$--level systems
can probabilistically simulate another one when arbitrary local operations and
classical communication are allowed. We provide necessary and sufficient
conditions for the simulation to be possible. Probabilistic interconvertability
is used to define an equivalence relation between gates. We show that this
relation induces a finite number of classes, that we identify. In the case of
two qubits, two classes of non--local operations exist. We choose the CNOT and
SWAP as representatives of these classes. We show how the CNOT [SWAP] can be
deterministically converted into any operation of its class. We also calculate
the optimal probability of obtaining the CNOT [SWAP] from any operation of the
corresponding class and provide a protocol to achieve this task.


title: Photoconductance Quantization in a Single-Photon Detector

abstract:
  We have made a single-photon detector that relies on photoconductive gain in
a narrow electron channel in an AlGaAs/GaAs 2-dimensional electron gas. Given
that the electron channel is 1-dimensional, the photo-induced conductance has
plateaus at multiples of the quantum conductance 2e$^{2}$/h. Super-imposed on
these broad conductance plateaus are many sharp, small, conductance steps
associated with single-photon absorption events that produce individual
photo-carriers. This type of photoconductive detector could measure a single
photon, while safely storing and protecting the spin degree of freedom of its
photo-carrier. This function is valuable for a quantum repeater that would
allow very long distance teleportation of quantum information.


title:
Atom correlations and spin squeezing near the Heisenberg limit: finite
  system size effect and decoherence

abstract:
  We analyze a model for spin squeezing based on the so-called counter-twisting
Hamiltonian, including the effects of dissipation and finite system size. We
discuss the conditions under which the Heisenberg limit, i.e. phase sensitivity
$\propto 1/N$, can be achieved. A specific implementation of this model based
on atom-atom interactions via quantized photon exchange is presented in detail.
The resulting excitation corresponds to the creation of spin-flipped atomic
pairs and can be used for fast generation of entangled atomic ensembles, spin
squeezing and apllications in quantum information processing. The conditions
for achieving strong spin squeezing with this mechanism are also analyzed.


title:
ROM-based quantum computation: Experimental explorations using Nuclear
  Magnetic Resonance, and future prospects

abstract:
  ROM-based quantum computation (QC) is an alternative to oracle-based QC. It
has the advantages of being less ``magical'', and being more suited to
implementing space-efficient computation (i.e. computation using the minimum
number of writable qubits). Here we consider a number of small (one and
two-qubit) quantum algorithms illustrating different aspects of ROM-based QC.
They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a
one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary
multiplication algorithm; and (d) a two-qubit ROM-based version of the
Deutsch-Jozsa algorithm. For each algorithm we present experimental
verification using NMR ensemble QC. The average fidelities for the
implementation were in the ranges 0.9 - 0.97 for the one-qubit algorithms, and
0.84 - 0.94 for the two-qubit algorithms. We conclude with a discussion of
future prospects for ROM-based quantum computation. We propose a four-qubit
algorithm, using Grover's iterate, for solving a miniature ``real-world''
problem relating to the lengths of paths in a network.


title: Squeezing and feedback

abstract:
  Electro-optical feedback has many features in common with optical
nonlinearities and hence is relevant to the generation of squeezing. First, I
discuss theoretical and experimental results for traveling-wave feedback,
emphasizing how the ``in-loop'' squeezing (also known as ``squashing'') differs
from free squeezing. Although such feedback, based on ordinary (demolition)
photodetection cannot create free squeezing, it can be used to manipulate it.
Then I treat feedback based on nonlinear quantum optical measurements (of which
non-demolition measurements are one example). These {\em are} able to produce
free squeezing, as shown in a number of experiments. Following that I discuss
theories showing that intracavity squeezing can be increased using ordinary
feedback, and produced using QND-based feedback. Finally, I return to
``squashed'' fields and present recent results showing that the reduced in-loop
fluctuations can suppress atomic decay in a manner analogous to the effect for
squeezed fields.


title: Quantum Trajectories for Realistic Detection

abstract:
  Quantum trajectories describe the stochastic evolution of an open quantum
system conditioned on continuous monitoring of its output, such as by an ideal
photodetector. Here we derive (non-Markovian) quantum trajectories for
realistic photodetection, including the effects of efficiency, dead time,
bandwidth, electronic noise, and dark counts. We apply our theory to a
realistic cavity QED scenario and investigate the impact of such detector
imperfections on the conditional evolution of the system state. A practical
theory of quantum trajectories with realistic detection will be essential for
experimental and technological applications of quantum feedback in many areas.


title:
Tomography of multimode quantum systems with quadratic Hamiltonians and
  multivariable Hermite polynomials

abstract:
  The systems with multimode nonstationary Hamiltonians quadratic in position
and momentum operators are reviewed. The tomographic probability distributions
(tomograms) for the Fock states and Gaussian states of the quadratic systems
are discussed. The tomograms for the Fock states are expressed in terms of
multivariable Hermite polynomials. Using the obvious physical relations some
new formulas for multivariable Hermite polynomials are found. Examples of
oscillator and charge moving in electromagnetic field are presented.


title: Entanglement cost of mixed states

abstract:
  We compute the entanglement cost of several families of bipartite mixed
states, including arbitrary mixtures of two Bell states. This is achieved by
developing a technique that allows us to ascertain the additivity of the
entanglement of formation for any state supported on specific subspaces. As a
side result, the proof of the irreversibility in asymptotic local manipulations
of entanglement is extended to two-qubit systems.


title:
Eigenstates of Operating Quantum Computer: Hypersensitivity to Static
  Imperfections

abstract:
  We study the properties of eigenstates of an operating quantum computer which
simulates the dynamical evolution in the regime of quantum chaos. Even if the
quantum algorithm is polynomial in number of qubits $n_q$, it is shown that the
ideal eigenstates become mixed and strongly modified by static imperfections
above a certain threshold which drops exponentially with $n_q$. Above this
threshold the quantum eigenstate entropy grows linearly with $n_q$ but the
computation remains reliable during a time scale which is polynomial in the
imperfection strength and in $n_q$.


title: Using Cloning to Solve NP Complete Problems

abstract:
  Assuming a cloning oracle, satisfiability, which is an NP complete problem,
is shown to belong to $BPP^C$ and $BQP^C$ (depending on the ability of the
oracle C to clone either a binary random variable or a qubit). The same result
is extended in the case of an approximate cloning oracle, thus establishing
that $NP \subseteq BPP^C \subseteq BQP^C$ and $NP \subseteq BPP^{AC} \subseteq
BQP^{AC}$, where C and AC are the exact and approximate cloning oracles,
respectively. Although exact cloning is impossible in quantum systems,
approximate cloning remains a possibility. However, the best known methods for
approximate cloning (based on unitary evolution) do not currently achieve the
desired precision levels. And it remains an open question whether they could be
improved when non-linear (or non-unitary) operators are used. Finally, a
straightforward attempt to dispense with cloning, replacing it by unitary
evolution, is proved to be impossible.


title:
A perspectival version of the modal interpretation of quantum mechanics
  and the origin of macroscopic behavior

abstract:
  We study the process of observation (measurement), within the framework of a
`perspectival' (`relational', `relative state') version of the modal
interpretation of quantum mechanics. We show that if we assume certain features
of discreteness and determinism in the operation of the measuring device (which
could be a part of the observer's nerve system), this gives rise to classical
characteristics of the observed properties, in the first place to spatial
localization. We investigate to what extent semi-classical behavior of the
object system itself (as opposed to the observational system) is needed for the
emergence of classicality. Decoherence is an essential element in the mechanism
of observation that we assume, but it turns out that in our approach no
environment-induced decoherence on the level of the object system is required
for the emergence of classical properties.


title:
Implementation of the Deutsch-Jozsa algorithm with Josephson charge
  qubits

abstract:
  We investigate the realization of a simple solid-state quantum computer by
implementing the Deutsch-Jozsa algorithm in a system of Josephson charge
qubits. Starting from a procedure to carry out the one-qubit Deutsch-Jozsa
algorithm we show how the N-qubit version of the Bernstein-Vazirani algorithm
can be realized. For the implementation of the three-qubit Deutsch-Jozsa
algorithm we study in detail a setup which allows to produce entangled states.


title: Locality and topology in the molecular Aharonov-Bohm effect

abstract:
  It is shown that the molecular Aharonov-Bohm effect is neither nonlocal nor
topological in the sense of the standard magnetic Aharonov-Bohm effect. It is
further argued that there is a close relationship between the molecular
Aharonov-Bohm effect and the Aharonov-Casher effect for an electrically neutral
spin$-{1/2}$ particle encircling a line of charge.


title: Uniqueness of Entanglement Measure and Thermodynamics

abstract:
  We apply the axiomatic approach to thermodynamics presented by Giles to
derive a unique measure of entanglement for bi-partite pure states. This
implies that local manipulations of entanglement in quantum information theory
and adiabatic transformations of states in thermodynamics have the same
underlying mathematical structure. We discuss possible extensions of our
results to mixed and multi-partite states.


title:
Quasi-order of clocks and synchronism and quantum bounds for copying
  timing information

abstract:
  The statistical state of any (classical or quantum) system with non-trivial
time evolution can be interpreted as the pointer of a clock. The quality of
such a clock is given by the statistical distinguishability of its states at
different times. If a clock is used as a resource for producing another one the
latter can at most have the quality of the resource. We show that this
principle, formalized by a quasi-order, implies constraints on many physical
processes. Similarly, the degree to which two (quantum or classical) clocks are
synchronized can be formalized by a quasi-order of synchronism.
  Copying timing information is restricted by quantum no-cloning and
no-broadcasting theorems since classical clocks can only exist in the limit of
infinite energy. We show this quantitatively by comparing the Fisher timing
information of two output systems to the input's timing information. For
classical signal processing in the quantum regime our results imply that a
signal looses its localization in time if it is amplified and distributed to
many devices.


title: Sub-Planck Structure, Decoherence, and Many-Body Environments

abstract:
  In a recent paper [Nature 412, 712 (2001)], Zurek has argued that (1) time
evolution typically causes chaotic quantum systems to generate structure that
varies on the scale of phase-space volume elements of size $(\hbar^2/A)^d$,
where A is a classical action characteristic of the state and d is the number
of degrees of freedom, and that (2) this structure implies that a small change
in a phase-space coordinate X by an amount $\delta X \sim \hbar X/A$
generically results in an orthogonal state. While we agree with (1), we argue
that (2) is not correct if the number of degrees of freedom is small. Our
arguments are based on the Berry-Voros ansatz for the structure of energy
eigenstates in chaotic systems. We find, however, that (2) becomes valid if the
number of degrees of freedom is large. This implies that many-body environments
may be crucial for the phenomenon of quantum decoherence.


title:
Entangled-Photon Generation from Parametric Down-Conversion in Media
  with Inhomogeneous Nonlinearity

abstract:
  We develop and experimentally verify a theory of Type-II spontaneous
parametric down-conversion (SPDC) in media with inhomogeneous distributions of
second-order nonlinearity. As a special case, we explore interference effects
from SPDC generated in a cascade of two bulk crystals separated by an air gap.
The polarization quantum-interference pattern is found to vary strongly with
the spacing between the two crystals. This is found to be a cooperative effect
due to two mechanisms: the chromatic dispersion of the medium separating the
crystals and spatiotemporal effects which arise from the inclusion of
transverse wave vectors. These effects provide two concomitant avenues for
controlling the quantum state generated in SPDC. We expect these results to be
of interest for the development of quantum technologies and the generation of
SPDC in periodically varying nonlinear materials.


title:
Error correction code for protecting three-qubit quantum information
  against erasures

abstract:
  We present a quantum error correction code which protects three quantum bits
(qubits) of quantum information against one erasure, i.e., a single-qubit
arbitrary error at a known position. To accomplish this, we encode the original
state by distributing quantum information over six qubits which is the minimal
number for the present task (see reference [1]). The encoding and error
recovery operations for such a code are presented. It is noted that the present
code is also a three-qubit quantum hidded information code over each qubit. In
addition, an encoding scheme for hiding $n$-qubit quantum information over each
qubit is proposed.


title: Coherent States for Unusual Potentials

abstract:
  The program to construct minimum-uncertainty coherent states for general
potentials works transparently with solvable analytic potentials. However, when
an analytic potential is not completely solvable, like for a double-well or the
linear (gravitational) potential, there can be a conundrum. Motivated by
supersymmetry concepts in higher dimensions, we show how these conundrums can
be overcome.


title:
Simulations of the adiabatic quantum optimization for the Set Partition
  Problem

abstract:
  We analyze the complexity of the quantum optimization algorithm based on
adiabatic evolution for the set partition problem. We introduce a cost function
defined on a logarithmic scale of the partition residues so that the total
number of values of the cost function is of the order of the problem size. We
simulate the behavior of the algorithm by numerical solution of the
time-dependent Schroedinger equation as well as the stationary equation for the
adiabatic eigenvalues. The numerical results for the time-dependent quantum
evolution indicate that the complexity of the algorithm scales exponentially
with the problem size.This result appears to contradict the recent numerical
results for complexity of quantum adiabatic algorithm applied to a different
NP-complete problem (Farhi et al, Science 292, p.472 (2001)).