title:
From the paradoxes of the standard wave-packet analysis to the
  definition of tunneling times for particles

abstract:
  We develop a new variant of the wave-packet analysis and solve the tunneling
time problem for one particle. Our approach suggests an individual asymptotic
description of the quantum subensembles of transmitted and reflected particles
both at the final and initial stage of tunneling. We find the initial states of
both subensembles, which are non-orthogonal. The latter reflects ultimately the
fact that at the initial stage of tunneling it is impossible to predict whether
a particle will be transmitted through or reflected off the barrier. At the
same time, in this case, one can say about the to-be-transmitted and
to-be-reflected subensembles of particles. We show that before the interaction
of the incident packet with the barrier both the number of particles and the
expectation value of the particle's momentum are constant for each subensemble.
Besides, these asymptotic quantities coincide with those of the corresponding
scattered subensemble. On the basis of this formalism we define individual
delay times for both scattering channels. Taking into account the spreading of
wave packets, we define the low bound of the scattering time to describe the
whole quantum ensemble of particles. All three characteristic times are derived
in terms of the expectation values of the position and momentum operators. The
condition which must be fulfilled for completed scattering events is derived.
We propose also the scheme of a {\it gedanken} experiment that allows one to
verify our approach.


title: Quantum Chaos at Finite Temperature

abstract:
  We use the quantum action to study quantum chaos at finite temperature. We
present a numerical study of a classically chaotic 2-D Hamiltonian system -
harmonic oscillators with anharmonic coupling. We construct the quantum action
non-perturbatively and find temperature dependent quantum corrections in the
action parameters. We compare Poincar\'{e} sections of the quantum action at
finite temperature with those of the classical action.


title: A Quantum Structure Description of the Liar Paradox

abstract:
  In this article we propose an approach that models the truth behavior of
cognitive entities (i.e. sets of connected propositions) by taking into account
in a very explicit way the possible influence of the cognitive person (the one
that interacts with the considered cognitive entity). Hereby we specifically
apply the mathematical formalism of quantum mechanics because of the fact that
this formalism allows the description of real contextual influences, i.e. the
influence of the measuring apparatus on the physical entity. We concentrated on
the typical situation of the liar paradox and have shown that (1) the
truth-false state of this liar paradox can be represented by a quantum vector
of the non-product type in a finite dimensional complex Hilbert space and the
different cognitive interactions by the actions of the corresponding quantum
projections, (2) the typical oscillations between false and truth - the paradox
-is now quantum dynamically described by a Schrodinger equation. We analyse
possible philosophical implications of this result.


title: Quantum Mechanics: Structures, Axioms and Paradoxes

abstract:
  We present an analysis of quantum mechanics and its problems and paradoxes
taking into account the results that have been obtained during the last two
decades by investigations in the field of `quantum structures research'. We
concentrate mostly on the results of our group FUND at Brussels Free
University. By means of a spin 1/2 model where the quantum probability is
generated by the presence of fluctuations on the interactions between measuring
apparatus and physical system, we show that the quantum structure can find its
origin in the presence of these fluctuations. This appraoch, that we have
called the 'hidden measurement approach', makes it possible to construct
systems that are in between quantum and classical. We show that two of the
traditional axioms of quantum axiomatics are not satisfied for these 'in
between quantum and classical' situations, and how this structural shortcoming
of standard quantum mechanics is at the origin of most of the quantum
paradoxes. We show that in this approach the EPR paradox identifies a genuine
incompleteness of standard quantum mechanics, however not an incompleteness
that means the lacking of hidden variables, but an incompleteness pointing at
the impossibility for standard quantum mechanics to describe separated quantum
systems. We indicate in which way, by redefining the meaning of density states,
standard quantum mechanics can be completed. We put forward in which way the
axiomatic approach to quantum mechanics can be compared to the traditional
axiomatic approach to relativity theory, and how this might lead to studying
another road to unification of both theories.


title: Quantum probabilities as Bayesian probabilities

abstract:
  In the Bayesian approach to probability theory, probability quantifies a
degree of belief for a single trial, without any a priori connection to
limiting frequencies. In this paper we show that, despite being prescribed by a
fundamental law, probabilities for individual quantum systems can be understood
within the Bayesian approach. We argue that the distinction between classical
and quantum probabilities lies not in their definition, but in the nature of
the information they encode. In the classical world, maximal information about
a physical system is complete in the sense of providing definite answers for
all possible questions that can be asked of the system. In the quantum world,
maximal information is not complete and cannot be completed. Using this
distinction, we show that any Bayesian probability assignment in quantum
mechanics must have the form of the quantum probability rule, that maximal
information about a quantum system leads to a unique quantum-state assignment,
and that quantum theory provides a stronger connection between probability and
measured frequency than can be justified classically. Finally we give a
Bayesian formulation of quantum-state tomography.


title: Quasi-exactly solvable quartic Bose Hamiltonians

abstract:
  We consider Hamiltonians, which are even polynomials of the forth order with
the respect to Bose operators. We find subspaces, preserved by the action of
Hamiltonian These subspaces, being finite-dimensional, include, nonetheless,
states with an \QTR{it}{infinite} number of quasi-particles, corresponding to
the original Bose operators. The basis functions look rather simple in the
coherent state representation and are expressed in terms of the degenerate
hypergeometric function with respect to the complex variable labeling the
representation. In some particular degenerate cases they turn (up to the power
factor) into the trigonometric or hyperbolic functions, Bessel functions or
combinations of the exponent and Hermit polynomials. We find explicitly the
relationship between coefficients at different powers of Bose operators that
ensure quasi-exact solvability of Hamiltonian.


title: Equilibria of Replicator Dynamics in Quantum Games

abstract:
  An evolutionarily stable strategy (ESS) was originally defined as a static
concept but later given a dynamic characterization. A well known theorem in
evolutionary game theory says that an ESS is an attractor of replicator
dynamics but not every attractor is an ESS. We search for a dynamic
characterization of ESSs in quantum games and find that in certain asymmetric
bi-matrix games evolutionary stability of attractors can change as the game
switches between its two forms, one classical and the other quantum.


title:
Entanglement by a beam splitter: nonclassicality as a prerequisite for
  entanglement

abstract:
  A beam splitter is a simple, readily available device which can act to
entangle the output optical fields. We show that a necessary condition for the
fields at the output of the beam splitter to be entangled is that the pure
input states exhibit nonclassical behavior. We generalize this proof for
arbitrary (pure or impure) Gaussian input states. Specifically, nonclassicality
of the input Gaussian fields is a necessary condition for entanglement of the
field modes with the help of the beam splitter. We conjecture that this is a
general property of the beam splitter: Nonclassicality of the inputs is a
necessary condition for entangling fields in the beam splitter.


title: Quantum Zeno-like effect due to competing decoherence mechanisms

abstract:
  We propose a selfconsistent quantum mechanical approach to study the dynamics
of a two-level system subject to random time evolution. This randomness gives
rise to competing effects between dissipative and non-dissipative decoherence
with a consequent slow down of the atomic decay rate.


title: Quantum Parametric Resonance

abstract:
  The quantum mechanical equivalent of parametric resonance is studied. A
simple model of a periodically kicked harmonic oscillator is introduced which
can be solved exactly. Classically stable and unstable regions in parameter
space are shown to correspond to Floquet operators with qualitatively different
properties. Their eigenfunctions, which are calculated exactly, exhibit a
transition: for parameter values with classically stable solutions the
eigenstates are normalizable while they cannot be normalized for parameter
values with classically instable solutions. Similarly, the spectrum of quasi
energies undergoes a specific transition. These observations remain valid
qualitatively for arbitrary linear systems exhibiting classically parametric
resonance such as the paradigm example of a frequency modulated pendulum
described by Mathieu's equation.


title: Bayes' theorem and quantum retrodiction

abstract:
  We derive on the basis of Bayes' theorem a simple but general expression for
the retrodicted premeasurement state associated with the result of any
measurement. The retrodictive density operator is the normalised probability
operator measure element associated with the result. We examine applications to
quantum optical cryptography and to the optical beam splitter.


title: Quantum Bargaining Games

abstract:
  We continue the analysis of quantum-like description of markets and
economics. The approach has roots in the recently developed quantum game theory
and quantum computing. The present paper is devoted to quantum bargaining games
which are a special class of quantum market games without institutionalized
clearinghouses.


title: A classical perspective on nonlocality in quantum field theory

abstract:
  A classical statistical field theory hidden variable model for the quantized
Klein-Gordon model is constructed that preserves relativistic signal locality
and is relativistically covariant, but is at the same time relativistically
nonlocal, paralleling the Hegerfeldt nonlocality of quantum theory. It is
argued that the relativistic nonlocality of this model is acceptable to
classical physics, but in any case the approach taken here characterizes the
nonlocality of the quantized Klein-Gordon model in terms of concepts from
classical statistical field theory.


title:
Supersymmetry and the relationship between a class of singular
  potentials in arbitrary dimensions

abstract:
  The eigenvalues of the potentials
$V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4
}}{r^{4}}$ and
$V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^
{6}}$, and of the special cases of these potentials such as the Kratzer and
Goldman-Krivchenkov potentials, are obtained in N-dimensional space. The
explicit dependence of these potentials in higher-dimensional space is
discussed, which have not been previously covered.


title:
On Some Peculiarities of Solving Nonstationary Problems of Quantum
  Mechanics

abstract:
  Exact solutions of several nonstationary problems of quantum mechanics are
obtained. It is shown that if the initial conditions of the problem correspond
to the localized-in-space particle, then it moves exactly along the classical
trajectory, and the wave packet is not spread in time.


title:
Unified treatment of screening Coulomb and anharmonic oscillator
  potentials in arbitrary dimensions

abstract:
  A mapping is obtained relating radial screened Coulomb systems with low
screening parameters to radial anharmonic oscillators in N-dimensional space.
Using the formalism of supersymmetric quantum mechanics, it is shown that exact
solutions of these potentials exist when the parameters satisfy certain
constraints.


title: Pairwise entanglement in symmetric multi-qubit systems

abstract:
  The concurrence, a quantitative measure of the entanglement between a pair of
particles, is determined for the case where the pair is extracted from a
symmetric state of N two-level systems. Examples are given for both pure and
mixed states of the N-particle system, and for a pair extracted from two
ensembles with correlated collective spins.


title: Detection and correction of errors with quantum tomography

abstract:
  It is shown that quantum tomography can detect and correct unlimited number
of errors during the evaluation of quantum algorithms on quantum computer.


title: Comments on "Quantum Control by Decompositions of SU(2)"

abstract:
  The purpose of the paper is to point out some typos and to observe that the
main result of V. Ramakrishna, K. Flores, H. Rabitz and R. J. Ober, Phys. Rev.
A Volume 62, 054309, 2000 remains valid (and this validity can be verified in a
constructive fashion) with only the requirement that the su(2) matrices A and B
in the paper in the title be linearly independent. An interpretation of this
constructive extension, in terms of Givens rotations of real Euclidean space,
is given.


title: Distinguishability of the Bell states

abstract:
  More than two multipartite orthogonal states cannot always be discriminated
(with certainty) if only local operations and classical communication (LOCC)
are allowed. Using an existing inequality among the measures of entanglement,
we show that any three Bell states cannot be discriminated by LOCC. Exploiting
the inequality, we calculate the distillable entanglement of a certain class of
(4\otimes 4) mixed states.


title:
On general relation between quantum ergodicity and fidelity of quantum
  dynamics

abstract:
  General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.


title: Can quantum chaos enhance stability of quantum computation?

abstract:
  We consider stability of a general quantum algorithm with respect to a fixed
but unknown residual interaction between qubits, and show a surprising fact,
namely that the average fidelity of quantum computation increases by decreasing
average time correlation function of the perturbing operator in sequences of
consecutive quantum gates. Our thinking is applied to the quantum Fourier
transformation where an alternative 'less regular' quantum algorithm is devised
which is qualitatively more robust against static random residual n-qubit
interaction.


title: Lindblad Evolution and Stochasticity: the Case of a Two-Level System

abstract:
  We consider the simple hypothesis of letting quantum systems have an inherent
random nature. Using well-known stochastic methods we thus derive a stochastic
evolution operator which let us define a stochastic density operator whose
expectation value under certain conditions satisfies a Lindblad equation. As
natural consequences of the former assumption decoherence and spontaneous
emission processes are obtained under the same conceptual scheme. A temptative
solution for the preferred basis problem is suggested. All this is illustrated
with a comprehensive study of a two-level quantum system evolution.


title: A Novel Approach to Quantum Heuristics for Structured Database Search

abstract:
  An algorithm for structured database searching is presented and used to solve
the set partition problem. O(n) oracle calls are required in order to obtain a
solution, but the probability that this solution is optimal decreases
exponentially with problem size. Each oracle call is followed by a measurement,
implying that it is necessary to maintain quantum coherence for only one oracle
call at a time.


title: Use of Mathematical Logical Concepts in Quantum Mechanics: An Example

abstract:
  The representation of numbers by product states in quantum mechanics can be
extended to the representation of words and word sequences in languages by
product states. This can be used to study quantum systems that generate text
that has meaning. A simple example of such a system, based on an example
described by Smullyan, is studied here. Based on a path interpretation for some
word states, definitions of truth, validity, consistency and completeness are
given and their properties studied. It is also shown that the relation between
the meaning, if any, of word states and the algorithmic complexity of the
process generating the states must be quite complex or nonexistent.


title: A quantum field theoretic description of the delayed choice experiment

abstract:
  Wheeler's delayed choice experiment, a well known manifestation of the
complementarity principle, has proved somewhat difficult to physically
interpret. We show that, restated in quantum field theoretic language, the
experiment submits to a simple explanation: that wave- or particle-nature is
imposed not at the slit plane but at the detector system. The intepretational
difficulty conventionally encountered is due to the assumption of enforcement
of complementarity at the former.


title: Communicating a direction using spin states

abstract:
  The communication of directions using quantum states is a useful laboratory
test for some basic facts of quantum information. For a system of spin-1/2
particles there are different quantum states that can encode directions. This
information can later be decoded by means of a generalized measurement. In this
talk we present the optimal strategies under different assumptions.


title: Violations of local realism by two entangled quNits

abstract:
  Results obtained in two recent papers, \cite{Kaszlikowski} and \cite{Durt},
seem to indicate that the nonlocal character of the correlations between the
outcomes of measurements performed on entangled systems separated in space is
not robust in the presence of noise. This is surprising, since entanglement
itself is robust. Here we revisit this problem and argue that the class of
gedanken-experiments considered in \cite{Kaszlikowski} and \cite{Durt} is too
restrictive. By considering a more general class, involving sequences of
measurements, we prove that the nonlocal correlations are in fact robust.


title: Canonical Transformations and Squeezing in Quantum Mechanics

abstract:
  In this Paper we present an approach to Quantum Mechanical Canonical
Transformations. Our main result is that Time Dependent Quantum Canonical
Transformations can always be cast in the form of Squeezing Operators. We
revise the main properties of these operators in regard to its Lie group
properties, how two of them can be combined to yield another operator of the
same class and how can also be decomposed and fragmented. In the second part of
the paper we show how this procedure works extremely well for the Time
Dependent Quantum Harmonic Oscillator. The issue of the systematic construction
of Quantum Canonical Transformations is also discussed along the lines of
Dirac, Wigner and Schwinger ideas and to the more recent work by Lee. The main
conclusion is that the Classical Phase Space Transformation can be maintained
in the operator formalism but the construction of the Quantum Canonical
Transformation is not clearly related to the Classical Generating Function of a
Classical Canonical Transformation. We propose the road of Squeezing Operators
rather than the old one attached to Quantum Operators constructed under the
guideline of the exponential of the Classical Generating Function.


title: Some Comments on Three Suggested Postulates for Quantum Theory

abstract:
  Three basic postulates for Quantum Theory are proposed, namely the
Probability, Maximum-Speed and Hilbert-Space postulates. Subsequently we show
how these postulates give rise to well-known and widely used quantum results,
as the probability rule and the linearity of quantum evolution. A discussion of
the postulates in the light of Bell's theorem is included which points towards
yet unsolved conceptual problems in the Foundations of Quantum Mechanics.


title:
Quantum Chaos at Finite Temperature - a New Approach via the Quantum
  Action

abstract:
  We address the problem of quantum chaos: Is there a rigorous, physically
meaningful definition of chaos in quantum physics? Can the tools of classical
chaos theory, like Lyapunov exponents, Poincar\'e sections etc. be carried over
to quantum systems? Can quantitative predictions be made? We show that the
recently proposed quantum action is well suited to answer those questions. As
an example we study chaotic behavior of the 2-D anharmonic oscillator and
compare classical with quantum chaos. Moreover, we study quantum chaos as
function of temperature (the classical system can be considered as the limit
where temperature goes to infinity).


title: Lower bounds for quantum communication complexity

abstract:
  We prove new lower bounds for bounded error quantum communication complexity.
Our methods are based on the Fourier transform of the considered functions.
First we generalize a method for proving classical communication complexity
lower bounds developed by Raz to the quantum case. Applying this method we give
an exponential separation between bounded error quantum communication
complexity and nondeterministic quantum communication complexity. We develop
several other lower bound methods based on the Fourier transform, notably
showing that \sqrt{\bar{s}(f)/\log n}, for the average sensitivity \bar{s}(f)
of a function f, yields a lower bound on the bounded error quantum
communication complexity of f(x AND y XOR z), where x is a Boolean word held by
Alice and y,z are Boolean words held by Bob. We then prove the first large
lower bounds on the bounded error quantum communication complexity of
functions, for which a polynomial quantum speedup is possible. For all the
functions we investigate, the only previously applied general lower bound
method based on discrepancy yields bounds that are O(\log n).


title: Anisotropic Spin Exchange in Pulsed Quantum Gates

abstract:
  We show how to eliminate the first-order effects of the spin-orbit
interaction in the performance of a two-qubit quantum gate. Our procedure
involves tailoring the time dependence of the coupling between neighboring
spins. We derive an effective Hamiltonian which permits a systematic analysis
of this tailoring. Time-symmetric pulsing of the coupling automatically
eliminates several undesirable terms in this Hamiltonian. Well chosen pulse
shapes can produce an effectively isotropic exchange gate, which can be used in
universal quantum computation with appropriate coding.


title: Trapped-Atom-Interferometer in a Magnetic Microtrap

abstract:
  We propose a configuration of a magnetic microtrap which can be used as an
interferometer for three-dimensionally trapped atoms. The interferometer is
realized via a dynamic splitting potential that transforms from a single well
into two separate wells and back. The ports of the interferometer are
neighboring vibrational states in the single well potential. We present a
one-dimensional model of this interferometer and compute the probability of
unwanted vibrational excitations for a realistic magnetic potential. We
optimize the speed of the splitting process in order suppress these excitations
and conclude that such interferometer device should be feasible with currently
available microtrap technique.


title: On the exact solutions of the Lipkin-Meshkov-Glick model

abstract:
  We present the many-particle Hamiltonian model of Lipkin, Meshkov and Glick
in the context of deformed polynomial algebras and show that its exact
solutions can be easily and naturally obtained within this formalism. The
Hamiltonian matrix of each $j$ multiplet can be split into two submatrices
associated to two distinct irreps of the deformed algebra. Their invariant
subspaces correspond to even and odd numbers of particle-hole excitations.


title:
Optimum detection for extracting maximum information from symmetric
  qubit sets

abstract:
  We demonstrate a class of optimum detection strategies for extracting the
maximum information from sets of equiprobable real symmetric qubit states of a
single photon. These optimum strategies have been predicted by Sasaki et al.
[Phys. Rev. A{\bf 59}, 3325 (1999)]. The peculiar aspect is that the detections
with at least three outputs suffice for optimum extraction of information
regardless of the number of signal elements. The cases of ternary (or trine),
quinary, and septenary polarization signals are studied where a standard von
Neumann detection (a projection onto a binary orthogonal basis) fails to access
the maximum information. Our experiments demonstrate that it is possible with
present technologies to attain about 96% of the theoretical limit.


title: Atomic wave packet basis for quantum information

abstract:
  We propose a wave packet basis for storing and processing several qubits of
quantum information in a single multilevel atom. Using radially localized wave
packet states in the Rydberg atom, we construct an orthogonal basis that is
related to the usual energy level basis by a quantum Fourier transform. A
transform-limited laser pulse that is short compared with the classical Kepler
period of the system interacts mainly with the wave packet state localized near
the atomic core, allowing selective control in this basis. We argue that wave
packet control in this regime is useful for multilevel quantum information
processing.


title: Quantum Foundations in the Light of Quantum Information

abstract:
  This paper reports three almost trivial theorems that nevertheless appear to
have significant import for quantum foundations studies. 1) A Gleason-like
derivation of the quantum probability law, but based on the positive
operator-valued measures as the basic notion of measurement (see also Busch,
quant-ph/9909073). Of note, this theorem also works for 2-dimensional vector
spaces and for vector spaces over the rational numbers, where the standard
Gleason theorem fails. 2) A way of rewriting the quantum collapse rule so that
it looks almost precisely identical to Bayes rule for updating probabilities in
classical probability theory. And 3) a derivation of the tensor-product rule
for combining quantum systems (and with it the very notion of quantum
entanglement) from Gleason-like considerations for local measurements on
bipartite systems along with classical communication.


title: The EPR-paradox in massive systems or about strange particles

abstract:
  We give an introduction to an entangled massive system, specifically the
neutral kaon system, which has similarities to the entangled two photon system,
but, however, also challenging differences.


title: Position measuring interactions and the Heisenberg uncertainty principle

abstract:
  An indirect measurement model is constructed for an approximately repeatable,
precise position measuring apparatus that violates the assertion, sometimes
called the Heisenberg uncertainty principle, that any position measuring
apparatus with noise epsilon brings the momentum disturbance no less than
hbar/2epsilon in any input state of the apparatus.


title:
Fibre bundle formulation of relativistic quantum mechanics. II.
  Covariant approach

abstract:
  We propose a fibre bundle formulation of the mathematical base of
relativistic quantum mechanics. At the present stage the bundle form of the
theory is equivalent to its conventional one, but it admits new types of
generalizations in different directions.
  In the present, second, part of our investigation, we consider a covariant
approach to bundle description of relativistic quantum mechanics.
  In it the wavefunctions are replaced with (state) sections of a suitably
chosen vector bundle over space-time whose (standard) fibre is the space of the
wavefunctions. Now the quantum evolution is described as a linear
transportation (by means of the transport along the identity map of the
space\nobreakdash-time) of the state sections in the (total) bundle space.
Connections between the (retarded) Green functions of the relativistic wave
equations and the evolution operators and transports are found. Especially the
Dirac and Klein-Gordon equations are considered.


title: Note on the Controllability of Molecular Systems

abstract:
  The reachable set for a finite dimensional quantum system is shown to be the
orbit of the group corresponding to the internal and control Hamiltonians, even
if this group is not compact.


title:
Optimal sequence of POVMs in the sense of Stein's lemma in quantum
  hypothesis testing

abstract:
  In this paper, we give another proof of quantum Stein's lemma by calculating
the information spectrum, and study an asymptotic optimal measurement in the
sense of Stein's lemma. We propose a projection measurement characterized by
the irreducible representation theory of the special linear group SL(H).
Specially, in spin 1/2 system, it is realized by a simultaneous measurement of
the total momentum and a momentum of a specified direction.


title: A space for the quantum world

abstract:
  Epistemic interpretations of quantum mechanics fail to address the puzzle
posed by the occurrence of probabilities in a fundamental physical theory. This
is a puzzle about the physical world, not a puzzle about our relation to the
physical world. Its solution requires a new concept of physical space,
presented in this article. An examination of how the mind and the brain
construct the phenomenal world reveals the psychological and neurobiological
reasons why we think about space in ways that are inadequate to the physical
world. The resulting notion that space is an intrinsically partitioned expanse
has up to now stood in the way of a consistent ontological interpretation.


title:
Bargmann invariants and off-diagonal geometric phases for multi-level
  quantum systems -- a unitary group approach

abstract:
  We investigate the geometric phases and the Bargmann invariants associated
with a multi-level quantum systems. In particular, we show that a full set of
`gauge-invariant' objects for an $n$-level system consists of $n$ geometric
phases and ${1/2}(n-1)(n-2)$ algebraically independent 4-vertex Bargmann
invariants. In the process of establishing this result we develop a canonical
form for U(n) matrices which is useful in its own right. We show that the
recently discovered `off-diagonal' geometric phases [N. Manini and F.
Pistolesi, Phys. Rev. Lett. 8, 3067 (2000)] can be completely analysed in terms
of the basic building blocks developed in this work. This result liberates the
off-diagonal phases from the assumption of adiabaticity used in arriving at
them.


title: Comparative study of the transient evolution of Hanle EIT/EIA resonances

abstract:
  The temporal evolutions of coherent resonances corresponding to
electromagnetically induced transparency (EIT) and absorption (EIA) were
observed in a Hanle absorption experiment carried on the $D_{2}$ lines of $%
^{87}$Rb vapor by suddenly turning the magnetic field on or off. The main
features of the experimental observations are well reproduced by a theoretical
model based on Bloch equation where the atomic level degeneracy has been fully
accounted for. Similar (opposite phase) evolutions were observed at low optical
field intensities for Hanle/EIT or Hanle/EIA resonances. Unlike the Hanle/EIA\
transients which are increasingly shorter for driving field intensities
approaching saturation, the $B\neq 0$ transient of the Hanle/EIT signal at
large driving field intensities present a long decay time approaching the
atomic transit time. Such counterintuitive behavior is interpreted as a
consequence of the Zeno effect.


title:
Observation of Nonclassical Photon Statistics due to Quantum
  Interference

abstract:
  The nonclassical effect of photon anti-bunching is observed in the mixed
field of a narrow band two-photon source and a coherent field under certain
condition. A variety of different features in photon statistics are found to be
the consequence of a two-photon interference effect with dependence on the
relative phase of the fields. Besides the anti-bunching effect, we find another
one of the features to be also nonclassical. These features emphasize the
importance of quantum entanglement.


title:
Translation-covariant Markovian master equation for a test particle in a
  quantum fluid

abstract:
  A recently proposed master equation in the Lindblad form is studied with
respect to covariance properties and existence of a stationary solution. The
master equation describes the interaction of a test particle with a quantum
fluid, the so-called Rayleigh gas, and is characterized by the appearance of a
two-point correlation function known as dynamic structure factor, which
reflects symmetry and statistical mechanics properties of the fluid. In the
case of a free gas all relevant physical parameters, such as fugacity, ratio
between the masses, momentum transfer and energy transfer are put into
evidence, giving an exact expansion of the dynamic structure factor. The limit
in which these quantities are small is then considered. In particular in the
Brownian limit a Fokker-Planck equation is obtained in which the corrections
due to quantum statistics can be explicitly evaluated and are given in terms of
the Bose function $g_0 (z)$ and the Fermi function $f_0 (z)$.

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


title:
The Precise Formula in a Sine Function Form of the norm of the Amplitude
  and the Necessary and Sufficient Phase Condition for Any Quantum Algorithm
  with Arbitrary Phase Rotations

abstract:
  In this paper we derived the precise formula in a sine function form of the
norm of the amplitude in the desired state, and by means of he precise formula
we presented the necessary and sufficient phase condition for any quantum
algorithm with arbitrary phase rotations. We also showed that the phase
condition: identical rotation angles, is a sufficient but not a necessary phase
condition.


title: Pointlessness and dangerousness of the postulates of quantum mechanics

abstract:
  The formalism of quantum mechanics produces spectacular results, but its
rules, its parameters are empirical, either deduced from classical physics, or
from experimental results rather than from the postulates. Thus, quantum
mechanics is purely phenomenological; for instance, the computation of the
eigenvalues of the energy is generally a simple interpolation in the discrete
space of the quantum numbers. The attempts to show that quantum electrodynamics
is more precise than classical electrodynamics are based on wrong computations.
The lack of paradoxes in the classical theory, the appearance of classical,
true interpretations of the wave-particle duality justify the criticism of
Ehrenfest and Einstein.
  The obscurity of the quantum concepts leads to wrong conclusions that
handicap the development of physics. Just as building a laser was considered
absurd before the first maser worked, the concept of photon leads to deny a
type of coherent Raman scattering necessary to understand some redshifts of
spectra in astrophysics, and able to destroy the two fundamental proofs to the
expansion of the universe.


title: Quantum neural network

abstract:
  It is suggested that a quantum neural network (QNN), a type of artificial
neural network, can be built using the principles of quantum information
processing. The input and output qubits in the QNN can be implemented by
optical modes with different polarization, the weights of the QNN can be
implemented by optical beam splitters and phase shifters


title: General Phase Matching Condition for Quantum Searching

abstract:
  We present a general phase matching condition for the quantum search
algorithm with arbitrary unitary transformation and arbitrary phase rotations.
We show by an explicit expression that the phase matching condition depends
both on the unitary transformation U and the initial state. Assuming that the
initial amplitude distribution is an arbitrary superposition sin\theta_0 |1> +
cos\theta_0 e^{i\delta} |2> with |1> = {1 / sin\beta} \sum_k |\tau_k>
<\tau_k|U|0> and |2> = {1 / cos\beta} \sum_{i \ne \tau}|i> <i|U|0>, where
|\tau_k> is a marked state and \sin\beta = \sqrt{\sum_k|U_{\tau_k 0}|^2} is
determined by the matrix elements of unitary transformation U between |\tau_k>
and the |0> state, then the general phase matching condition is tan{\theta / 2}
[cos 2\beta + tan\theta_0 cos\delta sin 2\beta]= tan{\phi / 2} [1-tan\theta_0
sin\delta sin 2\beta tan{\theta / 2}], where \theta and \phi are the phase
rotation angles for |0> and |\tau_k>, respectively. This generalizes previous
conclusions in which the dependence of phase matching condition on $U$ and the
initial state has been disguised. We show that several phase conditions
previously discussed in the literature are special cases of this general one,
which clarifies the question of which condition should be regarded as exact.


title: Can spectral and local information decide separability?

abstract:
  We discuss the discriminating power of separability criteria, which are based
on the spectrum of a quantum state and its reductions. Common examples are
entropic inequalities utilizing conditional Tsallis or Renyi entropies. We
prove that these inequalities are implied by the reduction criterion for any
positive value of the entropic parameters. We show however, that arbitrary sets
of criteria based on spectral and local information can never be sufficient by
establishing a separable, isospectral and locally undistinguishable counterpart
for any Werner state in odd dimensions. For the case of two qubit systems we
show that a simple controlled phase gate operation can produce an isospectral,
entangled state out of a separable one, which has the same reductions.


title: Quantum Search by Local Adiabatic Evolution

abstract:
  The adiabatic theorem has been recently used to design quantum algorithms of
a new kind, where the quantum computer evolves slowly enough so that it remains
near its instantaneous ground state which tends to the solution [Farhi et al.,
quant-ph/0001106]. We apply this time-dependent Hamiltonian approach to the
Grover's problem, i. e., searching a marked item in an unstructured database.
We find that, by adjusting the evolution rate of the Hamiltonian so as to keep
the evolution adiabatic on each infinitesimal time interval, the total running
time is of order $\sqrt{N}$, where $N$ is the number of items in the database.
We thus recover the advantage of Grover's standard algorithm as compared to a
classical search, scaling as $N$. This is in contrast with the constant-rate
adiabatic approach developed by Farhi et al., where the requirement of
adiabaticity is expressed only globally, resulting in a time of order $N$.


title: On the local unitary equivalence of states of multi-partite systems

abstract:
  Two pure states of a multi-partite system are alway are related by a unitary
transformation acting on the Hilbert space of the whole system. This
transformation involves multi-partite transformations. On the other hand some
quantum information protocols such as the quantum teleportation and quantum
dense coding are based on equivalence of some classes of states of bi-partite
systems under the action of local (one-particle) unitary operations. In this
paper we address the question: ``Under what conditions are the two states
states, $\varrho$ and $\sigma$, of a multi-partite system locally unitary
equivalent?'' We present a set of conditions which have to be satisfied in
order that the two states are locally unitary equivalent. In addition, we study
whether it is possible to prepare a state of a multi-qudit system. which is
divided into two parts A and B, by unitary operations acting only on the
systems A and B, separately.


title: Unconditional Security of Practical Quantum Key Distribution

abstract:
  We present a complete protocol for BB84 quantum key distribution for a
realistic setting (noise, loss, multi-photon signals of the source) that covers
many of todays experimental implementations. The security of this protocol is
shown against an eavesdropper having unrestricted power to manipulate the
signals coherently on their path from sender to receiver. The protocol and the
security proof take into account the effects concerning the finite size of the
generated key.


title: Correlations in quantum systems and branch points in the complex plane

abstract:
  Branch points in the complex plane are responsible for avoided level
crossings in closed and open quantum systems. They create not only an exchange
of the wave functions but also a mixing of the states of a quantum system at
high level density. The influence of branch points in the complex plane on the
low-lying states of the system is small.


title: Atomic Retrodiction

abstract:
  Measurement of a quantum system provides information concerning the state in
which it was prepared. In this paper we show how the retrodictive formalism can
be used to evaluate the probability associated with any one of a given set of
preparation events. We illustrate our method by calculating the retrodictive
density operator for a two-level atom coupled to the electromagnetic field.


title: Simple method for excitation of a Bose-Einstein condensate

abstract:
  An appropriate, time-dependent modification of the trapping potential may be
sufficient to create effectively collective excitations in a cold atom
Bose-Einstein condensate. The proposed method is complementary to earlier
suggestions and should allow the creation of both dark solitons and vortices.


title:
Simple applications of fundamental solution method in 1D quantum
  mechanics A talk given at the conference on: "Geometry Symmetry and Mechanics
  I" Lisbon, 11-16 July 2001

abstract:
  A method of fundamental solutions has been used to show its effectiveness in
solving some well known problems of 1D quantum mechanics (barrier penetrations,
over-barrier reflections, resonance states), i.e. those in which we look for
exponentially small contributions to semiclassical expansions for considered
quantities. Its usefulness for adiabatic transitions in two energy level
systems is also mentioned.


title: Bell inequality and CP violation in the neutral kaon system

abstract:
  For the entangled neutral kaon system we formulate a Bell inequality
sensitive to CP violation in mixing. Via this Bell inequality we obtain a bound
on the leptonic CP asymmetry which is violated by experimental data.
Furthermore, we connect the Bell inequality with a decoherence approach and
find a lower bound on the decoherence parameter which practically corresponds
to Furry's hypothesis.


title:
On the "Fake" Inferred Entanglement Associated with the Maximum Entropy
  Inference of Quantum States

abstract:
  The inference of entangled quantum states by recourse to the maximum entropy
principle is considered in connection with the recently pointed out problem of
fake inferred entanglement [R. Horodecki, {\it et al.}, Phys. Rev. A {\it 59}
(1999) 1799]. We show that there are operators $\hat A$, both diagonal and non
diagonal in the Bell basis, such that when the expectation value $<\hat A>$ is
taken as prior information the problem of fake entanglement is not solved by
adding a new constraint associated with the mean value of $\hat A^2$ (unlike
what happens when the partial information is given by the expectation value of
a Bell operator). The fake entanglement generated by the maximum entropy
principle is also studied quantitatively by comparing the entanglement of
formation of the inferred state with that of the original one.


title: Fidelity and the communication of quantum information

abstract:
  We compare and contrast the error probability and fidelity as measures of the
quality of the receiver's measurement strategy for a quantum communications
system. The error probability is a measure of the ability to retrieve {\it
classical} information and the fidelity measures the retrieval of {\it quantum}
information. We present the optimal measurement strategies for maximising the
fidelity given a source that encodes information on the symmetric qubit-states.


title: Cherenkov radiation and superluminal particles

abstract:
  Any charged particle moving faster than light through a medium emits
Cherenkov radiation. We show that charged particles moving faster than light
through the v a c u u m emit Cherenkov radiation. How can a particle move
faster than light? The w e a k speed of a charged particle can exceed the speed
of light. By definition, the weak velocity is <b|v|a>/<b|a> where v is the
velocity operator and |a> and |b> are, respectively, the states of a particle
before and after a velocity measurement. We discuss the consistency of weak
values and show that superluminal weak speed is consistent with relativistic
causality.


title: Thermodynamical analogues in quantum information theory

abstract:
  The first step in quantum information theory is the identification of
entanglement as a valuable resource. The next step is learning how to exploit
this resource efficiently. We learn how to exploit entanglement efficiently by
applying analogues of thermodynamical concepts. These concepts include
reversibility, entropy, and the distinction between intensive and extensive
quantities. We discuss some of these analogues and show how they lead to a
measure of entanglement for pure states. We also ask whether these analogues
are more than analogues, and note that, l o c a l l y, entropy of entanglement
is thermodynamical entropy.


title: Manipulation of photon statistics of highly degenerate chaotic radiation

abstract:
  Highly degenerate chaotic radiation has a Gaussian density matrix and a large
occupation number of modes $f $. If it is passed through a weakly transmitting
barrier, its counting statistics is close to Poissonian. We show that a second
identical barrier, in series with the first, drastically modifies the
statistics. The variance of the photocount is increased above the mean by a
factor $f$ times a numerical coefficient. The photocount distribution reaches a
limiting form with a Gaussian body and highly asymmetric tails. These are
general consequences of the combination of weak transmission and multiple
scattering.


title:
On Bohr's response to the clock-in-the-box thought experiment of
  Einstein

abstract:
  The recent analysis of De la Torre, Daleo and Garcia-Mata of the reply of
Bohr to the famous clock-in-the-box challenge of Einstein is criticized.


title: An optical conveyor belt for single neutral atoms

abstract:
  Using optical dipole forces we have realized controlled transport of a single
or any desired small number of neutral atoms over a distance of a centimeter
with sub-micrometer precision. A standing wave dipole trap is loaded with a
prescribed number of cesium atoms from a magneto-optical trap. Mutual detuning
of the counter-propagating laser beams moves the interference pattern, allowing
us to accelerate and stop the atoms at preselected points along the standing
wave. The transportation efficiency is close to 100%. This optical "single-atom
conveyor belt" represents a versatile tool for future experiments requiring
deterministic delivery of a prescribed number of atoms on demand.


title:
Weak localization of light by cold atoms: the impact of quantum internal
  structure

abstract:
  Since the work of Anderson on localization, interference effects for the
propagation of a wave in the presence of disorder have been extensively
studied, as exemplified in coherent backscattering (CBS) of light. In the
multiple scattering of light by a disordered sample of thermal atoms,
interference effects are usually washed out by the fast atomic motion. This is
no longer true for cold atoms where CBS has recently been observed. However,
the internal structure of the atoms strongly influences the interference
properties. In this paper, we consider light scattering by an atomic dipole
transition with arbitrary degeneracy and study its impact on coherent
backscattering. We show that the interference contrast is strongly reduced.
Assuming a uniform statistical distribution over internal degrees of freedom,
we compute analytically the single and double scattering contributions to the
intensity in the weak localization regime. The so-called ladder and crossed
diagrams are generalized to the case of atoms and permit to calculate
enhancement factors and backscattering intensity profiles for polarized light
and any closed atomic dipole transition.


title: Greenberger-Horne-Zeilinger paradoxes for many qudits

abstract:
  We construct GHZ contradictions for three or more parties sharing an
entangled state, the dimension d of each subsystem being an even integer
greater than 2. The simplest example that goes beyond the standard GHZ paradox
(three qubits) involves five ququats (d=4). We then examine the criteria a GHZ
paradox must satisfy in order to be genuinely M-partite and d-dimensional.


title:
A feasible quantum optical experiment capable of refuting
  noncontextuality for single photons

abstract:
  Elaborating on a previous work by Simon et al. [PRL 85, 1783 (2000)] we
propose a realizable quantum optical single-photon experiment using standard
present day technology, capable of discriminating maximally between the
predictions of quantum mechanics (QM) and noncontextual hidden variable
theories (NCHV). Quantum mechanics predicts a gross violation (up to a factor
of 2) of the noncontextual Bell-like inequality associated with the proposed
experiment. An actual maximal violation of this inequality would demonstrate
(modulo fair sampling) an all-or-nothing type contradiction between QM and
NCHV.


title: Conditional quantum dynamics with several observers

abstract:
  We consider several observers who monitor different parts of the environment
of a single quantum system and use their data to deduce its state. We derive a
set of conditional stochastic master equations that describe the evolution of
the density matrices each observer ascribes to the system under the Markov
approximation, and show that this problem can be reduced to the case of a
single "super-observer", who has access to all the acquired data. The key
problem - consistency of the sets of data acquired by different observers - is
then reduced to the probability that a given combination of data sets will be
ever detected by the "super-observer". The resulting conditional master
equations are applied to several physical examples: homodyne detection of
phonons in quantum Brownian motion, photo-detection and homodyne detection of
resonance fluorescence from a two-level atom. We introduce {\it relative
purity} to quantify the correlations between the information about the system
gathered by different observers from their measurements of the environment. We
find that observers gain the most information about the state of the system and
they agree the most about it when they measure the environment observables with
eigenstates most closely correlated with the optimally predictable {\it pointer
basis} of the system.


title: Effects of geometry and topology on some quantum mechanical systems

abstract:
  We study the behaviour of a nonrelativistic quantum particle interacting with
different potentials in the spacetimes of topological defects. We find the
energy spectra and show how they differ from their free-space values.


title:
Optimal simulation of two-qubit Hamiltonians using general local
  operations

abstract:
  We consider the simulation of the dynamics of one nonlocal Hamiltonian by
another, allowing arbitrary local resources but no entanglement nor classical
communication. We characterize notions of simulation, and proceed to focus on
deterministic simulation involving one copy of the system. More specifically,
two otherwise isolated systems $A$ and $B$ interact by a nonlocal Hamiltonian
$H \neq H_A+H_B$. We consider the achievable space of Hamiltonians $H'$ such
that the evolution $e^{-iH't}$ can be simulated by the interaction $H$
interspersed with local operations. For any dimensions of $A$ and $B$, and any
nonlocal Hamiltonians $H$ and $H'$, there exists a scale factor $s$ such that
for all times $t$ the evolution $e^{-iH'st}$ can be simulated by $H$ acting for
time $t$ interspersed with local operations. For 2-qubit Hamiltonians $H$ and
$H'$, we calculate the optimal $s$ and give protocols achieving it. The optimal
protocols do not require local ancillas, and can be understood geometrically in
terms of a polyhedron defined by a partial order on the set of 2-qubit
Hamiltonians.


title: Efficient Quantum Computing of Complex Dynamics

abstract:
  We propose a quantum algorithm which uses the number of qubits in an optimal
way and efficiently simulates a physical model with rich and complex dynamics
described by the quantum sawtooth map. The numerical study of the effect of
static imperfections in the quantum computer hardware shows that the main
elements of the phase space structures are accurately reproduced up to a time
scale which is polynomial in the number of qubits. The errors generated by
these imperfections are more dangerous than the errors of random noise in gate
operations.


title: Sheafifying Consistent Histories

abstract:
  Isham's topos-theoretic perspective on the logic of the consistent-histories
theory is extended in two ways. First, the presheaves of consistent sets of
history propositions in the topos proposed by Isham are endowed with a
Vietoris-type of topology and subsequently they are sheafified with respect to
it. The category resulting from this sheafification procedure is the topos of
sheaves of sets varying continuously over the Vietoris-topologized base poset
category of Boolean subalgebras of the universal orthoalgebra of quantum
history propositions. The second extension of Isham's topos consists in
endowing the stalks of the aforementioned sheaves, which were originally
inhabited by structureless sets, with further algebraic structure, that also
enjoys a quantum causal interpretation, so as to arrive at the topos of
consistent-histories of quantum causal sets. The resulting quantum causal
histories topos is compared with Markopoulou's quantum causal histories, with
Mallios and this author's finitary spacetime sheaves of quantum causal sets, as
well as with Butterfield and Isham's topos perspective on the Kochen-Specker
theorem of quantum logic.


title:
Perturbation Theory and Numerical Modeling of Quantum Logic Operations
  with a Large Number of Qubits

abstract:
  The perturbation theory is developed based on small parameters which
naturally appear in solid state quantum computation. We report the simulations
of the dynamics of quantum logic operations with a large number of qubits (up
to 1000). A nuclear spin chain is considered in which selective excitations of
spins are provided by having a uniform gradient of the external magnetic field.
Quantum logic operations are utilized by applying resonant electromagnetic
pulses. The spins interact with their nearest neighbors. We simulate the
creation of the long-distance entanglement between remote qubits in the spin
chain. Our method enables us to minimize unwanted non-resonant effects in a
controlled way. The method we use cannot simulate complicated quantum logic (a
quantum computer is required to do this), but it can be useful to test the
experimental performance of simple quantum logic operations. We show that: (a)
the probability distribution of unwanted states has a ``band'' structure, (b)
the directions of spins in typical unwanted states are highly correlated, and
(c) many of the unwanted states are high-energy states of a quantum computer (a
spin chain). Our approach can be applied to simple quantum logic gates and
fragments of quantum algorithms involving a large number of qubits.


title: Field Quantization, Photons and Non-Hermitean Modes

abstract:
  Field quantization in three dimensional unstable optical systems is treated
by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes in
both the cavity and external regions. The cavity non-Hermitean modes (NHM) are
treated using the paraxial and monochromaticity approximations. The NHM
bi-orthogonality relationships are used in a standard canonical quantization
procedure based on introducing generalised coordinates and momenta for the
electromagnetic (EM) field. The quantum EM field is equivalent to a set of
quantum harmonic oscillators (QHO), associated with either the cavity or the
external region NHM. This confirms the validity of the photon model in unstable
optical systems, though the annihilation and creation operators for each QHO
are not Hermitean adjoints. The quantum Hamiltonian for the EM field is the sum
of non-commuting cavity and external region contributions, each of which is sum
of independent QHO Hamiltonians for each NHM, but the external field
Hamiltonian also includes a coupling term responsible for external NHM photon
exchange processes. Cavity energy gain and loss processes is associated with
the non-commutativity of cavity and external region operators, given in terms
of surface integrals involving cavity and external region NHM functions on the
cavity-external region boundary. The spontaneous decay of a two-level atom
inside an unstable cavity is treated using the essential states approach and
the rotating wave approximation. Atomic transitions leading to cavity NHM
photon absorption have a different coupling constant to those leading to photon
emission, a feature resulting from the use of NHM functions. Under certain
conditions the decay rate is enhanced by the Petermann factor.


title: Subquantum Models: Basic Principles, Effects and Tests

abstract:
  We present models in which the indeterministic feature of Quantum Mechanics
is represented in the form of definite physical mechanisms. Our way is
completely different from so-called hidden parameter models, namely, we start
from a certain variant of QM - deterministic QM - which has most features
similar to QM, but the evolution in this theory is deterministic. Then we
introduce the subquantum medium composed of so-called space-like objects. The
interaction of a deterministic QM-particle with this medium is represented by
the random force, but it is the random force governed by the probability
amplitude distribution. This is the quantum random force and it is very
different from classical random force. This implies that in our models there
are no Bell`s inequalities and that our models (depending on a certain
parameter tau) can be arbitrarily close to QM. The parameter tau defines a
relaxation time and on time intervals shorter than tau, the evolution violates
Heisenberg`s uncertainty principle and it is almost deterministic - spreading
of the wave packet is much slower than in QM. Such type of short-time effects
form the bases of proposed tests, which can, in principle, define limits of
validity of QM. The proposed experiments are related to the behavior of quantum
objects on short time intervals, where we expect the behavior different from
QM. The main proposed feature is violation of uncertainty relations on short
time intervals.


title: Simulation and reversal of n-qubit Hamiltonians using Hadamard matrices

abstract:
  The ability to simulate one Hamiltonian with another is an important
primitive in quantum information processing. In this paper, a simulation method
for arbitrary $\sigma_z \otimes \sigma_z$ interaction based on Hadamard
matrices (quant-ph/9904100) is generalized for any pairwise interaction. We
describe two applications of the generalized framework. First, we obtain a
class of protocols for selecting an arbitrary interaction term in an n-qubit
Hamiltonian. This class includes the scheme given in quant-ph/0106064v2.
Second, we obtain a class of protocols for inverting an arbitrary, possibly
unknown n-qubit Hamiltonian, generalizing the result in quant-ph/0106085v1.


title:
Optimization of coherent attacks in generalizations of the BB84 quantum
  bit commitment protocol

abstract:
  It is well known that no quantum bit commitment protocol is unconditionally
secure. Nonetheless, there can be non-trivial upper bounds on both Bob's
probability of correctly estimating Alice's commitment and Alice's probability
of successfully unveiling whatever bit she desires. In this paper, we seek to
determine these bounds for generalizations of the BB84 bit commitment protocol.
In such protocols, an honest Alice commits to a bit by randomly choosing a
state from a specified set and submitting this to Bob, and later unveils the
bit to Bob by announcing the chosen state, at which point Bob measures the
projector onto the state. Bob's optimal cheating strategy can be easily deduced
from well known results in the theory of quantum state estimation. We show how
to understand Alice's most general cheating strategy, (which involves her
submitting to Bob one half of an entangled state) in terms of a theorem of
Hughston, Jozsa and Wootters. We also show how the problem of optimizing
Alice's cheating strategy for a fixed submitted state can be mapped onto a
problem of state estimation. Finally, using the Bloch ball representation of
qubit states, we identify the optimal coherent attack for a class of protocols
that can be implemented with just a single qubit. These results provide a tight
upper bound on Alice's probability of successfully unveiling whatever bit she
desires in the protocol proposed by Aharonov et al., and lead us to identify a
qubit protocol with even greater security.


title: One-parameter Darboux-transformed quantum actions in Thermodynamics

abstract:
  We use nonrelativistic supersymmetry, mainly Darboux transformations of the
general (one-parameter) type, for the quantum oscillator thermodynamic actions.
Interesting Darboux generalizations of the fundamental Planck and pure vacuum
cases are discussed in some detail with relevant plots. It is shown that the
one-parameter Darboux-transformed Thermodynamics refers to superpositions of
boson and fermion excitations of positive and negative absolute temperature,
respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048
regarding a single mode oscillator Carnot cycle are extended in the same
Darboux perspective. We also conjecture a Darboux generalization of the
fluctuation-dissipation theorem


title: The stuff the world is made of: physics and reality

abstract:
  Taking into account the results that we have been obtained during the last
decade in the foundations of quantum mechanic we put forward a view on reality
that we call the 'creation discovery view'. In this view it is made explicit
that a measurement is an act of a macroscopic physical entity on a
microphysical entity that entails the creation of new elements of reality as
well as the detection of existing elements of reality. Within this view most of
the quantum mechanical paradoxes are due to structural shortcomings of the
standard quantum theory, which means that our analysis agrees with the claim
made in the Einstein Podolsky Rosen paper, namely that standards quantum
mechanics is an incomplete theory. This incompleteness is however not due to
the absence of hidden variables but to the impossibility for standard quantum
mechanics to describe separated quantum entities. Nonlocality appears as a
genuine property of nature in our view and makes it necessary to reconsider the
role of space in reality. Our proposal for a new interpretation for space makes
it possible to put forward an new hypothesis for why it has not been possible
to unify quantum mechanics and relativity theory.


title:
Nonsequential positive-operator-valued measurements on entangled mixed
  states do not always violate a Bell inequality

abstract:
  We present a local-hidden-variable model for positive-operator-valued
measurements (an LHVPOV model) on a class of entangled generalized Werner
states, thus demonstrating that such measurements do not always violate a
Bell-type inequality. We also show that, in general, if the state $\rho'$ can
be obtained from $\rho$ with certainty by local quantum operations without
classical communication then an LHVPOV model for the state $\rho$ implies the
existence of such a model for $\rho'$.


title: Reply to Comment on "Completely positive quantum dissipation"

abstract:
  This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001)
028901) on a paper written by the author (B. Vacchini, ``Completely positive
quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).


title: Brownian Motion: The Quantum Perspective

abstract:
  We briefly go through the problem of the quantum description of Brownian
motion, concentrating on recent results about the connection between dynamics
of the particle and dynamic structure factor of the medium.


title:
Quantum-scissors device for optical state truncation: A proposal for
  practical realization

abstract:
  We propose a realizable experimental scheme to prepare superposition of the
vacuum and one-photon states by truncating an input coherent state. The scheme
is based on the quantum scissors device proposed by Pegg, Phillips, and Barnett
[Phys. Rev. Lett. 81, 1604 (1998)] and uses photon-counting detectors, a
single-photon source, and linear optical elements. Realistic features of the
photon counting and single-photon generation are taken into account and
possible error sources are discussed together with their effect on the fidelity
and efficiency of the truncation process. Wigner function and phase
distribution of the generated states are given and discussed for the evaluation
of the proposed scheme.


title: Is quantum decoherence reality or appearance?

abstract:
  It has been experimentally demonstrated that quantum coherence can persist in
macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the
challenge of this new fact, in this article QM in its standard form is assumed
to be extended by one beable (hidden variable), i. e., a quantum observable
with always definite values in nature (but usually only statistically given in
the quantum state). Localization is taken as the most plausible beable. The
paradoxical aspects of conventional QM take now a different form. Suitably
defining the notion of "subject" fully within the QM formalism, proving the
quantum conditional subsystem-state theorem, and choosing the
relative-decoherence interpretation of QM, the paradoxes formally disappear,
leaving one with decoherence relative to the definite values of the beable;
thus being only appearance, not absolute reality in QM. Relative to a different
subject one has perseverance of coherence. Hence, in this approach it is
claimed that decoherence and coherence, both exist in reality, but are not
"seen" by the same subject, and "subject" is, in this interpretation,
indispensable. The two mentioned, apparently contradictory phenomena, are in
this way decoupled from each other, contradiction is avoided, and any one of
the two can be treated in the way that is usual in QM.


title: Multipartite bound entangled states that violate Bell's inequality

abstract:
  We study the relation between distillability of multipartite states and
violation of Bell's inequality. We prove that there exist multipartite bound
entangled states (i.e. non-separable, non-distillable states) that violate a
multipartite Bell inequality. This implies that (i) violation of Bell's
inequality is not a sufficient condition for distillability and (ii) some bound
entangled states cannot be described by a local hidden variable model.


title: When only two thirds of the entanglement can be distilled

abstract:
  We provide an example of distillable bipartite mixed state such that, even in
the asymptotic limit, more pure-state entanglement is required to create it
than can be distilled from it. Thus, we show that the irreversibility in the
processes of formation and distillation of bipartite states, recently proved in
[G. Vidal, J.I. Cirac, Phys. Rev. Lett. 86, (2001) 5803-5806], is not limited
to bound-entangled states.


title:
Entanglement enhanced information transmission over a quantum channel
  with correlated noise

abstract:
  We show that entanglement is a useful resource to enhance the mutual
information of the depolarizing channel when the noise on consecutive uses of
the channel has some partial correlations. We obtain a threshold in the degree
of memory, depending on the shrinking factor of the channel, above which a
higher amount of classical information is transmitted with entangled signals.


title: A Systematic Formulation of Slow Polaritons in Atomic Gases

abstract:
  We formulate a theory of slow polaritons in atomic gases and apply it to the
slowing down, storing, and redirecting of laser pulses in an EIT medium. The
normal modes of the coupled matter and radiation are determined through a full
diagonalization of the dissipationless Hamiltonian. Away from the EIT resonance
where the polaritons acquire an excited-state contribution, lifetimes are
introduced as a secondary step. With detuning included various four-wave mixing
possibilities are analyzed. We investigate specifically the possibility of
reverting a stopped polariton by reversing the control beam.


title: Fuzziness in Quantum Mechanics

abstract:
  It is shown that quantum mechanics can be regarded as what one might call a
"fuzzy" mechanics whose underlying logic is the fuzzy one, in contradistinction
to the classical "crisp" logic. Therefore classical mechanics can be viewed as
a crisp limit of a "fuzzy" quantum mechanics. Based on these considerations it
is possible to arrive at the Schroedinger equation directly from the
Hamilton-Jacobi equation. The link between these equations is based on the fact
that a unique ("crisp") trajectory of a classical particle emerges out of a
continuum of possible paths collapsing to a single trajectory according to the
principle of least action. This can be interpreted as a consequence of an
assumption that a quantum "particle" "resides" in every path of the continuum
of paths which collapse to a single(unique) trajectory of an observed classical
motion. A wave function then is treated as a function describing a
deterministic entity having a fuzzy character. As a consequence of such an
interpretation, the complimentarity principle and wave-particle duality can be
abandoned in favor of a fuzzy deterministic microoobject.


title: Quantum entanglement in spinor Bose-Einstein condensates

abstract:
  We propose a scheme to generate and detect various kinds of quantum
entanglement in a spin-1 Bose-Einstein condensate. It is shown that substantial
many-particle entanglement can be generated directly in the spin-1 condensate
by free dynamical evolution with a properly prepared initial state. The scheme
also provides a simple method to generate three-mode entanglement in the
second-quantization picture and to detect the continuous variable type of
entanglement between two effective modes in the spin-1 condensate.


title: Entanglement teleportation via Bell Mixture

abstract:
  We investigate the teleportation of the bipartite entangled states through
two equally noisy quantum channels, namely mixture of Bell states. There is a
particular mixed state channel for which all pure entanglement in a known
Schmidt basis remain entangled after teleportation and it happens till the
channel state remains entangled. Werner state channel lacks both these
features. The relation of these noisy channels with violation of Bell's
inequality and 2-E inequality is studied.


title: Tests of Bell Inequalities

abstract:
  According to recent reports, the last loopholes in testing Bell's inequality
are closed. It is argued that the really important task in this field has not
been tackled yet and that the leading experiments claiming to close locality
and detection efficiency loopholes, although making a very significant
progress, have conceptual drawbacks. The important task is constructing quantum
devices which will allow winning games of certain correlated replies against
any classical team. A novel game of this type is proposed.


title:
Experimental Implementation of the Deutsch-Jozsa Algorithm for
  Three-Qubit Functions using Pure Coherent Molecular Superpositions

abstract:
  The Deutsch-Jozsa algorithm is experimentally demonstrated for three-qubit
functions using pure coherent superpositions of Li$_{2}$ rovibrational
eigenstates. The function's character, either constant or balanced, is
evaluated by first imprinting the function, using a phase-shaped femtosecond
pulse, on a coherent superposition of the molecular states, and then projecting
the superposition onto an ionic final state, using a second femtosecond pulse
at a specific time delay.


title: Suppression of arbitrary internal coupling in a quantum register

abstract:
  For the implementation of a quantum computer it is necessary to exercise
complete control over the Hamiltonian of the used physical system. For NMR
quantum computing the effectively acting Hamiltonian can be manipulated via
pulse sequences. Here we examine a register consisting of N selectively
addressable spins with pairwise coupling between each spin pair. We show that
complete decoupling of the spins is possible independent of the particular form
of the spin-spin interaction. The proposed method based on orthogonal arrays is
efficient in the sense that the effort regarding time and amount of pulses
increases only polynomially with the size N of the register. However, the
effect of external control errors in terms of inaccurate control pulses
eventually limits the achievable precision.


title: Functional Techniques in Classical Mechanics

abstract:
  In 1931 Koopman and von Neumann extended previous work of Liouville and
provided an operatorial version of Classical Mechanics (CM). In this talk we
will review a path-integral formulation of this operatorial version of CM. In
particular we will study the geometrical nature of the many auxiliary variables
present and of the unexpected universal symmetries generated by the functional
technique.


title: Classical Analog of Electromagnetically Induced Transparency

abstract:
  We present a classical analog for Electromagnetically Induced Transparency
(EIT). In a system of just two coupled harmonic oscillators subject to a
harmonic driving force we can reproduce the phenomenology observed in EIT. We
describe a simple experiment performed with two linearly coupled RLC circuits
which can be taught in an undergraduate laboratory class.


title: Deformation of quantum mechanics in fractional-dimensional space

abstract:
  A new kind of deformed calculus (the D-deformed calculus) that takes place in
fractional-dimensional spaces is presented. The D-deformed calculus is shown to
be an appropriate tool for treating fractional-dimensional systems in a simple
way and quite analogous to their corresponding one-dimensional partners. Two
simple systems, the free particle and the harmonic oscillator in fractional-
dimensional spaces are reconsidered into the framework of the D-deformed
quantum mechanics. Confined states in a D-deformed quantum well are studied.
D-deformed coherent states are also found.


title:
On the Dynamical Invariants and the Geometric Phases for a General Spin
  System in a Changing Magnetic Field

abstract:
  We consider a class of general spin Hamiltonians of the form
$H_s(t)=H_0(t)+H'(t)$ where $H_0(t)$ and $H'(t)$ describe the dipole
interaction of the spins with an arbitrary time-dependent magnetic field and
the internal interaction of the spins, respectively. We show that if $H'(t)$ is
rotationally invariant, then $H_s(t)$ admits the same dynamical invariant as
$H_0(t)$. A direct application of this observation is a straightforward
rederivation of the results of Yan et al [Phys. Lett. A, Vol: 251 (1999) 289
and Vol: 259 (1999) 207] on the Heisenberg spin system in a changing magnetic
field.


title:
A Theory of Quantum Preparation and the Corresponding Advantage of the
  Relative-Collapse Interpretation of Quantum Mechanics as Compared to the
  Conventional One

abstract:
  Analyzing two standard preparators, the Stern-Gerlach and the
hole-in-the-screen ones, it is demonstrated that four entities are the basic
ingredients of the theory: the composite-system preparator-plus-object state
(coming about as a result of a suitable interaction between the subsystems), a
suitable preparator observable, one of its characteristic projectors called the
triggering event, and, finally, the conditional object state corresponding to
the occurrence of the triggering event. The concepts of a conditional state and
of retrospective apparent ideal occurrence are discussed in the conventional
interpretation of quantum mechanics. In the general theory of a preparator in
this interpretation first-kind and second-kind preparators are distinguished.
They are described by the same entities in the same way, but in terms of
different physical mechanisms. In this article the relative-collapse
interpretation is extended to encompass also preparators (besides measuring
apparatuses). In this interpretation also the mechanisms become the same and
one has only one kind of preparators.


title: On the topology of adiabatic passage

abstract:
  We examine the topology of eigenenergy surfaces characterizing the population
transfer processes based on adiabatic passage. We show that this topology is
the essential feature for the analysis of the population transfers and the
prediction of its final result. We reinterpret diverse known processes, such as
stimulated Raman adiabatic passage (STIRAP), frequency-chirped adiabatic
passage and Stark-chirped rapid adiabatic passage (SCRAP). Moreover, using this
picture, we display new related possibilities of transfer. In particular, we
show that we can selectively control the level which will be populated in
STIRAP process in Lambda or V systems by the choice of the peak amplitudes or
the pulse sequence.


title: Quantum dissipative chaos in the statistics of excitation numbers

abstract:
  A quantum manifestation of chaotic classical dynamics is found in the
framework of oscillatory numbers statistics for the model of nonlinear
dissipative oscillator. It is shown by numerical simulation of an ensemble of
quantum trajectories that the probability distributions and variances of
oscillatory number states are strongly transformed in the order-to-chaos
transition. The nonclassical, sub-Poissonian statistics of oscillatory
excitation numbers is established for chaotic dissipative dynamics in the
framework of Fano factor and Wigner functions. These results are proposed for
testing and experimental studing of quantum dissipative chaos.


title: Doubly--dressed atomic wave packets

abstract:
  The problems of cavity atom optics in the presence of an external strong
coherent field are formulated as the problems of potential scattering of
doubly-dressed atomic wave packets. Two types of potentials produced by various
multiphoton Raman processes in a high-finesse cavity are examined. As an
application the deflection of dressed atomic wave by a cavity mode is
investigated. New momentum distribution of the atoms is derived that depends
from the parameters of coherent field as well as photon states in the cavity.


title: Quantum Dense Coding Exploiting Bright EPR Beam

abstract:
  Highly efficient quantum dense coding for continuous variables has been
experimentally accomplished by means of exploiting bright EPR beam with
anticorrelation of amplitude quadratures and correlation of phase quadratures,
which is generated from a nondegenerate optical parametric amplifier operating
in the state of deamplification. Two bits of classical information are encoded
on two quadratures of a half of bright EPR beam at the sender Alice and
transmitted to the receiver Bob via one qubit of the shared quantum state after
encoding. The amplitude and phase signals are simultaneously decoded with the
other half of EPR beam by the direct measurement of the Bell-state at Bob. The
signal to noise ratios of the simultaneously measured amplitude and phase
signals are improved 5.4dB and 4.8dB with respect to that of the shot noise
limit respectively. A high degree of immunity to unauthorized eavesdropping of
the presented quantum communication scheme is experimentally demonstrated.


title: Non-sequential triple ionization in strong fields

abstract:
  We consider the final stage of triple ionization of atoms in a strong
linearly polarized laser field. We propose that for intensities below the
saturation value for triple ionization the process is dominated by the
simultaneous escape of three electrons from a highly excited intermediate
complex. We identify within a classical model two pathways to triple
ionization, one with a triangular configuration of electrons and one with a
more linear one. Both are saddles in phase space. A stability analysis
indicates that the triangular configuration has the larger cross sections and
should be the dominant one. Trajectory simulations within the dominant symmetry
subspace reproduce the experimentally observed distribution of ion momenta
parallel to the polarization axis.


title: Is the Universe Really So Simple?

abstract:
  The intriguing suggestion of Tegmark (1996) that the universe--contrary to
all our experiences and expectations--contains only a small amount of
information due to an extremely high degree of internal symmetry is critically
examined. It is shown that there are several physical processes, notably
Hawking evaporation of black holes and non-zero decoherence time effects
described by Plaga, as well as thought experiments of Deutsch and Tegmark
himself, which can be construed as arguments against the low-information
universe hypothesis. In addition, an extreme form of physical reductionism is
entailed by this hypothesis, and therefore any possible argumentation against
such reductionism would count against it either. Some ramifications for both
quantum mechanics and cosmology are briefly discussed.


title: Decoherence and linear entropy increase in the quantum baker's map

abstract:
  We show that the coarse-grained quantum baker's map exhibits a linear entropy
increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the
classical chaotic baker's map. The starting point of our analysis is a symbolic
representation of the map on a string of $N$ qubits, i.e., an $N$-bit register
of a quantum computer. To coarse-grain the quantum evolution, we make use of
the decoherent histories formalism. As a byproduct, we show that the condition
of medium decoherence holds asymptotically for the coarse-grained quantum
baker's map.


title:
Sufficient conditions for three-particle entanglement and their tests in
  recent experiments

abstract:
  We point out a loophole problem in some recent experimental claims to produce
three-particle entanglement. The problem consists in the question whether
mixtures of two-particle entangled states might suffice to explain the
experimental data.
  In an attempt to close this loophole, we review two sufficient conditions
that distinguish between N-particle states in which all N particles are
entangled to each other and states in which only M particles are entangled
(with M<N). It is shown that three recent experiments to obtain three-particle
entangled states (Bouwmeester et al., Pan et al., and Rauschenbeutel et al.) do
not meet these conditions. We conclude that the question whether these
experiments provide confirmation of three-particle entanglement remains
unresolved. We also propose modifications of the experiments that would make
such confirmation feasible.


title: On quantum teleportation with beam-splitter-generated entanglement

abstract:
  Following the lead of Cochrane, Milburn, and Munro [Phys. Rev. A {\bf 62},
062307 (2000)], we investigate theoretically quantum teleportation by means of
the number-sum and phase-difference variables. We study Fock-state entanglement
generated by a beam splitter and show that two-mode Fock-state inputs can be
entangled by a beam splitter into close approximations of maximally entangled
eigenstates of the phase difference and the photon-number sum
(Einstein-Podolsky-Rosen -- EPR -- states). Such states could be experimentally
feasible with on-demand single-photon sources. We show that the teleportation
fidelity can reach near unity when such ``quasi-EPR'' states are used as the
quantum channel.


title:
How to share a continuous-variable quantum secret by optical
  interferometry

abstract:
  We develop the theory of continuous-variable quantum secret sharing and
propose its interferometric realization using passive and active optical
elements. In the ideal case of infinite squeezing, a fidelity ${\cal F}$ of
unity can be achieved with respect to reconstructing the quantum secret. We
quantify the reduction in fidelity for the (2,3) threshold scheme due to finite
squeezing and establish the condition for verifying that genuine quantum secret
sharing has occurred.


title: Coherent Atom Interactions Mediated by Dark-State Polaritons

abstract:
  We suggest a technique to induce effective, controllable interactions between
atoms that is based on Raman scattering into an optical mode propagating with a
slow group velocity. The resulting excitation corresponds to the creation of
spin-flipped atomic pairs in a way that is analogous to correlated photon
emission in optical parametric amplification. The technique can be used for
fast generation of entangled atomic ensembles, spin squeezing and applications
in quantum information processing.


title:
Universal dynamical control of quantum mechanical decay: Modulation of
  the coupling to the continuum

abstract:
  We derive and investigate an expression for the dynamically modified decay of
states coupled to an arbitrary continuum. This expression is universally valid
for weak temporal perturbations. The resulting insights can serve as useful
recipes for optimized control of decay and decoherence.


title: Cloning and Cryptography with Quantum Continuous Variables

abstract:
  The cloning of quantum variables with continuous spectra is investigated. We
define a Gaussian 1-to-2 cloning machine, which copies equally well two
conjugate variables such as position and momentum or the two quadrature
components of a light mode. The resulting cloning fidelity for coherent states,
namely $F=2/3$, is shown to be optimal. An asymmetric version of this Gaussian
cloner is then used to assess the security of a continuous-variable quantum key
distribution scheme that allows two remote parties to share a Gaussian key. The
information versus disturbance tradeoff underlying this continuous quantum
cryptographic scheme is then analyzed for the optimal individual attack.
Methods to convert the resulting Gaussian keys into secret key bits are also
studied. The extension of the Gaussian cloner to optimal $N$-to-$M$ continuous
cloners is then discussed, and it is shown how to implement these cloners for
light modes, using a phase-insensitive optical amplifier and beam splitters.
Finally, a phase-conjugated inputs $(N,N')$-to-$(M,M')$ continuous cloner is
defined, yielding $M$ clones and $M'$ anticlones from $N$ replicas of a
coherent state and $N'$ replicas of its phase-conjugate (with $M'-M=N'-N$).
This novel kind of cloners is shown to outperform the standard $N$-to-$M$
cloners in some situations.


title: The classical counterpart of entanglement

abstract:
  We define and explore the classical counterpart of entanglement in complete
analogy with quantum mechanics. Using a basis independent measure of entropy in
the classical Hilbert space of densities that are propagated by the
Frobenius-Perron operator, we demonstrate that at short times the quantum and
classical entropies share identical power laws and qualitative behaviors.


title:
A possible way to look at the last and future events for two-level
  system

abstract:
  In view of a three-dimensional picture (3D) of probability to find a particle
at a plane of the frequency and the time (PTF) becomes that process of
absorption and process of radiation for two - level system have different
direction on the time. Both processes are in the past or in the future
depending on named transition due to reversible model of the two-level atom.
The opportunity to know the last history of the resonant event for the
absorption process is for quantum interference interaction or for the resonant
radiation. On the contrary, to predict the resonant event in the future is
possible only by use near resonant atom-field absorption or by use radiation at
a fixed time. The problem of life time for a particle is entered through time
of spontaneous radiation connected with trajectory of the quantum transition.
It is offered to connect a trajectory of a particle during quantum transitions
with distribution of probability to find a particle. The conception of the
spectral history for events due to probability distribution is introduced for
next discussion.


title:
Optical mode characterization of single photons prepared via conditional
  measurements on a biphoton state

abstract:
  A detailed theoretical analysis of the spatiotemporal mode of a single photon
prepared via conditional measurements on a photon pair generated in the process
of parametric down-conversion is presented. The maximum efficiency of coupling
the photon into a transform-limited classical optical mode is calculated and
ways for its optimization are determined. An experimentally feasible technique
of generating the optimally matching classical mode is proposed. The theory is
applied to a recent experiment on pulsed homodyne tomography of the
single-photon Fock state (A. I. Lvovsky et al., Phys Rev. Lett. 87, 050402
(2001) - preprint at quant-ph/0101051)


title: Quantum Optimization for Combinatorial Searches

abstract:
  I propose a "quantum annealing" heuristic for the problem of combinatorial
search among a frustrated set of states characterized by a cost function to be
minimized. The algorithm is probabilistic, with postselection of the
measurement result. A unique parameter playing the role of an effective
temperature governs the computational load and the overall quality of the
optimization. Any level of accuracy can be reached with a computational load
independent of the dimension {\it N} of the search set by choosing the
effective temperature correspondingly low. This is much better than classical
search heuristics, which typically involve computation times growing as powers
of log({\it N})


title: A classical analogue of entanglement

abstract:
  We show that quantum entanglement has a very close classical analogue, namely
secret classical correlations. The fundamental analogy stems from the behavior
of quantum entanglement under local operations and classical communication and
the behavior of secret correlations under local operations and public
communication. A large number of derived analogies follow. In particular
teleportation is analogous to the one-time-pad, the concept of ``pure state''
exists in the classical domain, entanglement concentration and dilution are
essentially classical secrecy protocols, and single copy entanglement
manipulations have such a close classical analog that the majorization results
are reproduced in the classical setting. This analogy allows one to import
questions from the quantum domain into the classical one, and vice-versa,
helping to get a better understanding of both. Also, by identifying classical
aspects of quantum entanglement it allows one to identify those aspects of
entanglement which are uniquely quantum mechanical.


title:
Hamilton-Jacobi Formulation of KS Entropy for Classical and Quantum
  Dynamics

abstract:
  A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is
developed. It is numerically efficient and reveals a close relation between the
KS invariant and the classical action. This formulation is extended to the
quantum domain using the Madelung-Bohm orbits associated with the Schroedinger
equation. The resulting quantum KS invariant for a given orbit equals the mean
decay rate of the probability density along the orbit, while its ensemble
average measures the mean growth rate of configuration-space information for
the quantum system.


title: Electron Entanglement via a Quantum Dot

abstract:
  This Letter presents a method of electron entanglement generation. The system
under consideration is a single-level quantum dot with one input and two output
leads. The leads are arranged such that the dot is empty, single electron
tunneling is suppressed by energy conservation, and two-electron virtual
co-tunneling is allowed. This yields a pure, non-local spin-singlet state at
the output leads. Coulomb interaction is the nonlinearity essential for
entanglement generation, and, in its absence, the singlet state vanishes. This
type of electron entanglement is a four-wave mixing process analogous to the
photon entanglement generated by a Chi-3 parametric amplifier.


title: Impossibility of comparing and sorting quantum states

abstract:
  Is there any point of principle that prohibits us from doing one or more
forms of quantum information processing? It is now well known that an unknown
quantum state can neither be copied nor deleted perfectly. Given a set of
states which are not necessarily orthogonal, is it possible to compare any two
states from the set, given some reasonable ordering of such states? Is it
possible to sort them in some specific order? In the context of quantum
computation, it is shown here that there is no quantum circuit implementing a
unitary transformation, for comparing and sorting an unrestricted set of
quantum states.


title:
Quantum cryptography using photon source based on postselection from
  entangled two-photon states

abstract:
  A photon source based on postselection from entangled photon pairs produced
by parametric frequency down-conversion is suggested. Its ability to provide
good approximations of single-photon states is examined. Application of this
source in quantum cryptography for quantum key distribution is discussed.
Advantages of the source compared to other currently used sources are
clarified. Future prospects of the photon source are outlined.


title:
Laser cooling with electromagnetically induced transparency: Application
  to trapped samples of ions or neutral atoms

abstract:
  A novel method of ground state laser cooling of trapped atoms utilizes the
absorption profile of a three (or multi-) level system which is tailored by a
quantum interference. With cooling rates comparable to conventional sideband
cooling, lower final temperatures may be achieved. The method was
experimentally implemented to cool a single Ca$^+$ ion to its vibrational
ground state. Since a broad band of vibrational frequencies can be cooled
simultaneously, the technique will be particularly useful for the cooling of
larger ion strings, thereby being of great practical importance for
initializing a quantum register based on trapped ions. We also discuss its
application to different level schemes and for ground state cooling of neutral
atoms trapped by a far detuned standing wave laser field.


title:
On the classical character of control fields in quantum information
  processing

abstract:
  Control fields in quantum information processing are virtually always, almost
by definition, assumed to be classical. In reality, however, when such a field
is used to manipulate the quantum state of qubits, the qubits never remain
completely unentangled with the field. For quantum information processing this
is an undesirable property, as it precludes perfect quantum computing and
quantum communication. Here we consider the interaction of atomic qubits with
laser fields and quantify atom-field entanglement in various cases of interest.
We find that the entanglement decreases with the average number of photons
$\bar{n}$ in a laser beam as $E\propto\log_2 \bar{n}/\bar{n}$ for
$\bar{n}\to\infty$.


title:
Quantum subroutine problem and the robustness of quantum complexity
  classes

abstract:
  This paper positively solves the quantum subroutine problem for fully quantum
oracles. The quantum subroutine problem asks whether a quantum computer with an
efficiently computable oracle can be efficiently simulated by a non-oracle
quantum computer. We extends the earlier results obtained by Bennett,
Bernstein, Brassard, and Vazirani, and by Aharonov, Kitaev, and Nisan to the
case where the oracle evaluates a unitary operator and the computer is allowed
to be in the superposition of a query state and a non-query state during
computation. We also prove the robustness of {\bf EQP}, {\bf BQP}, and {\bf
ZQP} under the above general formulation, extending the earlier results on the
robustness of {\bf BQP} shown by Bennett et al.


title: Quantum Measurement, Information, and Completely Positive Maps

abstract:
  Axiomatic approach to measurement theory is developed. All the possible
statistical properties of apparatuses measuring an observable with
nondegenerate spectrum allowed in standard quantum mechanics are characterized.