title: Higher Order Gamow States with Exponential Decay

abstract:
  We derive Gamow vectors from S-matrix poles of higher multiplicity in analogy
to the Gamow vectors describing resonances from first-order poles. With these
vectors we construct a density operator that describes resonances associated
with higher order poles that obey an exponential decay law. It turns out that
this operator formed by these higher order Gamow vectors has a unique
structure.


title: Quantum measurements with a quantum computer

abstract:
  We present a scheme in which an ion trap quantum computer can be used to make
arbitrarily accurate measurements of the quadrature phase variables for the
collective vibrational motion of the ion. The electronic states of the ion
become the `apparatus', and the method is based on regarding the `apparatus' as
a quantum computer register which can be prepared in appropriate states by
running a Fourier transform algorithm on the data stored within it. The
resolution of the measurement rises exponentially with the number of ions used.


title: Lindblad Approach to Nonlinear Jaynes-Cummings Dynamics of a Trapped Ion

abstract:
  The Lindblad approach to open quantum systems is introduced for studying the
dynamics of a single trapped ion prepared in nonclassical motional states and
subjected to continuous measurement of its internal population. This results in
an inhibition of the dynamics similar to the one occurring in the quantum Zeno
effect. In particular, modifications to the Jaynes-Cummings collapses and
revivals arising from an initial coherent state of motion in various regimes of
interaction with the driving laser are dealt in detail.


title: Using a quantum computer to investigate quantum chaos

abstract:
  We show that the quantum baker's map, a prototypical map invented for
theoretical studies of quantum chaos, has a very simple realization in terms of
quantum gates. Chaos in the quantum baker's map could be investigated
experimentally on a quantum computer based on only 3 qubits.


title: Synchronizing Quantum Paths of a Universal Quantum Computer

abstract: This paper has been withdrawn, and will be superseded by another submission.


title: Linearly-independent quantum states can be cloned

abstract:
  A fundamental question in quantum mechanics is, whether it is possible to
replicate an arbitrary unknown quantum state. Then famous quantum no-cloning
theorem [Nature 299, 802 (1982)] says no to the question. But it leaves open
the following question: If the state is not arbitrary, but secretly chosen from
a certain set $\$={ | \Psi _1> ,| \Psi_2> ,... ,| \Psi _n> } $, whether is the
cloning possible? This question is of great practical significance because of
its applications in quantum information theory. If the states $| \Psi_1>, |
\Psi_2>,...$ and $| \Psi_n> $ are linearly-dependent, similar to the proof of
the no-cloning theorem, the linearity of quantum mechanics forbids such
replication. In this paper, we show that, if the states $| \Psi_1>, | \Psi _2>,
...$ and $| \Psi_n> $ are linearly-independent, they do can be cloned by a
unitary-reduction process.


title: The Geometric Phase and Ray Space Isometries

abstract:
  We study the behaviour of the geometric phase under isometries of the ray
space. This leads to a better understanding of a theorem first proved by
Wigner: isometries of the ray space can always be realised as projections of
unitary or anti-unitary transformations on the Hilbert space. We suggest that
the construction involved in Wigner's proof is best viewed as an use of the
Pancharatnam connection to ``lift'' a ray space isometry to the Hilbert space.


title: Trace forms for the generalized Wigner functions

abstract:
  We derive simple formulas connecting the generalized Wigner functions for
$s$-ordering with the density matrix, and vice-versa. These formulas proved
very useful for quantum mechanical applications, as, for example, for
connecting master equations with Fokker-Planck equations, or for evaluating the
quantum state from Monte Carlo simulations of Fokker-Planck equations, and
finally for studying positivity of the generalized Wigner functions in the
complex plane.


title: Optical von Neumann measurement

abstract:
  We present an optical scheme that realizes the standard von Neumann
measurement model, providing an indirect measurement of a quadrature of the
field with controllable Gaussian state-reduction. The scheme is made of simple
optical elements, as laser sources, beam splitters, and phase sensitive
amplifiers, along with a feedback mechanism that uses a Pockels cell. We show
that the von Neumann measurement is achieved without the need of working in a
ultra-short pulsed regime.


title: Quantum state manipulation of trapped atomic ions

abstract:
  A single laser-cooled and trapped 9Be+ ion is used to investigate methods of
coherent quantum-state synthesis and quantum logic. We create and characterize
nonclassical states of motion including "Schroedinger-cat" states. A
fundamental quantum logic gate is realized which uses two states of the
quantized ion motion and two ion internal states as qubits. We explore some of
the applications for, and problems in realizing, quantum computation based on
multiple trapped ions.


title:
Thomas Rotation and Polarised Light: A non-Abelian Geometric Phase in
  Optics

abstract:
  We describe a non-Abelian Berry phase in polarisation optics, suggested by an
analogy due to Nityananda between boosts in special relativity and the effect
of elliptic dichroism on polarised light. The analogy permits a simple optical
realization of the non-Abelian gauge field describing Thomas rotation. We also
show how Thomas rotation can be understood geometrically on the Poincar\'{e}
sphere in terms of the Pancharatnam phase.


title: Origin of quantum randomness in the pilot wave quantum mechanics

abstract:
  We account for the origin of the laws of quantum probabilities in the de
Broglie-Bohm (pilot wave) formulation of quantum theory by considering the
property of ergodicity likely to characterise the dynamics of microscopic
quantum systems.


title: The Quantum Tomographic Roulette Wheel

abstract:
  Random-phase homodyne tomography of the field intensity is a concrete example
of the Quantum Roulette of Helstrom. In this paper we give the explicit POM of
such measurement and compare it with direct photodetection and heterodyne
detection. Effects of nonunit quantum efficiency are also considered. Naimark
extensions for the roulette POM are analyzed and its experimental realization
is discussed.


title: Hamiltonians for Quantum Computing

abstract:
  We argue that the analog nature of quantum computing makes the usual design
approach of constructing complicated logical operations from many simple gates
inappropriate. Instead, we propose to design multi-spin quantum gates in which
the input and output two-state systems (spins) are not necessarily identical.
We outline the design criteria for such devices and then review recent results
for single-unit Hamiltonians that accomplish the NOT and XOR functions.


title: Quantum mechanical counterpart of nonlinear optics

abstract:
  Raman-type laser excitation of a trapped atom allows one to realize the
quantum mechanical counterpart of phenomena of nonlinear optics, such as
Kerr-type nonlinearities, parametric amplification, and multi-mode mixing.
Additionally, huge nonlinearities emerge from the interference of the atomic
wave function with the laser waves. They lead to a partitioning of the phase
space accompanied by a significantly different action of the time evolution in
neighboring phase-space zones. For example, a nonlinearly modified coherent
"displacement" of the motional quantum state may induce strong amplitude
squeezing and quantum interferences.


title: Determination of entangled quantum states of a trapped atom

abstract:
  We propose a method for measuring entangled vibronic quantum states of a
trapped atom. It is based on the nonlinear dynamics of the system that appears
by resonantly driving a weak electronic transition. The proposed technique
allows the direct sampling of a Wigner-function matrix, displaying all knowable
information on the quantum correlations of the motional and electronic degrees
of freedom of the atom. It opens novel possibilities for testing fundamental
predictions of the quantum theory concerning interaction phenomena.


title: Artificial Neural Network Methods in Quantum Mechanics

abstract:
  In a previous article we have shown how one can employ Artificial Neural
Networks (ANNs) in order to solve non-homogeneous ordinary and partial
differential equations. In the present work we consider the solution of
eigenvalue problems for differential and integrodifferential operators, using
ANNs. We start by considering the Schr\"odinger equation for the Morse
potential that has an analytically known solution, to test the accuracy of the
method. We then proceed with the Schr\"odinger and the Dirac equations for a
muonic atom, as well as with a non-local Schr\"odinger integrodifferential
equation that models the $n+\alpha$ system in the framework of the resonating
group method. In two dimensions we consider the well studied Henon-Heiles
Hamiltonian and in three dimensions the model problem of three coupled
anharmonic oscillators. The method in all of the treated cases proved to be
highly accurate, robust and efficient. Hence it is a promising tool for
tackling problems of higher complexity and dimensionality.

categories: quant-ph comp-gas nlin.CG physics.comp-ph


title: Quantum State Reduction and the Quantum Bayes Principle

abstract:
  This paper gives new foundations of quantum state reduction without appealing
to the projection postulate for the probe measurement. For this purpose, the
quantum Bayes principle is formulated as the most fundamental principle for
determining the state of a quantum system, and the joint probability
distribution for the outcomes of local successive measurements on a
noninteracting entangled system is derived without assuming the projection
postulate.


title: Reliable Quantum Computers

abstract:
  The new field of quantum error correction has developed spectacularly since
its origin less than two years ago. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment. Recovery from errors can work effectively even if occasional
mistakes occur during the recovery procedure. Furthermore, encoded quantum
information can be processed without serious propagation of errors. Hence, an
arbitrarily long quantum computation can be performed reliably, provided that
the average probability of error per quantum gate is less than a certain
critical value, the accuracy threshold. A quantum computer storing about 10^6
qubits, with a probability of error per quantum gate of order 10^{-6}, would be
a formidable factoring engine. Even a smaller, less accurate quantum computer
would be able to perform many useful tasks. (This paper is based on a talk
presented at the ITP Conference on Quantum Coherence and Decoherence, 15-18
December 1996.)


title: Quantum Computing: Pro and Con

abstract:
  I assess the potential of quantum computation. Broad and important
applications must be found to justify construction of a quantum computer; I
review some of the known quantum algorithms and consider the prospects for
finding new ones. Quantum computers are notoriously susceptible to making
errors; I discuss recently developed fault-tolerant procedures that enable a
quantum computer with noisy gates to perform reliably. Quantum computing
hardware is still in its infancy; I comment on the specifications that should
be met by future hardware. Over the past few years, work on quantum computation
has erected a new classification of computational complexity, has generated
profound insights into the nature of decoherence, and has stimulated the
formulation of new techniques in high-precision experimental physics. A broad
interdisciplinary effort will be needed if quantum computers are to fulfill
their destiny as the world's fastest computing devices. (This paper is an
expanded version of remarks that were prepared for a panel discussion at the
ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)


title: Quantum Entanglement and Communication Complexity

abstract:
  We consider a variation of the multi-party communication complexity scenario
where the parties are supplied with an extra resource: particles in an
entangled quantum state. We show that, although a prior quantum entanglement
cannot be used to simulate a communication channel, it can reduce the
communication complexity of functions in some cases. Specifically, we show
that, for a particular function among three parties (each of which possesses
part of the function's input), a prior quantum entanglement enables them to
learn the value of the function with only three bits of communication occurring
among the parties, whereas, without quantum entanglement, four bits of
communication are necessary. We also show that, for a particular two-party
probabilistic communication complexity problem, quantum entanglement results in
less communication than is required with only classical random correlations
(instead of quantum entanglement). These results are a noteworthy contrast to
the well-known fact that quantum entanglement cannot be used to actually
simulate communication among remote parties.


title: Phase Operator Problem and Macroscopic Extension of Quantum Mechanics

abstract:
  To find the Hermitian phase operatorof a single-mode electromagnetic field in
quantum mechanics, the Schroedinger representation is extended to a larger
Hilbert space augmented by states with infinite excitation by nonstandard
analysis. The Hermitian phase operator is shown to exist on the extended
Hilbert space. This operator is naturally considered as the controversial limit
of the approximate phase operators on finite dimensional spaces proposed by
Pegg and Barnett. The spectral measure of this operator is a Naimark extension
of the optimal probability operator-valued measure for the phase parameter
found by Helstrom. Eventually, the two promising approaches to the statistics
of the phase in quantum mechanics is unified by means of the Hermitian phase
operator in the macroscopic extension of the Schroedinger representation.


title: Realization of nonlinear oscillators with a trapped ion

abstract:
  We consider a trapped ion with a quantized center-of-mass motion in 2D trap
potential. With external laser fields the effective (non)linear coupling of two
orthogonal vibrational modes can be established via stimulated Raman
transition. Nonclassical vibrational states such as squeezed states or two-mode
entangled states (Schroedinger cat-like states) can be generated. When the
vibrational modes are entangled with internal energy levels the
Greenberger-Horne-Zeilinger (GHZ) states can be prepared.


title: Data processing in quantum information theory

abstract:
  The strengthened data processing inequality have been proved. The general
theory have been illustrated on the simple example.


title: Remarks on Bounds for Quantum Codes

abstract:
  We present some results that show that bounds from classical coding theory
still work in many cases of quantum coding theory.


title: Optimal Universal and State-Dependent Quantum Cloning

abstract:
  We establish the best possible approximation to a perfect quantum cloning
machine which produces two clones out of a single input. We analyze both
universal and state-dependent cloners. The maximal fidelity of cloning is shown
to be 5/6 for universal cloners. It can be achieved either by a special unitary
evolution or by a novel teleportation scheme. We construct the optimal
state-dependent cloners operating on any prescribed two non-orthogonal states,
discuss their fidelities and the use of auxiliary physical resources in the
process of cloning. The optimal universal cloners permit us to derive a new
upper bound on the quantum capacity of the depolarizing quantum channel.


title:
On the nonlinearity interpretation of q- and f-deformation and some
  applications

abstract:
  q-oscillators are associated to the simplest non-commutative example of Hopf
algebra and may be considered to be the basic building blocks for the symmetry
algebras of completely integrable theories. They may also be interpreted as a
special type of spectral nonlinearity, which may be generalized to a wider
class of f-oscillator algebras. In the framework of this nonlinear
interpretation, we discuss the structure of the stochastic process associated
to q-deformation, the role of the q-oscillator as a spectrum-generating algebra
for fast growing point spectrum, the deformation of fermion operators in
solid-state models and the charge-dependent mass of excitations in f-deformed
relativistic quantum fields.


title: Collision states and scar effects in charged three-body problems

abstract:
  Semiclassical methods form a bridge between classical systems and their
quantum counterparts. An interesting phenomenon discovered in this connection
is the scar effect, whereby energy eigenstates display enhancement structures
resembling the path of unstable periodic orbits. This paper deals with
collision states in charged three-body problems, in periodic media, which are
scarred by unstable classical orbits. The scar effect has a potential for
practical applications because orbits corresponding to zero measure classical
configurations may be reached and stabilized by resonant excitation. It may be
used, for example, to induce reactions that are favoured by unstable
configurations.


title: Single quantum querying of a database

abstract:
  We present a class of fast quantum algorithms, based on Bernstein and
Vazirani's parity problem, that retrieve the entire contents of a quantum
database $Y$ in a single query. The class includes binary search problems and
coin-weighing problems. Our methods far exceed the efficiency of classical
algorithms which are bounded by the classical information-theoretic bound. We
show the connection between classical algorithms based on several compression
codes and our quantum-mechanical method.


title: Supersymmetry in Stochastic Processes with Higher-Order Time Derivatives

abstract:
  A supersymmetric path integral representation is developed for stochastic
processes whose Langevin equation contains any number N of time derivatives,
thus generalizing the Langevin equation with inertia studied by Kramers, where
N=2. The supersymmetric action contains N fermion fields with first-order time
derivatives whose path integral is evaluated for fermionless asymptotic states.


title: A simple quantum channel having superadditivity of channel capacity

abstract:
  When classical information is sent through a quantum channel of nonorthogonal
states, there is a possibility that transmittable classical information exceeds
a channel capacity in a single use of the initial channel by extending it into
multi-product channel. In this paper, it is shown that this remarkable feature
of a quantum channel, so-called superadditivity, appears even in as low as the
third extended coding of the simplest binary input channel. A physical
implementation of this channel is indicated based on cavity QED techniques.


title: Noiseless Quantum Codes

abstract:
  In this paper we study a model quantum register $\cal R$ made of $N$ replicas
(cells) of a given finite-dimensional quantum system S. Assuming that all cells
are coupled with a common environment with equal strength we show that, for $N$
large enough, in the Hilbert space of $\cal R$ there exists a linear subspace
${\cal C}_N$ which is dynamically decoupled from the environment. The states in
${\cal C}_N$ evolve unitarily and are therefore decoherence-dissipation free.
The space ${\cal C}_N$ realizes a noiseless quantum code in which information
can be stored, in principle, for arbitrarily long time without being affected
by errors.


title: Dissipation and Decoherence in a Quantum Register

abstract:
  A model for a quantum register $\cal R$ made of $N$ replicas of a
$d$-dimensional quantum system (cell) coupled with the environment, is studied
by means of a Born-Markov Master Equation (ME). Dissipation and decoherence are
discussed in various cases in which a sub-decoherent enconding can be
rigorously found. For the qubit case ($d=2$) we have solved, for small $N,$ the
ME by numerical direct integration and studied, as a function of the coherence
length $\xi_c$ of the bath, fidelity and decoherence rates of states of the
register. For large enough $\xi_c$ the singlet states of the global $su(2)$
pseudo-spin algebra of the register (noiseless at $\xi_c=\infty$) are shown to
have a much smaller decoherence rates than the rest of the Hilbert space.


title: Optimal Quantum Cloning Machines

abstract:
  We present Quantum Cloning Machines (QCM) that transform N identical qubits
into $M>N$ identical copies and we prove that the fidelity (quality) of these
copies is optimal. The connection between cloning and measurement is discussed
in detail. When the number of clones M tends towards infinity, the fidelity of
each clone tends towards the optimal fidelity that can be obtained by a
measurement on the input qubits. More generally, the QCM are universal devices
to translate quantum information into classical information.


title: Non-partial Reality

abstract:
  Study on pre- and postselected quantum system indicates that ``product rule''
and ``sum rule'' for elements of reality should be abandoned. We show that this
so-called non-partial realism can refute arguments against hidden variables in
a unified way, and might save local realism.


title:
Redefintions of Histories by Measurements - An Explanation of
  "Nonlocality" Observed in EPR-Bohm Experiments

abstract:
  It is proved in the frame of standard quantum mechanics that selection of
different ensembles emerging from measurements of an observable leads to
identification of corresponding reductions of the initial, premeasured state.
This solves the problem of ``nonlocality`` observed in EPR-Bohm-type
experiments.


title: Quantum-type Coherence as a Combination of Symmetry and Semantics

abstract:
  It is shown that quantum-type coherence, leading to indeterminism and
interference of probabilities, may in principle exist in the absence of the
Planck constant and a Hamiltonian. Such coherence is a combined effect of a
symmetry (not necessary physical) and semantics. The crucial condition is that
symmetries should apply to logical statements about observables. A theoretical
example of a non-quantum system with quantum-type properties is analysed.


title: Asymptotic State Vector Collapse and QED Nonequivalent Representations

abstract:
  The state vector evolution in the interaction of measured pure state with the
collective quantum system or the field is analyzed in a nonperturbative QED
formalism. As the model example the measurement of the electron final state
scattered on nucleus or neutrino is considered. The produced electromagnetic
bremsstrahlung contains the unrestricted number of soft photons resulting in
the total radiation flux becoming the classical observable, which means the
state vector collapse. The evolution from the initial to the final system state
is nonunitary and formally irreversible in the limit of the infinite time.


title: Can absolute freedom save quantum mechanics?

abstract:
  A classical system violating the Bell inequality is discussed. The system is
local, deterministic, observers have free will, and detectors are ideal so that
no data are lost. The trick is based on two elements. First, a state of one
observer is locally influenced by a "particle". Second, random variables used
in the experiment are complementary. A relation of this effect to nonlocality
is discussed.


title: Stabilizer Codes and Quantum Error Correction

abstract:
  Controlling operational errors and decoherence is one of the major challenges
facing the field of quantum computation and other attempts to create specified
many-particle entangled states. The field of quantum error correction has
developed to meet this challenge. A group-theoretical structure and associated
subclass of quantum codes, the stabilizer codes, has proved particularly
fruitful in producing codes and in understanding the structure of both specific
codes and classes of codes. I will give an overview of the field of quantum
error correction and the formalism of stabilizer codes. In the context of
stabilizer codes, I will discuss a number of known codes, the capacity of a
quantum channel, bounds on quantum codes, and fault-tolerant quantum
computation.


title: Bell inequality and complementarity loophole

abstract:
  A simple classical, deterministic, local situation violating the Bell
inequality is described. The detectors used in the experiment are ideal and the
observers who decide which pair of measuring devices to choose for a given pair
of particles have free will. The construction uses random variables which are
not jointly measurable in a single run of an experiment and the hidden
variables have a nonsymmetric probability density. Such random variables are
complementary but still fully classical. An assumption that classical random
variables cannot satisfy any form of complementarity principle is false, and
this is the loophole used in this example. A relationship to the detector
inefficiency loophole is discussed.


title: On Quantum Communication Channels with Constrained Inputs

abstract:
  The purpose of this work is to extend the result of previous papers
quant-ph/9611023, quant-ph/9703013 to quantum channels with additive
constraints onto the input signal, by showing that the capacity of such channel
is equal to the supremum of the entropy bound with respect to all apriori
distributions satisfying the constraint. We also make an extension to channels
with continuous alphabet. As an application we prove the formula for the
capacity of the quantum Gaussian channel with constrained energy of the signal,
establishing the asymptotic equivalence of this channel to the semiclassical
photon channel. We also study the lower bounds for the reliability function of
the pure-state Gaussian channel.


title: On Tracial Operator Representations of Quantum Decoherence Functionals

abstract:
  A general `quantum history theory' can be characterised by the space of
histories and by the space of decoherence functionals. In this note we consider
the situation where the space of histories is given by the lattice of
projection operators on an infinite dimensional Hilbert space $H$. We study
operator representations for decoherence functionals on this space of
histories. We first give necessary and sufficient conditions for a decoherence
functional being representable by a trace class operator on $H \otimes H$, an
infinite dimensional analogue of the Isham-Linden-Schreckenberg representation
for finite dimensions. Since this excludes many decoherence functionals of
physical interest, we then identify the large and physically important class of
decoherence functionals which can be represented, canonically, by bounded
operators on $H \otimes H$.


title:
How to Probe for Dynamical Structure in the Collapse of Entangled States
  Using Nuclear Magnetic Resonance

abstract:
  The spin state of two magnetically inequivalent protons in contiguous atoms
of a molecule becomes entangeled by the indirect spin-spin interaction
(j-coupling). The degree of entanglement oscillates at the beat frequency
resulting from the splitting of a degeneracy. This beating is manifest in NMR
spectroscopy as an envelope of the transverse magnetization and should be
visible in the free induction decay signal. The period (approximately 1 sec) is
long enough for interference between the linear dynamics and collapse of the
wave-function induced by a Stern-Gerlach inhomogeneity to significantly alter
the shape of that envelope. Various dynamical collapse theories can be
distinguished by their observably different predictions with respect to this
alteration. Adverse effects of detuning due to the Stern-Gerlach inhomogeneity
can be reduced to an acceptable level by having a sufficiently thin sample or a
strong rf field.


title: About the quantum mechanical speeding up of classical algorithms

abstract:
  This work introduces a relative diffusion transformation (RDT) - a simple
unitary transformation which acts in a subspace, localized by an oracle. Such a
transformation can not be fulfilled on quantum Turing machines with this oracle
in polynomial time in general case. It is proved, that every function
computable in time T and space S on classical 1-dimensional cellular automaton,
can be computed with certainty in time O(S \sqrt T) on quantum computer with
RDTs over the parts of intermediate products of classical computation. This
requires multiprocessor, which consists of \sqrt T quantum devices each of O(S)
size, working in parallel-serial mode and interacting by classical lows.


title: Gravitation at the mesoscopic scale

abstract:
  Free fall experiments are discussed by using test masses associated to
quantum states not necessarily possessing a classical counterpart. The times of
flight of the Galileian experiments using classical test masses are replaced in
the quantum case by probability distributions which, although still not defined
in an uncontroversial manner, become manifestly dependent upon the mass and the
initial state. Such a dependence is also expected in non inertial frames of
reference if the weak equivalence principle still holds. This last could be
tested, merging recent achievements in mesoscopic physics, by using cooled
atoms in free fall and accelerated frames initially prepared in nonclassical
quantum states.


title:
Quantum computers can search arbitrarily large databases by a single
  query

abstract:
  This paper shows that a quantum mechanical algorithm that can query
information relating to multiple items of the database, can search a database
in a single query (a query is defined as any question to the database to which
the database has to return a (YES/NO) answer). A classical algorithm will be
limited to the information theoretic bound of at least O(log N) queries (which
it would achieve by using a binary search).


title: Computable functions, quantum measurements, and quantum dynamics

abstract:
  We construct quantum mechanical observables and unitary operators which, if
implemented in physical systems as measurements and dynamical evolutions, would
contradict the Church-Turing thesis which lies at the foundation of computer
science. We conclude that either the Church-Turing thesis needs revision, or
that only restricted classes of observables may be realized, in principle, as
measurements, and that only restricted classes of unitary operators may be
realized, in principle, as dynamics.


title:
Production of photons by the parametric resonance in the dynamical
  Casimir effect

abstract:
  We calculate the number of photons produced by the parametric resonance in a
cavity with vibrating walls. We consider the case that the frequency of
vibrating wall is $n \omega_1 (n=1,2,3,...)$ which is a generalization of other
works considering only $2 \omega_1$, where $\omega_1$ is the fundamental-mode
frequency of the electromagnetic field in the cavity. For the calculation of
time-evolution of quantum fields, we introduce a new method which is borrowed
from the time-dependent perturbation theory of the usual quantum mechanics.
This perturbation method makes it possible to calculate the photon number for
any $n$ and to observe clearly the effect of the parametric resonance.


title:
Hyperfinite-Dimensional Representations of Canonical Commutation
  Relation

abstract:
  This paper presents some methods of representing canonical commutation
relations in terms of hyperfinite-dimensional matrices, which are constructed
by nonstandard analysis. The first method uses representations of a nonstandard
extension of finite Heisenberg group, called hyperfinite Heisenberg group. The
second is based on hyperfinite-dimensional representations of so(3). Then, the
cases of infinite degree of freedom are argued in terms of the algebra of
hyperfinite parafermi oscillators, which is mathematically equivalent to a
hyperfinite-dimensional representation of so(n).


title: Bell-Kochen-Specker theorem: A proof with 18 vectors

abstract:
  We present a ``state-independent'' proof of the Bell-Kochen-Specker theorem
using only 18 four-dimensional vectors, which is a record for this kind of
proof. This set of vectors contains subsets which allow us to develop a
``state-specific'' proof with 10 vectors (also a record) and a
``probabilistic'' proof with 7 vectors which reflects the algebraic structure
of Hardy's nonlocality theorem.


title: New variants of the Bell-Kochen-Specker theorem

abstract:
  We discuss two new demonstrations of the Bell-Kochen-Specker theorem: a
state-independent proof using 14 four-dimensional propositions, based on a
suggestion made by Clifton, and a state-specific proof involving 5 propositions
on the singlet state of two spin-1/2 particles.


title:
Hypersensitivity to perturbation: An information-theoretical
  characterization of classical and quantum chaos

abstract:
  Hypersensitivity to perturbation is a criterion for chaos based on the
question of how much information about a perturbing environment is needed to
keep the entropy of a Hamiltonian system from increasing. In this paper we give
a brief overview of our work on hypersensitivity to perturbation in classical
and quantum systems.


title: Quantum Robots and Quantum Computers

abstract:
  Validation of a presumably universal theory, such as quantum mechanics,
requires a quantum mechanical description of systems that carry out theoretical
calculations and experiments. The description of quantum computers is under
active development. No description of systems to carry out experiments has been
given. A small step in this direction is taken here by giving a description of
quantum robots as mobile systems with on board quantum computers that interact
with environments. Some properties of these systems are discussed. A specific
model based on the literature descriptions of quantum Turing machines is
presented.


title: Quantum Statistical Thermodynamics of Two-Level Systems

abstract:
  We study four distinct families of Gibbs canonical distributions defined on
the standard complex, quaternionic, real and classical (nonquantum) two-level
systems. The structure function or density of states for any two-level system
is a simple power (1, 3, 0 or -1) of the length of its polarization vector,
while the magnitude of the energy of the system, in all four cases, is the
negative of the logarithm of the determinant of the corresponding
two-dimensional density matrix. Functional relationships (proportional to
ratios of gamma functions) are found between the average polarizations with
respect to the Gibbs distributions and the effective polarization temperature
parameters. In the standard complex case, this yields an interesting
alternative, meeting certain probabilistic requirements recently set forth by
Lavenda, to the more conventional (hyperbolic tangent) Brillouin function of
paramagnetism (which, Lavenda argues, fails to meet such specifications).


title: Saddle scars: Existence and applications

abstract:
  A quantum scar is a wave function which displays an high intensity in the
region of a classical unstable periodic orbit. Saddle scars are states related
to the unstable harmonic motions along the stable manifold of a saddle point of
the potential. Using a semiclassical method it is shown that, independently of
the overall structure of the potential, the local dynamics of the saddle point
is sufficient to insure the general existence of this type of scars and their
factorized structure is obtained. Potentially useful situations are identified,
where these states appear (directly or in disguise) and might be used for
quantum control purposes.


title: Minimum uncertainty for antisymmetric wave functions

abstract:
  We study how the entropic uncertainty relation for position and momentum
conjugate variables is minimized in the subspace of one-dimensional
antisymmetric wave functions. Based partially on numerical evidence and
partially on analytical results, a conjecture is presented for the sharp bound
and for the minimizers. Conjectures are also presented for the corresponding
sharp Hausdorff-Young inequality.


title:
No-hidden-variables proof for two spin-1/2 particles preselected and
  postselected in unentangled states

abstract:
  It is a well-known fact that all the statistical predictions of quantum
mechanics on the state of any physical system represented by a two-dimensional
Hilbert space can always be duplicated by a noncontextual hidden-variables
model. In this paper, I show that, in some cases, when we consider an
additional independent (unentangled) two-dimensional system, the quantum
description of the resulting composite system cannot be reproduced using
noncontextual hidden variables. In particular, a no-hidden-variables proof is
presented for two individual spin-1/2 particles preselected in an uncorrelated
state AB and postselected in another uncorrelated state aB, B being the same
state for the second particle in both preselection and postselection.


title: Ground State Laser Cooling Beyond the Lamb-Dicke Limit

abstract:
  We propose a laser cooling scheme that allows to cool a single atom confined
in a harmonic potential to the trap ground state $|0>$. The scheme assumes
strong confinement, where the oscillation frequency in the trap is larger than
the effective spontaneous decay width, but is not restricted to the Lamb-Dicke
limit, i.e. the size of the trap ground state can be larger than the optical
wavelength. This cooling scheme may be useful in the context of quantum
computations with ions and Bose-Einstein condensation.


title: The Logic of Quantum Mechanics Derived from Classical General Relativity

abstract:
  For the first time it is shown that the logic of quantum mechanics can be
derived from Classical Physics. An orthomodular lattice of propositions,
characteristic of quantum logic, is constructed for manifolds in Einstein's
theory of general relativity. A particle is modelled by a topologically
non-trivial 4-manifold with closed timelike curves - a 4-geon, rather than as
an evolving 3-manifold. It is then possible for both the state preparation and
measurement apparatus to constrain the results of experiments. It is shown that
propositions about the results of measurements can satisfy a non-distributive
logic rather than the Boolean logic of classical systems. Reasonable
assumptions about the role of the measurement apparatus leads to an
orthomodular lattice of propositions characteristic of quantum logic.


title: Quantum Computation Based on Retarded and Advanced Propagation

abstract:
  Computation is currently seen as a forward propagator that evolves (retards)
a completely defined initial vector into a corresponding final vector. Initial
and final vectors map the (logical) input and output of a reversible Boolean
network respectively, whereas forward propagation maps a one-way propagation of
logical implication, from input to output. Conversely, hard NP-complete
problems are characterized by a two-way propagation of logical implication from
input to output and vice versa, given that both are partly defined from the
beginning. Logical implication can be propagated forward and backward in a
computation by constructing the gate array corresponding to the entire
reversible Boolean network and constraining output bits as well as input bits.
The possibility of modeling the physical process undergone by such a network by
using a retarded and advanced in time propagation scheme is investigated. PACS
numbers: 89.70.+c, 02.50.-r, 03.65.-w, 89.80.+h


title:
Perturbative expansions for the fidelities and spatially correlated
  dissipation of quantum bits

abstract:
  We construct generally applicable short-time perturbative expansions for some
fidelities, such as the input-output fidelity, the entanglement fidelity, and
the average fidelity. Successive terms of these expansions yield characteristic
times for the damping of the fidelities involving successive powers of the
Hamiltonian. The second-order results, which represent the damping rates of the
fidelities, are extensively discussed. As an interesting application of these
expansions, we use them to study the spatially-correlated dissipation of
quantum bits. Spatial correlations in the dissipation are described by a
correlation function. Explicit conditions are derived for independent
decoherence and for collective decoherence.


title:
Dynamics of Dissipative Two-Level Systems in the Stochastic
  Approximation

abstract:
  The dynamics of the spin-boson Hamiltonian is considered in the stochastic
approximation. The Hamiltonian describes a two-level system coupled to an
environment and is widely used in physics, chemistry and the theory of quantum
measurement. We demonstrate that the method of the stochastic approximation
which is a general method of consideration of dynamics of an arbitrary system
interacting with environment is powerful enough to reproduce qualitatively
striking results by Leggett at al. found earlier for this model. The result
include an exact expression of the dynamics in terms of the spectral density
and show an appearance of two most interesting regimes for the system, i.e.
pure oscillating and pure damping ones. Correlators describing environment are
also computed.


title: Optical Simulation of Quantum Logic

abstract:
  A systematic method for simulating small-scale quantum circuits by use of
linear optical devices is presented. It relies on the representation of several
quantum bits by a single photon, and on the implementation of universal quantum
gates using simple optical components (beam splitters, phase shifters, etc.).
This suggests that the optical realization of small quantum networks is
reasonable given the present technology in quantum optics, and could be a
useful technique for testing simple quantum algorithms or error-correction
schemes. The optical circuit for quantum teleportation is presented as an
illustration.


title: Quantum mechanics in the noncontractible space

abstract:
  We show that the impact of the fundamental length in quantum mechanics can be
studied within the formalism of Berry's geometrical phase with the line
broadening as a resulting physical effect.


title: Radon transform and pattern functions in quantum tomography

abstract:
  The two-dimensional Radon transform of the Wigner quasiprobability is
introduced in canonical form and the functions playing a role in its inversion
are discussed. The transformation properties of this Radon transform with
respect to displacement and squeezing of states are studied and it is shown
that the last is equivalent to a symplectic transformation of the variables of
the Radon transform with the contragredient matrix to the transformation of the
variables in the Wigner quasiprobability. The reconstruction of the density
operator from the Radon transform and the direct reconstruction of its
Fock-state matrix elements and of its normally ordered moments are discussed.
It is found that for finite-order moments the integration over the angle can be
reduced to a finite sum over a discrete set of angles. The reconstruction of
the Fock-state matrix elements from the normally ordered moments leads to a new
representation of the pattern functions by convergent series over even or odd
Hermite polynomials which is appropriate for practical calculations. The
structure of the pattern functions as first derivatives of the products of
normalizable and nonnormalizable eigenfunctions to the number operator is
considered from the point of view of this new representation.


title: Quantum Chaos in a Yang-Mills-Higgs System

abstract:
  We study the energy fluctuations of a spatially homogeneous SU(2)
Yang-Mills-Higgs system. In particular, we analyze the nearest-neighbour
spacing distribution which shows a Wigner-Poisson transition by increasing the
value of the Higgs field in the vacuum. This transition is a clear quantum
signature of the classical chaos-order transition of the system.


title: Adiabatic quantum computation with Cooper pairs

abstract:
  We propose a new variant of the controlled-NOT quantum logic gate based on
adiabatic level-crossing dynamics of the q-bits. The gate has a natural
implementation in terms of the Cooper pair transport in arrays of small
Josephson tunnel junctions. An important advantage of the adiabatic approach is
that the gate dynamics is insensitive to the unavoidable spread of junction
parameters.


title: An Operational Approach to Quantum State Reduction

abstract:
  An operational approach to quantum state reduction, the state change of the
measured system caused by a measurement of an observable conditional upon the
outcome of measurement, is founded without assuming the projection postulate in
any stages of the measuring process. Whereas the conventional formula assumes
that the probe measurement satisfies the projection postulate, a new formula
for determining the state reduction shows that the state reduction does not
depend on how the probe observable is measured, or in particular does not
depend on whether the probe measurement satisfies the projection postulate or
not, contrary to the longstanding attempts in showing how the macroscopic
nature of probe detection provokes state reduction.


title:
Barut-Girardello coherent states for sp(N,C) and multimode Schr\"odinger
  cat states

abstract:
  Overcomplete families of states of the type of Barut-Girardello coherent
states (BG CS) are constructed for noncompact algebras $u(p,q)$ and $sp(N,C)$
in quadratic bosonic representation. The $sp(N,C)$ BG CS are obtained in the
form of multimode ordinary Schr\"odinger cat states. A set of such macroscopic
superpositions is pointed out which is overcomplete in the whole $N$ mode
Hilbert space (while the associated $sp(N,C)$ representation is reducible). The
multimode squared amplitude Schr\"odinger cat states are introduced as
macroscopic superpositions of the obtained $sp(N,C)$ BG CS.}


title:
Light Propagation in Nonlinear Waveguide and Classical Two-Dimensional
  Oscillator

abstract:
  The quantum optical problem of the propagation of electromagnetic waves in a
nonlinear waveguide is related to the solutions of the classical nonstationary
harmonic oscillator using the method of linear integrals of motion [ Malkin
et.al., Phys Rev. 2D (1970) p.1371 ]. An explicit solution of the classical
oscillator with a varying frequency, corresponding to the light propagation in
an anisotropic waveguide is obtained using the expressions for the quantum
field fluctuations. Substitutions have been found which allow to establish
connections of the linear and quadratic invariants of Malkin et.al. to several
types of invariants of quadratic systems, considered in later papers. These
substitutions give the opportunity to relate the corresponding quantum problem
to that of the classical two-dimensional nonstationary oscillator, which is
physically more informative.


title: Geometry of Thermodynamic States

abstract:
  A novel geometric formalism for statistical estimation is applied here to the
canonical distribution of classical statistical mechanics. In this scheme
thermodynamic states, or equivalently, statistical mechanical states, can be
characterised concisely in terms of the geometry of a submanifold ${\cal M}$ of
the unit sphere ${\cal S}$ in a real Hilbert space ${\cal H}$. The measurement
of a thermodynamic variable then corresponds to the reduction of a state vector
in ${\cal H}$ to an eigenstate, where the transition probability is the
Boltzmann weight. We derive a set of uncertainty relations for conjugate
thermodynamic variables in the equilibrium thermodynamic states. These follow
as a consequence of a striking thermodynamic analogue of the Anandan-Aharonov
relations in quantum mechanics. As a result we are able to provide a resolution
to the controversy surrounding the status of `temperature fluctuations' in the
canonical ensemble. By consideration of the curvature of the thermodynamic
trajectory in its state space we are then able to derive a series of higher
order variance bounds, which we calculate explicitly to second order.


title:
Mimicking a Squeezed Bath Interaction: Quantum Reservoir Engineering
  with Atoms

abstract:
  The interaction of an atomic two-level system and a squeezed vacuum leads to
interesting novel effects in atomic dynamics, including line narrowing in
resonance fluorescence and absorption spectra, and a suppressed (enhanced)
decay of the in-phase and out-of phase component of the atomic polarization. On
the experimental side these predictions have so far eluded observation,
essentially due to the difficulty of embedding atoms in a 4 pi squeezed vacuum.
In this paper we show how to ``engineer'' a squeezed-bath-type interaction for
an effective two-level system. In the simplest example, our two-level atom is
represented by the two ground levels of an atom with angular momentum J=1/2 ->
J=1/2 transition (a four level system) which is driven by (weak) laser fields
and coupled to the vacuum reservoir of radiation modes. Interference between
the spontaneous emission channels in optical pumping leads to a squeezed bath
type coupling, and thus to symmetry breaking of decay on the Bloch sphere. With
this system it should be possible to observe the effects predicted in the
context of squeezed bath - atom interactions. The laser parameters allow one to
choose properties of the squeezed bath interaction, such as the (effective)
photon number expectation number N and the squeezing phase phi. We present
results of a detailed analytical and numerical study.


title: Testing complete positivity

abstract:
  We study the modified dynamical evolution of the neutral kaon system under
the condition of complete positivity. The accuracy of the data from planned
future experiments is expected to be sufficiently precise to test such a
hypothesis.


title: Quantum Mechanics helps in searching for a needle in a haystack

abstract:
  Quantum mechanics can speed up a range of search applications over unsorted
data. For example imagine a phone directory containing N names arranged in
completely random order. To find someone's phone number with a probability of
50%, any classical algorithm (whether deterministic or probabilistic) will need
to access the database a minimum of O(N) times. Quantum mechanical systems can
be in a superposition of states and simultaneously examine multiple names. By
properly adjusting the phases of various operations, successful computations
reinforce each other while others interfere randomly. As a result, the desired
phone number can be obtained in only O(sqrt(N)) accesses to the database.


title: Quantum Superposition States of Bose-Einstein Condensates

abstract:
  We propose a scheme to create a macroscopic ``Sch\"odinger cat'' state formed
by two interacting Bose condensates. In analogy with quantum optics, where the
control and engineering of quantum states can be maintained to a large extend,
we consider the present scheme to be an example of quantum atom optics at work.


title: Movement and Fluctuations of the Vacuum

abstract:
  Quantum fields possess zero-point or vacuum fluctuations which induce
mechanical effects, namely generalised Casimir forces, on any scatterer.
  Symmetries of vacuum therefore raise fundamental questions when confronted
with the principle of relativity of motion in vacuum. The specific case of
uniformly accelerated motion is particularly interesting, in connection with
the much debated question of the appearance of vacuum in accelerated frames.
The choice of Rindler representation, commonly used in General Relativity,
transforms vacuum fluctuations into thermal fluctuations, raising difficulties
of interpretation. In contrast, the conformal representation of uniformly
accelerated frames fits the symmetry properties of field propagation and
quantum vacuum and thus leads to extend the principle of relativity of motion
to uniform accelerations.
  Mirrors moving in vacuum with a non uniform acceleration are known to
radiate. The associated radiation reaction force is directly connected to
fluctuating forces felt by motionless mirrors through fluctuation-dissipation
relations. Scatterers in vacuum undergo a quantum Brownian motion which
describes irreducible quantum fluctuations. Vacuum fluctuations impose ultimate
limitations on measurements of position in space-time, and thus challenge the
very concept of space-time localisation within a quantum framework.
  For test masses greater than Planck mass, the ultimate limit in localisation
is determined by gravitational vacuum fluctuations. Not only positions in
space-time, but also geodesic distances, behave as quantum variables,
reflecting the necessary quantum nature of an underlying geometry.


title: Conformal Symmetry and Quantum Relativity

abstract:
  The relativistic conception of space and time is challenged by the quantum
nature of physical observables. It has been known for a long time that
Poincar\'e symmetry of field theory can be extended to the larger conformal
symmetry. We use these symmetries to define quantum observables associated with
positions in space-time, in the spirit of Einstein theory of relativity. This
conception of localisation may be applied to massive as well as massless
fields. Localisation observables are defined as to obey Lorentz covariant
commutations relations and in particular include a time observable conjugated
to energy. Whilst position components do not commute in presence of a
non-vanishing spin, they still satisfy quantum relations which generalise the
differential laws of classical relativity. We also give of these observables a
representation in terms of canonical spatial positions, canonical spin
components and a proper time operator conjugated to mass. These results plead
for a new representation not only of space-time localisation but also of
motion.


title: Generalised Heisenberg Relations

abstract:
  A geometric framework for quantum statistical estimation is used to establish
a series of higher order corrections to the Heisenberg uncertainty relations
associated with pairs of canonically conjugate variables. These corrections can
be expressed in terms of linear combinations of higher order cumulants for the
distributions, and thus vanish for Gaussian distributions. Estimates for
typical numerical values arising from these corrections are indicated in the
case of a gamma distribution.


title: Time scale, objectivity and irreversibility in quantum mechanics

abstract:
  It is argued that setting isolated systems as primary scope of field theory
and looking at particles as derived entities, the problem of an objective
anchorage of quantum mechanics can be solved and irreversibility acquires a
fundamental role. These general ideas are checked in the case of the Boltzmann
description of a dilute gas.


title: Quantum Bayesian Nets

abstract:
  We begin with a review of a well known class of networks, Classical Bayesian
(CB) nets (also called causal probabilistic nets by some). Given a situation
which includes randomness, CB nets are used to calculate the probabilities of
various hypotheses about the situation, conditioned on the available evidence.
We introduce a new class of networks, which we call Quantum Bayesian (QB) nets,
that generalize CB nets to the quantum mechanical regime. We explain how to use
QB nets to calculate quantum mechanical conditional probabilities (in case of
either sharp or fuzzy observations), and discuss the connection of QB nets to
Feynman Path integrals. We give examples of QB nets that involve a single
spin-half particle passing through a configuration of two or three
Stern-Gerlach magnets. For the examples given, we present the numerical values
of various conditional probabilities, as calculated by a general computer
program especially written for this purpose.


title: Quantization of a particle in a background Yang-Mills field

abstract:
  Two classes of observables defined on the configuration space of a particle
are quantized, and the effects of the Yang-Mills field are discussed in the
context of geometric quantization.


title:
A Linear Quantum Dynamic Theory for Coherent Output of Bose-Einstain
  Condensation

abstract:
  A model for the coherent output coupler of the Bose-Einstein condensed atoms
from a trap in the recent MIT experiment (Phys. Rev. Lett., 78 (1997) 582) is
established with a simple many-boson system of two states with linear coupling.
Its exact solution for the many-body problem shows a factorization of dynamical
evolution process, i.e., the wave function initially prepared in a direct
product of a vacuum state and a coherent state remains in a direct product of
two coherent states at any instance in the evolution of the total system. This
conclusion always holds even for a system with a finite average particle number
in the initial state. Its thermodynamical limit can be directly dealt with in
the Bogoliubov approximation and manifests that an ideal condensate in the trap
will remain in a coherent state after the r.f. interaction while the
output-coupler pulse of atoms is also in a coherent state, which means a
coherent output of atomic beam to form a macroscopic quantum state in a
propagating mode.


title: Correlations in interference and diffraction

abstract:
  Quantum formalism of Fraunhofer diffraction is obtained. The state of the
diffraction optical field is connected with the state of the incident optical
field by a diffraction factor. Based on this formalism, correlations of the
diffraction modes are calculated with different kinds of incident optical
fields. Influence of correlations of the incident modes on the diffraction
pattern is analyzed and an explanation of the ''ghost'' diffraction is
proposed.


title:
Quantum phenomena do not violate the principle of locality - a new
  interpretation with physical consequences -

abstract:
  A new interpretation of nonrelativistic quantum mechanics explains the
violation of Bell's inequality by maintaining realism and the principle of
locality.


title: Dynamical Manipulation for spin-1/2 Systems

abstract:
  By means of the inverse techniques we analyse the evolution of purely
spin-1/2 systems in homogeneous magnetic fields as well as the generation of
exact solutions. Some ``evolution loops'', dynamical processes for which any
state evolves cyclically, are presented, and their corresponding geometric
phases are evaluated


title: Decoherent Histories Approach to the Arrival Time Problem

abstract:
  We use the decoherent histories approach to quantum theory to compute the
probability of a non-relativistic particle crossing $x=0$ during an interval of
time. For a system consisting of a single non-relativistic particle, histories
coarse-grained according to whether or not they pass through spacetime regions
are generally not decoherent, except for very special initial states, and thus
probabilities cannot be assigned. Decoherence may, however, be achieved by
coupling the particle to an environment consisting of a set of harmonic
oscillators in a thermal bath. Probabilities for spacetime coarse grainings are
thus calculated by considering restricted density operator propagators of the
quantum Brownian motion model. We also show how to achieve decoherence by
replicating the system $N$ times and then projecting onto the number density of
particles that cross during a given time interval, and this gives an
alternative expression for the crossing probability. The latter approach shows
that the relative frequency for histories is approximately decoherent for
sufficiently large $N$, a result related to the Finkelstein-Graham-Hartle
theorem.


title: Quantum Coin Tossing

abstract:
  We show that a secure quantum protocol for coin tossing exist. The existence
of quantum coin tossing support the conjecture of D.Mayers [Phys.Rev.Lett. 78,
3414(1997)] that only asymmetrical tasks as quantum bit commitment are
impossible.


title: Partial Factorization of Wave Function for A Quantum Dissipation System

abstract:
  The microscopic approach quantum dissipation process presented by Yu and Sun
[Phys. Rev., A49(1994)592, A51(1995)1845] is developed to analyze the wave
function structure of dynamic evolution of a typical dissipative system, a
single mode boson soaked in a bath of many bosons. In this paper, the wave
function of total system is explicitly obtained as a product of two components
of the system and the bath in the coherent state representation. It not only
describes the influence of the bath on the variable of the system through the
Brownian motion, but also manifests the back- action of the system on the bath
and the effects of the mutual interaction among the bosons of the bath. Due to
the back-action, the total wave function can only be partially factorizable
even for the Brownian motion can be ignored in certain senses, such as the
cases with weak coupling and large detuning


title: Time development of a wave packet and the time delay

abstract:
  A one-dimensional scattering problem off a $\delta$-shaped potential is
solved analytically and the time development of a wave packet is derived from
the time-dependent Schr\"odinger equation. The exact and explicit expression of
the scattered wave packet supplies us with interesting information about the
"time delay" by potential scattering in the asymptotic region. It is
demonstrated that a wave packet scattered by a spin-flipping potential can give
us quite a different value for the delay times from that obtained without
spin-degrees of freedom.


title:
Some properties of quantum reiliablity function for quantum
  communication channel

abstract:
  This paper presents some examples of quantum reliability function for the
quantum communication system in which classical information is transmitted by
quantum states. In addition, the quantum Cut off rate is defined. They will be
compared with Gallager's reliability function for the same system.


title: The non-Markovian stochastic Schrodinger equation for open systems

abstract:
  We present the non-Markovian generalization of the widely used stochastic
Schrodinger equation. Our result allows to describe open quantum systems in
terms of stochastic state vectors rather than density operators, without
approximation. Moreover, it unifies two recent independent attempts towards a
stochastic description of non-Markovian open systems, based on path integrals
on the one hand and coherent states on the other. The latter approach utilizes
the analytical properties of coherent states and enables a microscopic
interpretation of the stochastic states. The alternative first approach is
based on the general description of open systems using path integrals as
originated by Feynman and Vernon.


title:
Vacuum Fluctuations and Decoherence in Mesoscopic and Microscopic
  Systems

abstract:
  We discuss recent experimental evidence of decoherence in a laboratory
mesoscopic system in a cavity, from which we draw analogies with the
decoherence that we argue is induced by microscopic quantum-gravity
fluctuations in the space-time background. We emphasize the parallel r\^oles
played in both cases by dissipation through non-trivial vacuum fluctuations
that trigger the collapse of an initially coherent quantum state. We review a
phenomenological parametrization of possible effects of this kind in the
neutral kaon system, where they would induce CPT violation, and describe some
epxerimental tests.


title: On the Complexity of Quantum Searching Using Complex Queries

abstract:
  We discuss the quantum search algorithm using complex queries that has
recently been published by Grover (quant-ph/9706005). We recall the algorithm
adding some details showing which complex query has to be evaluated. Based on
this version of the algorithm we discuss its complexity.


title: Effective Pure States for Bulk Quantum Computation

abstract:
  In bulk quantum computation one can manipulate a large number of
indistinguishable quantum computers by parallel unitary operations and measure
expectation values of certain observables with limited sensitivity. The initial
state of each computer in the ensemble is known but not pure. Methods for
obtaining effective pure input states by a series of manipulations have been
described by Gershenfeld and Chuang (logical labeling) and Cory et al. (spatial
averaging) for the case of quantum computation with nuclear magnetic resonance.
We give a different technique called temporal averaging. This method is based
on classical randomization, requires no ancilla qubits and can be implemented
in nuclear magnetic resonance without using gradient fields. We introduce
several temporal averaging algorithms suitable for both high temperature and
low temperature bulk quantum computing and analyze the signal to noise behavior
of each.


title: On the failure of Bell's theorem

abstract:
  Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's
theorem and point out a loophole in it. We also demonstrate on this example
that quantum mechanics is a local realistic theory.


title: Evaluation of Vacuum Energy for Tensor Fields on Spherical Spaces

abstract:
  The effective one-loop potential on $R^{m+1}\times S^N$ spaces for massless
tensor fields is evaluated. The Casimir energy is given as a value of $\zeta-$
function by means of which regularization is made. In even- dimensional spaces
the vacuum energy contains divergent terms coming from poles of $\zeta(s,q)$ at
$s=1$, whereas in odd-dimensional spaces it becomes finite.


title:
Eigenvalue Problem for Schroedinger Operators and Time-Dependent
  Harmonic Oscillator

abstract:
  It is shown that the eigenvalue problem for the Hamiltonians of the standard
form, $H=p^2/(2m)+V(x)$, is equivalent to the classical dynamical equation for
certain harmonic oscillators with time-dependent frequency. This is another
indication of the central role played by time-dependent harmonic oscillators in
quantum mechanics. The utility of the known results for eigenvalue problem in
the solution of the dynamical equations of a class of time-dependent harmonic
oscillators is also pointed out.


title: Exact solution for generalized pairing

abstract:
  An infinite dimensional algebra, which is useful for deriving exact solutions
of the generalized pairing problem, is introduced. A formalism for
diagonalizing the corresponding Hamiltonian is also proposed. The theory is
illustrated with some numerical examples.


title:
Multiphoton localization and propagating quantum gap solitons in a
  frequency gap medium

abstract:
  The many-particle spectrum of an isotropic frequency gap medium doped with
impurity resonance atoms is studied using the Bethe ansatz technique. The
spectrum is shown to contain pairs of quantum correlated ``gap excitations''
and their heavy bound complexes (``gap solitons''), enabling the propagation of
quantum information within the classically forbidden gap. In addition,
multiparticle localization of the radiation and the medium polarization occurs
when such a gap soliton is pinned to the impurity atom.


title:
Introduction of a Quantum of Time ("chronon"), and its Consequences for
  Quantum Mechanics

abstract:
  In this review-article, we discuss the consequences of the introduction of a
quantum of time tau_0 in the formalism of non-relativistic quantum mechanics
(QM) by referring ourselves in particular to the theory of the "chronon" as
proposed by P.Caldirola. Such an interesting "finite difference" theory,
forwards --at the classical level-- a solution for the motion of a particle
endowed with a non-negligible charge in an external electromagnetic field,
overcoming all the known difficulties met by Abraham-Lorentz's and Dirac's
approaches (and even allowing a clear answer to the question whether a free
falling charged particle does or does not emit radiation), and --at the quantum
level-- yields a remarkable mass spectrum for leptons. After having briefly
reviewed Caldirola's approach, we compare one another the new Schroedinger,
Heisenberg and density-operator (Liouville-von Neumann) pictures resulting from
it. Moreover, for each representation, three (retarded, symmetric and advanced)
formulations are possible, which refer either to times t and t-tau_0, or to
times t-tau_0/2 and t+tau_0/2, or to times t and t+tau_0, respectively. It is
interesting to notice that, e.g., the "retarded" QM does naturally appear to
describe QM with friction, i.e., to describe dissipative quantum systems (like
a particle moving in an absorbing medium). In this sense, discretized QM is
much richer than the ordinary one. When the density matrix formalism is applied
to the solution of the measurement problem in QM, very interesting results are
met, so as a natural explication of "decoherence".


title: The Structure of the SWKB Series

abstract:
  The supersymmetric-WKB series is shown to be such that the SWKB quantisation
condition has corrections in powers of h^2 only and with explicit overall
factors of E. The results also suggest more efficient methods of calculating
the corrections.


title: Quantum Channel Capacity of Very Noisy Channels

abstract:
  We present a family of additive quantum error-correcting codes whose
capacities exceeds that of quantum random coding (hashing) for very noisy
channels. These codes provide non-zero capacity in a depolarizing channel for
fidelity parameters $f$ when $f> .80944$. Random coding has non-zero capacity
only for $f>.81071$; by analogy to the classical Shannon coding limit, this
value had previously been conjectured to be a lower bound. We use the method
introduced by Shor and Smolin of concatenating a non-random (cat) code within a
random code to obtain good codes. The cat code with block size five is shown to
be optimal for single concatenation. The best known multiple-concatenated code
we found has a block size of 25. We derive a general relation between the
capacity attainable by these concatenation schemes and the coherent information
of the inner code states.


title: Quantum Computation and Decision Trees

abstract:
  Many interesting computational problems can be reformulated in terms of
decision trees. A natural classical algorithm is to then run a random walk on
the tree, starting at the root, to see if the tree contains a node n levels
from the root. We devise a quantum mechanical algorithm that evolves a state,
initially localized at the root, through the tree. We prove that if the
classical strategy succeeds in reaching level n in time polynomial in n, then
so does the quantum algorithm. Moreover, we find examples of trees for which
the classical algorithm requires time exponential in n, but for which the
quantum algorithm succeeds in polynomial time. The examples we have so far,
however, could also be solved in polynomial time by different classical
algorithms.


title: Schrodinger Equation and Phase Space in Quantum Mechanics

abstract:
  Using classical statistics, Schrodinger equation in quantum mechanics is
derived from complex space model. Phase-space probability amplitude, that can
be defined on classical point of view, has connections to probability amplitude
in internal space and to wave function in quantum mechanics. In addition, the
physical entity of wave function in quantum mechanics is confirmed once again.


title:
Information-theoretic approach to quantum error correction and
  reversible measurement

abstract:
  Quantum operations provide a general description of the state changes allowed
by quantum mechanics. The reversal of quantum operations is important for
quantum error-correcting codes, teleportation, and reversing quantum
measurements. We derive information-theoretic conditions and equivalent
algebraic conditions that are necessary and sufficient for a general quantum
operation to be reversible. We analyze the thermodynamic cost of error
correction and show that error correction can be regarded as a kind of
``Maxwell demon,'' for which there is an entropy cost associated with
information obtained from measurements performed during error correction. A
prescription for thermodynamically efficient error correction is given.


title: Quantum Networking with Optical Fibres

abstract:
  I propose a scheme which allows for reliable transfer of quantum information
between two atoms via an optical fibre in the presence of decoherence. The
scheme is based on performing an adiabatic passage through two cavities which
remain in their respective vacuum states during the whole operation. The scheme
may be useful for networking several ion-trap quantum computers, thereby
increasing the number of quantum bits involved in a computation.


title: Entanglement purification via separable superoperators

abstract:
  One of the fundamental concepts of quantum information theory is that of
entanglement purification; that is, the transformation of a partially entangled
state into a smaller-dimensional, more completely entangled state. Of
particular interest are protocols for entanglement purification (EPPs) that
alternate purely local operations with one- or two-way classical communication.
In the present work, we consider a more general, but simpler, class of
transformations, called separable superoperators. Since every EPP is a
separable superoperator, bounds on separable superoperators apply as well to
EPPs; we use this fact to give a new upper bound on the rate of EPPs on
Bell-diagonal states, and thus on the capacity of Bell-diagonal channels.


title: "Minus c" Symmetry in Classical and Quantum Theories

abstract:
  It is shown that the transformations of the charge conjugation in classical
electrodynamics and in quantum theory can be interpreted as the consequences of
the symmetry of Maxwell and Dirac equations with respect to the inversion of
the speed of light: c to -c; t to t; (x,y,z) to (x,y,z), where c is the speed
of light; t is the time; x, y, z are the spatial variables.
  The elements of physical interpretation are given.


title: Matrix Hamiltonians: SUSY approach to hidden symmetries

abstract:
  A new supersymmetric approach to the analysis of dynamical symmetries for
matrix quantum systems is presented. Contrary to standard one dimensional
quantum mechanics where there is no role for an additional symmetry due to
nondegeneracy, matrix hamiltonians allow for non-trivial residual symmetries.
This approach is based on a generalization of the intertwining relations
familiar in SUSY Quantum Mechanics. The corresponding matrix supercharges, of
first or of second order in derivatives, lead to an algebra which incorporates
an additional block diagonal differential matrix operator (referred to as a
"hidden" symmetry operator) found to commute with the superhamiltonian. We
discuss some physical interpretations of such dynamical systems in terms of
spin 1/2 particle in a magnetic field or in terms of coupled channel problem.
Particular attention is paid to the case of transparent matrix potentials.


title:
A Nonperturbative Perspective on Inner Product Quantization: Highly
  Accurate Solutions to the Schr{\"o}dinger Equation

abstract:
  We devise a new and highly accurate quantization procedure for the inner
product representation, both in configuration and momentum space. Utilizing the
representation $\Psi(\xi) = \sum_{i}a_i[E]\xi^i R_{\beta}(\xi)$, for an
appropriate reference function, $R_{\beta}(\xi)$, we demonstrate that the
(convergent) zeroes of the coefficient functions, $a_i[E] = 0$, approximate the
exact bound/resonance state energies with increasing accuracy as $i \to
\infty$. The validity of the approach is shown to be based on an extension of
the Hill determinant quantization procedure. Our method has been applied, with
remarkable success, to various quantum mechanical problems.


title: Puzzlement about thermal redshift

abstract:
  Discussed is the classical theoretical description of the experimentally
established thermal redshift of spectral lines. Straightforward calculation of
the observable spectrum from a canonical ensamble of monochromatic radiators
yileds overall blueshift rather than redshift. It is concluded that the
customary explanation of the thermal redshift as a second order Doppler effect
does not bear closer examination, and that in fact, the phenomenon ''thermal
redshift'' is not yet fully uderstood in classical terms.


title:
''Averaged'' statistical thermodynamics, energy equipartition and the
  third law

abstract:
  Arguments are presented that the assumption, implicit to traditional
statistical thermodynamics, that at zero temperature all erratic motions cease,
should be dispensed with. Assuming instead a random ultrarelativistic
unobservable motion, similar to zitterbewegung, it is demonstrated that in an
ideal gas of classical particles the energy equipartition fails in a way that
complies with the third law of thermodynamics.


title:
Exact two-loop vacuum polarization correctionto the Lamb shift in
  hydrogen-like ions

abstract:
  We present a calculation scheme for the two-loop vacuum polarization
correction of order $\alpha^2$ to the Lamb shift of hydrogen-like high-Z atoms.
The interaction with the external Coulomb field is taken into account to all
orders in $(Z\alpha)$. By means of a modified potential approach the problem is
reduced to the evaluation of effective one-loop vacuum polarization potentials.
An expression for the energy shift is deduced within the framework of partial
wave decomposition performing appropriate subtractions. Exact results for the
two-loop vacuum polarization contribution to the Lamb shift of K- and L-shell
electron states in hydrogen-like Lead and Uranium are presented.


title:
Generation of single-mode SU(1,1) intelligent states and an analytic
  approach to their quantum statistical properties

abstract:
  We discuss a scheme for generation of single-mode photon states associated
with the two-photon realization of the SU(1,1) algebra. This scheme is based on
the process of non-degenerate down-conversion with the signal prepared
initially in the squeezed vacuum state and with a measurement of the photon
number in one of the output modes. We focus on the generation and properties of
single-mode SU(1,1) intelligent states which minimize the uncertainty relations
for Hermitian generators of the group. Properties of the intelligent states are
studied by using a ``weak'' extension of the analytic representation in the
unit disk. Then we are able to obtain exact analytical expressions for
expectation values describing quantum statistical properties of the SU(1,1)
intelligent states. Attention is mainly devoted to the study of photon
statistics and linear and quadratic squeezing.


title: A General Theory of Phase-Space Quasiprobability Distributions

abstract:
  We present a general theory of quasiprobability distributions on phase spaces
of quantum systems whose dynamical symmetry groups are (finite-dimensional) Lie
groups. The family of distributions on a phase space is postulated to satisfy
the Stratonovich-Weyl correspondence with a generalized traciality condition.
The corresponding family of the Stratonovich-Weyl kernels is constructed
explicitly. In the presented theory we use the concept of the generalized
coherent states, that brings physical insight into the mathematical formalism.


title: A Polynomial-Time Quantum Algorithm for Collision Problem

abstract:
  In this paper, we give a quantum algorithm which solves collision problem in
an expected polynomial time. Especially, when the function is two-to-one, we
present a quantum algorithm which can find a collision with certainty in a
worst-case polynomial time. We also give a quantum algorithm which solves claw
problem with certainty in a worst-case polynomial time.


title: Measuring the Cyclotron State of a Trapped Electron

abstract:
  We propose the cyclotron state retrieval of an electron trapped in a Penning
trap by using different measurement schemes based on suitable modifications of
the applied electromagnetic fields and exploiting the axial degree of freedom
as a probe. A test for matter-antimatter symmetry of the quantum state is
proposed.


title: Density matrix interpretation of solutions of Lie-Nambu equations

abstract:
  The spectrum of a density matrix $\rho(t)$ is conserved by a Lie-Nambu
dynamics if $\rho(t)$ is a self-adjoint and Hilbert-Schmidt solution of a
nonlinear triple-bracket equation. This generalizes to arbitrary separable
(positive- and indefinite-metric) Hilbert spaces the previous result which was
valid for finite-dimensional Hilbert spaces.


title: On the Improvement of Frequency Stardards with Quantum Entanglement

abstract:
  The optimal precision of frequency measurements in the presence of
decoherence is discussed. We analyze different preparations of n two level
systems as well as different measurement procedures. We show that standard
Ramsey spectroscopy on uncorrelated atoms and optimal measurements on maximally
entangled states provide the same resolution. The best resolution is achieved
using partially entangled preparations with a high degree of symmetry.


abstract:
  Vacuum polarization screening corrections to the ground state energy of
two-electron ions are calculated in the range $Z=20-100$. The calculations are
carried out for a finite nucleus charge distribution.


title:
Problems about Causality in Fermi's Two-Atom Model and Possible
  Resolutions

abstract:
  In order to check finite propagation speed Fermi, in 1932, had considered two
atoms A and B separated by some distance R. At time t=0, A is in an excited
state, B in its ground state, and no photons are present. Fermi's idea was to
calculate the excitation probability of B. In a model-independent way and with
minimal assumptions - Hilbert space and positive energy only - it is proved,
not just for atoms but for any systems A and B, that the excitation probability
of B is nonzero immediately after t=0. Possible ways out to avoid a
contradiction to finite propagation speed are discussed. The notions of strong
and weak Einstein causality are introduced.


title: Quantum Computation in Quantum-Hall Systems

abstract:
  We describe a quantum information processor (quantum computer) based on the
hyperfine interactions between the conduction electrons and nuclear spins
embedded in a two-dimensional electron system in the quantum-Hall regime.
Nuclear spins can be controlled individually by electromagnetic pulses. Their
interactions, which are of the spin-exchange type, can be possibly switched on
and off pair-wise dynamically, for nearest neighbors, by controlling
impurities. We also propose the way to feed in the initial data and explore
ideas for reading off the final results.


title: Beyond the Standard "Marginalizations" of Wigner Function

abstract:
  We discuss the problem of finding "marginal" distributions within different
tomographic approaches to quantum state measurement, and we establish
analytical connections among them.


title:
Generalized coherent states are unique Bell states of quantum systems
  with Lie group symmetries

abstract:
  We consider quantum systems, whose dynamical symmetry groups are semisimple
Lie groups, which can be split or decay into two subsystems of the same
symmetry. We prove that the only states of such a system that factorize upon
splitting are the generalized coherent states. Since Bell's inequality is never
violated by the direct product state, when the system prepared in the
generalized coherent state is split, no quantum correlations are created.
Therefore, the generalized coherent states are the unique Bell states, i.e.,
the pure quantum states preserving the fundamental classical property of
satisfying Bell's inequality upon splitting.


title: Trapping Quantum Coherence in Local Energy Minima

abstract:
  Clusters of solid-state quantum devices have long-living metastable states of
local energy minima which may be used to store quantum information. The low to
vanishing rate of dissipation fulfils the prerequisite to maintain quantum
coherence. Then physical symmetrization of the devices could minimize the
couplings of the clusters to environmental degrees of freedom so to reduce the
rate of decoherence. Combined with various other error correction mechanisms
and methods, such designs and optimizations could render solid-state devices
useful for quantum information processing, which have the advantages of
flexibility in state manipulation and system scaling.


title: Fault-tolerant quantum computation by anyons

abstract:
  A two-dimensional quantum system with anyonic excitations can be considered
as a quantum computer. Unitary transformations can be performed by moving the
excitations around each other. Measurements can be performed by joining
excitations in pairs and observing the result of fusion. Such computation is
fault-tolerant by its physical nature.


title: Propagator for a time-dependent harmonic oscillator

abstract:
  This paper has been withdrawn, as the explicit form of the propagator can be
found in:
  V.V.Dodonov, I.A.Malkin and V.I.Man'ko, J.Phys.A 8 (1975) L19
  V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Int.J.Theor.Phys. 14 (1975) 37, Sec.3
  V.V.Dodonov, I.A.Malkin and V.I.Man'ko, Theor.Math.Phys. 24 (1975) 746, Sec.2
  I am grateful to Professor Victor Dodonov for bringing this to my attention.


title: Entropic bounds on coding for noisy quantum channels

abstract:
  In analogy with its classical counterpart, a noisy quantum channel is
characterized by a loss, a quantity that depends on the channel input and the
quantum operation performed by the channel. The loss reflects the transmission
quality: if the loss is zero, quantum information can be perfectly transmitted
at a rate measured by the quantum source entropy. By using block coding based
on sequences of n entangled symbols, the average loss (defined as the overall
loss of the joint n-symbol channel divided by n, when n tends to infinity) can
be made lower than the loss for a single use of the channel. In this context,
we examine several upper bounds on the rate at which quantum information can be
transmitted reliably via a noisy channel, that is, with an asymptotically
vanishing average loss while the one-symbol loss of the channel is non-zero.
These bounds on the channel capacity rely on the entropic Singleton bound on
quantum error-correcting codes [Phys. Rev. A 56, 1721 (1997)]. Finally, we
analyze the Singleton bounds when the noisy quantum channel is supplemented
with a classical auxiliary channel.


title:
Internal structures of electrons and photons and some consequences in
  relativistic physics

abstract:
  The theoretical foundations of quantum mechanics and de Broglie-Bohm
mechanics are analyzed and it is shown that both theories employ a formal
approach to microphysics. By using a realistic approach it can be established
that the internal structures of particles comply with a wave-equation.
Including external potentials yields the Schrodinger equation, which, in this
context, is arbitrary due to internal energy components. The uncertainty
relations are an expression of this, fundamental, arbitrariness. Electrons and
photons can be described by an identical formalism, providing formulations
equivalent to the Maxwell equations. Electrostatic interactions justify the
initial assumption of electron-wave stability: the stability of electron waves
can be referred to vanishing intrinsic fields of interaction. Aspect's
experimental proof of non-locality is rejected, because these measurements
imply a violation of the uncertainty relations. The paper finally points out
some fundamental difficulties for a fully covariant formulation of quantum
electrodynamics, which seem to be related to the existing infinity problems in
this field.


title:
Quasiclassical Path-Integral Approach to Quantum Mechanics Associated
  with a Semisimple Lee Algebra

abstract:
  A closed (in terms of classical data) expression for a transition amplitude
between two generalized coherent states associated with a semisimple Lee
algebra underlying the system is derived for large values of the representation
highest weight, which corresponds to the quasiclssical approximation.
Consideration is based upon a path-integral formalism adjusted to quantization
of symplectic coherent-state manifolds that appear as one-rank coadjoint
orbits.


title: Quantum Entanglement: Criteria and Collective Tests

abstract:
  The state of a quantum system, consisting of two distinct subsystems, is
called separable if it can be prepared by two distant experimenters who receive
instructions from a common source, via classical communication channels. A
necessary condition is derived and is shown to be more sensitive than Bell's
inequality for detecting quantum inseparability. Moreover, collective tests of
Bell's inequality (namely, tests that involve several composite systems
simultaneously) may sometimes lead to a violation of Bell's inequality, even if
the latter is satisfied when each composite system is tested separately.


title: On the Localization of One-Photon States

abstract:
  Single photon states with arbitrarily fast asymptotic power-law fall-off of
energy density and photodetection rate are explicitly constructed. This goes
beyond the recently discovered tenth power-law of the Hellwarth-Nouchi photon
which itself superseded the long-standing seventh power-law of the Amrein
photon.


title:
Universal Algorithm for Optimal Estimation of Quantum States from Finite
  Ensembles

abstract:
  We present a universal algorithm for the optimal quantum state estimation of
an arbitrary finite dimensional system. The algorithm specifies a physically
realizable positive operator valued measurement (POVM) on a finite number of
identically prepared systems. We illustrate the general formalism by applying
it to different scenarios of the state estimation of N independent and
identically prepared two-level systems (qubits).


title: Angular Velocity Operator and Barnett-Pegg Formalism

abstract:
  We define a new operator within Barnett-Pegg formalism for phase angle. The
physical predictions for this operator correspond to those expected of an
angular velocity operator. Examples studied are particle on a circle with and
without magnetic field and quantum harmonic oscillator.


title: Ghost interference and diffraction based on the beam splitter

abstract:
  A simple scheme is proposed for observing the ghost interference and
diffraction. The signal and the idler beams are produced by a beam splitter
with the incident light being in a thermal state. A slit is inserted into the
signal beam. We derive rigorously that interference-diffraction patterns can be
observed in the first-order correlation by scanning the probe in the idler
beam.


title: Quantum Automata and Quantum Grammars

abstract:
  To study quantum computation, it might be helpful to generalize structures
from language and automata theory to the quantum case. To that end, we propose
quantum versions of finite-state and push-down automata, and regular and
context-free grammars. We find analogs of several classical theorems, including
pumping lemmas, closure properties, rational and algebraic generating
functions, and Greibach normal form. We also show that there are quantum
context-free languages that are not context-free.


title:
Coherent states for the anharmonic oscillator and classical phase space
  trajectories

abstract:
  Unique set of coherent states for the anharmonic oscillator is obtained by
requiring i. under the quantum mechanical time evolution a coherent state
evolves into another, governed by trajectory in the classical phase space (of a
related hamiltonian); ii. the resolution of identity involves exactly the
classical phase space measure.The rules are invariant under unitary
transformations of the quantum theory and canonical transformations of the
classical theory. The states are almost, but not quite, minimal uncertainty
wave packets. The construction can be generalized to quantum versions of
integrable classical theories.


title: Quantum Algorithms and the Fourier Transform

abstract:
  The quantum algorithms of Deutsch, Simon and Shor are described in a way
which highlights their dependence on the Fourier transform. The general
construction of the Fourier transform on an Abelian group is outlined and this
provides a unified way of understanding the efficacy of these algorithms.
Finally we describe an efficient quantum factoring algorithm based on a general
formalism of Kitaev and contrast its structure to the ingredients of Shor's
algorithm.


title: Entanglement and Quantum Computation

abstract:
  We argue that entanglement is the essential non-classical ingredient which
provides the computational speed-up in quantum algorithms as compared to
algorithms based on the processes of classical physics.


title: Entanglement Measures and Purification Procedures

abstract:
  We generalize previously proposed conditions each measure of entanglement has
to satisfy. We present a class of entanglement measures that satisfy these
conditions and show that the Quantum Relative Entropy and Bures Metric generate
two measures of this class. We calculate the measures of entanglement for a
number of mixed two spin 1/2 systems using the Quantum Relative Entropy, and
provide an efficient numerical method to obtain the measures of entanglement in
this case. In addition, we prove a number of properties of our entanglement
measure which have important physical implications. We briefly explain the
statistical basis of our measure of entanglement in the case of the Quantum
Relative Entropy. We then argue that our entanglement measure determines an
upper bound to the number of singlets that can be obtained by any purification
procedure and that distillable entanglement is in general smaller than the
entanglement of creation.


title: Lorentz-Invariant Hamiltonian and Riemann Hypothesis

abstract:
  We have given some arguments that a two-dimensional Lorentz-invariant
Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of
the Riemann zeta function. Some eigenfunction of the Hamiltonian corresponding
to infinite-dimensional representation of the Lorentz group have many
interesting properties. Especially, a relationship exists between the zero zeta
function condition and the absence of trivial representations in the wave
function.


title: Kinetics of Bose-Einstein Condensation in a Trap

abstract:
  The formation process of a Bose-Einstein condensate in a trap is described
using a master equation based on quantum kinetic theory, which can be well
approximated by a description using only the condensate mode in interaction
with a thermalized bath of noncondensate atoms. A rate equation of the form n =
2W(n)[(1-exp((mu_n - mu)/kT))n + 1] is derived, in which the difference between
the condensate chemical potential mu_n and the bath chemical potential mu gives
the essential behavior. Solutions of this equation, in conjunction with the
theoretical description of the process of evaporative cooling, give a
characteristic latency period for condensate formation and appear to be
consistent with the observed behavior of both rubidium and sodium condensate
formation.


title: Concentrating entanglement by local actions---beyond mean values

abstract:
  Suppose two distant observers Alice and Bob share a pure bipartite quantum
state. By applying local operations and communicating with each other using a
classical channel, Alice and Bob can manipulate it into some other states.
Previous investigations of entanglement manipulations have been largely limited
to a small number of strategies and their average outcomes. Here we consider a
general entanglement manipulation strategy and go beyond the average property.
For a pure entangled state shared between two separated persons Alice and Bob,
we show that the mathematical interchange symmetry of the Schmidt decomposition
can be promoted into a physical symmetry between the actions of Alice and Bob.
Consequently, the most general (multi-step two-way-communications) strategy of
entanglement manipulation of a pure state is, in fact, equivalent to a strategy
involving only a single (generalized) measurement by Alice followed by one-way
communications of its result to Bob. We also prove that strategies with one-way
communications are generally more powerful than those without communications.
In summary, one-way communications is necessary and sufficient for the
entanglement manipulations of a pure bipartite state. The supremum probability
of obtaining a maximally entangled state (of any dimension) from an arbitrary
state is determined and a strategy for achieving this probability is
constructed explicitly. One important question is whether collective
manipulations in quantum mechanics can greatly enhance the probability of large
deviations from the average behavior. We answer this question in the negative
for a specific problem.


title:
Intrinsic chaoticity in stable classical systems and quantum
  fluctuations

abstract: The paper has been withdrawn


title: W(infty)-Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization

abstract:
  The differential structure of operator bases used in various forms of the
Weyl-Wigner-Groenewold-Moyal (WWGM) quantization is analyzed and a
derivative-based approach, alternative to the conventional integral-based one
is developed. Thus the fundamental quantum relations follow in a simpler and
unified manner. An explicit formula for the ordered products of the
Heisenberg-Weyl algebra is obtained. The W(infty) -covariance of the
WWGM-quantization in its most general form is established. It is shown that the
group action of W(infty) that is realized in the classical phase space induces
on bases operators in the corresponding Hilbert space a similarity
transformation generated by the corresponding quantum W(infty) which provides a
projective representation of the former $W_{\infty}$. Explicit expressions for
the algebra generators in the classical phase space and in the Hilbert space
are given. It is made manifest that this W(infty)-covariance of the
WWGM-quantization is a genuine property of the operator bases.


title: Quantum separability, time reversal and canonical decompositions

abstract:
  We propose an interpretation of quantum separability based on a physical
principle: local time reversal. It immediately leads to a simple
characterization of separable quantum states that reproduces results known to
hold for binary composite systems and which thereby is complete for low
dimensions. We then describe a constructive algorithm for finding the canonical
decomposition of separable and non separable mixed states of dimensions 2x2 and
2x3.