title: Schroedinger's Interpolating Dynamics and Burgers' Flows

abstract:
  We discuss a connection (and a proper place in this framework) of the
unforced and deterministically forced Burgers equation for local velocity
fields of certain flows, with probabilistic solutions of the so-called
Schr\"{o}dinger interpolation problem. The latter allows to reconstruct the
microscopic dynamics of the system from the available probability density data,
or the input-output statistics in the phenomenological situations. An issue of
deducing the most likely dynamics (and matter transport) scenario from the
given initial and terminal probability density data, appropriate e.g. for
studying chaos in terms of densities, is here exemplified in conjunction with
Born's statistical interpretation postulate in quantum theory, that yields
stochastic processes which are compatible with the Schr\"{o}dinger picture free
quantum evolution.


title: The k-fermions as objects interpolating between fermions and bosons

abstract:
  Operators, refered to as k-fermion operators, that interpolate between boson
and fermion operators are introduced through the consideration of two
noncommuting quon algebras. The deformation parameters for these quon algebras
are roots of unity connected to an integer k. The case k=2 corresponds to
fermions and the limiting case k going to infinity to bosons. Generalized
coherent states and supercoherent states are investigated. The Dirac quantum
phase operator and the Fairlie-Fletcher-Zachos algebra are also considered.

categories: quant-ph hep-th math-ph math.MP math.QA q-alg


title:
Zero-Temperature Casimir Fluctuations and the Limits of Force Microscope
  Sensitivity

abstract:
  It is predicted that in force microscopy the quantum fluctuations responsible
for the Casimir force can be directly observed as temperature-independent force
fluctuations having spectral density $9\pi/(40\ln(4/e)) \hbar \delta k$, where
$\hbar$ is Planck's constant and $\delta k$ is the observed change in spring
constant as the microscope tip approaches a sample. For typical operating
parameters the predicted force noise is of order $10^{-18}$ Newton in one Hertz
of bandwidth. The Second Law is respected via the fluctuation-dissipation
theorem. For small tip-sample separations the cantilever damping is predicted
to increase as temperature is reduced, a behavior that is reminiscent of the
Kondo effect.


title: Accidental Degeneracy and Berry Phase of Resonant States

abstract:
  We study the complex geometric phase acquired by the resonant states of an
open quantum system which evolves irreversibly in a slowly time dependent
environment. In analogy with the case of bound states, the Berry phase factors
of resonant states are holonomy group elements of a complex line bundle with
structure group C*. In sharp contrast with bound states, accidental
degeneracies of resonances produce a continuous closed line of singularities
formally equivalent to a continuous distribution of "magnetic" charge on a
"diabolical" circle, in consequence, we find different classes of topologically
inequivalent non-trivial closed paths in parameter space.


title:
Mapping of the $B_N$-type Calogero-Sutherland-Moser system to decoupled
  Harmonic Oscillators

abstract:
  The $B_N$-type Calogero-Sutherland-Moser system in one-dimension is shown to
be equivalent to a set of decoupled oscillators by a similarity transformation.
This result is used to show the connection of the $A_N$ and $B_N$ type models
and explain the degeneracy structure of the later. We identify the commuting
constants of motion and the generators of a linear $W_\infty$ algebra
associated with the $B_N$ system.


title: Phase of the quantum oscillator

abstract:
  Requirements of a conjugate operator are emphasized, especially in its role
in uncertainty relations.It is argued that in many contexts it is necessary to
extend the Hilbert space in order to define a conjugate operator as in gauge
theories. Example of a particle in a box is analysed. This is closely related
to the quantum oscillator through cosine states of Susskind and Glogower.It is
used to justify London's phase wave functions albeit as part of a larger
Hilbert space. A new definition phase uncertainty neccessiated by periodicity
is proposed.It is close to the usual r.m.s. definition.Corresponding number-
phase uncertainty relation is obtained and its implications are discussed.
Hilbert space of an oscillator is identified with the Hilbert space of a planar
rotor with a $Z_2$ gauge invariance.This is used to construct states analogous
to the cosine and sine states and to illustrate unitary equivalence of Hilbert
spaces.


title: Continuous measurements, quantum trajectories, and decoherent histories

abstract:
  Quantum open systems are described in the Markovian limit by master equations
in Lindblad form. I argue that common ``quantum trajectory'' techniques
corresponding to continuous measurement schemes, which solve the master
equation by unraveling its evolution into stochastic trajectories in Hilbert
space, correspond closely to particular sets of decoherent (or consistent)
histories. This is illustrated by a simple model of photon counting. An
equivalence is shown for these models between standard quantum jumps and the
orthogonal jumps of Di\'osi, which have already been shown to correspond to
decoherent histories. This correspondence is compared to simple treatments of
trajectories based on repeated or continuous measurements.


title: Liouville Integrability of the Schroedinger Equation

abstract:
  Canonical coordinates for both the Schroedinger and the nonlinear
Schroedinger equations are introduced, making more transparent their
Hamiltonian structures. It is shown that the Schroedinger equation, considered
as a classical field theory, shares with the nonlinear Schroedinger, and more
generally with Liouville completely integrable field theories, the existence of
a "recursion operator" which allows for the construction of infinitely many
conserved functionals pairwise commuting with respect to the corresponding
Poisson bracket. The approach may provide a good starting point to get a clear
interpretation of Quantum Mechanics in the general setting, provided by
Stone-von Neumann theorem, of Symplectic Mechanics. It may give new tools to
solve in the general case the inverse problem of Quantum Mechanics.


title: The Problem of Measurement and the Theory of Quantum State Reduction

abstract:
  A new approach to the problem of measurement in quantum mechanics is
proposed. In this approach, the process of measurement is described in the
Heisenberg picture and divided into two stages. The first stage is to transduce
the measured observable to the probe observable. The second stage is to amplify
the probe observable to the macroscopic meter observable. Quantum state
reduction is derived, based on the quantum Bayes principle, from the
object-apparatus interaction in the first stage. The dynamical process of the
second stage is described as a quantum amplification with infinite gain based
on nonstandard analysis.


title: Baker-Campbell-Hausdorff relation for special unitary groups SU(N)

abstract:
  Multiplication of two elements of the special unitary group SU(N) determines
uniquely a third group element. A BAker-Campbell-Hausdorff relation is derived
which expresses the group parameters of the product (written as an exponential)
in terms of the parameters of the exponential factors. This requires the eigen-
values of three (N-by-N) matrices. Consequently, the relation can be stated
analytically up to N=4, in principle. Similarity transformations encoding the
time evolution of quantum mechanical observables, for example, can be worked
out by the same means.


title:
Experimental issues in coherent quantum-state manipulation of trapped
  atomic ions

abstract:
  Methods for, and limitations to, the generation of entangled states of
trapped atomic ions are examined. As much as possible, state manipulations are
described in terms of quantum logic operations since the conditional dynamics
implicit in quantum logic is central to the creation of entanglement. Keeping
with current interest, some experimental issues in the proposal for trapped-ion
quantum computation by I. Cirac and P. Zoller (University of Innsbruck) are
discussed. Several possible decoherence mechanisms are examined and what may be
the more important of these are identified. Some potential applications for
entangled states of trapped-ions which lie outside the immediate realm of
quantum computation are also discussed.


title:
Atomic versus molecular diffraction: Influence of break-ups and finite
  size

abstract:
  Atomic diffraction through double slits and transmission gratings is well
described in terms of the associated de Broglie waves and classical wave
optics. However, for weakly bound and relatively large systems, such as the
He_2 dimer, this might no longer hold true due to the possibility of break-up
processes and finite-size effects. We therefore study the diffraction of weakly
bound two-particle systems. If the bar and slit widths of the grating are much
larger than the diameter of the two-particle system we recover the usual optics
results. For smaller widths, however, deviations therefrom occur. We find that
the location of possible diffraction peaks is indeed still governed by the
usual grating function from optics, but the peaks may have a lower intensity.
This is not unexpected when break-up processes are allowed. More unusually
though, diffraction peaks which would be absent for de Broglie waves may
reappear. The results are illustrated for diffraction of He_2.


title: Ensemble versus individual system in quantum optics

abstract:
  Modern techniques allow experiments on a single atom or system, with new
phenomena and new challenges for the theoretician. We discuss what quantum
mechanics has to say about a single system. The quantum jump approach as well
as the role of quantum trajectories are outlined and a rather sophisticated
example is given.


title: The Spectral Theory of Perturbative Decays

abstract:
  In this paper, we propose a complex approach to evaluate a function sum of
two noncommuting non Hermitian operators. Then, it is proposed an explicit
expansion of the evolution operator in the case of the neutral K-meson system
under the influence of an external interaction. Then, the importance of the
procedure is pointed out to consider the algebraic expansion of the time
evolution operator whenever the dynamics decouples the internal transitions and
the center of mass motion.


title: Coherent States in Action

abstract:
  Quantum mechanical phase space path integrals are re-examined with regard to
the physical interpretation of the phase space variables involved. It is
demonstrated that the traditional phase space path integral implies a meaning
for the variables involved that is manifestly inconsistent. On the other hand,
a phase space path integral based on coherent states entails variables that
exhibit a self-consistent physical meaning.


title: Probability current tornado loops in three-dimensional scattering

abstract:
  We consider scattering of a three-dimensional particle on a finite family of
delta potentials. For some parameter values the scattering wavenctions exhibit
nodal lines in the form of closed loops, which may touch but do not entangle.
The corresponding probability current forms vortical singularities around these
lines; if the scattered particle is charged, this gives rise to magnetic flux
loops. The conclusions extend to scattering on hard obstacles or smooth
potentials.


title:
On the Structure of Additive Quantum Codes and the Existence of
  Nonadditive Codes

abstract:
  We first present a useful characterization of additive (stabilizer) quantum
error-correcting codes. Then we present several examples of We first present a
useful characterization of additive (stabilizer) quantum error--correcting
codes. Then we present several examples of nonadditive codes. We show that
there exist infinitely many non-trivial nonadditive codes with different
minimum distances, and high rates. In fact, we show that nonadditive codes that
correct t errors can reach the asymptotic rate R=1-2H(2t/n), where H(x) is the
binary entropy function. Finally, we introduce the notion of strongly
nonadditive codes (i.e., quantum codes with the following property: the trivial
code consisting of the entire Hilbert space is the only additive code that is
equivalent to any code containing the given code), and provide a construction
for an ((11,2,3)) strongly nonadditive code.


title: Is Quantum Mechaincs Non-Local?

abstract:
  Stapp has recently argued from a version of the Hardy type experiments that
quantum mechanics must be non-local, independent of any additional assumptions
like realism or hidden variables. I argue that either his conclusions do not
follow from his assumptions, or that his assumptions are not true of quantum
mechanics and can be interpreted as assigning an unwarranted level of reality
to the value of certain quantum attributes.


title: Gisin Nonlocality of the Doebner-Goldin 2-Particle Equation

abstract:
  Gisin's argument against deterministic nonlinear Schroedinger equations is
shown to be valid for every (formally) nonlinearizable case of the general
Doebner-Goldin 2-particle equation in the following form:
  The time-dependence of the position probability distribution of a particle
`behind the moon' may be instantaneously changed by an arbitrarily small
instantaneous change of the potential `inside the laboratory'.


title:
Laser cooling of single trapped atoms to the ground state: a dark state
  in position space

abstract:
  We propose a scheme that allows to laser cool trapped atoms to the ground
state of a one-dimensional confining potential. The scheme is based on the
creation of a dark state by designing the laser profile, so that the hottest
atoms are coherently pumped to another internal level, and then repumped back.
The scheme works beyond the Lamb-Dicke limit. We present results of a full
quantum treatment for a one-dimensional model.


title: Programming Complex Systems

abstract:
  Classical programming languages cannot model essential elements of complex
systems such as true random number generation. This paper develops a formal
programming language called the lambda-q calculus that addresses the
fundamental properties of complex systems. This formal language allows the
expression of quantumized algorithms, which are extensions of randomized
algorithms in that probabilities can be negative, and events can cancel out. An
illustration of the power of quantumized algorithms is the ability to
efficiently solve the satisfiability problem, something that many believe is
beyond the capability of classical computers. This paper proves that the
lambda-q calculus is not only capable of solving satisfiability but can also
simulate such complex systems as quantum computers. Since satisfiability is
believed to be beyond the capabilities of quantum computers, the lambda-q
calculus may be strictly stronger.


title: Time-Symmetrized Quantum Theory

abstract:
  A brief review of the time-symmetrized quantum formalism originated by
Aharonov, Bergmann and Lebowitz is presented. Symmetry of various measurements
under the time reversal is analyzed. Time-symmetrized counterfactuals are
introduced. It is argued that the time-symmetrized formalism demonstrates novel
profound features of quantum theory and that recent criticism of the formalism
is unfounded.


title:
Application of the Discrete Quantum - Classical System to the
  Information Transfer

abstract:
  The role and the form of detectors applicable to the quantum information
transfer are investigated. The detectors are described within the Event -
Enhanced Quantum Theory.


title: Quantum State Reconstruction of a Bose-Einstein Condensate

abstract:
  We propose a tomographic scheme to reconstruct the quantum state of a
Bose-Einstein condensate, exploiting the radiation field as a probe and
considering the atomic internal degrees of freedom. The density matrix in the
number state basis can be directly retrieved from the atom counting
probabilities.


title: Sonoluminescence: The Superradiance Paradigm

abstract:
  In this article we explain sonoluminescence from ideas borrowed from
superradiance. The model has no free parameters and the predicted energies of
quanta agree with experiment. It also hints why noble gases play a pivotal role
in the effect.


title: Asymptotic Quantum Parameter Estimation in Spin 1/2 System

abstract:
  For the precise estimation of the unknown quantum state, the independent
samples should be prepared. Can we reduce the error of the estimation by the
measurement using the quantum correlation between every sample? In this paper,
this question is treated in the parameter estimation for the unknown state.


title: Error Avoiding Quantum Codes

abstract:
  The existence is proved of a class of open quantum systems that admits a
linear subspace ${\cal C}$ of the space of states such that the restriction of
the dynamical semigroup to the states built over $\cal C$ is unitary. Such
subspace allows for error-avoiding (noiseless) enconding of quantum
information.


title:
An Indication From the Magnitude of CP Violations that Gravitation is a
  Possible Cause of Wave-Function Collapse

abstract:
  We consider experimental evidence for the hypothesis that the Planck energy,
$E_p \approx 10^{19}GeV$, sets the scale $\epsilon$ at which wave function
collapse causes deviations from linear Schr\"{o}dinger evolution. With a few
plausible assumptions about the collapse process, we first show that the
observed CP violation in $K_L$ decay implies a lower bound on $\epsilon$
remarkably close to $E_p$. If the bound is saturated, the entire CP violation
is due to collapse and a prediction made that the branching ratio for CP
violation in the B meson decay will be $\gamma \approx 10^{-5}$. We then show
that the assumptions are consequences of a simple non-linear, stochastic
modification of the Schr\"{o}dinger equation with $\epsilon$ setting the scale
of the non-linearity.


title: The maximum speed of dynamical evolution

abstract:
  We discuss the problem of counting the maximum number of distinct states that
an isolated physical system can pass through in a given period of time---its
maximum speed of dynamical evolution. Previous analyses have given bounds in
terms of the standard deviation of the energy of the system; here we give a
strict bound that depends only on E-E0, the system's average energy minus its
ground state energy. We also discuss bounds on information processing rates
implied by our bound on the speed of dynamical evolution. For example, adding
one Joule of energy to a given computer can never increase its processing rate
by more than about 3x10^33 operations per second.


title: Decoherence in ion traps due to laser intensity and phase fluctuations

abstract:
  We consider one source of decoherence for a single trapped ion due to
intensity and phase fluctuations in the exciting laser pulses. For simplicity
we assume that the stochastic processes involved are white noise processes,
which enables us to give a simple master equation description of this source of
decoherence. This master equation is averaged over the noise, and is sufficient
to describe the results of experiments that probe the oscillations in the
electronic populations as energy is exchanged between the internal and
electronic motion. Our results are in good qualitative agreement with recent
experiments and predict that the decoherence rate will depend on vibrational
quantum number in different ways depending on which vibrational excitation
sideband is used.


title:
Isotropic oscillator in the space of constant positive curvature.
  Interbasis expansions

abstract:
  The Schr\"odinger equation is thoroughly analysed for the isotropic
oscillator in the three-dimensional space of constant positive curvature in the
spherical and cylindrical systems of coordinates. The expansion coefficients
between the spherical and cylindrical bases of the oscillator are calculated.
It is shown that the relevant coefficients are expressed through the
generalised hypergeometric functions $_4F_3$ of the unit argument or $6_j$
Racah symbols extended over their indices to the region of real values.
Limiting transitions to a free motion and flat space are considered in detail.
Elliptic bases of the oscillator are constructed in the form of expansion over
the spherical and cylindrical bases. The corresponding expansion coefficients
are shown to obey the three-term recurrence relations.


title: Can a falling tree make a noise in two forests at the same time?

abstract:
  It is a commonplace to claim that quantum mechanics supports the old idea
that a tree falling in a forest makes no sound unless there is a listener
present. In fact, this conclusion is far from obvious. Furthermore, if a
tunnelling particle is observed in the barrier region, it collapses to a state
in which it is no longer tunnelling. Does this imply that while tunnelling, the
particle can not have any physical effects? I argue that this is not the case,
and moreover, speculate that it may be possible for a particle to have effects
on two spacelike separate apparatuses simultaneously. I discuss the measurable
consequences of such a feat, and speculate about possible statistical tests
which could distinguish this view of quantum mechanics from a ``corpuscular''
one. Brief remarks are made about an experiment underway at Toronto to
investigate these issues.


title: Vacuum fluctuations, accelerated motion and conformal frames

abstract:
  Radiation from a mirror moving in vacuum electromagnetic fields is shown to
vanish in the case of a uniformly accelerated motion. Such motions are related
to conformal coordinate transformations, which preserve correlation functions
characteristic of vacuum fluctuations. As a result, vacuum fluctuations remain
invariant under reflection upon a uniformly accelerated mirror, which therefore
does not radiate and experiences no radiation reaction force. Mechanical
effects of vacuum fluctuations thus exhibit an invariance with respect to
uniformly accelerated motions.


title: Renormalization Group Approach to the Dynamical Casimir Effect

abstract:
  In this paper we study the one dimensional dynamical Casimir effect. We
consider a one dimensional cavity formed by two mirrors, one of which performs
an oscillatory motion with a frequency resonant with the cavity. The naive
solution, perturbative in powers of the amplitude, contains secular terms.
Therefore it is valid only in the short time limit. Using a renormalization
group technique to resum these terms, we obtain an improved analytical solution
which is valid for longer times. We discuss the generation of peaks in the
density energy profile and show that the total energy inside the cavity
increases exponentially.


title: Bound and Unbound Wave Functions at Short Distances

abstract:
  There exists a simple relationship between a quantum-mechanical bound-state
wave function and that of nearby scattering states, when the scattering energy
is extrapolated to that of the bound state. This relationship is demonstrated
numerically for the case of a spherical well potential and analytically for
this and other soluble potentials. Provided that the potential is of finite
range and that the binding is weak, the theorem gives a useful approximation
for the short-distance behaviour of the scattering wave functions. The
connection between bound and scattering-state perturbation theory is
established in this limit.


title: Miller-Good Method for Symmetric Double Potential Wells

abstract:
  The ground state energy of the quartic anharmonic oscillator is calculated by
employing the Miller-Good method. For this purpose an extension of the
procedure is developed, which is suitable for considering four turning points
situations. A criterion for the selection of the auxiliary quantum mechanical
problem is also advanced.


title:
Connections Between Special Relativity, Charge Conservation, and Quantum
  Mechanics

abstract:
  Examination of the Einstein energy-momentum relationship suggests that simple
unbound forms of matter exist in a four-dimensional Euclidean space. Position,
momentum, velocity, and other vector quantities can be expressed as Euclidean
four-vectors, with the magnitude of the velocity vector having a constant
value, the speed of light. We see that charge may be simply a manifestation of
momentum in the new fourth direction, which implies that charge conservation is
a form of momentum conservation. The constancy of speed implies that all
elementary free particles can be described in the same manner as photons, by
means of a wave equation. The resulting wave mechanics (with a few small
assumptions) is simply the traditional form of quantum mechanics. If one begins
by assuming the wave nature of matter, it is shown that special relativistic
results follow simply. Thus we see evidence of a strong connection between
relativity and quantum mechanics. Comparisons between the theory presented here
and Kaluza-Klein theories reveal some similarities, but also many significant
differences between them.


title: The Church-Turing thesis as a guiding principle for physics

abstract:
  Two aspects of the physical side of the Church-Turing thesis are discussed.
The first issue is a variant of the Eleatic argument against motion, dealing
with Zeno squeezed time cycles of computers. The second argument reviews the
issue of one-to-one computation, that is, the bijective (unique and reversible)
evolution of computations and its relation to the measurement process.


title: Vibrational Decoherence in Ion Trap Quantum Computers

abstract:
  The ion trap quantum computer proposed by Cirac and Zoller is analyzed for
decoherence due to vibrations of the ions. An adiabatic approximation
exploiting the vast difference between the frequencies of the optical
intraionic transition and the vibrational modes is used to find the decoherence
time at any temperature T. The scaling of this decoherence time with the number
of ions is discussed, and compared to that due to spontaneous emission.


title: Multiparty Quantum Communication Complexity

abstract:
  Quantum entanglement cannot be used to achieve direct communication between
remote parties, but it can reduce the communication needed for some problems.
Let each of k parties hold some partial input data to some fixed k-variable
function f. The communication complexity of f is the minimum number of
classical bits required to be broadcasted for every party to know the value of
f on their inputs.
  We construct a function G such that for the one-round communication model and
three parties, G can be computed with n+1 bits of communication when the
parties share prior entanglement. We then show that without entangled
particles, the one-round communication complexity of G is (3/2)n + 1. Next we
generalize this function to a function F. We show that if the parties share
prior quantum entanglement, then the communication complexity of F is exactly
k. We also show that if no entangled particles are provided, then the
communication complexity of F is roughly k*log(k).
  These two results prove for the first time communication complexity
separations better than a constant number of bits.


title: Bures Metrics for Certain High-Dimensional Quantum Systems

abstract:
  Hubner's formula for the Bures (statistical distance) metric is applied to
both a one-parameter and a two-parameter series (n=2,...,7) of sets of 2^n x
2^n density matrices. In the doubly-parameterized series, the sets are
comprised of the n-fold tensor products --- corresponding to n independent,
identical quantum systems --- of the 2 x 2 density matrices with real entries.
The Gaussian curvatures of the corresponding Bures metrics are found to be
constants (4/n). In the second series of 2^n x 2^n density matrices studied,
the singly-parameterized sets are formed --- following a study of Krattenthaler
and Slater --- by averaging with respect to a certain Gibbs distribution, the
n-fold tensor products of the 2 x 2 density matrices with complex entries. For
n = 100, we are also able to compute the Bures distance between two arbitrary
(not necessarily neighboring) density matrices in this particular series,
making use of the eigenvalue formulas of Krattenthaler and Slater, together
with the knowledge that the 2^n x 2^n density matrices in this series commute.


title: Adaptive single-shot phase measurements: The full quantum theory

abstract:
  The phase of a single-mode field can be measured in a single-shot measurement
by interfering the field with an effectively classical local oscillator of
known phase. The standard technique is to have the local oscillator detuned
from the system (heterodyne detection) so that it is sometimes in phase and
sometimes in quadrature with the system over the course of the measurement.
This enables both quadratures of the system to be measured, from which the
phase can be estimated. One of us [H.M. Wiseman, Phys. Rev. Lett. 75, 4587
(1995)] has shown recently that it is possible to make a much better estimate
of the phase by using an adaptive technique in which a resonant local
oscillator has its phase adjusted by a feedback loop during the single-shot
measurement. In Ref.~[H.M. Wiseman and R.B. Killip, Phys. Rev. A 56, 944] we
presented a semiclassical analysis of a particular adaptive scheme, which
yielded asymptotic results for the phase variance of strong fields. In this
paper we present an exact quantum mechanical treatment. This is necessary for
calculating the phase variance for fields with small photon numbers, and also
for considering figures of merit other than the phase variance. Our results
show that an adaptive scheme is always superior to heterodyne detection as far
as the variance is concerned. However the tails of the probability distribution
are surprisingly high for this adaptive measurement, so that it does not always
result in a smaller probability of error in phase-based optical communication.


title:
Bayesian Thermostatistical Analyses of Two-Level Complex and
  Quaternionic Systems

abstract:
  The three and five-dimensional convex sets of two-level complex and
quaternionic quantum systems are studied in the Bayesian thermostatistical
framework introduced by Lavenda. Associated with a given parameterization of
each such set is a quantum Fisher (Helstrom) information matrix. The square
root of its determinant (adopting an ansatz of Harold Jeffreys) provides a
reparameterization-invariant prior measure over the set. Both such measures can
be properly normalized and their univariate marginal probability distributions
(which serve as structure functions) obtained. Gibbs (posterior) probability
distributions can then be found, using Poisson's integral representation of the
modified spherical Bessel functions. The square roots of the (classical) Fisher
information of these Gibbs distributions yield (unnormalized) priors over the
inverse temperature parameters.


title: Distortion of a Phase Space Under the Darboux Transformation

abstract:
  The Darboux transformation operator technique is applied to construct exactly
solvable anharmonic singular oscillator potentials and to study their coherent
states. Classical system corresponding to a transformed quantum system is
constructed with the help of the coherent states technique. It is shown that at
classical level the Darboux transformation may be treated as a transformation
of K\"ahler potential which leads to a distortion of the initial phase space.


title:
Electromagnetic fields in a 3D cavity and in a waveguide with
  oscillating walls

abstract:
  We consider classical and quantum electromagnetic fields in a
three-dimensional (3D) cavity and in a waveguide with oscillating boundaries of
the frequency $\Omega $. The photons created by the parametric resonance are
distributed in the wave number space around $\Omega/2 $ along the axis of the
oscillation. When classical waves propagate along the waveguide in the one
direction, we observe the amplification of the original waves and another wave
generation in the opposite direction by the oscillation of side walls. This can
be understood as the classical counterpart of the photon production. In the
case of two opposite walls oscillating with the same frequency but with a phase
difference, the interferences are shown to occur due to the phase difference in
the photon numbers and in the intensity of the generated waves.


title: Study of the spatial and temporal coherence of high order harmonics

abstract:
  We apply the theory of high-order harmonic generation by low-frequency laser
fields in the strong field approximation to the study of the spatial and
temporal coherence properties of the harmonics. We discuss the role of
dynamically induced phases of the atomic polarization in determining the
optimal phase matching conditions and angular distributions of harmonics. We
demonstrate that the phase matching and the spatial coherence can be controlled
by changing the focusing parameters of the fundamental laser beam. Then we
present a detailed study of the temporal and spectral properties of harmonics.
We discuss how the focusing conditions influence the individual harmonic
spectra and time profiles, and how the intensity dependence of the dynamically
induced phase leads to a chirp of the harmonic frequency. This phase modulation
can be used to control the temporal and spectral properties of the harmonic
radiation. Temporally, the harmonic chirped pulse can be recompressed to very
small durations. Spectrally, chirping of the fundamental beam may be employed
to compensate for the dynamically induced chirp and to control the individual
harmonic spectrum. Finally, we discuss the short pulse effects, in particular
nonadiabatic phenomena and the possibility of generating attosecond pulses.


title:
Coherence and Fluctuations in the Interaction between Moving Atoms and a
  Quantum Field

abstract:
  Mesoscopic physics deals with three fundamental issues: quantum coherence,
fluctuations and correlations. Here we analyze these issues for atom optics,
using a simplified model of an assembly of atoms (or detectors, which are
particles with some internal degree of freedom) moving in arbitrary
trajectories in a quantum field. Employing the influence functional formalism,
we study the self-consistent effect of the field on the atoms, and their mutual
interactions via coupling to the field. We derive the coupled Langevin
equations for the atom assemblage and analyze the relation of dissipative
dynamics of the atoms with the correlation and fluctuations of the quantum
field. This provides a useful theoretical framework for analysing the coherent
properties of atom-field systems.


title: Does Lorentz Boost Destroy Coherence?

abstract:
  It is shown that the time-energy uncertainty relation can be combined into
the position-momentum uncertainty relation covariantly in the quark model of
hadrons. This leads to a Lorentz-invariant form of the uncertainty relations.
This model explains that the quark model and the parton model are two different
manifestations of the same covariant model. In particular, this covariant model
explains why the coherent amplitudes in the quark model become incoherent,
after a Lorentz boost, in the parton model. It is shown that this lack of
coherence is consistent with the present form of quantum mechanics.


title: Open Quantum Systems, Entropy and Chaos

abstract:
  Entropy generation in quantum sytems is tied to the existence of a
nonclassical environment (heat bath or other) with which the system interacts.
The continuous `measuring' of the open system by its environment induces
decoherence of its wave function and entropy increase. Examples of
nonrelativistic quantum Brownian motion and of interacting scalar fields
illustrate these general concepts. It is shown that the Hartree-Fock
approximation around the bare classical limit can lead to spurious semiquantum
chaos, which may affect the determination of entropy production and
thermalization also in other cases.


title: Valleys in Quantum Mechanics

abstract:
  Conventionally, perturbative and non-perturbative calculations are performed
independently. In this paper, valleys in the configuration space in quantum
mechanics are investigated as a way to treat them in a unified manner. All the
known results of the interplay of them are reproduced naturally. The
prescription for separating the non-perturbative contribution from the
perturbative is given in terms of the analytic continuation of the valley
parameter. Our method is illustrated on a new series of examples with the
asymmetric double-well potential. We obtain the non-perturbative part
explicitly, which leads to the prediction of the large order behavior of the
perturbative series. We calculate the first 200 perturbative coefficients for a
wide range of parameters and confirm the agreement with the prediction of the
valley method.


title:
Anti-isospectral Transformations, Orthogonal Polynomials and
  Quasi-Exactly Solvable Problems

abstract:
  We consider the double sinh-Gordon potential which is a quasi-exactly
solvable problem and show that in this case one has two sets of Bender-Dunne
orthogonal polynomials . We study in some detail the various properties of
these polynomials and the corresponding quotient polynomials. In particular, we
show that the weight functions for these polynomials are not always positive.
We also study the orthogonal polynomials of the double sine-Gordon potential
which is related to the double sinh-Gordon case by an anti-isospectral
transformation. Finally we discover a new quasi-exactly solvable problem by
making use of the anti-isospectral transformation.


title: Parametrically amplified radiation in a cavity with an oscillating wall

abstract:
  We introduce a time-dependent perturbation method to calculate the number of
created particles in a 1D cavity with an oscillating wall of the frequency
$\Omega . $ This method makes it easy to find the dominant part of the solution
which results from the parametric resonance. The maximal number of particles
are created at the mode frequency $\Omega/2 . $ Using the Floquet theory, we
discuss the long-time behavior of the particle creation.


title: Interpreting the Quantum World

abstract:
  This is an "Essay-Review" of a book with the same title, by Jeffrey Bub
(Cambridge University Press, 1997).


title: Two-Structure Framework for Hamiltonian Dynamical Systems

abstract:
  The Lie product and the order relation are viewed as defining structures for
Hamiltonian dynamical systems. Their admissible combinations are singled out by
the requirement that the group of the Lie automorphisms be contained in the
group of the order automorphisms (Lie algebras with invariant cones). Taking
advantage of the reciprocal independence of the relevant structures, the
inclusion relation between the two automorphism groups can be reversed; a
procedure which leads to an entirely new formal language (ordered linear spaces
with invariant Lie products). Presumably it offers an alternative description
for quantum systems, radically different from the conventional algebraic
models.


title:
On the Spatial Density Matrix for the Centre of Mass of a one
  dimensional Perfect Gas

abstract:
  We examine the reduced density matrix of the centre of mass on position basis
considering a one-dimensional system of $N$ non-interacting distinguishable
particles in a infinitely deep square potential well. We find a class of pure
states of the system for which the off-diagonal elements of the matrix above go
to zero as $N$ increases. This property holds too for the state vectors which
are factorized in the single particle wave functions. In this last case, if the
average energy of each particle is less than a common bound, the diagonal
elements are distributed according to the normal law with a mean square
deviation which becomes smaller and smaller as $N$ increases towards infinity.
Therefore when the state vectors are of the type considered we cannot
experience spatial superpositions of the centre of mass and we may conclude
that position is a preferred basis for the collective variable.


title: Quantum State Reduction: An Operational Approach

abstract:
  A rigorous theory of quantum state reduction, the state change of the
measured system caused by a measurement conditional upon the outcome of
measurement, is developed fully within quantum mechanics without leading to the
vicious circle relative to the von Neumann chain. For the basis of the theory,
the local measurement theorem provides the joint probability distribution for
the outcomes of local successive measurements on a noninteracting entangled
system without assuming the projection postulate, and the quantum Bayes
principle enables us to determine operationally the quantum state from a given
information on the outcome of measurement.


title: Symmetries in nuclear, atomic and molecular spectroscopy

abstract:
  This paper addresses the three following questions. (i) How the structures of
group and of chain of groups enter nuclear, atomic and molecular spectroscopy?
(ii) How these structures can be exploited, in a quantum- mechanical framework,
in the problems of state labelling and (external) symmetry breaking? (iii) How
it is possible to associate a Wigner-Racah algebra to a group or a chain of
groups for making easier the calculation of quantum-mechanical matrix elements?
Numerous examples illustrate the philosophy of qualitative and quantitative
applications to spectroscopy.

categories: quant-ph cond-mat math-ph math.MP nucl-th physics.atm-clus physics.atom-ph physics.chem-ph


title: A new approach to the Cramer-Rao type bound of the pure state model

abstract:
  In this paper, new methodology -- direct approach -- for the determination of
the attainable CR type bound of the pure state model, is proposed and
successfully applied to the wide variety of pure state models, for example, the
2-dimensional arbitrary model, the coherent model with arbitrary dimension.
When the weight matrix is $SLD$ Fisher information, the bound is determined for
arbitrary pure state models. Manifestation of complex structure in the
Cramer-Rao type bound is also discussed.


title: Beables in Algebraic Quantum Mechanics

abstract:
  John Bell once argued that one ought to select, out of the 'observables' of
quantum theory, some subset of 'beables' that can be consistently ascribed
determinate values. Moreover, this subset should be selected so as to guarantee
(among other things) that we can dispense with the orthodox interpretation's
loose talk about 'measurement values': "...the probability of a beable being a
particular value would be calculated just as was formerly calculated the
probability of observing that value". Working in the framework of C*-algebras
(in particular, Segal algebras), I propose an algebraic characterization of
those subsets of bounded observables of a quantum system that can have beable
status with respect to any (fixed) state of the system. It turns out that
observables with beable status in a state need not all commute (a possibility
Bell himself does not consider), but they must at least form a certain kind of
'quasicommutative' subalgebra determined by the state. A virtue of the analysis
is that it applies to beables with continuous spectra, usually neglected in
discussions of the no-hidden-variables theorems. In the (very) special case
where the algebra of observables for a system is representable on a
finite-dimensional Hilbert space, I give a complete characterization of the
maximal beable subalgebras determined by any state of the system; the
infinite-dimensional case remains open. These results are discussed in relation
to previous results of a similar nature, to 'no-collapse' interpretations of
quantum mechanics, and to algebraic relativistic quantum field theory.


title:
Volume Elements of Monotone Metrics on the n x n Density Matrices as
  Densities-of-States for Thermodynamic Purposes. I

abstract:
  Among the monotone metrics on the (n^{2} - 1)-dimensional convex set of n x n
density matrices, as Petz and Sudar have recently elaborated, there are a
minimal (Bures) and a maximal one. We examine the proposition that it is
physically meaningful to treat the volume elements of these metrics as
densities-of-states for thermodynamic purposes. In the n = 2 (spin-1/2) case,
use of the maximal monotone metric, in fact, does lead to the adoption of the
Langevin (and not the Brillouin) functions, thus, completely conforming with a
recent probabilistic argument of Lavenda. Brody and Hughston also arrived at
the Langevin function in an analysis based on the Fubini-Study metric. It is a
matter of some interest, however, that in the first (subsequently modified)
version of their paper, they had reported a different result, one fully
consistent with the alternative use of the minimal monotone metric. In this
part I of our investigation, we first study scenarios involving partially
entangled spin-1/2 particles (n = 4, 6,...) and then a certain three-level
extension of the two-level systems. In part II, we examine, in full generality,
and with some limited analytical success, the cases n = 3 and 4.


title: Monge Distance between Quantum States

abstract:
  We define a metric in the space of quantum states taking the Monge distance
between corresponding Husimi distributions (Q--functions). This quantity
fulfills the axioms of a metric and satisfies the following semiclassical
property: the distance between two coherent states is equal to the Euclidean
distance between corresponding points in the classical phase space. We compute
analytically distances between certain states (coherent, squeezed, Fock and
thermal) and discuss a scheme for numerical computation of Monge distance for
two arbitrary quantum states.


title: Wigner function and decoherence

abstract:
  I briefly review the role of the Wigner function in the study of the
quantum-to-classical transition through interaction with the environment
(decoherence).


title: Pilot Wave Steerage: A Mechanism and Test

abstract:
  An intuitive, generic, physical model, or conceptual paradigm for pilot wave
steerage of particle beams based on Stochastic Electrodynamics is presented.
The utility of this model for understanding the Pauli Exclusion Principle is
briefly considered, and a possible experimental verification for the underlying
concepts is proposed. \\[7mm] Key words: Quantum Mechanics, Pilot Wave, Pauli
Exclusion Principle, Stochastic Electrodynamics


title:
Reply to Comment on ``Generating Functions for Hermite Polynomials of
  Arbitrary Order"

abstract:
  The results in the preceding comment are placed on a more general
mathematical foundation.


title: Towards Even and Odd Squeezed Number States

abstract:
  The time evolution of even and odd squeezed states, as well as that of
squeezed number states, has been given in simple, analytic form. This follows
experimental work on trapped ions which has demonstrated even and odd coherent
states, number states, and squeezed (but not displaced) ground states. We
review this situation and consider the extension to even and odd squeezed
number states. Questions of uncertainty relations are also discussed.


title: On multi-particle entanglement

abstract:
  We build, using group-theoretic methods, a general framework for approaching
multi-particle entanglement. As far as entanglement is concerned, two states of
n spin-1/2 particles are equivalent if they are on the same orbit of the group
of local rotations (U(2)^n). We give a method for finding the number of
parameters needed to describe inequivalent n spin-1/2 particles states. We also
describe how entanglement of states on a given orbit may be characterized by
the stability group of the action of the group of local rotations on any point
on the orbit.


title:
A Model for the Production of Regular Fluorescent Light from Coherently
  Driven Atoms

abstract:
  It has been shown in recent years that incoherent pumping through multiple
atomic levels provides a mechanism for the production of highly anti-bunched
light, and that as the number of incoherent steps is increased the light
becomes increasingly regular. We show that in a resonance fluorescence
situation, a multi-level atom may be multiply coherently driven so that the
fluorescent light is highly anti-bunched. We show that as the number of
coherently driven levels is increased, the spontaneous emissions may be made
increasingly more regular. We present a systematic method for designing the
level structure and driving required to produce highly anti-bunched light in
this manner for an arbitrary even number of levels.


title:
Spectra and generalized eigenfunctions of the one- and two-mode
  squeezing operators in quantum optics

abstract:
  The spectra and generalized eigenfunctions of the hyperbolic and parabolic
generators of the standard representation of SU(1,1) in the one-mode boson
Hilbert space are derived. The eigenfunctions are given in three different
forms, corresponding to the coordinate, photon number, and Fock-Bargmann
representations of the state vectors. The possible spectra of general second
degree Hamiltonians are determined. Some corresponding results in the two-mode
case are also given. - In the Appendix we prove completeness and orthonormality
relations for the polynomials giving the number representation expansion
coefficients of the generalized eigenfunctions of the hyperbolic generator (=
squeezing generator). These polynomials are special cases of Pollaczek
polynomials.


title: Front Propagation in Evanescent Media

abstract:
  We investigate the time evolution of waves in evanescent media generated by a
source within this medium and observed at some distance away from the location
of the source. The aim is to find a velocity which describes a causal process
and is thus, for a medium with relativistic dispersion, limited by the velocity
of light. The wave function consists of a broad frequency forerunner generated
by the onset of the source, and of a monochromatic front which carries the
oscillation frequency of the source. For a medium with Schr\"{o}dinger-like
dispersion the monochromatic front propagates with a velocity which is in
agreement with the traversal time, and in the relativistic case the velocity of
the fronts is limited by the velocity of light. For sources with a sharp onset,
the forerunners are not attenuated and in magnitude far exceed the
monochromatic front. In contrast, for sources which are frequency-band limited,
the forerunners are also attenuated and become comparable to the monochromatic
front: like in the propagating case, there exists a time at which a broad
frequency forerunner is augmented by a monochromatic wave.


title: Hyperentangled States

abstract:
  We investigate a new class of entangled states, which we call
'hyperentangled',that have EPR correlations identical to those in the vacuum
state of a relativistic quantum field. We show that whenever hyperentangled
states exist in any quantum theory, they are dense in its state space. We also
give prescriptions for constructing hyperentangled states that involve an
arbitrarily large collection of systems.


title: Analog quantum error correction

abstract:
  Quantum error-correction routines are developed for continuous quantum
variables such as position and momentum. The result of such analog quantum
error correction is the construction of composite continuous quantum variables
that are largely immune to the effects of noise and decoherence.


title:
Relativistic nonlocality (RNL) in experiments with moving polarizers and
  2 non-before impacts

abstract:
  Relativistic nonlocality (RNL) is a recently proposed relativistic nonlocal
description which unifies relativity of simultaneity and superluminal
nonlocality (without superluminal signaling). In this article RNL is applied to
experiments with so-called 2 non-before impacts, leading to new rules of
calculating the joint probabilities, and predictions conflicting with quantum
mechanics. A real experiment using fast moving polarizing beam-splitters is
proposed.


title: Unconditionally Secure Quantum Bit Commitment

abstract:
  This paper has been withdrawn: it does not evade the no-go results of Mayers,
Lo and Chau, to whom I am most grateful for helpful correspondences.


title: Unconditionally Secure Multi-Party Computation

abstract: This paper was withdrawn on 20.11.97.


title: Unconditionally Secure All-Or-Nothing Disclosure of Secrets

abstract: This paper was withdrawn on 20.11.97.


title: Secure Multi-Party Addition via Quantum States

abstract: This paper was withdrawn on 20.11.97.


title: Uhlmann's parallelism in quantum estimation theory

abstract:
  Two important classes of the quantum statistical model, the locally
quasi-classical model and the quasi-classical model, are introduced from the
estimation theoretical viewpoint, and they are characterized geometrically by
the vanishing conditions of the relative phase factor (RPF), implying the close
tie between Uhlmann parallel transport and the quantum estimation theory.


title:
Higher power squeezed states, Jacobi matrices, and the Hamburger moment
  problem

abstract:
  k:th power (amplitude-)squeezed states are defined as the normalized states
giving equality in the Schroedinger-Robertson uncertainty relation for the real
and imaginary parts of the k:th power of the one-mode annihilation operator.
Equivalently they are the set of normalized eigenstates (for all possible
complex eigenvalues) of the Bogolubov transformed "k:th power annihilation
operators". Expressed in the number representation the eigenvalue equation
leads to a three term recursion relation for the expansion coefficients, which
can be explicitly solved in the cases k = 1, 2. The solutions are essentially
Hermite and Pollaczek polynomials, respectively. k = 1 gives the ordinary
squeezed states, i.e. displaced squeezed vacua. For k equal to or larger than
three, where no explicit solution has been found, the recursion relation for
the symmetric operator given by the real part of the k:th power of the
annihilation operator defines a Jacobi matrix corresponding to a classical
Hamburger moment problem, which is undetermined. This implies that the operator
has an infinity of self-adjoint extensions, all with disjoint discrete spectra.
The corresponding squeezed states are well-defined, however.


title: Do we need photons in parametric down conversion?

abstract:
  The phenomenon of parametric down conversion from the vacuum may be
understood as a process in classical electrodynamics, in which a nonlinear
crystal couples the modes of the pumping field with those of the zeropoint, or
"vacuum" field. This is an entirely local theory of the phenomenon, in contrast
with the presently accepted nonlocal theory. The new theory predicts a hitherto
unsuspected phenomenon - parametric up conversion from the vacuum.


title: A local realist theory of parametric down conversion

abstract:
  In a series of articles we have shown that all parametric-down- conversion
processes, both of type-I and type-II, may be described by a positive Wigner
density. These results, together with our description of how light detectors
subtract the zeropoint radiation, indicated the possibility of a completely
local realist theory of all these processes. In the present article we show how
the down-converted fields may be described as retarded fields, generated by
currents inside the nonlinear crystal, thereby achieving such a theory. Most of
its predictions coincide with the standard nonlocal theory. However, the
intensities of the down converted signals do not correspond exactly with the
photon pairs of the nonlocal theory. For example, in a blue- red down
conversion we would find 1.03 red "photons" for every blue one. The theory also
predicts a new phenomenon, namely parametric up conversion from the vacuum.


title: Continuous Time and Consistent Histories

abstract:
  We discuss the use of histories labelled by a continuous time in the approach
to consistent-histories quantum theory in which propositions about the history
of the system are represented by projection operators on a Hilbert space. This
extends earlier work by two of us \cite{IL95} where we showed how a continuous
time parameter leads to a history algebra that is isomorphic to the canonical
algebra of a quantum field theory. We describe how the appropriate
representation of the history algebra may be chosen by requiring the existence
of projection operators that represent propositions about time average of the
energy. We also show that the history description of quantum mechanics contains
an operator corresponding to velocity that is quite distinct from the momentum
operator. Finally, the discussion is extended to give a preliminary account of
quantum field theory in this approach to the consistent histories formalism.


title: The quantum capacity is properly defined without encodings

abstract:
  We show that no source encoding is needed in the definition of the capacity
of a quantum channel for carrying quantum information. This allows us to use
the coherent information maximized over all sources and and block sizes, but
not encodings, to bound the quantum capacity. We perform an explicit
calculation of this maximum coherent information for the quantum erasure
channel and apply the bound in order find the erasure channel's capacity
without relying on an unproven assumption as in an earlier paper.


title: Security against eavesdropping in quantum cryptography

abstract:
  In this article we deal with the security of the BB84 quantum cryptography
protocol over noisy channels using generalized privacy amplification. For this
we estimate the fraction of bits needed to be discarded during the privacy
amplification step. This estimate is given for two scenarios, both of which
assume the eavesdropper to access each of the signals independently and take
error correction into account. One scenario does not allow a delay of the
eavesdropper's measurement of a measurement probe until he receives additional
classical information. In this scenario we achieve a sharp bound. The other
scenario allows a measurement delay, so that the general attack of an
eavesdropper on individual signals is covered. This bound is not sharp but
allows a practical implementation of the protocol.


title: Single-electron computing without dissipation

abstract:
  A possibility to perform single-electron computing without dissipation in the
array of tunnel-coupled quantum dots is studied theoretically, taking the spin
gate NOT (inverter) as an example. It is shown that the logical operation can
be realized at the stage of unitary evolution of electron subsystem, though
complete switching of the inverter cannot be achieved in a reasonable time at
realistic values of model parameters. An optimal input magnetic field is found
as a function of inter-dot tunneling energy and intra-dot Coulomb repulsion
energy.


title: Quantum Mechanical Square Root Speedup in a Structured Search Problem

abstract:
  An unstructured search for one item out of N can be performed quantum
mechanically in time of order square root of N whereas classically this
requires of order N steps. This raises the question of whether square root
speedup persists in problems with more structure. In this note we focus on one
example of a structured problem and find a quantum algorithm which takes time
of order the square root of the classical time.


title: Central charges in regular mechanics

abstract:
  We consider the algebra associated to a group of transformations which are
symmetries of a regular mechanical system (i.e. system free of constraints).
For time dependent coordinate transformations we show that a central extension
may appear at the classical level which is coordinate and momentum independent.
A cochain formalism naturally arises in the argument and extends the usual
configuration space cochain concepts to phase space.


title: On the effectiveness of Gamow's method for calculating decay rates

abstract:
  We examine Gamow's method for calculating the decay rate of a wave function
initially located within a potential well. Using elementary techniques, we
examine a very simple, exactly solvable model, in order to show why it is so
reliable for calculating decay rates, in spite of its conceptual problems. We
also discuss the regime of validity of the exponential decay law.


title: Statistics for Particles Having Internal Quantum State

abstract:
  A new kind of quantum statistics which interpolates between Bose and Fermi
statistics is proposed beginning with the assumption that the quantum state of
a many-particle system is a functional on the internal space of the particles.
The quantum commutation relations for such particle creation and annihilation
operators are derived, and statistical partition function and thermodynamical
properties of an ideal gas of the particles are investigated. The application
of this quantum statistics for the ensemble of extremal black holes are
discussed.


title:
Three-dimensional quantization of the electromagnetic field in
  dispersive and absorbing inhomogeneous dielectrics

abstract:
  A quantization scheme for the phenomenological Maxwell theory of the full
electromagnetic field in an inhomogeneous three-dimensional, dispersive and
absorbing dielectric medium is developed. The classical Maxwell equations with
spatially varying and Kramers-Kronig consistent permittivity are regarded as
operator-valued field equations, introducing additional current- and
charge-density operator fields in order to take into account the noise
associated with the dissipation in the medium. It is shown that the equal-time
commutation relations between the fundamental electromagnetic fields $\hat E$
and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ in the Coulomb gauge
can be expressed in terms of the Green tensor of the classical problem. From
the Green tensors for bulk material and an inhomogeneous medium consisting of
two bulk dielectrics with a common planar interface it is explicitly proven
that the well-known equal-time commutation relations of QED are preserved.


title: Is Quantum Bit Commitment Really Impossible?

abstract: This paper has been withdrawn.


title: Complementarity and Young's interference fringes from two atoms

abstract:
  The interference pattern of the resonance fluorescence from a J=1/2 to J=1/2
transition of two identical atoms confined in a three-dimensional harmonic
potential is calculated. Thermal motion of the atoms is included. Agreement is
obtained with experiments [Eichmann et al., Phys. Rev. Lett. 70, 2359 (1993)].
Contrary to some theoretical predictions, but in agreement with the present
calculations, a fringe visibility greater than 50% can be observed with
polarization-selective detection. The dependence of the fringe visibility on
polarization has a simple interpretation, based on whether or not it is
possible in principle to determine which atom emitted the photon.


title:
Type-II parametric down conversion in the Wigner-function formalism.
  Entanglement and Bell's inequalities

abstract:
  We continue the analysis of our previous articles which were devoted to
type-I parametric down conversion, the extension to type-II being
straightforward. We show that entanglement, in the Wigner representation, is
just a correlation that involves both signal and vacuum fluctuations. An
analysis of the detection process opens the way to a complete description of
parametric down conversion in terms of pure Maxwell electromagnetic waves.


title: A framework for fast quantum mechanical algorithms

abstract:
  A framework is presented for the design and analysis of quantum mechanical
algorithms, the sqrt(N) step quantum search algorithm is an immediate
consequence of this framework. It leads to several other search-type
applications - several examples are presented. Also, it leads to quantum
mechanical algorithms for problems not immediately connected with search - two
such algorithms are presented for estimating the mean and median of statistical
distributions. Both algorithms require fewer steps than the fastest possible
classical algorithms; also both are considerably simpler and faster than
existing quantum mechanical algorithms for the respective problems.


title: Timing, ``Accidentals'' and Other Artifacts in EPR Experiments

abstract:
  Subtraction of ``accidentals'' in Einstein-Podolsky-Rosen experiments
frequently changes results compatible with local realism into ones that appear
to demonstrate non-locality. The validity of the procedure depends on the
unproven assumption of the independence of emission events. Other possible
sources of bias include enhancement, imperfect synchronisation, over-reliance
on rotational invariance, and the well-known detection loophole. Investigation
of existing results may be more fruitful than attempts at loophole-free Bell
tests, improving our understanding of light.


title: A reductionistic approach to quantum computation

abstract:
  In the reductionistic approach, mechanisms are divided into simpler parts
interconnected in some standard way (e.g. by a mechanical transmission). We
explore the possibility of porting reductionism in quantum operations.
Conceptually, first parts are made independent of each other by assuming that
all ``transmissions'' are removed. The overall state would thus become a
superposition of tensor products of the eigenstates of the independent parts.
Transmissions are restored by projecting off all the tensor products which
violate them. This would be performed by particle statistics; the plausibility
of this scheme is based on the interpretation of particle statistics as
projection. The problem of the satisfiability of a Boolean network is
approached in this way. This form of quantum reductionism appears to be able of
taming the quantum whole without clipping its richness.


title: The myth of the photon

abstract:
  We have shown that all "single-photon" and "photon-pair" states, produced in
atomic transitions, and in parametric down conversion by nonlinear optical
crystals, may be represented by positive Wigner densities of the relevant sets
of mode amplitudes. The light fields of all such states are represented as a
real probability ensemble (not a pseudoensemble) of solutions of the
unquantized Maxwell equation.
  The local realist analysis of light-detection events in spatially separated
detectors requires a theory of detection which goes beyond the currently
fashionable single-mode photon theory. It also requires us to recognize that
there is a payoff between detector efficiency and signal-noise discrimination.
Using such a theory, we have demonstrated that all experimental data, both in
atomic cascades and in parametric down conversions, have a consistent local
realist explanation based on the unquantized Maxwell field.
  Finally we discuss current attempts to demonstrate Schroedinger-cat-like
behaviour of microwave cavities interacting with Rydberg atoms. Here also we
demonstrate that there is no experimental evidence which cannot be described by
the unquantized Maxwell field.
  We conclude that misuse of the Photon Concept has resulted in a mistaken
recognition of "nonlocal" phenomena.


title: Quantum self-dual codes and symmetric matrices

abstract:
  This paper has been withdrawn since a Gilbert-Varshamov bound for general
quantum codes has already appeared in Ekert and Macchiavello, Prys. Rev. Lett.
77, p. 2585, and a Gilbert-Varshamov bound for stabilizer codes connected with
orthogonal geometry, or equivalently, with symmetric matrices as in this paper,
has been proved by Calredbank, Rains, Shor and Sloane, Phys. Rev. Lett. 78, p.
405. I would like to thank Robert Calderbank for pointing out these references
to me.


title: Dynamics for Density Operator Interpretations of Quantum Theory

abstract:
  We first introduce and discuss density operator interpretations of quantum
theory as a special case of a more general class of interpretations, giving
special attention to a version that we call the `atomic version'. We then
review some crucial parts of the theory of stochastic processes (the proper
context in which to discuss dynamics), and develop a general framework for
specifying a dynamics for density operator interpretations. This framework
admits infinitely many empirically equivalent dynamics. We give some examples,
and discuss some of the properties of one of them.


title: Error correction for continuous quantum variables

abstract:
  We propose an error correction coding algorithm for continuous quantum
variables. We use this algorithm to construct a highly efficient 5-wavepacket
code which can correct arbitrary single wavepacket errors. We show that this
class of continuous variable codes is robust against imprecision in the error
syndromes. A potential implemetation of the scheme is presented.


title: Photoemissive sources and quantum stochastic calculus

abstract:
  Just at the beginning of quantum stochastic calculus Hudson and Parthasarathy
proposed a quantum stochastic Schrodinger equation linked to dilations of
quantum dynamical semigroups. Such an equation has found applications in
physics, mainly in quantum optics, but not in its full generality. It has been
used to give, at least approximately, the dynamics of photoemissive sources
such as an atom absorbing and emitting light or matter in an optical cavity,
which exchanges light with the surrounding free space. But in these cases the
possibility of introducing the gauge (or number) process in the dynamical
equation has not been considered. In this paper we show, in the case of the
simplest photoemissive source, namely a two-level atom stimulated by a laser,
how the full Hudson-Parthasarathy equation allows to describe in a consistent
way not only absorption and emission, but also the elastic scattering of the
light by the atom. Morever, we study the differential and total cross sections
for the scattering of laser light by the atom, as a function of the frequency
of the stimulating laser. The resulting line-shape is very interesting. Not
only a Lorentzian shape is permitted, but the full variety of Fano profiles can
be obtained. The dependence of the line shape on the intensity of the
stimulating laser is computed; in particular, the resonance position turns out
to be intensity dependent, a phenomenon known as lamp shift.


title:
Separable and entangled states of composite quantum systems; Rigorous
  description

abstract:
  We present a general description of separable states in Quantum Mechanics. In
particular, our result gives an easy proof that inseparabitity (or
entanglement) is a pure quantum (noncommutative) notion. This implies that
distinction between separability and inseparabitity has sense only for
composite systems consisting of pure quantum subsystems. Moreover, we provide
the unified characterization of pure-state entanglement and mixed-state
entanglement.


title: Nonlocal character of quantum theory?

abstract:
  In a recent article under the above title (but without the question mark)
Henry Stapp presented arguments which lead him to conclude that under suitable
conditions ``the truth of a statement that refers only to phenomena confined to
an earlier time'' must ``depend on which measurement an experimenter freely
chooses to perform at a later time.'' I point out that the reasoning leading to
this conclusion relies on an essential ambiguity regarding the meaning of the
expression ``statement that refers only to phenomena confined to an earlier
time'' when such a statement contains counterfactual conditionals. As a result
the argumentation does not justify the conclusion that there can be frames of
reference in which future choices can affect present facts. But it does provide
an instructive and interestingly different opportunity to illustrate a central
point of Bohr's reply to Einstein, Podolsky, and Rosen.


title: Structure of nonlinear gauge transformations

abstract:
  Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations
(NGT) defined in terms of a wave function $\psi(x)$ do not form a group. To get
a group property one has to consider transformations that act differently on
different branches of the complex argument function and the knowledge of the
value of $\psi(x)$ is not sufficient for a well defined NGT. NGT that are well
defined in terms of $\psi(x)$ form a semigroup parametrized by a real number
$\gamma$ and a nonzero $\lambda$ which is either an integer or $-1\leq
\lambda\leq 1$. An extension of NGT to projectors and general density matrices
leads to NGT with complex $\gamma$. Both linearity of evolution and Hermiticity
of density matrices are gauge dependent properties.


title: Lie-Nambu and beyond

abstract:
  Linear quantum mechanics can be regarded as a particular example of a
nonlinear Nambu-type theory. Some elements of this approach are presented.


title: Photon counting sampling of phase space

abstract:
  The recently proposed scheme for direct sampling of the quantum phase space
by photon counting is discussed within the Wigner function formalism.


title: A new stochastic interpretation of quantum mechanics

abstract:
  The reinterpretation of quantum mechanical formalism in terms of a classical
model with a continuous material "$\Psi$-field" acting upon a point-like
particle which is subjected to large friction and random forces is proposed.
This model gives a mechanism for sudden "quantum jumps" and provides a simple
explanation of "Schr\"odinger Cat" phenomena.


title: Thermalisation of Quantum States

abstract:
  An exact stochastic model for the thermalisation of quantum states is
proposed. The model has various physically appealing properties. The dynamics
are characterised by an underlying Schrodinger evolution, together with a
nonlinear term driving the system towards an asymptotic equilibrium state and a
stochastic term reflecting fluctuations. There are two free parameters, one of
which can be identified with the heat bath temperature, while the other
determines the characteristic time scale for thermalisation. Exact expressions
are derived for the evolutionary dynamics of the system energy, the system
entropy, and the associated density operator.


title:
Resolving the space-time structure of sonoluminescence by intensity
  interferometry

abstract:
  We analyze the spatial and temporal resolving power of two-photon intensity
interferometry for the light emitting source in single bubble sonoluminescence
(SBSL). We show that bubble sizes between several 10 nm and 3 um can be
resolved by measuring the transverse correlation function, but that a direct
determination of the flash duration via the longitudinal correlation function
works only for SBSL pulses which are shorter than 0.1 ps. Larger pulse lengths
can be determined indirectly from the intercept of the angular correlator at
equal photon frequencies. The dynamics of the bubble is not accessible by
two-photon interferometry.


title: Strictly isospectral supersymmetry and Schroedinger general zero modes

abstract:
  The connection between the strictly isospectral construction in
supersymmetric quantum mechanics and the general zero mode solutions of the
Schroedinger equation is explained by introducing slightly generalized
first-order intertwining operators. We also present a multiple-parameter
generalization of the strictly isospectral construction in the same perspective


title:
Mermin's Suggestion and the Nature of Bohr's Action-at-a-Distance
  Influence

abstract:
  Mermin suggests comparing my recent proof of quantum nonlocality to Bohr's
reply to Einstein, Podolsky, and Rosen. Doing so leads naturally to the insight
that the nonlocal influence deduced from the analysis of the Hardy experiment
is the same as the nonlocal influence deduced by Bohr, and used by him to block
the application of the criterion of physical reality proposed by Einstein,
Podolsky, and Rosen. However, the greater sophistication of the Hardy
experiment, as contrasted to the experiment considered by Bohr and the three
authors, exposes more clearly than before the nature of this influence, and
thereby strengthens Bohr's position.


title: Revivals of Quantum Wave Packets

abstract:
  We present a generic treatment of wave-packet revivals for quantum-mechanical
systems. This treatment permits a classification of certain ideal revival
types. For example, wave packets for a particle in a one-dimensional box are
shown to exhibit perfect revivals. We also examine the revival structure of
wave packets for quantum systems with energies that depend on two quantum
numbers. Wave packets in these systems exhibit quantum beats in the initial
motion as well as new types of long-term revivals. As an example, we consider
the revival structure of a particle in a two-dimensional box.


title: Does a quantum particle know the time?

abstract:
  We study the spatial regularity of the fundamental solution E(t,x) of the
Schr\"odinger equation on the circle in a scale of Besov spaces. Although the
fundamental solution is not smooth, we reveal a fine change of regularity of
E(t,x) at different times t. For rational t, E(t,x) is a weighted sum of
delta-functions, and, therefore, exhibits the same regularity as at t=0. For
irrational t, the regularity of E(t,x) is better and depends on how well t is
approximated by rationals. For badly approximated t (e.g., when t is a
quadratic irrational, or, more generally, when t has bounded quotients in its
continued fraction expansion), E(t,x) is a "1/2-derivative" more regular than
E(0,x). For a generic irrational t, E(t,x) is almost "1/2-derivative" more
regular. However, the better t is approximated by rationals, the lower is the
regularity of E(t,x). We describe different thin classes of irrationals which
prescribe their particular regularity to the fundamental solution. These
classes are singled out and characterized by the behavior of the continued
fraction expansions of their members.


title:
A Quantum-Theoretic Analog for a Pair of Noncommuting Observables of the
  Semiclassical Brillouin Function

abstract:
  We study, with the use of numerical integration, a noncommutative extension
of a quantum-theoretic model (an alternative to the semiclassical Brillouin
function), recently presented by Brody and Hughston and, independently, Slater,
for the thermodynamic behavior of a spin-1/2 particle. Differences between the
(broadly similar) predictions yielded by this extended model and those obtained
from its conventional (semiclassical/Jaynesian) entropy-maximization
counterpart are examined.


title: On quantum theories of the mind

abstract:
  Replies are given to arguments advanced in this journal that claim to show
that it is to nonlinear classical mechanics rather than quantum mechanics that
one must look for the physical underpinnings of consciousness.


title: Why Quantum Bit Commitment And Ideal Quantum Coin Tossing Are Impossible

abstract:
  There had been well known claims of unconditionally secure quantum protocols
for bit commitment. However, we, and independently Mayers, showed that all
proposed quantum bit commitment schemes are, in principle, insecure because the
sender, Alice, can almost always cheat successfully by using an
Einstein-Podolsky-Rosen (EPR) type of attack and delaying her measurements. One
might wonder if secure quantum bit commitment protocols exist at all. We answer
this question by showing that the same type of attack by Alice will, in
principle, break any bit commitment scheme. The cheating strategy generally
requires a quantum computer. We emphasize the generality of this ``no-go
theorem'': Unconditionally secure bit commitment schemes based on quantum
mechanics---fully quantum, classical or quantum but with measurements---are all
ruled out by this result. Since bit commitment is a useful primitive for
building up more sophisticated protocols such as zero-knowledge proofs, our
results cast very serious doubt on the security of quantum cryptography in the
so-called ``post-cold-war'' applications. We also show that ideal quantum coin
tossing is impossible because of the EPR attack. This no-go theorem for ideal
quantum coin tossing may help to shed some lights on the possibility of
non-ideal protocols.


title:
Barut-Girardello coherent states for u(p,q) and sp(N,R) and their
  macroscopic superpositions

abstract:
  The Barut-Girardello coherent states (BG CS) representation is extended to
the noncompact algebras u(p,q) and sp(N,R) in (reducible) quadratic boson
realizations. The sp(N,R) BG CS take the form of multimode ordinary
Schr\"odinger cat states. Macroscopic superpositions of 2^{n-1} sp(N,R) CS (2^n
canonical CS, n=1,2,...) are pointed out which are overcomplete in the N-mode
Hilbert space and the relation between the canonical CS and the u(p,q) BG-type
CS representations is established. The sets of u(p,q) and sp(N,R) BG CS and
their discrete superpositions contain many states studied in quantum optics
(even and odd N-mode CS, pair CS) and provide an approach to quadrature
squeezing, alternative to that of intelligent states. New subsets of weakly and
strongly nonclassical states are pointed out and their statistical properties
(first- and second-order squeezing, photon number distributions) are discussed.
For specific values of the angle parameters and small amplitude of the
canonical CS components these states approaches multimode Fock states with one,
two or three bosons/photons. It is shown that eigenstates of a squared
non-Hermitian operator A^2 (generalized cat states) can exhibit squeezing of
the quadratures of A.


title: Optimized quantum-optical communications in the presence of loss

abstract:
  We consider the effect of loss on quantum-optical communication channels. The
channel based on direct detection of number states, which for a lossless
transmission line would achieve the ultimate quantum channel capacity, is
easily degraded by loss. The same holds true for the channel based on homodyne
detection of squeezed states, which also is very fragile to loss. On the
contrary, the ``classical'' channel based on heterodyne detection of coherent
states is loss-invariant. We optimize the a priori probability for the
squeezed-state and the number-state channels, taking the effect of loss into
account. In the low power regime we achieve a sizeable improvement of the
mutual information, and both the squeezed-state and the number-state channels
overcome the capacity of the coherent-state channel. In particular, the
squeezed-state channel beats the classical channel for total average number of
photons $N<8$. However, for sufficiently high power the classical channel
always performs as the best one. For the number-state channel we show that with
a loss $\eta\lesssim .6$ the optimized a priori probability departs from the
usual thermal-like behavior, and develops gaps of zero probability, with a
considerable improvement of the mutual information (up to 70 % of improvement
at low power for attenuation $\eta=.15$).


title: On the computation of quantum characteristic exponents

abstract:
  A quantum characteristic exponent may be defined, with the same operational
meaning as the classical Lyapunov exponent when the latter is expressed as a
functional of densities. Existence conditions and supporting measure properties
are discussed as well as the problems encountered in the numerical computation
of the quantum exponents. Although an example of true quantum chaos may be
exhibited, the taming effect of quantum mechanics on chaos is quite apparent in
the computation of the quantum exponents. However, even when the exponents
vanish, the functionals used for their definition may still provide a
characterization of distinct complexity classes for quantum behavior.


title: Quantum Bit Commitment from a Computation Bound

abstract: This paper is withdrawn. See quant-ph/9806031 for a discussion.


title: Grover's quantum searching algorithm is optimal

abstract:
  I improve the tight bound on quantum searching by Boyer et al.
(quant-ph/9605034) to a matching bound, thus showing that for any probability
of success Grovers quantum searching algorithm is optimal. E.g. for near
certain success we have to query the oracle pi/4 sqrt{N} times, where N is the
size of the search space. I also show that unfortunately quantum searching
cannot be parallelized better than by assigning different parts of the search
space to independent quantum computers. Earlier results left open the
possibility of a more efficient parallelization.


title:
Surface effects influencing the single-atom spontaneous emission in a
  linear atomic chain

abstract:
  As a contribution to quantum optics in the vicinity of surfaces we study the
single atom spontaneous emission in a linear chain of two-level atoms. The
electromagnetic field is thereby treated with the help of integro-differential
equations which take into account the interaction with the other atoms in the
chain. The life time of the excited atom, the frequency shift of the atomic
transition and the angular distribution of emitted photons are worked out. They
depend on the position of the emitting atom. As compared with the single atom
in free space, considerable modifications occur for atoms a few interatomic
distances away from the ends of the chain.


title: On the nature of the quantum states of macroscopic systems

abstract:
  It is assumed that the quantum state that may describe a macroscopic system
at a given instant of time is one of the eigenstates of the reduced density
matrix calculated from the wave function of the system plus its environment.
This implies that the above quantum state is a member of a special orthonormed
set of states. Using a suitable Monte-Carlo simulation, this property is shown
to be consistent with the extremely small standard deviation for the
coordinates and the momenta of macroscopic systems. Consequences for
statistical mechanics and possible observable effects are discussed.


title: Revivals of Rydberg Wave Packets

abstract:
  We examine the revival structure of Rydberg wave packets. These wave packets
exhibit initial classical periodic motion followed by a sequence of collapse,
fractional/full revivals, and fractional/full superrevivals. The effects of
quantum defects on wave packets in alkali-metal atoms and a squeezed-state
description of the initial wave packets are also described. We then examine the
revival structure of Rydberg wave packets in the presence of an external
electric field, i.e., the revival structure of Stark wave packets. These wave
packets have energies that depend on two quantum numbers and exhibit new types
of interference behavior.


title: The myth of the down converted photon

abstract:
  Parametric down conversion (PDC) is widely interpreted in terms of photons,
but, even among supporters of this interpretation, many properties of the
photon pairs have been described as "mind-boggling" and even "absurd". In this
article we argue that a classical description of the light field, taking
account of its vacuum fluctuations, leads us to a consistent and rational
account of all PDC phenomena. "Nonlocality" in quantum optics is simply an
artifact of the Photon Concept. We also predict a new phenomenon, namely the
appearance of a second, or satellite PDC rainbow.


title:
Permanently Secure Quantum Bit Commitment from a Temporary Computation
  Bound

abstract: This paper has been withdrawn. See quant-ph/9806031 for a discussion.


title: Nonlocality and Bohr's reply to EPR

abstract:
  Henry Stapp's commentary (quant-ph/9711060) does not capture the point I was
trying to make in my essay (quant-ph/9711052) on how a subtle flaw in his
``proof of quantum nonlocality'' clearly illustrates a central issue in Bohr's
reply to EPR. I therefore wish to emphasize what I do and do not say in that
essay and even, with some trepidation, what Bohr did and did not say in his
reply to EPR.


title: Models to Reduce the Complexity of Simulating a Quantum Computer

abstract:
  Recently Quantum Computation has generated a lot of interest due to the
discovery of a quantum algorithm which can factor large numbers in polynomial
time. The usefulness of a quantum com puter is limited by the effect of errors.
Simulation is a useful tool for determining the feasibility of quantum
computers in the presence of errors. The size of a quantum computer that can be
simulat ed is small because faithfully modeling a quantum computer requires an
exponential amount of storage and number of operations. In this paper we define
simulation models to study the feasibility of quantum computers. The most
detailed of these models is based directly on a proposed imple mentation. We
also define less detailed models which are exponentially less complex but still
pro duce accurate results. Finally we show that the two different types of
errors, decoherence and inaccuracies, are uncorrelated. This decreases the
number of simulations which must be per formed.


title: Prevention of dissipation with two particles

abstract:
  An error prevention procedure based on two-particle encoding is proposed for
protecting an arbitrary unknown quantum state from dissipation, such as phase
damping and amplitude damping. The schemes, which exhibits manifestation of the
quantum Zeno effect, is effective whether quantum bits are decohered
independently or cooperatively. We derive the working condition of the scheme
and argue that this procedure has feasible practical implementation.


title:
A Possible Einstein-Podolsky-Rosen Probe of the Momentum-Position
  Uncertainty Relation

abstract:
  It is suggested that a measurement of the products of photoemission by alkali
atoms excited after extraction from a trap, might, using the EPR strategy, show
a significant violation of the momentum-position uncertainty relation. If this
failed, as is quite likely, possible causes, such as retroactive propagation of
influences and retrodiction failure, could be tested on the proposed apparatus.


title: Fabrication of Magnetic Charge From Excited States of H-atom

abstract:
  It is shown that the excited states of hydrogen atom in a uniform electric
field (Stark States) posess magnetic charge whose magnitude is given by a
Dirac-Saha type relation: $$ {eg\over \hbar c} = \sqrt 3 n $$ An experiment is
proposed to fabricate such states and to detect their magnetic charge.


title: Semiclassical Green Function in Mixed Spaces

abstract:
  A explicit formula on semiclassical Green functions in mixed position and
momentum spaces is given, which is based on Maslov's multi-dimensional
semiclassical theory. The general formula includes both coordinate and momentum
representations of Green functions as two special cases of the form.


title: Questions on quantization

abstract:
  We pose 22 relatively general questions about quantization in the operator
algebra setting. In the process we briefly survey some recent developments.


title: Wave atom optics theory of the Collective Atomic-Recoil Laser

abstract:
  We present a wave atom optics theory of the Collective Atomic-Recoil Laser,
where the atomic center-of-mass motion is treated quantum mechanically. It
extends the previous ray atom optics theory, which treated the center-of-mass
atomic motion classically, to the realm of ultracold atoms. For the case of a
far off resonant pump laser we derive an analytical solution which gives the
linear response of the CARL system for both the quantum and classical regimes.
A linear stability analysis reveals significant qualitative differences between
these two regimes, which arise from the effects of diffraction on the atomic
center-of-mass motion.


title: Quantum computers can search rapidly by using almost any transformation

abstract:
  A quantum computer has a clear advantage over a classical computer for
exhaustive search. The quantum mechanical algorithm for exhaustive search was
originally derived by using subtle properties of a particular quantum
mechanical operation called the Walsh-Hadamard (W-H) transform. This paper
shows that this algorithm can be implemented by replacing the W-H transform by
almost any quantum mechanical operation. This leads to several new applications
where it improves the number of steps by a square-root. It also broadens the
scope for implementation since it demonstrates quantum mechanical algorithms
that can readily adapt to available technology.


title: Quantum gates with "hot" trapped ions

abstract:
  We propose a scheme to perform a fundamental two-qubit gate between two
trapped ions using ideas from atom interferometry. As opposed to the scheme
considered by J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995), it
does not require laser cooling to the motional ground state.


title: Quantum-Mechanical Supersymmetry in Traps

abstract:
  We discuss the application of quantum-mechanical supersymmetry to particle
traps. The supersymmetric-partner wave functions may be used to describe a
valence fermion in a trap system with an isotropic harmonic-oscillator
potential. Interactions with the core are incorporated analytically. The close
similarity of this approach to the application of supersymmetry in atomic
systems is made explicit by means of a radial mapping between the two systems.


title:
On a Generalized Oscillator: Invariance Algebra and Interbasis
  Expansions

abstract:
  This article deals with a quantum-mechanical system which generalizes the
ordinary isotropic harmonic oscillator system. We give the coefficients
connecting the polar and Cartesian bases for D=2 and the coefficients
connecting the Cartesian and cylindrical bases as well as the cylindrical and
spherical bases for D=3. These interbasis expansion coefficients are found to
be analytic continuations to real values of their arguments of the
Clebsch-Gordan coefficients for the group SU(2). For D=2, the superintegrable
character for the generalized oscillator system is investigated from the points
of view of a quadratic invariance algebra.

categories: quant-ph math-ph math.MP physics.atm-clus physics.atom-ph physics.chem-ph


title: Localization of Quantum States at the Cyclotron Resonance

abstract:
  A new type of localization - localization over the quantum resonance cells -
in an intrinsically degenerate system is explored by using the quasienergy
eigenstates.


title: Protection of information in quantum qatabases

abstract:
  The conventional protection of information by cryptographical keys makes no
sense if a key can be quickly discovered by an unauthorized person. This way of
penetration to the protected systems was made possible by a quantum computers
in view of results of P.Shor and L.Grover. This work presents the method of
protection of an information in a database from a spy even he knows all about
its control system and has a quantum computer, whereas a database can not
distinguish between operations of spy and legal user.


title: A Scheme to Probe the Decoherence of a Macroscopic Object

abstract:
  We propose a quantum optical version of Schr\"{o}dinger's famous gedanken
experiment in which the state of a microscopic system (a cavity field) becomes
entangled with and disentangled from the state of a massive object (a movable
mirror). Despite the fact that a mixture of Schr\"{o}dinger cat states is
produced during the evolution (due to the fact that the macroscopic mirror
starts off in a thermal state), this setup allows us to systematically probe
the rules by which a superposition of spatially separated states of a
macroscopic object decoheres. The parameter regime required to test
environment-induced decoherence models is found to be close to those currently
realizable, while that required to detect gravitationally induced collapse is
well beyond current technology.


title: Algebraic Approach to Shape Invariance

abstract:
  The integrability condition called shape invariance is shown to have an
underlying algebraic structure and the associated Lie algebras are identified.
These shape-invariance algebras transform the parameters of the potentials such
as strength and range. Shape-invariance algebras, in general, are shown to be
infinite-dimensional. The conditions under which they become finite-dimensional
are explored.


title: Optimal universal quantum cloning and state estimation

abstract:
  We derive a tight upper bound for the fidelity of a universal N to M qubit
cloner, valid for any M \geq N, where the output of the cloner is required to
be supported on the symmetric subspace. Our proof is based on the concatenation
of two cloners and the connection between quantum cloning and quantum state
estimation. We generalise the operation of a quantum cloner to mixed and/or
entangled input qubits described by a density matrix supported on the symmetric
subspace of the constituent qubits. We also extend the validity of optimal
state estimation methods to inputs of this kind.


title: Optimal Signal-to-Quantum Noise Ratio for Nonclassical Number States

abstract:
  We analyze the properties of nonclassical number states, specifically
squeezed number states D(a)S(z)|n >, and find their maximum signal-to-quantum
noise ratio. It is shown that the optimal signal-to-quantum noise ratio for
these states decreases as 1/(2n+1)2, where n is the photon number, from the
optimal value as derived by Yuen.


title: Implementations of Quantum Logic: Fundamental and Experimental Limits

abstract:
  Quantum information processing rests on our ability to manipulate quantum
superpositions through coherent unitary transformations. In reality the quantum
information processor (a linear ion trap, or cavity qed implementation for
example) exists in a dissipative environment. Dephasing, and other technical
sources of noise, as well as more fundamental sources of dissipation severely
restrict quantum processing capabilities. The strength of the coherent coupling
needed to implement quantum logic is not always independent of dissipation. The
limitations these dissipative influences present will be described and the need
for efficient error correction noted. Even if long and involved quantum
computations turn out to be hard to realize, one can perform interesting
manipulations of entanglement involving only a few gates and qubits, of which
we give examples. Quantum communication also involves manipulations of
entanglement which are simpler to implement than elaborate computations. We
briefly analyse the notion of the capacity of a quantum communication channel.


title:
Three Body Multichannel Scattering as a Model of Irreversible Quantum
  Mechanics

abstract:
  The new formulation of the theory of multichannel scattering on the example
of collinear model is proposed. It is shown, that in the closed three-body
scattering system the principle of quantum determinism in general case breaks
down and we have a micro- irreversible quantum mechanics.