title:
Quantum Mechanics as a Classical Theory IX: The Formation of Operators
  and Quantum Phase-Space Densities

abstract:
  In our previous papers we were interested in making a reconstruction of
quantum mechanics according to classical mechanics. In this paper we suspend
this program for a while and turn our attention to a theme in the frontier of
quantum mechanics itself---that is, the formation of operators. We then
investigate all the subtleties involved in forming operators from their
classical counterparts. We show, using the formalism of quantum phase-space
distributions, that our formation method, which is equivalent to Weyl's rule,
gives the correct answer. Since this method implies that eigenstates are not
dispersion-free we argue for modifications in the orthodox view. Many
properties of the quantum phase-space distributions are also investigated and
discussed in the realm of our classical approach. We then strengthen the
conclusions of our previous papers that quantum mechanics is merely an
extremely good approximation of classical statistical mechanics performed upon
the configuration space.


title:
A Supersymmetric Treatment of a Particle Subjected to a Ring-shaped
  Potential

abstract:
  The ring-shaped Hartmann potential $V = \eta \sigma^{2} \epsilon_{0} \left(
\frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right)$ was
introduced in quantum chemistry to describe ring-shaped molecules like benzene.
In this article, fundamental concepts of supersymmetric quantum mechanics
(SUSYQM) are discussed.
  The energy eigenvalues and (radial) eigenfunctions of the Hartmann potential
are subsequently rederived using the techniques of SUSYQM.


title:
Quantum optical input--output relations for dispersive and lossy
  multi-slab dielectric plates

abstract:
  Using the Green function approach to the problem of quantization of the
phenomenological Maxwell theory, the propagation of quantized radiation through
dispersive and absorptive multilayer dielectric plates is studied.
Input--output relations are derived, with special emphasis on the determination
of the quantum noise generators associated with the absorption of radiation
inside the dielectric matter. The input--output relations are used to express
arbitrary correlation functions of the outgoing field in terms of correlation
functions of the incoming field and those of the noise generators. To
illustrate the theory, the effect of a single-slab plate on the mean
photon-number densities in the frequency domain is discussed in more detail.


title:
Simple Quantum Mechanical Phenomena and the Feynman Real Time Path
  Integral

abstract:
  The path integral formalism gives a very illustrative and intuitive
understanding of quantum mechanics but due to its difficult sum over phases one
usually prefers Schr\"odinger's approach. We will show that it is possible to
calculate simple quantum phenomena by performing Feynman's sum over all paths
staying entirely in real time. Once the propagator is obtained it is
particularly easy to get the energy spectrum or the evolution of any
wavefunction.


title: On Quantum Field Brownian Motion, Decoherence and Semiquantum Chaos

abstract:
  Entropy production in quantum (field) systems requiring environment-induced
decoherence is described in a Gaussian variational approximation. The new
phenomenon of Semiquantum Chaos is reported. (Presented at the International
Conference on Nonlinear Dynamics, Chaotic and Complex Systems, Zakopane
(Poland), 7-12.11.95.)

categories: quant-ph chao-dyn hep-th nlin.CD nucl-th


title:
Realistic lower bounds for the factorization time of large numbers on a
  quantum computer

abstract:
  We investigate the time T a quantum computer requires to factorize a given
number dependent on the number of bits L required to represent this number. We
stress the fact that in most cases one has to take into account that the
execution time of a single quantum gate is related to the decoherence time of
the qubits that are involved in the computation. Although exhibited here only
for special systems, this inter-dependence of decoherence and computation time
seems to be a restriction in many current models for quantum computers and
leads to the result that the computation time T scales much stronger with L
than previously expected.


title: On Uniqueness of the Jump Process in Quantum Measurement Theory

abstract:
  We prove that, contrary to the standard quantum theory of continuous
observation, in the formalism of Event Enhanced Quantum Theory the stochastic
process generating individual sample histories of pairs (observed quantum
system, observing classical apparatus) is unique. This result gives a rigorous
basis to the previous heuristic argument of Blanchard and Jadczyk. Possible
implications of this result are discussed.


title: Bell Inequalities with Postselection

abstract:
  Experimental tests of Bell inequalities ought to take into account all
detection events. If the latter are postselected, and only some of these events
are included in the statistical analysis, a Bell inequality may be violated,
even by purely classical correlations. The paradoxical properties of Werner
states, recently pointed out by Popescu, can be explained as the result of a
postselection of the detection events, or, equivalently, as due to the
preparation of a new state by means of a nonlocal process.


title: Quantum Evoluton and Space-time Structure

abstract:
  The hilbert-space structure of quantum mechanics is related to the causal
structure of space-time. The usual measurement hypotheses apparently preclude
nonlinear or stochastic quantum evolution. By admitting a difference in the
calculus of joint probabilities of events in space-time according to whether
the separation is space-like or time-like, a relativistic nonlinear or
stochastic quantum theory may be possible.


title: Coherent states of quantum non-linear systems

abstract:
  Quantum dynamics of integrable systems is discussed. Localized wave packets
generalizing the conventional coherent states of minimal uncertainty are
constructed. The wave packet moves along a certain trajectory and does not
change its shape for times of order $\frac{1}{\hbar}$.


title: Statistical Mechanics of $qp$-Bosons in $D$ Dimensions

abstract:
  This paper is concerned with statistical properties of a gas of $qp$-bosons
without interaction. Some thermodynamical functions for such a system in $D$
dimensions are derived. Bose-Einstein condensation is discussed in terms of the
parameters $q$ and $p$. Finally, the second-order correlation function of a gas
of photons is calculated.


title:
Maxwell Electromagnetic Theory, Planck's Radiation Law and Bose-Einstein
  Statistics

abstract:
  We give an example in which it is possible to understand quantum statistics
using classical concepts. This is done by studying the interaction of charged
matter oscillators with the thermal and zeropoint electromagnetic fields
characteristic of quantum electrodynamics and classical stochastic
electrodynamics. Planck's formula for the spectral distribution and the
elements of energy $ \hbar\omega $ are interpreted without resorting to
discontinuities. We also show the aspects in which our model calculation
complement other derivations of blackbody radiation spectrum without quantum
assumptions.


title:
Testing temporal Bell inequalities through repeated measurements in
  rf-SQUIDs

abstract:
  Temporal Bell-like inequalities are derived taking into account the influence
of the measurement apparatus on the observed magnetic flux in a rf-SQUID.
Quantum measurement theory is shown to predict violations of these inequalities
only when the flux states corresponding to opposite current senses are not
distinguishable. Thus rf-SQUIDs cannot help to discriminate realism and quantum
mechanics at the macroscopic level.


title: Chaos in the Quantum Measurement Record

abstract:
  We investigate measures of chaos in the measurement record of a quantum
system which is being observed. Such measures are attractive because they can
be directly connected to experiment. Two measures of chaos in the measurement
record are defined and investigated numerically for the case of a quantum
kicked top. A smooth transition between chaotic and regular behavior is found.


title:
Polynomial Lie Algebras $sl_{pd}(2)$ in Action: Smooth $sl(2)$ Mappings
  and Approximations

abstract:
  We examine applications of polynomial Lie algebras $sl_{pd}(2)$ to solve
physical tasks in $G_{inv}$-invariant models of coupled subsystems in quantum
physics. A general operator formalism is given to solve spectral problems using
expansions of generalized coherent states, eigenfunctions and other physically
important quantities by power series in the $sl_{pd}(2)$ coset generators
$V_{\pm}$. We also discuss some mappings and approximations related to the
familiar $sl(2)$ algebra formalism. On this way a new closed analytical
expression is found for energy spectra which coincides with exact solutions in
certain cases and, in general, manifests an availability of incommensurable
eigenfrequencies related to a nearly chaotic dynamics of systems under study.


title: On the Problem of Chaos Conservation in Quantum Physics

abstract:
  We develop a new method of constructing a large N asymptotic series in powers
of $N^{-1/2}$ for the function of N arguments which is a solution to the Cauchy
problem for the equation of a special type. Many-particle Wigner,
Schr\"{o}dinger and Liouville equations for a system of a large number of
particles are of this type, when the external potential is of order O(1), while
the coefficient of the particle interaction potential is 1/N; the potentials
can be arbitrary smooth bounded functions. We apply this method to equations
for N-particle states corresponding to the N-th tensor power of an abstract
Hamiltonian algebra of observables. In particular, we show for the case of
multiparticle Schr\"{o}dinger-like equations that the property of N-particle
wave function to be approximately equal at large N to the product of
one-particle wave functions does not conserve under time evolution, while the
same property for the correlation functions of the finite order is known to
conserve(such hypothesis being the quantum analog of the chaos conservation
hypothesis put forward by M.Kac in 1956 was proved by the analysis of the
BBGKY-like hierarchy of equations). In order to find a leading asymptotics for
the N-particle wave function, one should use not only the solution to the well-
known Hartree equation being derivable from the BBGKY approach but also the
solution to another (Riccati-type) equation presented in this paper. We also
consider another interesting case when one adds to the N-particle system under
consideration one more particle interacting with the system with the
coefficient of the interaction potential of order O(1).It happens that in this
case one should investigate not a single Hartree-like equation but a set of
such equations, and the chaos will not conserve even for the correlators.


title: Projection Postulate and Atomic Quantum Zeno Effect

abstract:
  The projection postulate has been used to predict a slow-down of the time
evolution of the state of a system under rapidly repeated measurements, and
ultimately a freezing of the state. To test this so-called quantum Zeno effect
an experiment was performed by Itano et al. (Phys. Rev. A 41, 2295 (1990)) in
which an atomic-level measurement was realized by means of a short laser pulse.
The relevance of the results has given rise to controversies in the literature.
In particular the projection postulate and its applicability in this experiment
have been cast into doubt. In this paper we show analytically that for a wide
range of parameters such a short laser pulse acts as an effective level
measurement to which the usual projection postulate applies with high accuracy.
The corrections to the ideal reductions and their accumulation over n pulses
are calculated. Our conclusion is that the projection postulate is an excellent
pragmatic tool for a quick and simple understanding of the slow-down of time
evolution in experiments of this type. However, corrections have to be
included, and an actual freezing does not seem possible because of the finite
duration of measurements.


title: Quantum State Diffusion and Time Correlation Functions

abstract:
  In computing the spectra of quantum mechanical systems one encounters the
Fourier transforms of time correlation functions, as given by the quantum
regression theorem for systems described by master equations. Quantum state
diffusion (QSD) gives a useful method of solving these problems by unraveling
the master equation into stochastic trajectories; but there is no generally
accepted definition of a time correlation function for a single QSD trajectory.
In this paper we show how QSD can be used to calculate these spectra directly;
by formally solving the equations which arise, we arrive at a natural
definition for a two-time correlation function in QSD, which depends explicitly
on both the stochastic noise of the particular trajectory and the time of
measurement, and which agrees in the mean with the ensemble average definition
of correlation functions.


title: Time-Reversal and Irreversibility

abstract:
  The time reversal and irreversibility in conventional quantum mechanics are
compared with those of the rigged Hilbert space quantum mechanics. We discuss
the time evolution of Gamow and Gamow-Jordan vectors and show that the rigged
Hilbert space case admits a new kind of irreversibility which does not appear
in the conventional case. The origin of this irreversibility can be traced back
to different initial-boundary conditions for the states and observables. It is
shown that this irreversibility does not contradict the experimentally tested
consequences of the time-reversal invariance of the conventional case but
instead we have to introduce a new time reversal operator.


title: Semiclassical Density Matrix Near the Top of a Barrier

abstract:
  Employing the path integral approach, we calculate the semiclassical
equilibrium density matrix of a particle moving in a nonlinear potential field
for coordinates near the top of a potential barrier. As the temperature is
decreased, near a critical temperature $T_c$ the harmonic approximation for the
fluctuation path integral fails. This is due to a caustic arising at a
bifurcation point of the classical paths. We provide a selfconsistent scheme to
treat the large quantum fluctuations leading to a nonlinear fluctuation
potential. The procedure differs from methods used near caustics of the real
time propagator. The semiclassical density matrix is determined explicitly for
the case of asymmetric barriers from high temperatures down to temperatures
somewhat below $T_c$.
  Pacs: 03.65.Sq, 05.30.-d


title: On the quantum probability flux through surfaces

abstract:
  We remark that the often ignored quantum probability current is fundamental
for a genuine understanding of scattering phenomena and, in particular, for the
statistics of the time and position of the first exit of a quantum particle
from a given region, which may be simply expressed in terms of the current.
This simple formula for these statistics does not appear as such in the
literature. It is proposed that the formula, which is very different from the
usual quantum mechanical measurement formulas, be verified experimentally. A
full understanding of the quantum current and the associated formula is
provided by Bohmian mechanics.


title:
Dynamic Polarization of the LiH Molecule in Strong Light Field in
  Anomalous-Dispersion Domain

abstract:
  A new method is proposed to calculate the polarization vector of a molecule
in a monochromatic external field in the anomalous-despersion domain. The
method takes into account the instantaneous switching of the field. A simple
modification of the method allows one to consider a more general switching
procedure. As an illustration of the method Fourier components of the
polarization vector of the LiH molecule in the anomalous -dispersion domain is
calculated.


title: Quantum Hamilton-Jacobi formalism and the bound state spectra

abstract:
  It is well known in classical mechanics that, the frequencies of a periodic
system can be obtained rather easily through the action variable, without
completely solving the equation of motion. The equivalent quantum action
variable appearing in the quantum Hamilton-Jacobi formalism, can, analogously
provide the energy eigenvalues of a bound state problem, without having to
solve the corresponding Schr\"odinger equation explicitly. This elegant and
useful method is elucidated here in the context of some known and not so well
known solvable potentials. It is also shown, how this method provides an
understanding, as to why approximate quantization schemes such as ordinary and
supersymmetric WKB, can give exact answers for certain potentials.


title: On Exactness Of The Supersymmetric WKB Approximation Scheme

abstract:
  Exactness of the lowest order supersymmetric WKB (SWKB) quantization
condition $\int^{x_2}_{x_1} \sqrt{E-\omega^2(x)} dx = n \hbar \pi$, for certain
potentials, is examined, using complex integration technique. Comparison of the
above scheme with a similar, but {\it exact} quantization condition, $\oint_c
p(x,E) dx = 2\pi n \hbar$, originating from the quantum Hamilton-Jacobi
formalism reveals that, the locations and the residues of the poles that
contribute to these integrals match identically, for both of these cases. As
these poles completely determine the eigenvalues in these two cases, the
exactness of the SWKB for these potentials is accounted for. Three non-exact
cases are also analysed; the origin of this non-exactness is shown to be due
the presence of additional singularities in $\sqrt{E-\omega^2(x)}$, like branch
cuts in the $x-$plane.


title:
Characterisations of Classical and Non-classical states of Quantised
  Radiation

abstract:
  A new operator based condition for distinguishing classical from
non-classical states of quantised radiation is developed. It exploits the fact
that the normal ordering rule of correspondence to go from classical to quantum
dynamical variables does not in general maintain positivity. It is shown that
the approach naturally leads to distinguishing several layers of increasing
nonclassicality, with more layers as the number of modes increases. A
generalisation of the notion of subpoissonian statistics for two-mode radiation
fields is achieved by analysing completely all correlations and fluctuations in
quadratic combinations of mode annihilation and creation operators conserving
the total photon number. This generalisation is nontrivial and intrinsically
two-mode as it goes beyond all possible single mode projections of the two-mode
field. The nonclassicality of pair coherent states, squeezed vacuum and
squeezed thermal states is analysed and contrasted with one another, comparing
the generalised subpoissonian statistics with extant signatures of nonclassical
behaviour.


title:
A Non-critical String (Liouville) Approach to Brain Microtubules: State
  Vector reduction, Memory coding and Capacity

abstract:
  Microtubule (MT) networks, subneural paracrystalline cytosceletal structures,
seem to play a fundamental role in the neurons. We cast here the complicated MT
dynamics in the form of a $1+1$-dimensional non-critical string theory, thus
enabling us to provide a consistent quantum treatment of MTs, including
enviromental {\em friction} effects. Quantum space-time effects, as described
by non-critical string theory, trigger then an {\em organized collapse} of the
coherent states down to a specific or {\em conscious state}. The whole process
we estimate to take ${\cal O}(1\,{\rm sec})$. The {\em microscopic arrow of
time}, endemic in non-critical string theory, and apparent here in the
self-collapse process, provides a satisfactory and simple resolution to the
age-old problem of how the, central to our feelings of awareness, sensation of
the progression of time is generated. In addition, the complete integrability
of the stringy model for MT we advocate in this work proves sufficient in
providing a satisfactory solution to memory coding and capacity. Such features
might turn out to be important for a model of the brain as a quantum computer.


title: Negative entropy and information in quantum mechanics

abstract:
  A framework for a quantum mechanical information theory is introduced that is
based entirely on density operators, and gives rise to a unified description of
classical correlation and quantum entanglement. Unlike in classical (Shannon)
information theory, quantum (von Neumann) conditional entropies can be negative
when considering quantum entangled systems, a fact related to quantum
non-separability. The possibility that negative (virtual) information can be
carried by entangled particles suggests a consistent interpretation of quantum
informational processes.


title:
Quantum State Disturbance vs. Information Gain: Uncertainty Relations
  for Quantum Information

abstract:
  When an observer wants to identify a quantum state, which is known to be one
of a given set of non-orthogonal states, the act of observation causes a
disturbance to that state. We investigate the tradeoff between the information
gain and that disturbance. This issue has important applications in quantum
cryptography. The optimal detection method, for a given tolerated disturbance,
is explicitly found in the case of two equiprobable non-orthogonal pure states.


title: Consistent Histories and Operational Quantum Physics

abstract:
  In this work a generalization of the consistent histories approach to quantum
mechanics is presented. We first critically review the consistent histories
approach to nonrelativistic quantum mechanics in a mathematically rigorous way
and give some general comments about it. We investigate to what extent the
consistent histories scheme is compatible with the results of the operational
formulation of quantum mechanics. According to the operational approach
nonrelativistic quantum mechanics is most generally formulated in terms of
effects, states and operations. We formulate a generalized consistent histories
theory using the concepts and the terminology which have proven useful in the
operational formulation of quantum mechanics. The logical rule of the logical
interpretation of quantum mechanics is generalized to the present context. The
algebraic structure of the generalized theory is studied in detail.


title:
Phase Space Localization and Approach to Thermal Equilibrium for a Class
  of Open Systems

abstract:
  We analyse the evolution of a quantum oscillator in a finite temperature
environment using the quantum state diffusion (QSD) picture. Following a
treatment similar to that of reference [7] we identify stationary solutions of
the corresponding It\^o equation. We prove their global stability and compute
typical time scales characterizing the localization process. The recovery of
the density matrix in approximately diagonal form enables us to verify the
approach to thermal equilibrium in the long time limit and we comment on the
connection between QSD and the decoherent histories approach.


title: A simple quantum oblivious transfer protocol

abstract:
  A simple and efficient protocol for quantum oblivious transfer is proposed.
The protocol can easily be implemented with present technology and is secure
against cheaters with unlimited computing power provided the receiver does not
have the technology to store the particles for an arbitrarily long period of
time. The proposed protocol is a significant improvement over the previous
protocols. Unlike the protocol of Cr\'epeau and Kilian which is secure if only
if the spin of the particle is measured along the $x$ or the $y$ axis, the
present protocol is perfectly secure no matter along which axes the spin of the
particles are measured, and unlike the protocol of Bennett et al. which
requires tens of thousand of particles, the present protocol requires only two
particles.


title: Bohmian Mechanics and the Quantum Revolution

abstract:
  This is a review-essay on ``Speakable and Unspeakable in Quantum Mechanics''
by John Bell and ``The Undivided Universe: An Ontological Interpretation of
Quantum Mechanics'' by David Bohm and Basil Hiley. The views of these authors
concerning the character of quantum theory and quantum reality---and, in
particular, their approaches to the issues of nonlocality, the possibility of
hidden variables, and the nature of and desiderata for a satisfactory
scientific explanation of quantum phenomena---are contrasted, with each other
and with the orthodox approach to these issues.


title:
Does the Wave Function Provide a Complete Description of Physical
  Reality?

abstract:
  This is the introduction to the section on Quantum Mechanics in the
centennial collection of noteworthy articles appearing in The Physical Review
and Physical Review Letters through 1983, since it all began in 1893. The
selections for this section are "Can Quantum-Mechanical Description of Physical
Reality Be Considered Complete?" by Einstein, Podolsky and Rosen; Bohr's
response, with the same title; Bohm's first hidden variables paper: "A
Suggested Interpretation of the Quantum Theory in Terms of `Hidden' Variables.
I"; Aharonov and Bohm's "Significance of Electromagnetic Potentials in the
Quantum Theory"; and "Experimental Test of Bell's Inequalities Using
Time-Varying Analyzers" by Aspect, Dalibard and Roger.


title: Geometric Phases, Coherent States and Resonant Hamiltonian

abstract:
  We study characteristic aspects of the geometric phase which is associated
with the generalized coherent states. This is determined by special orbits in
the parameter space defining the coherent state, which is obtained as a
solution of the variational equation governed by a simple model Hamiltonian
called the "resonant Hamiltonian". Three typical coherent states are
considered: SU(2), SU(1,1) and Heisenberg-Weyl. A possible experimental
detection of the phases is proposed in such a way that the geometric phases can
be discriminated from the dynamical phase.


title: Minimum-Uncertainty Angular Wave Packets and Quantized Mean Values

abstract:
  Uncertainty relations between a bounded coordinate operator and a conjugate
momentum operator frequently appear in quantum mechanics. We prove that
physically reasonable minimum-uncertainty solutions to such relations have
quantized expectation values of the conjugate momentum. This implies, for
example, that the mean angular momentum is quantized for any
minimum-uncertainty state obtained from any uncertainty relation involving the
angular-momentum operator and a conjugate coordinate. Experiments specifically
seeking to create minimum-uncertainty states localized in angular coordinates
therefore must produce packets with integer angular momentum.


title: Bohmian Mechanics and the Meaning of the Wave Function

abstract:
  We outline how Bohmian mechanics works: how it deals with various issues in
the foundations of quantum mechanics and how it is related to the usual quantum
formalism. We then turn to some objections to Bohmian mechanics, for example
the fact that in Bohmian mechanics there is no back action of particle
configurations upon wave functions. These lead us to our main concern: a more
careful consideration of the meaning of the wave function in quantum mechanics,
as suggested by a Bohmian perspective. We propose that the reason, on the
universal level, that there is no action of configurations upon wave functions,
as there seems to be between all other elements of physical reality, is that
the wave function of the universe is not an element of physical reality. We
propose that the wave function belongs to an altogether different category of
existence than that of substantive physical entities, and that its existence is
nomological rather than material. We propose, in other words, that the wave
function is a component of physical law rather than of the reality described by
the law.


title: Good Quantum Error-Correcting Codes Exist

abstract:
  A quantum error-correcting code is defined to be a unitary mapping (encoding)
of k qubits (2-state quantum systems) into a subspace of the quantum state
space of n qubits such that if any t of the qubits undergo arbitrary
decoherence, not necessarily independently, the resulting n qubits can be used
to faithfully reconstruct the original quantum state of the k encoded qubits.
Quantum error-correcting codes are shown to exist with asymptotic rate k/n = 1
- 2H(2t/n) where H(p) is the binary entropy function -p log p - (1-p) log
(1-p). Upper bounds on this asymptotic rate are given.


title:
Comment on ``Quantum Phase of Induced Dipoles Moving in a Magnetic
  Field''

abstract:
  It has recently been suggested that an Aharonov-Bohm phase should be capable
of detection using beams of neutral polarizable particles. A more careful
analysis of the proposed experiment suffices to show, however, that it cannot
be performed regardless of the strength of the external electric and magnetic
fields.


title:
Quantum Mechanics as a Classical Theory X: Quantization in Generalized
  Coordinates

abstract:
  In this tenth paper of the series we aim at showing that our formalism, using
the Wigner-Moyal Infinitesimal Transformation together with classical
mechanics, endows us with the ways to quantize a system in any coordinate
representation we wish. This result is necessary if one even think about making
general relativistic extensions of the quantum formalism. Besides, physics
shall not be dependent on the specific representation we use and this result is
necessary to make quantum theory consistent and complete.


title: Particle Path Formulation of Quantum Mechanics

abstract:
  An extension of the classical action principle obtained in the framework of
the gauge transformations, is used to describe the motion of a particle. This
extension assigns many, but not all, paths to a particle. Properties of the
particle paths are shown to impart wave like behaviour to a particle in motion
and to imply various other assumptions and conjectures attributed to the
formalism of Quantum Mechanics. The Klein-Gordon and other similar equations
are derived by incorporating these properties in the path-integral formalism.


title: Decoherence of Hydrodynamic Histories: A Simple Spin Model

abstract:
  In the context of the decoherent histories approach to the quantum mechanics
of closed systems, Gell-Mann and Hartle have argued that the variables
typically characterizing the quasiclassical domain of a large complex system
are the integrals over small volumes of locally conserved densities --
hydrodynamic variables. The aim of this paper is to exhibit some simple models
in which approximate decoherence arises as a result of local conservation. We
derive a formula which shows the explicit connection between local conservation
and approximate decoherence. We then consider a class of models consisting of a
large number of weakly interacting components, in which the projections onto
local densities may be decomposed into projections onto one of two alternatives
of the individual components. The main example we consider is a one-dimensional
chain of locally coupled spins, and the projections are onto the total spin in
a subsection of the chain. We compute the decoherence functional for histories
of local densities, in the limit when the number of components is very large.
We find that decoherence requires two things: the smearing volumes must be
sufficiently large to ensure approximate conservation, and the local densities
must be partitioned into sufficiently large ranges to ensure protection against
quantum fluctuations.


title: Weak-Measurement Elements of Reality

abstract:
  A brief review of the attempts to define ``elements of reality'' in the
framework of quantum theory is presented. It is noted that most definitions of
elements of reality have in common the feature to be a definite outcome of some
measurement. Elements of reality are extended to pre- and post-selected systems
and to measurements which fulfill certain criteria of weakness of the coupling.
Some features of the newly introduced concepts are discussed.


title:
On the Nature of the Change in the Wave Function in a Measurement in
  Quantum Mechanics

abstract:
  Generally a central role has been assigned to an unavoidable physical
interaction between the measuring instrument and the physical entity measured
in the change in the wave function that often occurs in measurement in quantum
mechanics. A survey of textbooks on quantum mechanics by authors such as Dicke
and Witke (1960), Eisberg and Resnick (1985), Gasiorowicz (1974), Goswami
(1992), and Liboff (1993) supports this point. Furthermore, in line with the
view of Bohr and Feynman, generally the unavoidable interaction between a
measuring instrument and the physical entity measured is considered responsible
for the uncertainty principle. A gedankenexperiment using Feynman's double-hole
interference scenario shows that physical interaction is not necessary to
effect the change in the wave function that occurs in measurement in quantum
mechanics. Instead, the general case is that knowledge is linked to the change
in the wave function, not a physical interaction between the physical existent
measured and the measuring instrument. Empirical work on electron shelving that
involves null measurements, or what Renninger called negative observations
(Zeitschrift fur Physik, vol. 158, p. 417), supports these points. Work on
electron shelving is reported by Dehmelt and his colleagues (Physical Review
Letters, vol. 56, p. 2797), Wineland and his colleagues (Physical Review
Letters, vol. 57, p. 1699), and Sauter, Neuhauser, Blatt, and Toschek (Physical
Review Letters, vol. 57, p. 1696).


title: Quantum Philosophy: The Flight from Reason in Science

abstract:
  This is a talk concerning the irrationality of prominent physicists with
regard to the foundations of quantum mechanics, delivered at a conference on
the irrationality of the postmodern attack on science by nonscientists.


title: Pole_Factorization Theorem in Quantum Electrodynamics

abstract:
  In quantum electrodynamics a classical part of the S-matrix is normally
factored out in order to obtain a quantum remainder that can be treated
perturbatively without the occurrence of infrared divergences. However, this
separation, as usually performed, introduces spurious large-distance effects
that produce an apparent breakdown of the important correspondence between
stable particles and poles of the S-matrix, and, consequently, lead to apparent
violations of the correspondence principle and to incorrect results for
computations in the mesoscopic domain lying between the atomic and classical
regimes. An improved computational technique is described that allows valid
results to be obtained in this domain, and that leads, for the quantum
remainder, in the cases studied, to a physical-region singularity structure
that, as regards the most singular parts, is the same as the normal
physical-region analytic structure in theories in which all particles have
non-zero mass. The key innovations are to define the classical part in
coordinate space, rather than in momentum space, and to define there a
separation of the photon-electron coupling into its classical and quantum parts
that has the following properties: 1) The contributions from the terms
containing only classical couplings can be summed to all orders to give a
unitary operator that generates the coherent state that corresponds to the
appropriate classical process, and 2) The quantum remainder can be rigorously
shown to exhibit, as regards its most singular parts, the normal analytic
structure.


title: Quantum statistics of trapped bosons

abstract:
  The computer code on which this paper relied contained an error. When
corrected, the Monte Carlo evaluation of the ground state occupation is
consistent with the conventional grand canonical calculation. Hence, the
original version of this paper has been withdrawn.


title:
Stochastic Schr\"odinger equation from an interaction with the
  environment

abstract:
  We consider a class of models describing a quantum oscillator in interaction
with an environment. We show that models of continuous spontaneous localization
based on a stochastic Schr\"odinger equation can be derived as an approximation
to purely deterministic Hamiltonian systems. We show an exponential decay of
off-diagonal matrix elements in the energy representation.


title: Introducing spin to classical phase space

abstract:
  The kinematic degrees of freedom of spinning particles are analyzed and an
explicit construction of the phase space and the simplectic structure that
accomodates them is presented. A Poincare invariant theory of classical
spinning particles that generalizes the work of Proca and Barut to arbitrary
spin is given using spinor variables. Second quantization is naturally
connected to the unphysical nature of zitterbewegung. Position variables can
not be disentangled from spin in a canonical way, nor can the phase space be
reduced to the usual description $(x,p)$ and a vector spin.
  Pacs: 03.20.+i, 03.65.Sq, 03.30.+p, 11.30.Cp


title: Considerations on Localization of Macroscopic Bodies

abstract:
  Position holds a very special role in understanding the classical behaviour
of macroscopic bodies on the basis of quantum principles. This lead us to
examine the localised states of a large condensed object in the context of a
realistic model. Following the argument that an isolated macroscopic body is
usually described by a linear superposition of low-lying energy eigenstates, it
has been found that localised states of this type correspond to a nearly
minimum-uncertainty state for the center of mass. An indication is also given
of the dependence of the center of mass position spread on the number of
constituent particles.
  This paper is not offered as an answer to the intriguing question of the
preferred role played by the position basis, but will hopefully provide some
contribution to the quantum modelling of multi-particle systems.


title: Naive Realism about Operators

abstract:
  A source of much difficulty and confusion in the interpretation of quantum
mechanics is a ``naive realism about operators.'' By this we refer to various
ways of taking too seriously the notion of operator-as-observable, and in
particular to the all too casual talk about ``measuring operators'' that occurs
when the subject is quantum mechanics. Without a specification of what should
be meant by ``measuring'' a quantum observable, such an expression can have no
clear meaning. A definite specification is provided by Bohmian mechanics, a
theory that emerges from Sch\"rodinger's equation for a system of particles
when we merely insist that ``particles'' means particles. Bohmian mechanics
clarifies the status and the role of operators as observables in quantum
mechanics by providing the operational details absent from standard quantum
mechanics. It thereby allows us to readily dismiss all the radical claims
traditionally enveloping the transition from the classical to the quantum
realm---for example, that we must abandon classical logic or classical
probability. The moral is rather simple: Beware naive realism, especially about
operators!


title:
Manifestly Covariant Approach to Bargmann-Wigner Fields (I): Generalized
  scalar products and Wigner states

abstract:
  Manifestly covariant formalism for Bargmann-Wigner fields is developed.
  It is shown that there exists some freedom in the choice of the form of the
Bargmann-Wigner scalar product: The general product depends implicitly on a
family of world-vectors. The standard choice of the product corresponds to
timelike and equal vectors which define a ``time" direction. The generalized
form shows that formulas are simpler if one chooses {\it null\/} directions.
This freedom is used to derive simple covariant formulas for momentum-space
wave functions (generalized Wigner states) corresponding to arbitrary mass and
spin and using eigenstates of the Pauli-Lubanski vector. The eigenstates which
make formulas the simplest correspond to projections of the Pauli-Lubanski
vector on {\it null\/} directions. The new formulation is an alternative to the
standard helicity formalism.


title: Nambu-Type Generalization of the Dirac Equation

abstract:
  Nonlinear generalization of the Dirac equation extending the standard
paradigm of nonlinear Hamiltonians is discussed. ``Faster-than-light
telegraphs" are absent for all theories formulated within the new framework. A
new metric for infinite dimensional Lie algebras associated with Lie-Poisson
dynamics is introduced.


title:
Comment on "Why quantum mechanics cannot be formulated as a Markov
  process"

abstract:
  In the paper with the above title, D. T. Gillespie [Phys. Rev. A 49, 1607,
(1994)] claims that the theory of Markov stochastic processes cannot provide an
adequate mathematical framework for quantum mechanics. In conjunction with the
specific quantum dynamics considered there, we give a general analysis of the
associated dichotomic jump processes. If we assume that Gillespie's
"measurement probabilities" \it are \rm the transition probabilities of a
stochastic process, then the process must have an invariant (time independent)
probability measure. Alternatively, if we demand the probability measure of the
process to follow the quantally implemented (via the Born statistical
postulate) evolution, then we arrive at the jump process which \it can \rm be
interpreted as a Markov process if restricted to a suitable duration time.
However, there is no corresponding Markov process consistent with the $Z_2$
event space assumption, if we require its existence for all times $t\in R_+$.


title: An Evolutionary Picture for Quantum Physics

abstract:
  In the orthodox language of Quantum Mechanics the observer occupies a central
position and the only "real events" are the measuring results. We argue here
that this narrow view is not forced upon us by the lessons of Quantum Physics.
An alternative language, closer to the intuitive picture of the working
physicist in many areas, is not only possible but warranted. It needs, however,
a different conceptual picture ultimately implying also a different
mathematical structure. Only a rudimentary outline of this picture will be
attempted here. The importance of idealizations, unavoidable in any scheme, is
emphasized. A brief discussion of the EPR-phenomenon is added.


title: Approximate Quantum Fourier Transform and Decoherence

abstract:
  We discuss the advantages of using the approximate quantum Fourier transform
(AQFT) in algorithms which involve periodicity estimations. We analyse quantum
networks performing AQFT in the presence of decoherence and show that extensive
approximations can be made before the accuracy of AQFT (as compared with
regular quantum Fourier transform) is compromised. We show that for some
computations an approximation may imply a better performance.


title: Darboux-Witten techniques for the Demkov-Ostrovsky problem

abstract:
  The bosonic strictly isospectral problem for Demkov-Ostrovsky (DO) effective
potentials in the radially nodeless sector is first solved in the
supersymmetric Darboux-Witten (DW) half line (or l-changing) procedure. As an
application, for the \kappa =1 class, if one goes back to optics examples, it
might be possible to think of a one-parameter family of Maxwell lenses having
the same optical scattering properties in the nodeless radial sector. Although
the relative changes in the index of refraction that one may introduce in this
way are at the level of several percents, at most, for all DO orbital quantum
numbers l\geq 0, the index profiles are different from the original Maxwell
one, possessing an inflection point within the lens. I pass then to the DW full
line (or N-changing) procedure, obtaining the corresponding Morse-type problem
for which the supersymmetric results are well established, and finally come
back to the half line with well-defined results


title: Distinguishability and Accessible Information in Quantum Theory

abstract:
  This document focuses on translating various information-theoretic measures
of distinguishability for probability distributions into measures of distin-
guishability for quantum states. These measures should have important appli-
cations in quantum cryptography and quantum computation theory. The results
reported include the following. An exact expression for the quantum fidelity
between two mixed states is derived. The optimal measurement that gives rise to
it is studied in detail. Several upper and lower bounds on the quantum mutual
information are derived via similar techniques and compared to each other. Of
note is a simple derivation of the important upper bound first proved by Holevo
and an explicit expression for another (tighter) upper bound that appears
implicitly in the same derivation. Several upper and lower bounds to the quan-
tum Kullback relative information are derived. The measures developed are also
applied to ferreting out the extent to which quantum systems must be disturbed
by information gathering measurements. This is tackled in two ways. The first
is in setting up a general formalism for describing the tradeoff between
inference and disturbance. The main point of this is that it gives a way of
expressing the problem so that it appears as algebraic as that of the problem
of finding quantum distinguishability measures. The second result on this theme
is a theorem that prohibits "broadcasting" an unknown (mixed) quantum state.
That is to say, there is no way to replicate an unknown quantum state onto two
separate quantum systems when each system is considered without regard to the
other. This includes the possibility of correlation or quantum entanglement
between the systems. This result is a significant extension and generalization
of the standard "no-cloning" theorem for pure states.


title: Factoring in a Dissipative Quantum Computer

abstract:
  We describe an array of quantum gates implementing Shor's algorithm for prime
factorization in a quantum computer. The array includes a circuit for modular
exponentiation with several subcomponents (such as controlled multipliers,
adders, etc) which are described in terms of elementary Toffoli gates. We
present a simple analysis of the impact of losses and decoherence on the
performance of this quantum factoring circuit. For that purpose, we simulate a
quantum computer which is running the program to factor N = 15 while
interacting with a dissipative environment. As a consequence of this
interaction randomly selected qubits may spontaneously decay. Using the results
of our numerical simulations we analyze the efficiency of some simple error
correction techniques.


title:
Impulsive quantum measurements: restricted path integral versus von
  Neumann collapse

abstract:
  The relation between the restricted path integral approach to quantum
measurement theory and the commonly accepted von Neumann wavefunction collapse
postulate is presented. It is argued that in the limit of impulsive
measurements the two approaches lead to the same predictions. The example of
repeated impulsive quantum measurements of position performed on a harmonic
oscillator is discussed in detail and the quantum nondemolition strategies are
recovered in both the approaches.


title: Correlated states and Schr\"odinger cats

abstract:
  The Schr\"odinger cat male and female states are discussed. The Wigner and
Q--functions of generalized correlated light are given. Linear transformator of
photon statistics is reviewed.


title: Interaction time of a wave packet interact with a potential barrier

abstract:
  We study the evolution of a wave packet impinging onto a one dimensional
potential barrier. The transmission and reflection times discussed in the
literature for stationary states do not correspond to the times required for
the emergence of a transmitted or a reflected packet. We propose new
definitions for the interaction (dwell) time and the transmission and
reflection times which are suitable for packets and fit better the actual time
evolution of the packet.


title: Quantum information: How much information in a state vector?

abstract:
  Quantum information refers to the distinctive information-processing
properties of quantum systems, which arise when information is stored in or
retrieved from nonorthogonal quantum states. More information is required to
prepare an ensemble of nonorthogonal quantum states than can be recovered from
the ensemble by measurements. Nonorthogonal quantum states cannot be
distinguished reliably, cannot be copied or cloned, and do not lead to exact
predictions for the results of measurements. These properties contrast sharply
with those of information stored in the microstates of a classical system.


title: Isospectral Hamiltonians and $W_{1+\infty}$ algebra

abstract:
  We discuss a spectrum generating algebra in the supersymmetric quantum
mechanical system which is defined as a series of solutions to a specific
differential equation. All Hamiltonians have equally spaced eigenvalues, and we
realize both positive and negative mode generators of a subalgebra of
$W_{1+\infty}$ without use of negative power of raising/lowering operators of
the system. All features in the supersymmetric case are generalized to the
parasupersymmetric systems of order 2.


title: Light scattering off cold, trapped bosons

abstract:
  The computer code on which this paper relied contained an error. When
corrected, the Monte Carlo evaluation of the ground state occupation is
consistent with the conventional grand canonical calculation. Hence, the
original version of this paper has been withdrawn.


title: Ideal Bose gas limit of trapped atoms


title: Multiple Particle Interference and Quantum Error Correction

abstract:
  The concept of multiple particle interference is discussed, using insights
provided by the classical theory of error correcting codes. This leads to a
discussion of error correction in a quantum communication channel or a quantum
computer. Methods of error correction in the quantum regime are presented, and
their limitations assessed. A quantum channel can recover from arbitrary
decoherence of x qubits if K bits of quantum information are encoded using n
quantum bits, where K/n can be greater than 1-2 H(2x/n), but must be less than
1 - 2 H(x/n). This implies exponential reduction of decoherence with only a
polynomial increase in the computing resources required. Therefore quantum
computation can be made free of errors in the presence of physically realistic
levels of decoherence. The methods also allow isolation of quantum
communication from noise and evesdropping (quantum privacy amplification).


title: Universal Superpositions of Coherent States and Self-Similar Potentials

abstract:
  A variety of coherent states of the harmonic oscillator is considered. It is
formed by a particular superposition of canonical coherent states. In the
simplest case, these superpositions are eigenfunctions of the annihilation
operator $A=P(d/dx+x)/\sqrt2$, where $P$ is the parity operator. Such $A$
arises naturally in the $q\to -1$ limit for a symmetry operator of a specific
self-similar potential obeying the $q$-Weyl algebra, $AA^\dagger-q^2A^\dagger
A=1$. Coherent states for this and other reflectionless potentials whose
discrete spectra consist of $N$ geometric series are analyzed. In the harmonic
oscillator limit the surviving part of these states takes the form of
orthonormal superpositions of $N$ canonical coherent states
$|\epsilon^k\alpha\rangle$, $k=0, 1, \dots, N-1$, where $\epsilon$ is a
primitive $N$th root of unity, $\epsilon^N=1$. A class of $q$-coherent states
related to the bilateral $q$-hypergeometric series and Ramanujan type integrals
is described. It includes a curious set of coherent states of the free
nonrelativistic particle which is interpreted as a $q$-algebraic system without
discrete spectrum. A special degenerate form of the symmetry algebras of
self-similar potentials is found to provide a natural $q$-analog of the Floquet
theory. Some properties of the factorization method, which is used throughout
the paper, are discussed from the differential Galois theory point of view.

categories: quant-ph cond-mat hep-th math.QA nlin.SI q-alg solv-int


title: Hypercomplex quantum mechanics

abstract:
  The fundamental axioms of the quantum theory do not explicitly identify the
algebraic structure of the linear space for which orthogonal subspaces
correspond to the propositions (equivalence classes of physical questions). The
projective geometry of the weakly modular orthocomplemented lattice of
propositions may be imbedded in a complex Hilbert space; this is the structure
which has traditionally been used. This paper reviews some work which has been
devoted to generalizing the target space of this imbedding to Hilbert modules
of a more general type. In particular, detailed discussion is given of the
simplest generalization of the complex Hilbert space, that of the quaternion
Hilbert module.


title: Method for Detecting Berry's Phase in a Modified Paul Trap

abstract:
  We modify the time-dependent electric potential of the Paul trap from a
sinusoidal waveform to a square waveform. The exact quantum motion and the
Berry's phase of an electron in the modified Paul trap are found in an
analytically closed form. We consider a scheme to detect the Berry's phase by a
Bohm-Aharonov-type interference experiment and point out a critical property
which renders it practicable.


title: Factorization, ladder operators and isospectral structures

abstract:
  Using the modified factorization method employed by Mielnik for the harmonic
oscillator, we show that isospectral structures associated with a second order
operator $H$, can always be constructed whenever $H$ could be factored, or
exist ladder operators for its eigenfunctions. Three examples are shown, and
properties like completeness and integrability are discused for the general
case.


title: Time-Frequency Transfer with Quantum Fields

abstract:
  Clock synchronisation relies on time-frequency transfer procedures which
involve quantum fields. We use the conformal symmetry of such fields to define
as quantum operators the time and frequency exchanged in transfer procedures
and to describe their transformation under transformations to inertial or
accelerated frames. We show that the classical laws of relativity are changed
when brought in the framework of quantum theory.


title: Supersymmetry and the Hartmann Potential of Theoretical Chemistry

abstract:
  The ring-shaped Hartmann potential $ V = \eta \sigma^{2} \epsilon_{0} \left(
\frac{2 a_{0}}{r} - \frac{\eta a_{0}^{2}}{r^{2} sin^{2} \theta} \right) $ was
introduced in quantum chemistry to describe ring-shaped molecules like benzene.
In this article, the supersymmetric features of the Hartmann potential are
discussed. We first review the results of a previous paper in which we
rederived the eigenvalues and radial eigenfunctions of the Hartmann potential
using a formulation of one-dimensional supersymmetric quantum mechanics
(SUSYQM) on the half-line $\left[ 0, \infty \right)$. A reformulation of SUSYQM
in the full line $\left( -\infty, \infty \right)$ is subsequently developed. It
is found that the second formulation makes a connection between states having
the same quantum number $L$ but different values of $\eta \sigma^{2}$ and
quantum number $N$. This is in contrast to the first formulation, which relates
states with identical values of the quantum number $N$ and $\eta \sigma^{2}$
but different values of the quantum number $L$.


title: What are quantum theorists doing at a conference on consciousness?

abstract:
  The reason why orthodox quantum theory necessarily invokes consciousness is
explained. Several procedures whereby the Born probability rule can be
introduced are discussed, and reasons are given for prefering one in which
consciousness selects a unique realised world. Consciousness is something
outside of the laws of physics (quantum mechanics), but it has a real effect
upon the experienced world. Finally, orthodox quantum theory is shown to
require that consciousness acts non-locally.


title: Radial Coulomb and Oscillator Systems in Arbitrary Dimensions

abstract:
  A mapping is obtained relating analytical radial Coulomb systems in any
dimension greater than one to analytical radial oscillators in any dimension.
This mapping, involving supersymmetry-based quantum-defect theory, is possible
for dimensions unavailable to conventional mappings. Among the special cases is
an injection from bound states of the three-dimensional radial Coulomb system
into a three-dimensional radial isotropic oscillator where one of the two
systems has an analytical quantum defect. The issue of mapping the continuum
states is briefly considered.


title:
Manifestly Covariant Approach to Bargmann-Wigner Fields (II): From
  spin-frames to Bargmann-Wigner spinors

abstract:
  The Bargmann-Wigner (BW) scalar product is a particular case of a larger
class of scalar products parametrized by a family of world-vectors. The choice
of null and $p$-dependent world-vectors leads to BW amplitudes which behave as
local $SU(2)$ spinors (BW-spinors) if {\it passive\/} transformations are
concerned. The choice of null directions leads to a simplified formalism which
allows for an application of ordinary, manifestly covariant spinor techniques
in the context of infinite dimensional unitary representations of the
Poincar\'e group.


title: Protective Measurements of Two-State Vectors

abstract:
  A recent result about measurability of a quantum state of a single quantum
system is generalized to the case of a single pre- and post-selected quantum
system described by a two-state vector. The protection required for such
measurement is achieved by coupling the quantum system to a pre- and
post-selected protected device yielding a nonhermitian effective Hamiltonian.


title: Time of Events in Quantum Theory

abstract:
  We enhance elementary quantum mechanics with three simple postulates that
enable us to define time observable. We discuss shortly justification of the
new postulates and illustrate the concept with the detailed analysis of a delta
function counter.

categories: quant-ph cond-mat funct-an gr-qc hep-th math.FA


title: Adiabatic Measurements on Metastable Systems

abstract:
  In several situations, most notably when describing metastable states, a
system can evolve according to an effective non hermitian Hamiltonian. To each
eigenvalue of a non hermitian Hamiltonian is associated an eigenstate
$\vert\phi\rangle$ which evolves forward in time and an eigenstate
$\langle{\psi}\vert$ which evolves backward in time. Quantum measurements on
such systems are analyzed in detail with particular emphasis on adiabatic
measurements in which the measuring device is coupled weakly to the system. It
is shown that in this case the outcome of the measurement of an observable $A$
is the weak value $\langle{\psi}\vert A\vert\phi\rangle /
\langle{\psi}\vert{\phi}\rangle $ associated to the two-state vector
$\langle{\psi}\vert$ $\vert\phi\rangle$ corresponding to one of the eigenvalues
of the non hermitian Hamiltonian. The possibility of performing such
measurements in a laboratory is discussed.


title: Non-linear Quantization of Integrable Classical Systems

abstract:
  It is demonstrated that the so-called "unavoidable quantum anomalies" can be
avoided in the farmework of a special non-linear quantization scheme. A simple
example is discussed in detail.


title:
Self-Adjoint Extensions of the Pauli Equation in the Presence of a
  Magnetic Monopole

abstract:
  We discuss the Hamiltonian for a nonrelativistic electron with spin in the
presence of an abelian magnetic monopole and note that it is not self-adjoint
in the lowest two angular momentum modes. We then use von Neumann's theory of
self-adjoint extensions to construct a self-adjoint operator with the same
functional form. In general, this operator will have eigenstates in which the
lowest two angular momentum modes mix, thereby removing conservation of angular
momentum. However, consistency with the solutions of the Dirac equation limits
the possibilities such that conservation of angular momentum is restored.
Because the same effect occurs for a spinless particle with a sufficiently
attractive inverse square potential, we also study this system. We use this
simpler Hamiltonian to compare the eigenfunctions corresponding to a particular
self-adjoint extension with the eigenfunctions satisfying a boundary condition
consistent with probability conservation.


title: New Trends in Quantum Computing

abstract:
  Classical and quantum information are very different. Together they can
perform feats that neither could achieve alone, such as quantum computing,
quantum cryptography and quantum teleportation. Some of the applications range
from helping to preventing spies from reading private communications. Among the
tools that will facilitate their implementation, we note quantum purification
and quantum error correction. Although some of these ideas are still beyond the
grasp of current technology, quantum cryptography has been implemented and the
prospects are encouraging for small-scale prototypes of quantum computation
devices before the end of the millennium.


title:
Analytical properties of scattering amplitudes in one-dimensional
  quantum theory

abstract:
  One-dimensional quantum scattering from a local potential barrier is
considered. Analytical properties of the scattering amplitudes have been
investigated by means of the integral equations equivalent to the Schrodinger
equations. The transition and reflection amplitudes are expressed in terms of
two complex functions of the incident energy, which are similar to the Jost
function in the partial-wave scattering. These functions are entire for
finite-range potentials and meromorphic for exponentially decreasing
potentials. The analytical properties result from locality of the potential in
the wave equation and represent the effect of causality in time dependence of
the scattering process.


title: Efficient Networks for Quantum Factoring

abstract:
  We consider how to optimize memory use and computation time in operating a
quantum computer. In particular, we estimate the number of memory qubits and
the number of operations required to perform factorization, using the algorithm
suggested by Shor. A $K$-bit number can be factored in time of order $K^3$
using a machine capable of storing $5K+1$ qubits. Evaluation of the modular
exponential function (the bottleneck of Shor's algorithm) could be achieved
with about $72 K^3$ elementary quantum gates; implementation using a linear ion
trap would require about $396 K^3$ laser pulses. A proof-of-principle
demonstration of quantum factoring (factorization of 15) could be performed
with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be
a useful computer, it will be a powerful device for exploring experimentally
the properties of entangled quantum states.


title: Quantum Tunneling in the Wigner Representation

abstract:
  Time dependence for barrier penetration is considered in the phase space. An
asymptotic phase-space propagator for nonrelativistic scattering on a one -
dimensional barrier is constructed. The propagator has a form universal for
various initial state preparations and local potential barriers. It is
manifestly causal and includes time-lag effects and quantum spreading. Specific
features of quantum dynamics which disappear in the standard semi-classical
approximation are revealed. The propagator may be applied to calculation of the
final momentum and coordinate distributions, for particles transmitted through
or reflected from the potential barrier, as well as for elucidating the
tunneling time problem.


title: Effects of Loss and Decoherence on a Simple Quantum Computer

abstract:
  We investigate the impact of loss (amplitude damping) and decoherence (phase
damping) on the performance of a simple quantum computer which solves the
one-bit Deutsch problem. The components of this machine are beamsplitters and
nonlinear optical Kerr cells, but errors primarily originate from the latter.
We develop models to describe the effect of these errors on a quantum optical
Fredkin gate. The results are used to analyze possible error correction
strategies in a complete quantum computer. We find that errors due to loss can
be avoided perfectly by appropriate design techniques, while decoherence can be
partially dealt with using projective error correction.


title: Perfect Quantum Error Correction Code

abstract:
  We present a quantum error correction code which protects a qubit of
information against general one qubit errors which maybe caused by the
interaction with the environment. To accomplish this, we encode the original
state by distributing quantum information over five qubits, the minimal number
required for this task. We give a simple circuit which takes the initial state
with four extra qubits in the state |0> to the encoded state. The circuit can
be converted into a decoding one by simply running it backward. Reading the
extra four qubits at the decoder's output we learn which one of the sixteen
alternatives (no error plus all fifteen possible 1-bit errors) was realized.
The original state of the encoded qubit can then be restored by a simple
unitary transformation.


title: Locality, Independence and the Pro-Liberty Bell

abstract:
  Construed as an argument against hidden variable theories, Bell's Theorem
assumes that hidden variables would be independent of future measurement
settings. This Independence Assumption (IA) is rarely questioned. Bell
considered relaxing it to avoid non-locality, but thought that the resulting
view left no room for free will. However, Bell seems to have failed to
distinguish two different strategies for giving up IA. One strategy takes for
granted the Principle of the Common Cause, which requires that a correlation
between hidden variables and measurement settings be explained by a joint
correlation with some unknown factor in their common past. The other strategy
rejects the Principle of the Common Cause, and argues that the required
correlation might be due to the known interaction between the object system and
the measuring device in their common future. Bell and most others who have
discussed these issues have focussed on the former strategy, but because the
two approaches have not been properly distinguished, it has not been well
appreciated that there is a quite different way to relax IA. This paper
distinguishes the two strategies, and argues that the latter is considerably
more appealing than the former.


title: Polarization in Quantum Computations

abstract:
  We propose a realization of quantum computing using polarized photons. The
information is coded in two polarization directions of the photons and
two-qubit operations are done using conditional Faraday effect. We investigate
the performance of the system as a computing device.


title: Error Correction in Quantum Communication

abstract:
  We show how procedures which can correct phase and amplitude errors can be
directly applied to correct errors due to quantum entanglement. We specify
general criteria for quantum error correction, introduce quantum versions of
the Hamming and the Gilbert-Varshamov bounds and comment on the practical
implementation of quantum codes.


title: Nearly Instantaneous Alternatives in Quantum Mechanics

abstract:
  Usual quantum mechanics predicts probabilities for the outcomes of
measurements carried out at definite moments of time. However, realistic
measurements do not take place in an instant, but are extended over a period of
time. The assumption of instantaneous alternatives in usual quantum mechanics
is an approximation whose validity can be investigated in the generalized
quantum mechanics of closed systems in which probabilities are predicted for
spacetime alternatives that extend over time. In this paper we investigate how
alternatives extended over time reduce to the usual instantaneous alternatives
in a simple model in non-relativistic quantum mechanics. Specifically, we show
how the decoherence of a particular set of spacetime alternatives becomes
automatic as the time over which they extend approaches zero and estimate how
large this time can be before the interference between the alternatives becomes
non-negligible. These results suggest that the time scale over which coarse
grainings of such quantities as the center of mass position of a massive body
may be extended in time before producing significant interference is much
longer than characteristic dynamical time scales.


title: Quantum computing Hamiltonian cycles

abstract:
  An algorithm for quantum computing Hamiltonian cycles of simple, cubic,
bipartite graphs is discussed. It is shown that it is possible to evolve a
quantum computer into an entanglement of states which map onto the set of all
possible paths originating from a chosen vertex, and furthermore to
subsequently project out all states not corresponding to Hamiltonian cycles.


title: Symplectic tomography as classical approach to quantum systems

abstract:
  By using a generalization of the optical tomography technique we describe the
dynamics of a quantum system in terms of equations for a purely classical
probability distribution which contains complete information about the system.


title: On The Space Reflections Definition Problem in a Magnetic Charge Theory

abstract:
  A new way to define the operation of P-inversion in the theory with a
magnetic charge is presented.


title: Is Quantum Bit Commitment Really Possible?

abstract:
  We show that all proposed quantum bit commitment schemes are insecure because
the sender, Alice, can almost always cheat successfully by using an
Einstein-Podolsky-Rosen type of attack and delaying her measurement until she
opens her commitment.


title: Poisson spaces with a transition probability

abstract:
  The common structure of the space of pure states $P$ of a classical or a
quantum mechanical system is that of a Poisson space with a transition
probability. This is a topological space equipped with a Poisson structure, as
well as with a function $p:P\times P-> [0,1]$, with certain properties. The
Poisson structure is connected with the transition probabilities through
unitarity (in a specific formulation intrinsic to the given context).
  In classical mechanics, where $p(\rho,\sigma)=\dl_{\rho\sigma}$, unitarity
  poses no restriction on the Poisson structure. Quantum mechanics is
characterized by a specific (complex Hilbert space) form of $p$, and by the
property that the irreducible components of $P$ as a transition probability
space coincide with the symplectic leaves of $P$ as a Poisson space. In
conjunction, these stipulations determine the Poisson structure of quantum
mechanics up to a multiplicative constant (identified with Planck's constant).
  Motivated by E.M. Alfsen, H. Hanche-Olsen and F.W. Shultz ({\em Acta Math.}
{\bf 144} (1980) 267-305) and F.W. Shultz ({\em Commun.\ Math.\ Phys.} {\bf 82}
(1982) 497-509), we give axioms guaranteeing that $P$ is the space of pure
states of a unital $C^*$-algebra. We give an explicit construction of this
algebra from $P$.


title: Quantum Interferometry: Some Basic Features Revisited

abstract:
  The reduction paradigm of quantum interferometry is reanalyzed. In contrast
to widespread opinion it is shown to be amenable to straightforward
mathematical treatment within ``every-users'' simple-minded single particle
quantum mechanics (without reduction postulate or the like), exploiting only
its probabilistic content.


title: Quantum transport in mesoscopic systems and the measurement problem

abstract:
  We study noninvasive measurement of stationary currents in mesoscopic
systems. It is shown that the measurement process is fully described by the
Schr\"odinger equation without any additional reduction postulate and without
the introduction of an observer. Nevertheless the possibility of observing a
particular state out of coherent superposition leads to collapse of the wave
function, even though the measured system is not distorted by interaction with
the detector. Experimental consequences are discussed.


title: Does the universe in fact contain almost no information?

abstract:
  At first sight, an accurate description of the state of the universe appears
to require a mind-bogglingly large and perhaps even infinite amount of
information, even if we restrict our attention to a small subsystem such as a
rabbit. In this paper, it is suggested that most of this information is merely
apparent, as seen from our subjective viewpoints, and that the algorithmic
information content of the universe as a whole is close to zero. It is argued
that if the Schr\"odinger equation is universally valid, then decoherence
together with the standard chaotic behavior of certain non-linear systems will
make the universe appear extremely complex to any self-aware subsets that
happen to inhabit it now, even if it was in a quite simple state shortly after
the big bang. For instance, gravitational instability would amplify the
microscopic primordial density fluctuations that are required by the Heisenberg
uncertainty principle into quite macroscopic inhomogeneities, forcing the
current wavefunction of the universe to contain such Byzantine superpositions
as our planet being in many macroscopically different places at once. Since
decoherence bars us from experiencing more than one macroscopic reality, we
would see seemingly complex constellations of stars etc, even if the initial
wavefunction of the universe was perfectly homogeneous and isotropic.


title: Schumacher's quantum data compression as a quantum computation

abstract:
  An explicit algorithm for performing Schumacher's noiseless compression of
quantum bits is given. This algorithm is based on a combinatorial expression
for a particular bijection among binary strings. The algorithm, which adheres
to the rules of reversible programming, is expressed in a high-level pseudocode
language. It is implemented using $O(n^3)$ two- and three-bit primitive
reversible operations, where $n$ is the length of the qubit strings to be
compressed. Also, the algorithm makes use of $O(n)$ auxiliary qubits; however,
space-saving techniques based on those proposed by Bennett are developed which
reduce this workspace to $O(\sqrt{n})$ while increasing the running time by
less than a factor of two.


title: The Edge Currents in IQHE

abstract:
  It is shown that an observed length in the potential drops across IQHE
samples is a universal length for a given magnetic field strength which has the
magnitude equal to the reciprocal magnitude of magnetic length and which
results from the quantum mechanical uncertainty relation in presence of
magnetic field. The analytic solution of Ohm's equation for the potential in
Corbino sample in IQHE is also given.


title: On The Quantum Theory of Hall Effect

abstract:
  We discuss a model of both classical and integer quantum Hall-effect which is
based on a semi-classical Schroedinger-Chern-Simons-action, where the
Ohm-equations result as equations of motion. The quantization of the classical
Chern-Simons-part of action under typical quantum Hall conditions results in
the quantized Hall conductivity. We show further that the classical Hall-effect
is described by a theory which arises as the classical limit of a theory of
quantum Hall-effect. The model explains also the preference and the domain of
the edge currents on the boundary of samples.


title: A Model Of The Integer Quantum Hall Effect

abstract:
  We discuss a model for the integer quantum Hall effect which is based on a
Schroedinger-Chern-Simons-action functional for a non-interacting system of
electrons in an electromagnetic field on a mutiply connected manifold. In this
model the integer values of the Hall conductivity arises in view of the
quantization of the Chern-Simons-action functional for electromagnetic
potential.


title: On The relation between Superconductivity and Quantum Hall Effect

abstract:
  We introduce a model of superconductivity and discuss its relation to the
quantum Hall-effect. This kind of relation is supported by the well known SQUID
results. The concept of pure gauge potential as it is involved in various
theoretical models concerning solid state effects in magnetic fields is also
discussed.


title: A General Fidelity Limit for Quantum Channels

abstract:
  We derive a general limit on the fidelity of a quantum channel conveying an
ensemble of pure states. Unlike previous results, this limit applies to
arbitrary coding and decoding schemes, including nonunitary decoding. This
establishes the converse of the quantum noiseless coding theorem for all such
schemes.


title: The Trouble with Quantum Bit Commitment

abstract:
  In a recent paper, Lo and Chau explain how to break a family of quantum bit
commitment schemes, and they claim that their attack applies to the 1993
protocol of Brassard, Cr\'epeau, Jozsa and Langlois (BCJL). The intuition
behind their attack is correct, and indeed they expose a weakness common to all
proposals of a certain kind, but the BCJL protocol does not fall in this
category. Nevertheless, it is true that the BCJL protocol is insecure, but the
required attack and proof are more subtle. Here we provide the first complete
proof that the BCJL protocol is insecure.


title: Correlation properties of quantum measurements

abstract:
  The kind of information provided by a measurement is determined in terms of
the correlation established between observables of the apparatus and the
measured system. Using the framework of quantum measurement theory, necessary
and sufficient conditions for a measurement interaction to produce strong
correlations are given and are found to be related to properties of the final
object and apparatus states. These general results are illustrated with
reference to the standard model of the quantum theory of measurement.


title:
Einstein-Podolsky-Rosen-Bohm experiment with massive particles as a test
  of relativistic center-of-mass position operator

abstract:
  The nonrelativistic singlet state average $\langle \psi|{\vec a}\cdot\vec
\sigma\otimes {\vec b}\cdot\vec \sigma|\psi\rangle =-\vec a\cdot\vec b $ can be
relativistically generalized if one defines spin {\it via\/} the relativistic
center-of-mass operator. The relativistic correction is quadratic in $v/c$ and
can be measured in Einstein-Podolsky-Rosen-Bohm-type experiments with massive
spin-1/2 particles. A deviation from the nonrelativistic formula would indicate
that for relativistic nonzero-spin particles centers of mass and charge do not
coincide.


title: On the concept of the tunneling time

abstract:
  Asymptotic time evolution of a wave packet describing a non-relativistic
particle incident on a potential barrier is considered, using the Wigner
phase-space distribution. The distortion of the trasmitted wave packet is
determined by two time-like parameters, given by the energy derivative of the
complex transmission amplitude. The result is consistent with various
definitions of the tunneling time (e.g. the B\"{u}ttiker-Landauer time, the
complex time and Wigner's phase time). The speed-up effect and the negative
dispersion are discussed, and new experimental implications are considered.


title: Bures and Statistical Distance for Squeezed Thermal States

abstract:
  We compute the Bures distance between two thermal squeezed states and deduce
the Statistical Distance metric. By computing the curvature of this metric we
can identify regions of parameter space most sensitive to changes in these
parameters and thus lead to optimum detection statistics.


title:
The Standard Model of Quantum Measurement Theory: History and
  Applications

abstract:
  The standard model of the quantum theory of measurement is based on an
interaction Hamiltonian in which the observable-to-be-measured is multiplied
with some observable of a probe system. This simple Ansatz has proved extremely
fruitful in the development of the foundations of quantum mechanics. While the
ensuing type of models has often been argued to be rather artificial, recent
advances in quantum optics have demonstrated their prinicpal and practical
feasibility. A brief historical review of the standard model together with an
outline of its virtues and limitations are presented as an illustration of the
mutual inspiration that has always taken place between foundational and
experimental research in quantum physics.


title: Time-of-arrival in quantum mechanics

abstract:
  We study the problem of computing the probability for the time-of-arrival of
a quantum particle at a given spatial position. We consider a solution to this
problem based on the spectral decomposition of the particle's (Heisenberg)
state into the eigenstates of a suitable operator, which we denote as the
``time-of-arrival'' operator. We discuss the general properties of this
operator. We construct the operator explicitly in the simple case of a free
nonrelativistic particle, and compare the probabilities it yields with the ones
estimated indirectly in terms of the flux of the Schr\"odinger current. We
derive a well defined uncertainty relation between time-of-arrival and energy;
this result shows that the well known arguments against the existence of such a
relation can be circumvented. Finally, we define a ``time-representation'' of
the quantum mechanics of a free particle, in which the time-of-arrival is
diagonal. Our results suggest that, contrary to what is commonly assumed,
quantum mechanics exhibits a hidden equivalence between independent (time) and
dependent (position) variables, analogous to the one revealed by the
parametrized formalism in classical mechanics.


title: Quantum error correction in the presence of spontaneous emission

abstract:
  We present a quantum error correcting code that is invariant under the
conditional time evolution between spontaneous emissions and which can correct
for one general error. The code presented here generalizes previous error
correction codes in that not all errors lead to different error syndromes. This
idea may lead to shorter codes than previously expected.


title: Collective tests for quantum nonlocality

abstract:
  Pairs of spin-1/2 particles are prepared in a Werner state (namely, a mixture
of singlet and random components). If the random component is large enough, the
statistical results of spin measurements that may be performed on each pair
separately can be reproduced by an algorithm involving local ``hidden''
variables. However, if several such pairs are tested simultaneously, a
violation of the Clauser-Horne-Shimony-Holt inequality may occur, and no local
hidden variable model is compatible with the results.


title: Quantum error correction of dephasing in 3 qubits

abstract:
  We show how to perform error correction of single qubit dephasing by encoding
a single qubit into a minimum of three. This may be performed in a manner
closely analogous to classical error correction schemes. Further, the resulting
quantum error correction schemes are trivially generalized to the minimal
encoding of arbitrarily many qubits so as to allow for multiqubit dephasing
correction under the sole condition that the environment acts independently on
each qubit.


title: On a physical realization of Chern-Simons Theory

abstract:
  The physical content of Chern-Simons-action is discussed and it is shown that
this action is proportional to the usual charged matter interaction term in
electrodynamics.


title: Efficient Simulation of Quantum Systems by Quantum Computers

abstract:
  We show that the time evolution of the wave function of a quantum mechanical
many particle system can be implemented very efficiently on a quantum computer.
The computational cost of such a simulation is comparable to the cost of a
conventional simulation of the corresponding classical system. We then sketch
how results of interest, like the energy spectrum of a system, can be obtained.
We also indicate that ultimately the simulation of quantum field theory might
be possible on large quantum computers.
  We want to demonstrate that in principle various interesting things can be
done. Actual applications will have to be worked out in detail also depending
on what kind of quantum computer may be available one day...


title: Homodyne detection for measuring coherent phase state distributions

abstract:
  Using coherent phase states, parameterized phase state distributions for a
single-mode radiation field are introduced and their integral relation to the
phase-parameterized field-strength distributions is studied. The integral
kernel is evaluated and the problem of direct sampling of the coherent phase
state distributions using balanced homodyne detection is considered. Numerical
simulations show that when the value of the smoothing parameter is not too
small the coherent phase state distributions can be obtained with sufficiently
well accuracy. With decreasing value of the smoothing parameter the
determination of the coherent phase state distributions may be an effort,
because both the numerical calculation of the sampling function and the
measurement of the field-strength distributions are required to be performed
with drastically increasing accuracy.


title: Simulations of Many-Body Quantum Systems by a Quantum Computer

abstract:
  We suggest that quantum computers can solve quantum many-body problems that
are impracticable to solve on a classical computer.


title:
The deformed uncertainty relation and the corresponding beam quality
  factor

abstract:
  By using the theory of deformed quantum mechanics, we study the deformed
light beam theoretically. The deformed beam quality factor $M_q^2$ is given
explicitly under the case of deformed light in coherent state. When the
deformation parameter $q$ being a root of unity, the beam quality factor $M_q^2
\leq 1$.


title:
Homodyne detection for measuring internal quantum correlations of
  optical pulses

abstract:
  A new method is described for determining the quantum correlations at
different times in optical pulses by using balanced homodyne detection. The
signal pulse and sequences of ultrashort test pulses are superimposed, where
for chosen distances between the test pulses their relative phases and
intensities are varied from measurement to measurement. The correlation
statistics of the signal pulse is obtained from the time-integrated difference
photocurrents measured.


title: Error Prevention Scheme with Four Particles

abstract:
  It is shown that a simplified version of the error correction code recently
suggested by Shor exhibits manifestation of the quantum Zeno effect. Thus,
under certain conditions, protection of an unknown quantum state is achieved.
Error prevention procedures based on four-particle and two-particle encoding
are proposed and it is argued that they have feasible practical
implementations.


title: Mathematical Techniques for Quantum Communication Theory

abstract:
  We present mathematical techniques for addressing two closely related
questions in quantum communication theory. In particular, we give a
statistically motivated derivation of the Bures-Uhlmann measure of
distinguishability for density operators, and we present a simplified proof of
the Holevo upper bound to the mutual information of quantum communication
channels. Both derivations give rise to novel quantum measurements.


title: Multiphoton Ionization as Time-Dependent Tunneling

abstract:
  A new semiclassical approach to ionization by an oscillating field is
presented. For a delta-function atom, an asymptotic analysis is performed with
respect to a quantity h, defined as the ratio of photon energy to ponderomotive
energy. This h appears formally equivalent to Planck's constant in a suitably
transformed Schroedinger equation and allows semiclassical methods to be
applicable. Systematically, a picture of tunneling wave packets in complex time
is developped, which by interference account for the typical ponderomotive
features of ionization curves. These analytical results are then compared to
numerical simulations and are shown to be in good agreement.


title: From quantum cellular automata to quantum lattice gases

abstract:
  A natural architecture for nanoscale quantum computation is that of a quantum
cellular automaton. Motivated by this observation, in this paper we begin an
investigation of exactly unitary cellular automata. After proving that there
can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in
one dimension, we weaken the homogeneity condition and show that there are
nontrivial, exactly unitary, partitioning cellular automata. We find a one
parameter family of evolution rules which are best interpreted as those for a
one particle quantum automaton. This model is naturally reformulated as a two
component cellular automaton which we demonstrate to limit to the Dirac
equation. We describe two generalizations of this automaton, the second of
which, to multiple interacting particles, is the correct definition of a
quantum lattice gas.


title:
Exponential and Laguerre Squeezed States for su(1,1) Algebra and
  Calogero-Sutherland Model

abstract:
  A class of squeezed states for the su(1,1) algebra is found and expressed by
the exponential and Laguerre-polynomial operators acting on the vacuum states.
As a special case it is proved that the Perelomov's coherent state is a
ladder-operator squeezed state and therefore a minimum uncertainty state. The
theory is applied to the two-particle Calogero-Sutherland model. We find some
new squeezed states and compared them with the classical trajectories. The
connection with some su(1,1) quantum optical systems (amplitude-squared
realization, Holstein-Primakoff realization, the two mode realization and a
four mode realization) is also discussed.


title: Separability Criterion for Density Matrices

abstract:
  A quantum system consisting of two subsystems is separable if its density
matrix can be written as $\rho=\sum_A w_A\,\rho_A'\otimes\rho_A''$, where
$\rho_A'$ and $\rho_A''$ are density matrices for the two subsytems. In this
Letter, it is shown that a necessary condition for separability is that a
matrix, obtained by partial transposition of $\rho$, has only non-negative
eigenvalues. This criterion is stronger than Bell's inequality.


title:
Quantum Error-Correcting Codes Need Not Completely Reveal the Error
  Syndrome

abstract:
  Quantum error-correcting codes so far proposed have not worked in the
presence of noise which introduces more than one bit of entropy per qubit sent
through a quantum channel, nor can any code which identifies the complete error
syndrome. We describe a code which does not find the complete error syndrome
and can be used for reliable transmission of quantum information through
channels which add more than one bit of entropy per transmitted bit. In the
case of the depolarizing channel our code can be used in a channel of fidelity
.8096. The best existing code worked only down to .8107.


title: A decision procedure for unitary linear quantum cellular automata

abstract:
  Linear quantum cellular automata were introduced recently as one of the
models of quantum computing. A basic postulate of quantum mechanics imposes a
strong constraint on any quantum machine: it has to be unitary, that is its
time evolution operator has to be a unitary transformation. In this paper we
give an efficient algorithm to decide if a linear quantum cellular automaton is
unitary. The complexity of the algorithm is O(n^((3r-1)/(r+1))) = O(n^3) in the
algebraic computational model if the automaton has a continuous neighborhood of
size r, where $n$ is the size of the input.


title: Simple New Axioms for Quantum Mechanics

abstract:
  The space P of pure states of any physical system, classical or quantum, is
identified as a Poisson space with a transition probability. The latter is a
function p: PxP -> [0,1]; in addition, a Poisson bracket is defined for
functions on P. These two structures are connected through unitarity. Classical
and quantum mechanics are each characterized by a simple axiom on the
transition probability p. Unitarity then determines the Poisson bracket of
quantum mechanics up to a multiplicative constant (identified with Planck's
constant). Superselection rules are naturally incorporated.


title:
On the absence of bound-state stabilization through short ultra-intense
  fields

abstract:
  We address the question of whether atomic bound states begin to stabilize in
the short ultra-intense field limit. We provide a general theory of ionization
probability and investigate its gauge invariance. For a wide range of
potentials we find an upper and lower bound by non-perturbative methods, which
clearly exclude the possibility that the ultra intense field might have a
stabilizing effect on the atom. For short pulses we find almost complete
ionization as the field strength increases.


title: Dark pair coherent states of the motion of a trapped ion

abstract:
  We propose a scheme for generating vibrational pair coherent states of the
motion of an ion in a two-dimensional trap. In our scheme, the trapped ion is
excited bichromatically by three laser beams along different directions in the
X-Y plane of the ion trap. We show that if the initial vibrational state is
given by a two-mode Fock state, the final steady state, indicated by the
extinction of the fluorescence emitted by the ion, is a pure state. The
motional state of the ion in the equilibrium realizes that of the
highly-correlated pair coherent state.


title: On the absence of homogeneous scalar unitary cellular automata

abstract:
  Failure to find homogeneous scalar unitary cellular automata (CA) in one
dimension led to consideration of only ``approximately unitary'' CA---which
motivated our recent proof of a No-go Lemma in one dimension. In this note we
extend the one dimensional result to prove the absence of nontrivial
homogeneous scalar unitary CA on Euclidean lattices in any dimension.


title: Small-angle scattering on a system of magnetic and electric charges

abstract:
  The generalization of the conformal scattering method for small-angle
scattering processes involving magnetic monopoles and ordinary charges is
constructed. Using this generalization we show that introducing of magnetic
charges corresponds to analytical continuation of the eikonal amplitude in the
complex charge plane (the imaginary part is proportional to the magnetic
charge). We calculate explicitly the eikonal amplitude for scattering on a dyon
and two monopoles in terms of confluent hypergeometric functions. The
singularities of the corresponding amplitudes (focal points) are studied in
details.


title: Insolubility of the Quantum Measurement Problem for Unsharp Observables

abstract:
  The quantum mechanical measurement problem is the difficulty of dealing with
the indefiniteness of the pointer observable at the conclusion of a measurement
process governed by unitary quantum dynamics. There has been hope to solve this
problem by eliminating idealizations from the characterization of measurement.
We state and prove two `insolubility theorems' that disappoint this hope. In
both the initial state of the apparatus is taken to be mixed rather than pure,
and the correlation of the object observable and the pointer observable is
allowed to be imperfect. In the {\it insolubility theorem for sharp
observables}, which is only a modest extension of previous results, the object
observable is taken to be an arbitrary projection valued measure. In the {\it
insolubility theorem for unsharp observables}, which is essentially new, the
object observable is taken to be a positive operator v alued measure. Both
theorems show that the measurement problem is not the consequence of neglecting
the ever-present imperfections of actual measurements.


title: Is the quantum state (an) observable?

abstract:
  We explore the sense in which the state of a physical system may or may not
be regarded (an) observable in quantum mechanics. Simple and general arguments
from various lines of approach are reviewed which demonstrate the following
no-go claims: (1) the structure of quantum mechanics precludes the
determination of the state of a single system by means of measurements
performed on that system only; (2) there is no way of using entangled
two-particle states to transmit superluminal signals. Employing the
representation of observables as general positive operator valued measures, our
analysis allows one to indicate whether optimal separation of different states
is achieved by means of sharp or unsharp observables.


title: The capacity of the noisy quantum channel

abstract:
  An upper limit is given to the amount of quantum information that can be
transmitted reliably down a noisy, decoherent quantum channel. A class of
quantum error-correcting codes is presented that allow the information
transmitted to attain this limit. The result is the quantum analog of Shannon's
bound and code for the noisy classical channel.


title: Improvement of measurement accuracy in SU(1,1) interferometers

abstract:
  We consider an SU(1,1) interferometer employing four-wave mixers that is fed
with two-mode states which are both coherent and intelligent states of the
SU(1,1) Lie group. It is shown that the phase sensitivity of the interferometer
can be essentially improved by using input states with a large photon-number
difference between the modes.


title: Parity-dependent squeezing of light

abstract:
  A parity-dependent squeezing operator is introduced which imposes different
SU(1,1) rotations on the even and odd subspaces of the harmonic oscillator
Hilbert space. This operator is used to define parity-dependent squeezed states
which exhibit highly nonclassical properties such as strong antibunching,
quadrature squeezing, strong oscillations in the photon-number distribution,
etc. In contrast to the usual squeezed states whose $Q$ and Wigner functions
are simply Gaussians, the parity-dependent squeezed states have much more
complicated $Q$ and Wigner functions that exhibit an interesting interference
in phase space. The generation of these states by parity-dependent quadratic
Hamiltonians is also discussed.


title: Symplectic Tomography of Nonclassical States of Trapped Ion

abstract:
  The marginal distribution of squeezed and rotated quadrature for two types of
nonclassical states of trapped ion -- for squeezed and correlated states and
for squeezed even and odd coherent states (squeezed Schr\"odinger cat states)
is studied. The obtained marginal distribution for the two types of states is
shown to satisfy classical dynamical equation equivalent to standard quantum
evolution equation for density matrix (wave function) derived in symplectic
tomography scheme.