title:
The Three-Box "Paradox" and Other Reasons to Reject the Counterfactual
  Usage of the ABL Rule

abstract:
  An apparent paradox proposed by Aharonov and Vaidman in which a single
particle can be found with certainty in two (or more) boxes is analyzed by way
of a simple thought experiment. It is found that the apparent paradox arises
from an invalid counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL)
rule, and effectively attributes conflicting properties not to the same
particle but to different particles. A connection is made between the present
analysis and the consistent histories formulation of Griffiths. Finally, a
critique is given of some recent counterarguments by
  Vaidman against the rejection of the counterfactual usage of the ABL rule.


title:
Quantum control of atomic systems by time-resolved homodyne detection of
  spontaneous emission

abstract:
  We describe the light-matter interaction of a single two level atom with the
electromagnetic vacuum in terms of field and dipole variables by considering
homodyne detection of the emitted fields. Spontaneous emission is then observed
as a continuous fluctuating force acting on the atomic dipole. The effect of
this force may be compensated and even reversed by feedback.


title:
Exactness of Conventional and Supersymmetric JWKB Formulae and Glo bal
  Symmetries of Stokes Graphs

abstract:
  It has been shown that the cases of the JWKB formulae in 1--dim QM quantizing
the energy levels exactly are results of essentially one global symmetry of
both potentials and their corresponding Stokes graphs. Namely, this is the
invariance of the latter on translations in the complex plain of the space
variable i.e. the potentials and the Stokes graphs have to be periodic. A
proliferation of turning points in the basic period strips (parallelograms) is
another limitation for the exactness of the JWKB formulae. A systematic
analyses of a single-well class of potentials satisfying suitable conditions
has been performed. Only ten potentials (with one or two real parameters)
quantized exactly by the JWKB formulae have been found all of them coinciding
(or being equivalent to) with the well-known ones found previously. It was
shown also that the exactness of the supersymmetric JWKB formulae is a
consequence of the corresponding exactness of the conventional ones and vice
versa. Because of the latter two exactly JWKB quantized potentials have been
additionally established. These results show that the exact SUSY JWKB formulae
choose the Comtet at al form of them independently of whether the supersymmetry
is broken or not. A close relation between the shape invariance property of
potentials considered and their meromorphic structure on the x-plane is also
demonstrated.


title: Localization induced by noise and non linearity

abstract:
  We introduce a model for a two configurations system, and we study the
transition from quantum to classical behaviour. We first consider the effect of
the interaction with the environment as an external noise and we show that it
produces decoherence and suppression of tunnelling. These features are widely
accepted as definition of classicality, while we believe that classicality
implies that quantum delocalized states spontaneously evolve into localized
ones. We than show that this evolution take place only when both noise and non
linearity in the equations are present.


title:
Incoherent and Coherent Eavesdropping in the 6-state Protocol of Quantum
  Cryptography

abstract:
  All incoherent as well as 2- and 3-qubit coherent eavesdropping strategies on
the 6 state protocol of quantum cryptography are classified. For a disturbance
of 1/6, the optimal incoherent eavesdropping strategy reduces to the universal
quantum cloning machine. Coherent eavesdropping cannot increase Eve's Shannon
information, neither on the entire string of bits, nor on the set of bits
received undisturbed by Bob. However, coherent eavesdropping can increase as
well Eve's Renyi information as her probability of guessing correctly all bits.
The case that Eve delays the measurement of her probe until after the public
discussion on error correction and privacy amplification is also considered. It
is argued that by doing so, Eve gains only a negligibly small additional
information.


title: Realism or Locality: Which Should We Abandon?

abstract:
  We reconsider the consequences of the observed violations of Bell's
inequalities. Two common responses to these violations are: (i) the rejection
of realism and the retention of locality, and (ii) the rejection of locality
and the retention of realism. Here we critique response (i). We argue that
locality contains an implicit form of realism, since in a world view that
embraces locality, spacetime, with its usual, fixed topology, has properties
independent of measurement. Hence we argue that response (i) is incomplete, in
that its rejection of realism is only partial.


title: Time-of-Arrival States

abstract:
  Although one can show formally that a time-of-arrival operator cannot exist,
one can modify the low momentum behaviour of the operator slightly so that it
is self-adjoint. We show that such a modification results in the difficulty
that the eigenstates are drastically altered. In an eigenstate of the modified
time-of-arrival operator, the particle, at the predicted time-of-arrival, is
found far away from the point of arrival with probability 1/2.


title:
Optimized perturbation method for the propagation in the anharmonic
  oscillator potential

abstract:
  The application of the optimized expansion for the quantum-mechanical
propagation in the anharmonic potential $\lambda x^4$ is discussed for real and
imaginary time. The first order results in the imaginary time formalism provide
approximations to the free energy and particle density which agree well with
the exact results in the whole range of temperatures.


title: A Canonical Quantization of the Baker's Map

abstract:
  We present here a canonical quantization for the baker's map. The method we
use is quite different from that used in Balazs and Voros (ref.
\QCITE{cite}{}{BV}) and Saraceno (ref. \QCITE{cite}{}{S}). We first construct a
natural ``baker covering map'' on the plane $\QTO{mathbb}{\mathbb{R}}^{2}$. We
then use as the quantum algebra of observables the subalgebra of operators on
$L^{2}(\QTO{mathbb}{\mathbb{R}}) $ generated by $\left\{\exp (2\pi i\hat{x})
,\exp (2\pi i\hat{p}) \right\} $ . We construct a unitary propagator such that
as $\hbar \to 0$ the classical dynamics is returned. For Planck's constant
$h=1/N$, we show that the dynamics can be reduced to the dynamics on an
$N$-dimensional Hilbert space, and the unitary $N\times N$ matrix propagator is
the same as given in ref. \QCITE{cite}{}{BV} except for a small correction of
order $h$. This correction is shown to preserve the classical symmetry $x\to
1-x$ and $p\to 1-p$ in the quantum dynamics for periodic boundary conditions.


title: Relativistic Quantum Field Theory with a Physical State Vector

abstract:
  Evolution of a physical quantum state vector is described as governed by two
distinct physical laws: Continuous, unitary time evolution and a
relativistically covariant reduction process. In previous literature, it was
concluded that a relativistically satisfactory version of the collapse
postulate is in contradiction with physical measurements of a non-local state
history. Here it is shown that such measurements are excluded when reduction is
formulated as a physical process and the measurement devices are included as
part of the state vector.


title:
Exact derivation of the Langevin and master equations for harmonic
  quantum Brownian motion

abstract:
  A many particle Hamiltonian, where the interaction term conserves the number
of particles, is considered. A master equation for the populations of the
different levels is derived in an exact way. It results in a local equation
with time-dependent coefficients, which can be identified with the transition
probabilities in the golden rule approximation. A reinterpretation of the model
as a set of coupled harmonic oscillators enables one to obtain for one of them
an exact local Langevin equation, with time-dependent coefficients.


title: The Gamow vectors and the Schwinger effect

abstract:
  We introduce a `proper time' formalism to study the instability of the vacuum
in a uniform external electric field due to particle production. This formalism
allows us to reduce a quantum field theoretical problem to a quantum-mechanical
one in a higher dimension. The instability results from the inverted oscillator
structure which appears in the Hamiltonian. We show that the `proper time'
unitary evolution splits into two semigroups. The semigroup associated with
decaying Gamov vectors is related to the Feynman boundary conditions for the
Green functions and the semigroup associated with growing Gamov vectors is
related to the Dyson boundary conditions.


title: Quantum Brownian motion. II

abstract:
  This paper is devoted to generalize some previous results presented in Gaioli
et al., Int. J. Theor. Phys. 36, 2167 (1997). We evaluate the autocorrelation
function of the stochastic acceleration and study the asymptotic evolution of
the mean occupation number of a harmonic oscillator playing the role of a
Brownian particle. We also analyze some deviations from the Bose population at
low temperatures and compare it with the deviations from the exponential decay
law of an unstable quantum system.


title: Realizing the quantum baker's map on an NMR quantum computer

abstract:
  By numerically simulating an implementation of the quantum baker's map on a
3-qubit NMR quantum computer based on the molecule trichloroethylene, we
demonstrate the feasibility of quantum chaos experiments on present-day quantum
computers. We give detailed descriptions of proposed experiments that
investigate (a) the rate of entropy increase due to decoherence and (b) the
phenomenon of hypersensitivity to perturbation.


title:
Continuous quantum measurement with observer: pure wavefunction
  evolution instead of decoherence

abstract:
  We consider a continuous measurement of a two-level system (double-dot) by
weakly coupled detector (tunnel point contact nearby). While usual treatment
leads to the gradual system decoherence due to the measurement, we show that
the knowledge of the measurement result can restore the pure wavefunction at
any time (this can be experimentally verified). The formalism allows to write a
simple Langevin equation for the random evolution of the system density matrix
which is reflected and caused by the stochastic detector output. Gradual
wavefunction ``collapse'' and quantum Zeno effect are naturally described by
the equation.


title: A Quantum Computational Learning Algorithm

abstract:
  An interesting classical result due to Jackson allows polynomial-time
learning of the function class DNF using membership queries. Since in most
practical learning situations access to a membership oracle is unrealistic,
this paper explores the possibility that quantum computation might allow a
learning algorithm for DNF that relies only on example queries. A natural
extension of Fourier-based learning into the quantum domain is presented. The
algorithm requires only an example oracle, and it runs in O(sqrt(2^n)) time, a
result that appears to be classically impossible. The algorithm is unique among
quantum algorithms in that it does not assume a priori knowledge of a function
and does not operate on a superposition that includes all possible states.


title: Quantum Associative Memory

abstract:
  This paper combines quantum computation with classical neural network theory
to produce a quantum computational learning algorithm. Quantum computation uses
microscopic quantum level effects to perform computational tasks and has
produced results that in some cases are exponentially faster than their
classical counterparts. The unique characteristics of quantum theory may also
be used to create a quantum associative memory with a capacity exponential in
the number of neurons. This paper combines two quantum computational algorithms
to produce such a quantum associative memory. The result is an exponential
increase in the capacity of the memory when compared to traditional associative
memories such as the Hopfield network. The paper covers necessary high-level
quantum mechanical and quantum computational ideas and introduces a quantum
associative memory. Theoretical analysis proves the utility of the memory, and
it is noted that a small version should be physically realizable in the near
future.


title: Initializing the Amplitude Distribution of a Quantum State

abstract:
  To date, quantum computational algorithms have operated on a superposition of
all basis states of a quantum system. Typically, this is because it is assumed
that some function f is known and implementable as a unitary evolution.
However, what if only some points of the function f are known? It then becomes
important to be able to encode only the knowledge that we have about f. This
paper presents an algorithm that requires a polynomial number of elementary
operations for initializing a quantum system to represent only the m known
points of a function f.


title:
What Do These Correlations Know About Reality? Nonlocality and the
  Absurd

abstract:
  In honor of Daniel Greenberger's 65th birthday I record for posterity two
superb examples of his wit, offer a proof of an important theorem on quantum
correlations that even those of us over 60 can understand, and suggest, by
trying to make it look silly, that invoking ``quantum nonlocality'' as an
explanation for such correlations may be too cheap a way out of the dilemma
they pose.


title: Quantum Mechanics on a Torus

abstract:
  We present here a canonical description for quantizing classical maps on a
torus. We prove theorems analagous to classical theorems on mixing and
ergodicity in terms of a quantum Koopman space $ L^2 (A_\hbar},\tau_\hbar) $
obtained as the completion of the algebra of observables $ A_\hbar $ in the
norm induced by the following inner product $(A,B) =\tau_{\hbar}(A^{\dagger}B)
$, where $\tau_{\hbar}$ is a linear functional on the algebra analogous to the
classical ``integral over phase space.'' We also derive explicit formulas
connecting this formulation to the $\theta $-torus decomposition of Bargmann
space introduced in ref. \QCITE{cite}{}{KLMR}.


title: Single Molecule Magnetic Resonance and Quantum Computation

abstract:
  It is proposed that nuclear (or electron) spins in a trapped molecule would
be well isolated from the environment and the state of each spin can be
measured by means of mechanical detection of magnetic resonance. Therefore
molecular traps make an entirely new approach possible for spin-resonance
quantum computation which can be conveniently scaled up. In the context of
magnetic resonance spectroscopy, a molecular trap promises the ultimate
sensitivity for single spin detection and an unprecedented spectral resolution
as well.


title: Time as an Observable

abstract:
  The role of time in quantum mechanics is discussed. The differences between
ordinary observables and an observable which corresponds to the time of an
event is examined. In particular, the time-of-arrival of a particle to a fixed
location is not an ordinary quantum mechanical observable. While we can measure
if the particle arrives, we argue that the time at which it arrives always has
an inherent ambiguity. The minimum inaccuracy of time-of-arrival measurements
is given by dt>1/E where E is the kinetic energy of the particle. The use of
time-of-arrival operators, as well as current operators, is examined
critically.


title: Variance of the Quantum Coordinates of an Event

abstract:
  We study the variances of the coordinates of an event considered as quantum
observables in a Poincare' covariant theory. The starting point is their
description in terms of a covariant positive-operator-valued measure on the
  Minkowski space-time. Besides the usual uncertainty relations, we find
stronger inequalities involving the mass and the centre-of-mass angular
momentum of the object that defines the event. We suggest that these
inequalities may help to clarify some of the arguments which have been given in
favour of a gravitational quantum limit to the accuracy of time and space
measurements.


title: Complex Parameters in Quantum Mechanics

abstract:
  The Schrodinger equation for stationary states in a central potential is
studied in an arbitrary number of spatial dimensions, say q. After
transformation into an equivalent equation, where the coefficient of the first
derivative vanishes, it is shown that in such equation the coefficient of the
second inverse power of r is an even function of a parameter, say lambda,
depending on a linear combination of q and of the angular momentum quantum
number, say l. Thus, the case of complex values of lambda, which is useful in
scattering theory, involves, in general, both a complex value of the parameter
originally viewed as the spatial dimension and complex values of the angular
momentum quantum number. The paper ends with a proof of the Levinson theorem in
an arbitrary number of spatial dimensions, when the potential includes a
non-local term which might be useful to understand the interaction between two
nucleons.


title: Exact time evolution in harmonic quantum Brownian motion

abstract:
  We consider a particular (exactly soluble) model of the one discussed in a
previous work. We show numerical results for the time evolution of the main
dynamical quantities and compare them with analytical results.


title: Quantum Brownian motion

abstract:
  We study the behavior of a subsystem (harmonic oscillator) in contact with a
thermal reservoir (finite set of uncoupled harmonic oscillators). We exactly
solve the eigenvalue problem and obtain the temporal evolution of the dynamical
variables of interest. We show how the subsystem goes to equilibrium and give
quantitative estimates of the Poincar\'e recurrence times. We study the
behavior of the subsystem mean ocuppation number in the limit of a dense bath
and compare it with the expected exponential decay law.


title: Twin-photon techniques for fiber measurements

abstract:
  The potential of twin photons generated by parametric down-conversion for
metrological applications are discussed. We present several experimental
results like the measurement of chromatic dispersion and polarization mode
dispersion in optical fibers.


title: Fast Quantum Fourier Transforms for a Class of Non-abelian Groups

abstract:
  An algorithm is presented allowing the construction of fast Fourier
transforms for any solvable group on a classical computer. The special
structure of the recursion formula being the core of this algorithm makes it a
good starting point to obtain systematically fast Fourier transforms for
solvable groups on a quantum computer. The inherent structure of the Hilbert
space imposed by the qubit architecture suggests to consider groups of order
2^n first (where n is the number of qubits). As an example, fast quantum
Fourier transforms for all 4 classes of non-abelian 2-groups with cyclic normal
subgroup of index 2 are explicitly constructed in terms of quantum circuits.
The (quantum) complexity of the Fourier transform for these groups of size 2^n
is O(n^2) in all cases.


title:
On the averaged quantum dynamics by white-noise Hamiltonians with and
  without dissipation

abstract:
  Exact results are derived on the averaged dynamics of a class of random
quantum-dynamical systems in continuous space. Each member of the class is
characterized by a Hamiltonian which is the sum of two parts. While one part is
deterministic, time-independent and quadratic, the Weyl-Wigner symbol of the
other part is a homogeneous Gaussian random field which is delta correlated in
time, but smoothly correlated in position and momentum. The averaged dynamics
of the resulting white-noise system is shown to be a monotone mixing increasing
quantum-dynamical semigroup. Its generator is computed explicitly. Typically,
in the course of time the mean energy of such a system grows linearly to
infinity. In the second part of the paper an extended model is studied, which,
in addition, accounts for dissipation by coupling the white-noise system
linearly to a quantum-mechanical harmonic heat bath. It is demonstrated that,
under suitable assumptions on the spectral density of the heat bath, the mean
energy then saturates for long times.


title: Space-time properties of free motion time-of-arrival eigenstates

abstract:
  The properties of the time-of-arrival operator for free motion introduced by
Aharonov and Bohm and of its self-adjoint variants are studied. The domains of
applicability of the different approaches are clarified. It is shown that the
arrival time of the eigenstates is not sharply defined. However, strongly
peaked real-space (normalized) wave packets constructed with narrow Gaussian
envelopes centred on one of the eigenstates provide an arbitrarily sharp
arrival time.


title: Fast quantum search algorithm and Bounds on it

abstract:
  We recast Grover's generalised search algorithm in a geometric language even
when the states are not approximately orthogonal. We provide a possible search
algorithm based on an arbitrary unitary transformation which can speed up the
steps still further. We discuss the lower and upper bounds on the transition
matrix elements when the unitary operator changes with time, thereby implying
that quantum search process can not be too fast or too slow. This is a
remarkable feature of quantum computation unlike classical one. Quantum
mechanical uncertainty relation puts bounds on search process. Also we mention
the problems of perturbation and other issues in time-dependent search
operation.


title:
Relativistic Trace Formula for Bound States in Terms of Classical
  Periodic Orbits

abstract:
  We set up a trace formula for the relativistic density of states in terms of
a topological sum of classical periodic orbits. The result is applicable to any
relativistic integrable system.


title: Bound Entanglement and Teleportation

abstract:
  Recently M. Horodecki, P. Horodecki and R. Horodecki have introduced a set of
density matrices of two spin-1 particles from which it is not possible to
distill any maximally entangled states, even though the density matrices are
entangled. Thus these density matrices do not allow reliable teleportation.
However it might nevertheless be the case that these states can be used for
teleportation, not reliably, but still with fidelity greater than that which
may be achieved with a classical scheme. We show that, at least for some of
these density matrices, teleportation cannot be achieved with better than
classical fidelity.


title:
A quantum algorithm providing exponential speed increase for finding
  eigenvalues and eigenvectors

abstract:
  We describe a new polynomial time quantum algorithm that uses the quantum
fast fourier transform to find eigenvalues and eigenvectors of a Hamiltonian
operator, and that can be applied in cases (commonly found in ab initio physics
and chemistry problems) for which all known classical algorithms require
exponential time. Applications of the algorithm to specific problems are
considered, and we find that classically intractable and interesting problems
from atomic physics may be solved with between 50 and 100 quantum bits.


title: Trapped Ion Quantum Computer Research at Los Alamos

abstract:
  We briefly review the development and theory of an experiment to investigate
quantum computation with trapped calcium ions. The ion trap, laser and ion
requirements are determined, and the parameters required for simple quantum
logic operations are described


title: Pulse controlled noise suppressed quantum computation

abstract:
  To make arbitrarily accurate quantum computation possible, practical
realization of quantum computers will require suppressing noise in quantum
memory and gate operations to make it below a threshold value. A scheme based
on realistic quantum computer models is described for suppressing noise in
quantum computation without the cost of stringent quantum computing resources.


title: Solution of Coulomb Path Integral in Momentum Space

abstract:
  The path integral for a point particle in a Coulomb potential is solved in
momentum space. The solution permits us to give for the first time a negative
answer to an old question of quantum mechanics in curved spaces raised in 1957
by DeWitt, whether the Hamiltonian of a particle in a curved space contains an
additional term proportional to the curvature scalar $R$. We show that this
would cause experimentally wrong level spacings in the hydrogen atom. Our
solution also gives a first experimental confirmation of the correctness of the
measure of integration in path integrals in curved space implied by a recently
discovered nonholonomic mapping principle.


title: On the analytical convergence of the QPA procedure

abstract:
  We present an analytical proof of the convergence of the ``quantum privacy
amplification'' procedure proposed by D. Deutsch et al. [Phys. Rev. Lett. 77,
2818 (1996)]. The proof specifies the range of states which can be purified by
this method.


title: Time-Symmetrized Counterfactuals in Quantum Theory

abstract:
  Recently, several authors have criticized the time-symmetrized quantum theory
originated by the work of Aharonov et al. (1964). The core of this criticism
was a proof, appearing in various forms, which showed that the counterfactual
interpretation of time-symmetrized quantum theory cannot be reconciled with
standard quantum theory. I argue here that the apparent contradiction is due to
a logical error. I analyze the concept of counterfactuals in quantum theory and
introduce time-symmetrized counterfactuals. These counterfactuals do not lead
to any contradiction with the predictions of quantum theory. I discuss
applications of time-symmetrized counterfactuals to several surprising examples
and show the usefulness of the time-symmetrized quantum formalism.


title: Epistemology of Quantization

abstract:
  A notion of quantization is proposed that is independent of the original
statistical interpretation of the distribution of energy in a photon gas or of
the quantization of angular momentum in hydrogen atom. Such a procedutre
implies the existance of finite space-time four-interval that any relativistic
preparation and measurement of a physical event requires. That finite
four-interval is also the epistemological source of QM uncertainty relations.
Furthermore, the consetrvation of helicity in the propagation of a photon is a
relativistic invariant, and is the origin of the "appearence" of a paradox of
nonlocal interaction in Bell's inequality [2,3,4] as shown in A. Aspect et all
[5] experiment. That is a spin of a photon is always correlated with its
momentum.


title: Entanglement monotones

abstract:
  In the context of quantifying entanglement we study those functions of a
multipartite state which do not increase under the set of local
transformations. A mathematical characterization of these monotone magnitudes
is presented. They are then related to optimal strategies of conversion of
shared states. More detailed results are presented for pure states of bipartite
systems. It is show that more than one measure are required simultaneously in
order to quantify completely the non-local resources contained in a bipartite
pure state, while examining how this fact does not hold in the so-called
asymptotic limit. Finally, monotonicity under local transformations is proposed
as the only natural requirement for measures of entanglement.


title: A Modification of Grover's Algorithm as a Fast Database Search

abstract:
  A modification of Grover's algorithm is proposed, which can be used directly
as a fast database search. An explicit two q-bit example is displayed in
detail. We discuss the case where the database has multiple entries
corresponding to the same target value.


title:
Stochastic wave function approach to the calculation of multitime
  correlation functions of open quantum systems

abstract:
  Within the framework of probability distributions on projective Hilbert space
a scheme for the calculation of multitime correlation functions is developed.
The starting point is the Markovian stochastic wave function description of an
open quantum system coupled to an environment consisting of an ensemble of
harmonic oscillators in arbitrary pure or mixed states. It is shown that matrix
elements of reduced Heisenberg picture operators and general time-ordered
correlation functions can be expressed by time-symmetric expectation values of
extended operators in a doubled Hilbert space. This representation allows the
construction of a stochastic process in the doubled Hilbert space which enables
the determination of arbitrary matrix elements and correlation functions. The
numerical efficiency of the resulting stochastic simulation algorithm is
investigated and compared with an alternative Monte Carlo wave function method
proposed first by Dalibard et al. [Phys. Rev. Lett. {\bf 68}, 580 (1992)]. By
means of a standard example the suggested algorithm is shown to be more
efficient numerically and to converge faster. Finally, some specific examples
from quantum optics are presented in order to illustrate the proposed method,
such as the coupling of a system to a vacuum, a squeezed vacuum within a finite
solid angle, and a thermal mixture of coherent states.


title:
Heisenberg picture operators in the stochastic wave function approach to
  open quantum systems

abstract:
  A fast simulation algorithm for the calculation of multitime correlation
functions of open quantum systems is presented. It is demonstrated that any
stochastic process which ``unravels'' the quantum Master equation can be used
for the calculation of matrix elements of reduced Heisenberg picture operators,
and thus for the calculation of multitime correlation functions, by extending
the stochastic process to a doubled Hilbert space. The numerical performance of
the stochastic simulation algorithm is investigated by means of a standard
example.


title:
Non-linear coherent states associated with conditionally exactly
  solvable problems

abstract:
  Recently, based on a supersymmetric approach, new classes of conditionally
exactly solvable problems have been found, which exhibit a symmetry structure
characterized by non-linear algebras. In this paper the associated
``non-linear'' coherent states are constructed and some of their properties are
discussed in detail.


title: Heisenberg picture operators in the quantum state diffusion model

abstract:
  A stochastic simulation algorithm for the computation of multitime
correlation functions which is based on the quantum state diffusion model of
open systems is developed. The crucial point of the proposed scheme is a
suitable extension of the quantum master equation to a doubled Hilbert space
which is then unraveled by a stochastic differential equation.


title:
Influence of Small Impurities on Low-Energy Electron Dynamics in
  Two-Dimensional Microscopic Bounded Region

abstract:
  In order to give some insight into a role of small impurities on the electron
motion in microscopic devices, we examine from a general viewpoint, the effect
of small obstacles on a particle motion at low energy inside microscopic
bounded regions. It will be shown that the obstacles disturb the electron
motion only if they are weakly attractive.

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


title: On the Absence of the Zeno Effect in Relativistic Quantum Field Theory

abstract:
  We study the time evolution of decaying particles in renormalizable models of
Relativistic Quantum Field Theory. Significant differences between the latter
and Non Relativistic Quantum Mechanics are found -in particular, the Zeno
effect seems to be absent in such RQFT models. Conventional renormalization
yields finite time behavior in some cases but fails to produce finite survival
probabilities in others.


title: Quantum synthesis of 3D vibrational states of trapped ions

abstract:
  A universal algorithm for a deterministic preparation of arbitrary
three--mode bosonic states is introduced. In particular, we consider
preparation of entangled quantum states of a vibrational motion of an ion
confined in a 3D trapping potential. The target states are established after a
proper sequence of laser stimulated Raman transitions. Stability of the
algorithm with respect to a technical noise is discussed and the distance
(fidelity) of outputs with respect to target states is studied.


title:
Controlling the flow of information in quantum cloners: Asymmetric
  cloning

abstract:
  We show that the distribution of information at the output of the quantum
cloner can be efficiently controlled via preparation of the quantum cloner. We
present a universal cloning network with the help of which asymmetric cloning
can be performed.


title: Higgs Field and Localization Problem

abstract:
  We analyze the role that the excited states of the Higgs field could play in
a possible solution to the so called localization problem of Quantum Theory. We
seek a solution to the aforementioned point without introducing additional
fundamental constants or extra hypotheses, as has been done in previous works.
  The electron and Higgs field do indeed have solitonic solutions. This last
feature renders, in the one-dimensional case, a solution to the localization
problem.


title: Optical control and entanglement of atomic Schroedinger fields

abstract:
  We develop a fully quantized model of a Bose-Einstein condensate driven by a
far off-resonant pump laser which interacts with a single mode of an optical
ring cavity. In the linear regime, the cavity mode exhibits spontaneous
exponential gain correlated with the appearance of two atomic field side-modes.
These side-modes and the cavity field are generated in a highly entangled
state, characterized by thermal intensity fluctuations in the individual modes,
but with two-mode correlation functions which violate certain classical
inequalities. By injecting an initial coherent field into the optical cavity
one can significantly decrease the intensity fluctuations at the expense of
reducing the correlations, thus allowing for optical control over the quantum
statistical properties of matter waves.


title: Generation of arbitrary quantum states of traveling fields

abstract:
  We show that any single-mode quantum state can be generated from the vacuum
by alternate application of the coherent displacement operator and the creation
operator. We propose an experimental implementation of the scheme for traveling
optical fields, which is based on field mixings and conditional measurements in
a beam splitter array, and calculate the probability of state generation.


title: Nonlocality Without Inequalities for all Pure Entangled States

abstract: This paper has been withdrawn by the authors.


title: General teleportation channel, singlet fraction and quasi-distillation

abstract:
  We prove a theorem on direct relation between the optimal fidelity $f_{max}$
of teleportation and the maximal singlet fraction $F_{max}$ attainable by means
of trace-preserving LQCC action (local quantum and classical communication).
For a given bipartite state acting on $C^d\otimes C^d$ we have $f_{max}=
{F_{max}d+1\over d+1}$. We assume completely general teleportation scheme
(trace preserving LQCC action over the pair and the third particle in unknown
state). The proof involves the isomorphism between quantum channels and a class
of bipartite states. We also exploit the technique of $U\otimes U^*$ twirling
states (random application of unitary transformation of the above form) and the
introduced analogous twirling of channels. We illustrate the power of the
theorem by showing that {\it any} bound entangled state does not provide better
fidelity of teleportation than for the purely classical channel. Subsequently,
we apply our tools to the problem of the so-called conclusive teleportation,
then reduced to the question of optimal conclusive increasing of singlet
fraction. We provide an example of state for which Alice and Bob have no chance
to obtain perfect singlet by LQCC action, but still singlet fraction
arbitrarily close to unity can be obtained with nonzero probability. We show
that a slight modification of the state has a threshold for singlet fraction
which cannot be exceeded anymore.


title: Quantum differential forms

abstract:
  Formalism of differential forms is developed for a variety of Quantum and
noncommutative situations.


title: Quantum Gambling

abstract:
  We present a two-party protocol for quantum gambling, a new task closely
related to coin tossing. The protocol allows two remote parties to play a
gambling game, such that in a certain limit it becomes a fair game. No
unconditionally secure classical method is known to accomplish this task.


title:
Mean-density Bogoliubov description of inhomogeneous Bose-condensed
  gases

abstract:
  A mean-density description of spatially-inhomogeneous Bose-condensed gases
based on Bogoliubov's method is introduced. The description assumes only a
large mean atomic density and so remains valid when the mean field collapses
due to phase diffusion. A spread in the number of particles in the condensate
is shown to lead to an anomalous coupling between the condensate and excited
modes. This coupling is due to the dependence of the condensate spatial
wavefunction on particle number and it could, in principle, be used for
reducing particle fluctuations in the condensate.


title:
Heisenberg picture approach to the invariants and the exact quantum
  motions for coupled parametric oscillators

abstract:
  For $N$-coupled generalized time-dependent oscillators, primary invariants
and a generalized invariant are found in terms of classical solutions. Exact
quantum motions satisfying the Heisenberg equation of motion are also found.
For number states and coherent states of the generalized invariant, the
uncertainties in positions and momenta are obtained.


title: An analytically solvable time dependent Jaynes Cummings model

abstract:
  Using the underlying su(2) algebra of the Jaynes-Cummings Model (JCM), we
construct a time dependent interaction term that allows analytical solution for
even off-resonance conditions. Exact solutions for the time evolution of any
state has been found. The effect of detuning on the Rabi oscillations and the
collapse and revival of inversion is indicated. It is also shown that at
resonance, the time dependent JCM is analytically solvable for an arbitrary
interaction term.


title: Locality problem, Bell's inequalities and EPR experiments

abstract:
  The question has been solved whether Bell's inequalities cover all possible
kinds of hidden-variable theories. It has been shown that the given nequalities
can be hardly derived when the changing space position of photon-pair source
together with the microscopic space structure of measuring devices are taken
into account; and when corresponding impact parameters (i.e., exact impact
points) of photons in individual measuring devices (polarizers) influence
measured values, in addition to usually considered characteristics.


title:
Finite Number and Finite Size Effects in Relativistic Bose-Einstein
  Condensation

abstract:
  Bose-Einstein condensation of a relativistic ideal Bose gas in a rectangular
cavity is studied. Finite size corrections to the critical temperature are
obtained by the heat kernel method. Using zeta-function regularization of
one-loop effective potential, lower dimensional critical temperatures are
calculated. In the presence of strong anisotropy, the condensation is shown to
occur in multisteps. The criteria of this behavior is that critical
temperatures corresponding to lower dimensional systems are smaller than the
three dimensional critical temperature.


title: Entanglement of projection and a new class of quantum erasers

abstract:
  We define a new measurement of entanglement, the entanglement of projection,
and find that it is natural to write the entanglements of formation and
assistance in terms of it. Our measure allows us to describe a new class of
quantum erasers which restore entanglement rather than just interference. Such
erasers can be implemented with simple quantum computer components. We propose
realistic optical versions of these erasers.


title:
Local, deterministic hidden variable theories based on a loophole in
  Bell's theorem

abstract:
  This paper furthers the long historical examination of and debate on the
foundations of quantum mechanics (QM) by presenting two local hidden variable
(LHV) rules in the context of the EPRB experiment which violate Bell's
inequality, but which are nevertheless local and deterministic under reasonable
definitions of the terms, and coincide approximately with the conventional QM
prediction. The theories are based on the general idea of probabilistic
detection of particles depending on an interaction of hidden variables within
the measuring device and particle, and relate mathematically to Fourier
analysis. The crucial discrepancy of variations in the hidden variable
distribution based on relative polarizer orientations is isolated which
invalidates assumptions in Bell-type theorems. The first theory can be analyzed
completely symbolically whereas the second was analyzed using numerical
methods. The properties of the second in particular are shown to be
approximately consistent with the reported results and uncertainties in all
three Aspect experiments. Variation in the total photon pairs detected over
orientations is shown to be a basic characteristic of these theories. Some
comments on the relevance of active vs. passive locality are made. Two sections
consider these ideas relative to energy conservation and the measurement
problem (collapse of the wavefunction). One section proposes new experiments.


title: Fisher information in quantum statistics

abstract:
  Braunstein and Caves (1994) proposed to use Helstrom's {\em quantum
information} number to define, meaningfully, a metric on the set of all
possible states of a given quantum system. They showed that the quantum
information is nothing else than the maximal Fisher information in a
measurement of the quantum system, maximized over all possible measurements.
Combining this fact with classical statistical results, they argued that the
quantum information determines the asymptotically optimal rate at which
neighbouring states on some smooth curve can be distinguished, based on
arbitrary measurements on $n$ identical copies of the given quantum system.
  We show that the measurement which maximizes the Fisher information typically
depends on the true, unknown, state of the quantum system. We close the
resulting loophole in the argument by showing that one can still achieve the
same, optimal, rate of distinguishability, by a two stage adaptive measurement
procedure.
  When we consider states lying not on a smooth curve, but on a manifold of
higher dimension, the situation becomes much more complex. We show that the
notion of ``distinguishability of close-by states'' depends strongly on the
measurement resources one allows oneself, and on a further specification of the
task at hand. The quantum information matrix no longer seems to play a central
role.


title: Squeezed Light Generation in Nonlinear System with Chaotic Dynamics

abstract:
  The squeezing in a nonlinear system with chaotic dynamics is considered. The
model describing interaction of collection of two-level atoms with a
single-mode of self-consistent field and an external field is analyzed. It is
shown that in the semiclassical limit, in contrast to the regular behaviour,
the chaotic dynamics result in: (i) an increase in squeezing, (ii) unstable
squeezing and contraction of time intervals of squeezing on large enough times.
The possibility of the experimental observation of the described effects is
discussed.

categories: quant-ph chao-dyn nlin.CD physics.optics


title:
Process, System, Causality, and Quantum Mechanics, A Psychoanalysis of
  Animal Faith

abstract:
  We shall argue in this paper that a central piece of modern physics does not
really belong to physics at all but to elementary probability theory. Given a
joint probability distribution J on a set of random variables containing x and
y, define a link between x and y to be the condition x=y on J. Define the {\it
state} D of a link x=y as the joint probability distribution matrix on x and y
without the link. The two core laws of quantum mechanics are the Born
probability rule, and the unitary dynamical law whose best known form is the
Schrodinger's equation. Von Neumann formulated these two laws in the language
of Hilbert space as prob(P) = trace(PD) and D'T = TD respectively, where P is a
projection, D and D' are (von Neumann) density matrices, and T is a unitary
transformation. We'll see that if we regard link states as density matrices,
the algebraic forms of these two core laws occur as completely general theorems
about links. When we extend probability theory by allowing cases to count
negatively, we find that the Hilbert space framework of quantum mechanics
proper emerges from the assumption that all D's are symmetrical in rows and
columns. On the other hand, Markovian systems emerge when we assume that one of
every linked variable pair has a uniform probability distribution. By
representing quantum and Markovian structure in this way, we see clearly both
how they differ, and also how they can coexist in natural harmony with each
other, as they must in quantum measurement, which we'll examine in some detail.
Looking beyond quantum mechanics, we see how both structures have their special
places in a much larger continuum of formal systems that we have yet to look
for in nature.


title: Method of quantum computation with ``hot'' trapped ions

abstract:
  We present a novel method of performing quantum logic gates in trapped ion
quantum computers which does not require the ions to be cooled down to their
vibrational center of mass (CM) mode ground state. Our scheme employs adiabatic
passages and the conditional phase shift first investigated by D'Helon and
Milburn (C.~D'Helon and G.J.~Milburn, Phys. Rev. A {\bf 54}, 5141 (1996)).


title: Lorentz-covariant quantum mechanics and preferred frame

abstract:
  In this paper the relativistic quantum mechanics is considered in the
framework of the nonstandard synchronization scheme for clocks. Such a
synchronization preserves Poincar{\'e} covariance but (at least formally)
distinguishes an inertial frame. This enables to avoid the problem of a
noncausal transmision of information related to breaking of the Bell's
inequalities in QM. Our analysis has been focused mainly on the problem of
existence of a proper position operator for massive particles. We have proved
that in our framework such an operator exists for particles with arbitrary
spin. It fulfills all the requirements: it is Hermitean and covariant, it has
commuting components and moreover its eigenvectors (localised states) are also
covariant. We have found the explicit form of the position operator and have
demonstrated that in the preferred frame our operator coincides with the
Newton--Wigner one. We have also defined a covariant spin operator and have
constructed an invariant spin square operator. Moreover, full algebra of
observables consisting of position operators, fourmomentum operators and spin
operators is manifestly Poincar\'e covariant in this framework. Our results
support expectations of other authors (Bell, Eberhard) that a consistent
formulation of quantum mechanics demands existence of a preferred frame.


title: Dynamical Cooling of Trapped Gases I: One Atom Problem

abstract:
  We study the laser cooling of one atom in an harmonic trap beyond the
Lamb-Dicke regime. By using sequences of laser pulses of different detunings we
show that the atom can be confined into just one state of the trap, either the
ground state or an excited state of the harmonic potential. The last can be
achieved because under certain conditions an excited state becomes a dark
state. We study the problem in one and two dimensions. For the latter case a
new cooling mechanism is possible, based on the destructive interference
between the effects of laser fields in different directions, which allows the
creation of variety of dark states. For both, one and two dimensional cases,
Monte Carlo simulations of the cooling dynamics are presented.


title: Born's Principle, Action-Reaction Problem and Arrow of Time

abstract:
  We try to obtain Born's principle as a result of a subquantum heat death,
using classical ${\cal H}$-theorem and the definition of a proper quantum
${\cal H}$-theorem, within the framwork of Bohm's theory. We shall show the
possibility of solving the problem of action-reaction asymmetry present in
Bohm's theory and the arrow of time problem in our procedure.


title: Path Integrals with Kinetic Coupling Potentials

abstract:
  Path integral solutions with kinetic coupling potentials $\propto p_1p_2$ are
evaluated. As examples I give a Morse oscillator, i.e., a model in molecular
physics, and the double pendulum in the harmonic approximation. The former is
solved by some well-known path integral techniques, whereas the latter by an
affine transformation.


title:
Dephasing of Josephson oscillations between two coupled Bose-Einstein
  condensates

abstract:
  We study the dynamics of the relative phase between two Bose-Einstein
condensates coupled via collisions and via a Josephson-like coupling. We derive
the equations of the motion for the relative phase and the relative number
operators from the second quantized Hamiltonian of the system using a quantum
field theoretical approach. We distinguish the cases in which the two
condensates are in the same trap or in two different traps and study the
influence of this difference on the first order correlation function of atomic
fields. In identical traps this function does not undergo dephasing. We
calculate the dephasing time for the case of different traps.


title: Quantum State Separation, Unambiguous Discrimination and Exact Cloning

abstract:
  Unambiguous discrimination and exact cloning reduce the square-overlap
between quantum states, exemplifying the more general type of procedure we term
state separation. We obtain the maximum probability with which two equiprobable
quantum states can be separated by an arbitrary degree, and find that the
established bounds on the success probabilities for discrimination and cloning
are special cases of this general bound. The latter also gives the maximum
probability of successfully producing N exact copies of a quantum system whose
state is chosen secretly from a known pair, given M initial realisations of the
state, where N>M. We also discuss the relationship between this bound and that
on unambiguous state discrimination.


title:
Are quantum teleportation and cryptography predicted by quantum
  mechanics?

abstract:
  It has been shown that the predictions of some new phenomena (e.g.,
teleportation and cryptography) are based on some assumptions added to the
quantum-mechanical model or modifying some of its basic axioms. The hitherto
experiments presented as a support of the mentioned phenomena may be hardly
regarded as sufficient, as they may be interpreted alternatively on the basis
of simple interference processes.


title:
Quantum Mechanical Black Holes: Towards a Unification of Quantum
  Mechanics and General Relativity

abstract:
  In this paper, starting from vortices we are finally lead to a treatment of
Fermions as Kerr-Newman type Black Holes wherein we identify the horizon at the
particle's Compton wavelength periphery. A naked singularity is avoided and the
singular processes inside the horizon of the Black Hole are identified with
Quantum Mechanical effects within the Compton wavelength. Inertial mass,
gravitation, electromagnetism and even QCD type interactions emerge from such a
description including relative strengths and also other features like the
anomalous gyromagnetic ratio, the discreteness of the charge, the reason why
the electron's field emerges from Newman's complex transformation in General
Relativity, a rationale for the left handedness of neutrinos and the
matter-antimatter imbalance. This model describes the most fundamental stable
Fermions viz., the electrons, neutrinos and approximately the quarks. It also
harmoniously unifies the hydrodynamical, monopole and classical relativistic
perspectives.


title:
q deformation by intertwining with application to the singular
  oscillator

abstract:
  We present a version of q-deformed calculus based on deformed counterparts of
Darboux intertwining operators. The case in which the deformed transformation
function is of the vacuum type is detailed, but the extension to counterparts
of excited states used as Darboux transformation functions is also formally
discussed. The method leads to second-order Fokker-Planck-like deformed
operators which may be considered as supersymmetric partners, though for a sort
of q-deformed open systems, i.e., those possessing q nonlocal drift terms,
potential part, as well as q-spreaded vacuum fluctuations. The undeformed limit
corresponds to the conservative case, since all q nonlocalities wash out. The
procedure is applied to the x^{-2} singular oscillator, for which we also
present a formal q generalization of the Bagrov-Samsonov coherent states


title: Variations on the Theme of the Greenberger-Horne-Zeilinger Proof

abstract:
  Three arguments based on the Greenberger-Horne-Zeilinger (GHZ) proof of the
nonexistence of local hidden variables are presented. The first is a
description of a simple game which a team that uses the GHZ method will always
win. The second uses counterfactuals in an attempt to show that quantum theory
is nonlocal in a stronger sense than is implied by the nonexistence of local
hidden variables and the third describes peculiar features of time-symmetrized
counterfactuals in quantum theory.


title: Probability and Entropy in Quantum Theory

abstract:
  Entropic arguments are shown to play a central role in the foundations of
quantum theory. We prove that probabilities are given by the modulus squared of
wave functions, and that the time evolution of states is linear and also
unitary.

categories: quant-ph cond-mat.stat-mech gr-qc math.PR


title: Entropy of Classical Histories

abstract:
  We consider a number of proposals for the entropy of sets of classical
coarse-grained histories based on the procedures of Jaynes, and prove a series
of inequalities relating these measures. We then examine these as a function of
the coarse-graining for various classical systems, and show explicitly that the
entropy is minimized by the finest-grained description of a set of histories.
We propose an extension of the second law of thermodynamics to the entropy of
histories. We briefly discuss the implications for decoherent or consistent
history formulations of quantum mechanics.


title: A Study of Parallel Self-Organizing Map

abstract:
  A Parallel Self-Organizing Map (Parallel-SOM) is proposed to modify Kohonen's
SOM in parallel computing environment. In this model, two separate layers of
neurons are connected together. The number of neurons in both layers and
connections between them is the product of the number of all elements of input
signals and the number of possible classification of the data. With this
structure the conventional repeated learning procedure is modified to learn
just once. The once learning manner is more similar to human learning and
memorizing activities. During training, weight updating is managed through a
sequence of operations among some transformation and operation matrices. Every
connection between neurons of input/output layers is considered as a
independent processor. In this way, all elements of the Euclidean distance
matrix and weight matrix are calculated simultaneously. The minimum distance of
every line of distance matrix can be found by Grover's search algorithm. This
synchronization feature improves the weight updating sequence significantly.
With a typical classification example, the convergence result demonstrates
efficient performance of Parallel-SOM. Theoretic analysis and proofs also show
some important properties of proposed model. Especially, the paper proves that
Parallel-SOM has the same convergence property as Kohonen's SOM, but the
complexity of former is reduced obviously.


title:
Continuous quantum measurement with particular output: pure wavefunction
  evolution instead of decoherence

abstract:
  We consider a continuous measurement of a two-level system (double-dot) by
weakly coupled detector (tunnel point contact nearby). While usual treatment
leads to the gradual system decoherence due to the measurement, we show that
the knowledge of the measurement result can restore the pure wavefunction at
any time (this can be experimentally verified). The formalism allows to write a
simple Langevin equation for the random evolution of the system density matrix
which is reflected and caused by the stochastic detector output. Gradual
wavefunction ``collapse'' and quantum Zeno effect are naturally described by
the equation.


title: Parallel Quantum Computation and Quantum Codes

abstract:
  We propose a definition of QNC, the quantum analog of the efficient parallel
class NC. We exhibit several useful gadgets and prove that various classes of
circuits can be parallelized to logarithmic depth, including circuits for
encoding and decoding standard quantum error-correcting codes, or more
generally any circuit consisting of controlled-not gates, controlled pi-shifts,
and Hadamard gates. Finally, while we note the Quantum Fourier Transform can be
parallelized to linear depth, we conjecture that an even simpler `staircase'
circuit cannot be parallelized to less than linear depth, and might be used to
prove that QNC < QP.


title:
An Alternative Algorithm for the Database Search Problem on a Quantum
  Computer

abstract: The paper has been withdrawn


title: Why can an electron mass vary from zero to infinity?

abstract:
  When a particle is in high speed or bound in the Coulomb potential of point
nucleus, the variation of its mass can be ascribed to the variation of relative
ratio of hiding antimatter to matter in the particle. At two limiting cases,
the ratio approaches to 1.


title: Unextendible Product Bases and Bound Entanglement

abstract:
  An unextendible product basis (UPB) for a multipartite quantum system is an
incomplete orthogonal product basis whose complementary subspace contains no
product state. We give examples of UPBs, and show that the uniform mixed state
over the subspace complementary to any UPB is a bound entangled state. We
exhibit a tripartite 2x2x2 UPB whose complementary mixed state has tripartite
entanglement but no bipartite entanglement, i.e. all three corresponding 2x4
bipartite mixed states are unentangled. We show that members of a UPB are not
perfectly distinguishable by local POVMs and classical communication.


title: The Universe of Fluctuations

abstract:
  We discuss the recent model of a Quantum Mechanical Black Hole (QMBH) which
describes the most fundamental known particles, the leptons and approximately
the quarks in terms of the Kerr-Newman Black Hole with a naked singularity
shielded by Zitterbewegung effects. This goes beyond the Zitterbewegung and
self interaction models of Barut and Bracken, Hestenes, Chacko and others and
provides a unified picture which amongst other things gives a rationale for and
an insight into: 1. The apparently inexplicable reason why complex space-time
transformations lead to the Kerr-Newman metric in General Relativity. 2. The
value of the fine structure constant. 3. The ratio between electromagnetic and
gravitational interaction strengths. 4. The anomalous gyromagnetic ratio for
the electron. 5. Why the neutrino is left-handed. 6. Why the charge is
discrete. In the spirit of Effective Field Theories, this model provides an
alternative formalism for Quantum Theory and also for its combination with
General Relativity. Finally a mechanism for the formation of these QMBH or
particles is explored within the framework of Stochastic Electrodynamics, QED
and Quantum Statistical Mechanics. The cosmological implications are then
examined. It turns out that a surprisingly large number of facts, including
some which were hitherto inexplicable, follow as a consequence of the model.
These include a theoretical deduction of the Mass, Radius and Age of the
Universe, also the values of Hubble's constant and the Cosmological constant.


title: Will small particles exhibit Brownian motion in the quantum vacuum?

abstract:
  The Brownian motion of small particles interacting with a field at a finite
temperature is a well-known and well-understood phenomenon. At zero
temperature, even though the thermal fluctuations are absent, quantum fields
still possess vacuum fluctuations. It is then interesting to ask whether a
small particle that is interacting with a quantum field will exhibit Brownian
motion when the quantum field is assumed to be in the vacuum state. In this
paper, we study the cases of a small charge and an imperfect mirror interacting
with a quantum scalar field in (1+1) dimensions. Treating the quantum field as
a classical stochastic variable, we write down a Langevin equation for the
particles. We show that the results we obtain from such an approach agree with
the results obtained from the fluctuation-dissipation theorem. Unlike the
finite temperature case, there exists no special frame of reference at zero
temperature and hence it is essential that the particles do not break Lorentz
invariance. We find that that the scalar charge breaks Lorentz invariance,
whereas the imperfect mirror does not. We conclude that small particles such as
the imperfect mirror {\it will} exhibit Brownian motion even in the quantum
vacuum, but this effect can be so small that it may prove to be difficult to
observe it experimentally.


title: Continuous quantum measurements of a particle in a Paul trap

abstract:
  We calculate the propagator of a particle caught in a Paul trap and subject
to the continuous quantum measurement of its position. The probabilities of the
measurement outputs, the possible trajectories of the particle, are also found.
This enables us to propose a series of experiments that would allow to confront
the predictions of one of the models that describe the interaction between a
measured quantum system and measuring device, namely the so called Restricted
Path-Integral Formalism, with the experiment.


title:
Some Aspects of Generalized Contact Interaction in One-Dimensional
  Quantum Mechanics

abstract:
  We construct a one-dimensional contact interaction ($\epsilon$ potential)
which induces the discontinuity of the wave function while keeping its
derivative continuous. By combining the $\epsilon$ potential and the Dirac's
$\delta$ function, we construct most general one-dimensional contact
interactions allowable under the time reversal symmetry. We present some
elementary results for the scattering problem which suggest a dual relation
between $\delta$ and $\epsilon$ potentials.

categories: quant-ph cond-mat hep-th nlin.SI nucl-th solv-int


title:
Charge Renormalization in a New Kind of Non-Local Quantum
  Electrodynamics

abstract:
  The goal of this message is to calculate radiative corrections to the
Sommerfeld fine structure constant in the framework of a new QED in which
particles are described by bilocal fields. The bare constant is 1/136 where 136
is a dimension of the dynamical group of the bihamiltonian system underlying
the suggested elementary particle theory. Our calculations in the second order
of perturbation theory give the renormalized Sommerfeld constant 1/137.0345. We
believe the difference (137.0359 - 137.0345) between corresponding experimental
and theoretical values may be understood as corrections of the fourth order.


title: Subdecoherent Information Encoding in a Quantum-Dot Array

abstract:
  A potential implementation of quantum-information schemes in semiconductor
nanostructures is studied. To this end, the formal theory of quantum encoding
for avoiding errors is recalled and the existence of noiseless states for model
systems is discussed. Based on this theoretical framework, we analyze the
possibility of designing noiseless quantum codes in realistic semiconductor
structures. In the specific implementation considered, information is encoded
in the lowest energy sector of charge excitations of a linear array of quantum
dots. The decoherence channel considered is electron-phonon coupling We show
that besides the well-known phonon bottleneck, reducing single-qubit
decoherence, suitable many-qubit initial preparation as well as register design
may enhance the decoherence time by several orders of magnitude. This behaviour
stems from the effective one-dimensional character of the phononic environment
in the relevant region of physical parameters.


title:
Schr\"{o}dinger Equation with the Potential $V(r)=a r^2+b r^{-4}+c
  r^{-6}$

abstract:
  By making use of an ${\it ansatz}$ for the eigenfunction, we obtain the exact
solutions to the Schr\"{o}dinger equation with the anharmonic potential,
$V(r)=a r^2+b r^{-4}+c r^{-6}$, both in three dimensions and in two dimensions,
where the parameters $a$, $b$, and $c$ in the potential satisfy some
constraints.


title: Levinson's Theorem for the Klein-Gordon Equation in Two Dimensions

abstract:
  The two-dimensional Levinson theorem for the Klein-Gordon equation with a
cylindrically symmetric potential $V(r)$ is established. It is shown that
$N_{m}\pi=\pi (n_{m}^{+}-n_{m}^{-})=
[\delta_{m}(M)+\beta_{1}]-[\delta_{m}(-M)+\beta_{2}]$, where $N_{m}$ denotes
the difference between the number of bound states of the particle $n_{m}^{+}$
and the ones of antiparticle $n_{m}^{-}$ with a fixed angular momentum $m$, and
the $\delta_{m}$ is named phase shifts. The constants $\beta_{1}$ and
$\beta_{2}$ are introduced to symbol the critical cases where the half bound
states occur at $E=\pm M$.


title:
An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR
  quantum computer

abstract:
  A new approach to the implementation of a quantum computer by high-resolution
nuclear magnetic resonance (NMR) is described. The key feature is that two or
more line-selective radio-frequency pulses are applied simultaneously. A
three-qubit quantum computer has been investigated using the 400 MHz NMR
spectrum of the three coupled protons in 2,3-dibromopropanoic acid. It has been
employed to implement the Deutsch-Jozsa algorithm for distinguishing between
constant and balanced functions. The extension to systems containing more
coupled spins is straightforward and does not require a more protracted
experiment.


title: Methods for Reliable Teleportation

abstract:
  Recent experimental results and proposals towards implementation of quantum
teleportation are discussed. It is proved that reliable (theoretically, 100%
probability of success) teleportation cannot be achieved using the methods
applied in recent experiments, i.e., without quantum systems interacting one
with the other. Teleportation proposal involving atoms and electro-magnetic
cavities are reviewed and the most feasible methods are described. In
particular, the language of nonlocal measurements has been applied which has
also been used for presenting a method for teleportation of quantum states of
systems with continuous variables.


title: Quantum Coherence Oscillations in Antiferromagnetic Chains

abstract:
  Macroscopic quantum coherence oscillations in mesoscopic antiferromagnets may
appear when the anisotropy potential creates a barrier between the
antiferromagnetic states with opposite orientations of the Neel vector. This
phenomenon is studied for the physical situation of the nuclear spin system of
eight Xe atoms arranged on a magnetic surface along a chain. The oscillation
period is calculated as a function of the chain constant. The environmental
decoherence effects at finite temperature are accounted assuming a dipole
coupling between the spin chain and the fluctuating magnetic field of the
surface. The numerical calculations indicate that the oscillations are damped
by a rate $\sim (N-1)/ \tau$, where $N$ is the number of spins and $\tau$ is
the relaxation time of a single spin.


title: Optimal Quantum Clocks

abstract:
  A quantum clock must satisfy two basic constraints. The first is a bound on
the time resolution of the clock given by the difference between its maximum
and minimum energy eigenvalues. The second follows from Holevo's bound on how
much classical information can be encoded in a quantum system. We show that
asymptotically, as the dimension of the Hilbert space of the clock tends to
infinity, both constraints can be satisfied simultaneously. The experimental
realization of such an optimal quantum clock using trapped ions is discussed.


title: Copying of entangled states and the degradation of correlations

abstract:
  We investigate the degree to which entanglement survives when a correlated
pair of two-state systems are copied using either local or non-local processes.
We show how the copying process degrades the entanglement, due to a residual
correlation between the copied output and the copying machine (itself made of
qubits).


title: Note on Explicit Formulae for the Bures Metric

abstract:
  The aim of this paper is to derive explicit formulae for the Riemannian Bures
metric on the manifold of (finite dimensional) nondegenerate density matrices.
The computation of the Bures metric using the presented equations does not
require any diagonalization procedure and uses matrix products, determinants
and traces, only.


title: Are There Dynamical Laws?

abstract:
  The nature of a physical law is examined, and it is suggested that there may
not be any fundamental dynamical laws. This explains the intrinsic
indeterminism of quantum theory. The probabilities for transition from a given
initial state to a final state then depends on the quantum geometry that is
determined by symmetries, which may exist as relations between states in the
absence of dynamical laws. This enables the experimentally well confirmed
quantum probabilities to be derived from the geometry of Hilbert space, and
gives rise to effective probabilistic laws. An arrow of time which is
consistent with the one given by the second law of thermodynamics, regarded as
an effective law, is obtained. Symmetries are used as the basis for a new
proposed paradigm of physics. This gives rise naturally to the gravitational
and gauge fields from the symmetry group of the standard model, and a general
procedure for obtaining interactions from any symmetry group.


title: Quantization of the Dirac Fibre: a New Way in the Particle Physics

abstract:
  The problem of ultraviolet divergences is analysed in the quantum field
theory. It was found that it has common roots with the problem of cosmological
singularity. In the context of fibre bundles the second quantization method is
represented as a procedure of the quantization for vector bundle cross-section.
It is shown to be quite a different quantization way called as a fibre
quantization which leads to an idea on existence of the non-standard dynamical
system, i.e. the relativistic be-Hamiltonian system. It takes place on
supersmall distances and is well described by the mathematical apparatus for
the non-unitary quantum scheme using a dual pair of topological vector spaces
in terms of the non-Hermitian form. The article contains the proof of the
theorem on radical changes in space and in matter structure taking place for a
very high density of matter: the phase transitions ``Lagrangian field system
(elementary particles) $\to$ relativistic bi-Hamiltonian system (Feynman's
partons)'' and ``continuum $\to$ discontinuum''.
  All required calculations in the framework of the proposed theory are
published in the Russian periodicals. The purpose of this article is to replace
the calculations by reasonings and concepts. The present article begins the
systematic exposition of principles of the theory.


title: Non-Fock Representations of Heisenberg Algebras

abstract:
  The purpose of this paper is to present the mathematical techniques of a new
quantum scheme using a dual pair of reflexive topological vector spaces in
terms of the non-Hermitian form. The scheme is shown to be a generalization of
the well-known unitary quantum theory and to describe jointly quantum objects
and physical vacuum.


title:
Stabilization of Deterministically Chaotic Systems by Interference and
  Quantum Measurements: The Ikeda Map Case

abstract:
  We propose a method which can effectively stabilize fixed points in the
classical and quantum dynamics of a phase-sensitive chaotic system with
feedback. It is based on feeding back a selected quantum sub-ensemble whose
phase and amplitude stabilize the otherwise chaotic dynamics. Although the
method is rather general, we apply it to realizations of the inherently chaotic
Ikeda map. One suggested realization involves the Mach-Zender interferometer
with Kerr nonlinearity. Another realization involves a trapped ion interacting
with laser fields.


title:
Trapping state restoration in the randomly-driven Jaynes-Cummings model
  by conditional measurements

abstract:
  We propose a scheme which can effectively restore fixed points in the quantum
dynamics of repeated Jaynes-Cummings interactions followed by atomic state
measurements, when the interaction times fluctuate randomly. It is based on
selection of superposed atomic states whose phase correlations tend to suppress
the phase fluctuations of each separate state. One suggested realization
involves the convergence of the cavity field distribution to a single Fock
state by conditional measurements performed on two-level atoms with fluctuating
velocities after they cross the cavity. Another realization involves a trapped
ion whose internal-motional state coupling fluctuates randomly. Its motional
state is made to converge to a Fock state by conditional measurements of the
internal state of the ion.


title:
Supersymmetric Method for Constructing Quasi-Exactly and
  Conditionally-Exactly Solvable Potentials

abstract:
  Using supersymmetric quantum mechanics we develop a new method for
constructing quasi-exactly solvable (QES) potentials with two known
eigenstates. This method is extended for constructing conditionally-exactly
solvable potentials (CES). The considered QES potentials at certain values of
parameters become exactly solvable and can be treated as CES ones.


title:
A mathematical foundation of quantum information and quantum computer
  -on quantum mutual entropy and entanglement-

abstract:
  The study of mutual entropy (information) and capacity in classica l system
was extensively done after Shannon by several authors like Kolmogor ov and
Gelfand. In quantum systems, there have been several definitions of t he mutual
entropy for classical input and quantum output. In 1983, the autho r defined
the fully quantum mechanical mutual entropy by means of the relati ve entropy
of Umegaki, and it has been used to compute the capacity of quant um channel
for quantum communication process; quantum input-quantum output.
  Recently, a correlated state in quantum syatems, so-called quantum entangled
state or quantum entanglement, are used to study quntum information, in part
icular, quantum computation, quantum teleportation, quantum cryptography.
  In this paper, we mainly discuss three things below: (1) We point out the di
fference between the capacity of quantum channel and that of classical-quant
um-classical channel. (2) So far the entangled state is merely defined as a
non-separable state, we give a wider definition of the entangled state and c
lassify the entangled states into three categories. (3) The quantum mutual e
ntropy for an entangled state is discussed. The above (2) and (3) are a join t
work with Belavkin.


title: Quantum-Non-Demolition Endoscopic Tomography

abstract:
  We present a new indirect method to measure the quantum state of a single
mode of the electromagnetic field in a cavity. Our proposal combines the idea
of (endoscopic) probing and that of tomography in the sense that the signal
field is coupled via a quantum-non-demolition Hamiltonian to a meter field on
which then quantum state tomography is performed using balanced homodyne
detection. This technique provides full information about the signal state. We
also discuss the influence of the measurement of the meter on the signal field.


title: A note on the paper, "Quarks or Leptons?"

abstract:
  In the context of a recent description of Fermions as Kerr-Newman type black
holes with Quantum Mechanical inputs, it is shown how the quark picture can be
recovered. The advantage is that in the process we obtain a rationale for such
features as the puzzling fractional charges of the quarks, their masses,
confinement and handedness in a unified scheme.


title: Low Dimensional Electrons

abstract:
  Motivated by recent work on nano tubes indicating one dimensional quantum
effects and studies of two dimensional electron gas, we consider a recent model
of Fermions as Kerr-Newman type black holes with quantum mechanical effects.
Such an anyonic fractionally charged quasi-electron picture is deduced and
identified with quarks.


title: Using Parity Kicks for Decoherence Control

abstract:
  We show how it is possible to suppress decoherence using tailored external
forcing acting as pulses. In the limit of infinitely frequent pulses
decoherence and dissipation are completely frozen; however, a significant
decoherence suppression is already obtained when the frequency of the pulses is
of the order of the reservoir typical frequency scale. This method could be
useful in particular to suppress the decoherence of the center-of-mass motion
in ion traps.


title: Approximate quantum counting on an NMR ensemble quantum computer

abstract:
  We demonstrate the implementation of a quantum algorithm for estimating the
number of matching items in a search operation using a two qubit nuclear
magnetic resonance (NMR) quantum computer.


title: Using Conditional Measurements to Combat Decoherence

abstract:
  With the help of some remarkable examples, it is shown that conditional
measurements performed on two-level atoms just after they have interacted with
a resonant cavity field mode are able to recover the coherence of number-state
superpositions, which is lost due to dissipation.


title: Dephasing and collapse in continuous measurement of a single system

abstract:
  We show that long standing debates on the collapse and the role of the
observer in quantum mechanics can be resolved experimentally via a
nondistructive continuous monitoring of a single quantum system. An example of
such a system, coupled with the point-contact detector is presented. The
detailed quantum mechanical analysis of the entire system (including the
detector) shows that under certain conditions the measurement collapse would
generate distinctive effects in the detector behavior, which can be
experimentally investigated.


title: Still Baking

abstract:
  We present here a simple proof of the non-existence of a non-periodic
invariant point for the quantum baker's map propagator presented in Rubin and
Salwen (Annals of Physics, 1998), for Planck's constant h=1/N and N a positive
integer.


title:
On the Path Integral Treatment for an Aharonov-Bohm Field on the
  Hyperbolic Plane

abstract:
  In this paper I discuss by means of path integrals the quantum dynamics of a
charged particle on the hyperbolic plane under the influence of an
Aharonov-Bohm gauge field. The path integral can be solved in terms of an
expansion of the homotopy classes of paths. I discuss the interference pattern
of scattering by an Aharonov-Bohm gauge field in the flat space limit, yielding
a characteristic oscillating behavior in terms of the field strength. In
addition, the cases of the isotropic Higgs-oscillator and the Kepler-Coulomb
potential on the hyperbolic plane are shortly sketched.


title: Quantum Carry-Save Arithmetic

abstract:
  This paper shows how to design efficient arithmetic elements out of quantum
gates using "carry-save" techniques borrowed from classical computer design.
This allows bit-parallel evaluation of all the arithmetic elements required for
Shor's algorithm, including modular arithmetic, deferring all carry propagation
until the end of the entire computation. This reduces the quantum gate delay
from O(N^3) to O(N log N) at a cost of increasing the number of qubits required
from O(N) to O(N^2).


title:
Realization scheme for continuous fuzzy measurement of energy and the
  monitoring of a quantum transition

abstract:
  The continuous fuzzy measurement of energy of a single two-level system
driven by a resonant external field is studied. An analysis is given in the
framework of the phenomenological restricted path integral approach (RPI)
(which reduces effectively to a Schrodinger equation with a complex
Hamiltonian) as well as with reference to the microphysical details of a class
of concrete physical realizations. Within the RPI approach it is demonstrated
that for appropriately adjusted fuzziness, information about the evolution of
the state of the system can be read off from the measurement readout E(t). It
is shown furthermore how a measurement of this type may be realized by a series
of weak and short interactions of the two-level system with a quantum
mechanical meter system. After each interaction a macroscopic measuring
apparatus causes the meter to transit into one of two states. The result is
used to generate the energy readout E(t). In this way a complete agreement with
the RPI approach is demonstrated which thus obtains an operational
interpretation.


title: Strong Converse to the Quantum Channel Coding Theorem

abstract:
  A lower bound on the probability of decoding error of quantum communication
channel is presented. The strong converse to the quantum channel coding theorem
is shown immediately from the lower bound. It is the same as Arimoto's method
exept for the difficulty due to non-commutativity.


title: Quantum radiation in a plane cavity with moving mirrors

abstract:
  We consider the electromagnetic vacuum field inside a perfect plane cavity
with moving mirrors, in the nonrelativistic approximation. We show that low
frequency photons are generated in pairs that satisfy simple properties
associated to the plane geometry. We calculate the photon generation rates for
each polarization as functions of the mechanical frequency by two independent
methods: on one hand from the analysis of the boundary conditions for moving
mirrors and with the aid of Green functions; and on the other hand by an
effective Hamiltonian approach. The angular and frequency spectra are discrete,
and emission rates for each allowed angular direction are obtained. We discuss
the dependence of the generation rates on the cavity length and show that the
effect is enhanced for short cavity lengths. We also compute the dissipative
force on the moving mirrors and show that it is related to the total radiated
energy as predicted by energy conservation.


title: Quantum repeaters based on entanglement purification

abstract:
  We study the use of entanglement purification for quantum communication over
long distances. For distances much longer than the coherence length of a
corresponding noisy quantum channel, the fidelity of transmission is usually so
low that standard purification methods are not applicable. It is however
possible to divide the channel into shorter segments that are purified
separately and then connected by the method of entanglement swapping. This
method can be much more efficient than schemes based on quantum error
correction, as it makes explicit use of two-way classical communication. An
important question is how the noise, introduced by imperfect local operations
(that constitute the protocols of purification and the entanglement swapping),
accumulates in such a compound channel, and how it can be kept below a certain
noise level. To treat this problem, we first study the applicability and the
efficiency of entanglement purification protocols in the situation of imperfect
local operations. We then present a scheme that allows entanglement
purification over arbitrary long channels and tolerates errors on the per-cent
level. It requires a polynomial overhead in time, and an overhead in local
resources that grows only logarithmically with the length of the channel.


title: Photon statistics of a random laser

abstract:
  A general relationship is presented between the statistics of thermal
radiation from a random medium and its scattering matrix S. Familiar results
for black-body radiation are recovered in the limit S to 0. The mean photocount
is proportional to the trace of 1-SS^dagger, in accordance with Kirchhoff's law
relating emissivity and absorptivity. Higher moments of the photocount
distribution are related to traces of powers of 1-SS^dagger, a generalization
of Kirchhoff's law. The theory can be applied to a random amplifying medium (or
"random laser") below the laser threshold, by evaluating the Bose-Einstein
function at a negative temperature. Anomalously large fluctuations are
predicted in the photocount upon approaching the laser threshold, as a
consequence of overlapping cavity modes with a broad distribution of spectral
widths.


title:
A topos perspective on the Kochen-Specker theorem: II. Conceptual
  Aspects, and Classical Analogues:

abstract:
  In a previous paper, we have proposed assigning as the value of a physical
quantity in quantum theory, a certain kind of set (a sieve) of quantities that
are functions of the given quantity. The motivation was in part physical---such
a valuation illuminates the Kochen-Specker theorem; and in part
mathematical---the valuation arises naturally in the topos theory of
presheaves.
  This paper discusses the conceptual aspects of this proposal. We also
undertake two other tasks. First, we explain how the proposed valuations could
arise much more generally than just in quantum physics; in particular, they
arise as naturally in classical physics. Second, we give another motivation for
such valuations (that applies equally to classical and quantum physics). This
arises from applying to propositions about the values of physical quantities
some general axioms governing partial truth for any kind of proposition.


title: A realistic interpretation for quantum mechanics

abstract:
  We propose a realistic and nonlocal interpretation for quantum mechanics,
which requires new mathematical, physical and philosophical foundations for
space-time. Our theory violates Bell's inequality. We also discuss the cat
paradox.


title:
Asymptotic quantum estimation theory for the displaced thermal states
  family

abstract:
  Concerning state estimation, we will compare two cases. In one case we cannot
use the quantum correlations between samples. In the other case, we can use
them. In addition, under the later case, we will propose a method which
simultaneously measures the complex amplitude and the expected photon number
for the displaced thermal states.


title: Quasi-classical dynamics of interacting Bose condensates

abstract:
  The dynamics of the composition of uniform Bose condensates involving two
species capable of reciprocal interconversion is treated in terms of a
collective quasi-spin model. This collective model quickly reduces to classical
form towards the thermodynamic limit. Quantum solutions are easily obtained
numerically short of this limit which give insight into the dynamically
relevant correlation processes.


title: Quantum Wavelet Transforms: Fast Algorithms and Complete Circuits

abstract:
  The quantum Fourier transform (QFT), a quantum analog of the classical
Fourier transform, has been shown to be a powerful tool in developing quantum
algorithms. However, in classical computing there is another class of unitary
transforms, the wavelet transforms, which are every bit as useful as the
Fourier transform. Wavelet transforms are used to expose the multi-scale
structure of a signal and are likely to be useful for quantum image processing
and quantum data compression. In this paper, we derive efficient, complete,
quantum circuits for two representative quantum wavelet transforms, the quantum
Haar and quantum Daubechies $D^{(4)}$ transforms. Our approach is to factor the
operators for these transforms into direct sums, direct products and dot
products of unitary matrices. In so doing, we find that permutation matrices, a
particular class of unitary matrices, play a pivotal role. Surprisingly, we
find that operations that are easy and inexpensive to implement classically are
not always easy and inexpensive to implement quantum mechanically, and vice
versa. In particular, the computational cost of performing certain permutation
matrices is ignored classically because they can be avoided explicitly.
However, quantum mechanically, these permutation operations must be performed
explicitly and hence their cost enters into the full complexity measure of the
quantum transform. We consider the particular set of permutation matrices
arising in quantum wavelet transforms and develop efficient quantum circuits
that implement them. This allows us to design efficient, complete quantum
circuits for the quantum wavelet transform.


title: Primal structure of Quantum Mechanics - A critique and an alternative

abstract:
  The basic premise of Quantum Mechanics, embodied in the doctrine of
wave-particle duality, assigns both, a particle and a wave structure to the
physical entities. The classical laws describing the motion of a particle and
the evolution of a wave are assumed to be correct. Gauge Mechanics treats the
discrete entities as particles, and their motion is described by an extension
of the corresponding classical laws. Quantum mechanical interpretations of
various observations and their implications, including some issues that are
usually ignored, are presented and compared here with the gauge mechanical
descriptions. The considerations are confined mainly to the conceptual
foundations and the internal consistency of these theories. Although no major
differences between their predictions have yet been noticed, some deviations
are expected, which are indicated. These cases may provide the testing grounds
for further investigations.


title: What is Surrealistic about Bohm Trajectories?

abstract:
  We discuss interferometers in Bohmian quantum mechanics. It is shown that,
with the correct configuration space, Bohm trajectories in a which way
interferometer are not surrealistic, but behaves exactly as common sense
suggests. Some remarks about a way to generalize Bohmian mechanics to treat
density matrix are also made.
  PACS: 03.65.Bz, 03.75.Dg
  Key words: Bohm Trajectories, Which Way Interferometers, ESSW


title: Long-range correlation of thermal radiation

abstract:
  A general theory is presented for the spatial correlations in the intensity
of the radiation emitted by a random medium in thermal equilibrium. We find
that a non-zero correlation persists over distances large compared to the
transverse coherence length of the thermal radiation. This long-range
correlation vanishes in the limit of an ideal black body. We analyze two types
of systems (a disordered waveguide and an optical cavity with chaotic
scattering) where it should be observable.


title: Berry's Phase in the Presence of a Non-Adiabatic Environment

abstract:
  We consider a two-level system coupled to an environment that evolves
non-adiabatically. We present a non-perturbative method for determining the
persistence amplitude whose phase contains all the corrections to Berry's phase
produced by the non-adiabatic motion of the environment. Specifically, it
includes the effects of transitions between the two energy levels to all orders
in the non-adiabatic coupling. The problem of determining all non-adiabatic
corrections is reduced to solving an ordinary differential equation to which
numerical methods should provide solutions in a variety of situations. We apply
our method to a particular example that can be realized as a magnetic resonance
experiment, thus raising the possibility of testing our results in the lab.


title: Higher-Order Methods for Quantum Simulations

abstract:
  To efficiently implement many-particle quantum simulations on quantum
computers we develop and present methods for inverting the
Campbell-Baker-Hausdorff lemma to 3rd and 4th order in the commutator. That is,
we reexpress exp{-i(H_1 + H_2 + ...)dt} as a product of factors exp(-i H_1 dt),
exp(-i H_2 dt), ... which is accurate to 3rd or 4th order in dt.


title: On Quantum Fidelities and Channel Capacities

abstract:
  We show the equivalence of two different notions of quantum channel capacity:
that which uses the entanglement fidelity as its criterion of success in
transmission, and that which uses the minimum fidelity of pure states in a
subspace of the input Hilbert space as its criterion. As a corollary, any
source with entropy rate less than the capacity may be transmitted with high
entanglement fidelity. We also show that a restricted class of encodings is
sufficient to transmit any quantum source which may be transmitted on a given
channel. This enables us to simplify a known upper bound for the channel
capacity. It also enables us to show that the availability of an auxiliary
classical channel from encoder to decoder does not increase the quantum
capacity.


title: Measurement and Its Mathematical Scale

abstract:
  It is argued that every measurement is made in a certain scale. The scale in
which present measuments are made is called present scale which gives present
knowledge. Quantities at the limits to present measurement may be observables
in other scales. Cantor's series of infinites is used to describe scales of
measurement. Continuum Hypothesis and Schroedinger Cat are discussed.


title: Spatial Asymmetry For Particle Pairs And The Spin-Statistics Theorem

abstract:
  We discuss the conditions under which identical particles may yet be
distinguishable and the relationship between particle permutation and exchange.
We show that we can always define permutation-symmetric state vectors. When the
particles are completely indistinguishable, then exchange is equivalent to
permutation and therefore the exchange eigenvalue for such
permutation-symmetric state vectors is always +1. Exchange asymmetry arises
when the particles are physically distinguishable, even though otherwise
identical, and can be computed from the transformations that arise when the
distinguishing features are reversed.
  There is a fundamental spatial asymmetry between the relative orientations of
any two vectors in a common frame of reference that persists even in the limit
that the vectors coincide. For a pair of particles this asymmetry between their
spin quantization frames renders them distinguishable even when otherwise
identical. In the conventional construction, this distinction is not properly
accounted for. Particle exchange is then equivalent to reversing this relative
orientation --- which requires a relative rotation by 2pi on the spin
quantization frame of one particle with respect to the other, thus resulting in
the conventional exchange phase.


title:
Interference effects in two-photon ATI by multiple orders high harmonics
  with random or locked phases

abstract:
  We numerically study 2-photon processes using a set of harmonics from a
Ti:Sapphire laser and in particular interference effects in the Above Threshold
Ionization spectra. We compare the situation where the harmonic phases are
assumed locked to the case where they have a random distribution. Suggestions
for possible experiments, using realistic parameters are discussed.


title: Three manifestations of the pulsed harmonic potential

abstract:
  We consider, in turn, three systems being acted upon by a regularly pulsed
harmonic potential (PHP). These are i) a classical particle, ii) a quantum
particle, and iii) a directed line. We contrast the mechanics of the first two
systems by parameterizing their bands of stability and periodicity. Interesting
differences due to quantum fluctuations are examined in detail. The
fluctuations of the directed line are calculated in the two cases of a binding
PHP, and an unbinding PHP. In the latter case there is a finite maximum line
length for a given potential strength.


title: Fast quantum verification for the formulas of predicate calculus

abstract:
  Quantum algorithm is constructed which verifies the formulas of predicate
calculus in time $O(\sqrt N)$ with bounded error probability, where $N$ is the
time required for classical algorithms. This algorithm uses the polynomial
number of simultaneous oracle queries. This is a modification of the result of
Buhrman, Cleve and Wigderson quant-ph/9802040.


title: An Introduction to Quantum Computing for Non-Physicists

abstract:
  Richard Feynman's observation that quantum mechanical effects could not be
simulated efficiently on a computer led to speculation that computation in
general could be done more efficiently if it used quantum effects. This
speculation appeared justified when Peter Shor described a polynomial time
quantum algorithm for factoring integers.
  In quantum systems, the computational space increases exponentially with the
size of the system which enables exponential parallelism. This parallelism
could lead to exponentially faster quantum algorithms than possible
classically. The catch is that accessing the results, which requires
measurement, proves tricky and requires new non-traditional programming
techniques.
  The aim of this paper is to guide computer scientists and other
non-physicists through the conceptual and notational barriers that separate
quantum computing from conventional computing. We introduce basic principles of
quantum mechanics to explain where the power of quantum computers comes from
and why it is difficult to harness. We describe quantum cryptography,
teleportation, and dense coding. Various approaches to harnessing the power of
quantum parallelism are explained, including Shor's algorithm, Grover's
algorithm, and Hogg's algorithms. We conclude with a discussion of quantum
error correction.


title:
Comment on "Consistency, amplitudes, and probabilities in quantum
  theory"

abstract:
  In a recent article [Phys. Rev. A 57, 1572 (1998)] Caticha has concluded that
``nonlinear variants of quantum mechanics are inconsistent.'' In this note we
identify what it is that nonlinear quantum theories have been shown to be
inconsistent with.