title: The Schrodinger particle in an oscillating spherical cavity

abstract:
  We study a Schrodinger particle in an infinite spherical well with an
oscillating wall. Parametric resonances emerge when the oscillation frequency
is equal to the energy difference between two eigenstates of the static cavity.
Whereas an analytic calculation based on a two-level system approximation
reproduces the numerical results at low driving amplitudes, epsilon, we observe
a drastic change of behaviour when epsilon > 0.1, when new resonance states
appear bearing no apparent relation to the eigenstates of the static system.


title:
Father Time. I. Does the Cosmic Microwave Background Radiation Provide a
  Universal Arrow of Time ?

abstract:
  The existence of a non-thermodynamic arrow of time was demonstrated in a
recent paper (Mod.Phys.Lett. A13, 1265 (1998)), in which a model of non-local
Quantum Electrodynamics was formulated through the principle of gauge
invariance. In this paper we show that the Cosmic Microwave Background
Radiation is capable of making every particle of the universe (except those
which are not acted upon by an electromagnetic field) follow this arrow of
time.


title: Minimal conditions for local pure-state entanglement manipulation

abstract:
  We find a minimal set of necessary and sufficient conditions for the
existence of a local procedure that converts a finite pure state into one of a
set of possible final states. This result provides a powerful method for
obtaining optimal local entanglement manipulation protocols for pure initial
states. As an example, we determine analytically the optimal distillable
entanglement for arbitrary finite pure states. We also construct an explicit
protocol achieving this bound.


title: Higher Order Methods for Simulations on Quantum Computers

abstract:
  To efficiently implement many-qubit gates for use in quantum simulations on
quantum computers we develop and present methods reexpressing exp[-i (H_1 + H_2
+ ...) \Delta t] as a product of factors exp[-i H_1 \Delta t], exp[-i H_2
\Delta t], ... which is accurate to 3rd or 4th order in \Delta t. The methods
we derive are an extended form of symplectic method and can also be used for
the integration of classical Hamiltonians on classical computers. We derive
both integral and irrational methods, and find the most efficient methods in
both cases.


title:
Generation of entanglement in a system of two dipole-interacting atoms
  by means of laser pulses

abstract:
  Effectiveness of using laser field to produce entanglement between two
dipole-interacting identical two-level atoms is considered in detail. The
entanglement is achieved by driving the system with a carefully designed laser
pulse transferring the system's population to one of the maximally entangled
Dicke states in a way analogous to population inversion by a resonant
$\pi$-pulse in a two-level atom. It is shown that for the optimally chosen
pulse frequency, power and duration, the fidelity of generating a maximally
entangled state approaches unity as the distance between the atoms goes to
zero.


title: Quantum search without entanglement

abstract:
  Entanglement of quantum variables is usually thought to be a prerequisite for
obtaining quantum speed-ups of information processing tasks such as searching
databases. This paper presents methods for quantum search that give a speed-up
over classical methods, but that do not require entanglement. These methods
rely instead on interference to provide a speed-up. Search without entanglement
comes at a cost: although they outperform analogous classical devices, the
quantum devices that perform the search are not universal quantum computers and
require exponentially greater overhead than a quantum computer that operates
using entanglement. Quantum search without entanglement is compared to
classical search using waves.


title:
Excited Binomial States and Excited Negative Binomial States of the
  Radiation Field and Some of their Statistical Properties

abstract:
  We introduce excited binomial states and excited negative binomial states of
the radiation field by repeated application of the photon creation operator on
binomial states and negative binomial states. They reduce to Fock states and
excited coherent states in certain limits and can be viewed as intermediate
states between Fock states and coherent states. We find that both the excited
binomial states and excited negative binomial states can be exactly normalized
in terms of hypergeometric functions. Base on this interesting character, some
of the statistical properties are discussed.


title: Coherent manipulation of two dipole-dipole interacting ions

abstract:
  We investigate to what extent two trapped ions can be manipulated coherently
when their coupling is mediated by a dipole-dipole interaction. We will show
how the resulting level shift induced by this interaction can be used to create
entanglement, while the decay of the states remains nearly negligible. This
will allow us to implement conditional dynamics (a CNOT gate) and single qubit
operations. We propose two different experimental realisations where a large
level shift can be achieved and discuss both the strengths and weaknesses of
this scheme from the point of view of a practical realization.


title: Time of arrival through a quantum barrier

abstract:
  We introduce a formalism for the calculation of the time of arrival t at a
detector of particles traveling through interacting environments. We develop a
general formulation that employs quantum canonical transformations from the
free to the interacting cases to compute t. We interpret our results in terms
of a Positive Operator Valued Measure. We then compute the probability
distribution in times of arrival at a detector of those particles that, after
their initial preparation, have undergone quantum tunneling or reflection due
to the presence of potential barriers. We obtain the expected retardation or
advancement for transmitted wave packets, and non-foreseen double bump
structures for some cases of reflection.


title: On Quantum Algorithms

abstract:
  Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. In effect, they follow the same logical paradigm as
(multi-particle) interferometers. We show how most known quantum algorithms,
including quantum algorithms for factorising and counting, may be cast in this
manner. Quantum searching is described as inducing a desired relative phase
between two eigenvectors to yield constructive interference on the sought
elements and destructive interference on the remaining terms.


title: Stochastic resonance for quantum channels

abstract:
  The concept of stochastic resonance in nonlinear dynamics is applied to
interpret the capacity of noisy quantum channels. The two-Pauli channel is used
to illustrate the idea. The fidelity of the channel is also considered. Noise
enhancement is found for the fidelity but not for the capacity.

categories: quant-ph chao-dyn cond-mat.stat-mech nlin.CD nlin.SI solv-int


title: Dynamical Stability and Quantum Chaos of Ions in a Linear Trap

abstract:
  The realization of a paradigm chaotic system, namely the harmonically driven
oscillator, in the quantum domain using cold trapped ions driven by lasers is
theoretically investigated. The simplest characteristics of regular and chaotic
dynamics are calculated. The possibilities of experimental realization are
discussed.


title:
Zeta function method and repulsive Casimir forces for an unusual pair of
  plates at finite temperature

abstract:
  We apply the generalized zeta function method to compute the Casimir energy
and pressure between an unusual pair of parallel plates at finite temperature,
namely: a perfectly conducting plate and an infinitely permeable one. The high
and low temperature limits of these quantities are discussed; relationships
between high and low temperature limits are estabkished by means of a modified
version of the temperature inversion symmetry.


title:
Quantum Computation with Quantum Dots and Terahertz Cavity Quantum
  Electrodynamics

abstract:
  A quantum computer is proposed in which information is stored in the two
lowest electronic states of doped quantum dots (QDs). Many QDs are located in a
microcavity. A pair of gates controls the energy levels in each QD. A
Controlled Not (CNOT) operation involving any pair of QDs can be effected by a
sequence of gate-voltage pulses which tune the QD energy levels into resonance
with frequencies of the cavity or a laser. The duration of a CNOT operation is
estimated to be much shorter than the time for an electron to decohere by
emitting an acoustic phonon.


title: Subtraction of ``accidentals'' and the validity of Bell tests

abstract:
  In some key Bell experiments, including two of the well-known ones by Alain
Aspect, 1981-2, it is only after the subtraction of ``accidentals'' from the
coincidence counts that we get violations of Bell tests. The data adjustment,
producing increases of up to 60% in the test statistics, has never been
adequately justified. Few published experiments give sufficient information for
the reader to make a fair assessment. There is a straightforward and well known
realist model that fits the unadjusted data very well. In this paper, the logic
of this realist model and the reasoning used by experimenters in justification
of the data adjustment are discussed. It is concluded that the evidence from
all Bell experiments is in urgent need of re-assessment, in the light of all
the known ``loopholes''. Invalid Bell tests have frequently been used,
neglecting improved ones derived by Clauser and Horne in 1974. ``Local causal''
explanations for the observations have been wrongfully neglected.


title:
Reconstructing the density matrix of a spin s through Stern-Gerlach
  measurements (II)

abstract:
  The density matrix of a spin s is fixed uniquely if the probabilities to
obtain the value s upon measuring n.S are known for 4s(s+1) appropriately
chosen directions n in space. These numbers are just the expectation values of
the density operator in coherent spin states, and they can be determined in an
experiment carried out with a Stern-Gerlach apparatus. Furthermore, the
experimental data can be inverted providing thus a parametrization of the
statistical operator by 4s(s+1) positive parameters.


title:
Reply on `comment on our paper `Single two-level ion in an
  anharmonic-oscillator trap: Time evolution of the Q function and population
  inversion ''

abstract:
  We show here that the model Hamiltonian used in our paper for ion vibrating
in a q-analog harmonic oscillator trap and interacting with a classical
single-mode light field is indeed obtained by replacing the usual bosonic
creation and annihilation operators of the harmonic trap model by their
q-deformed counterparts. The approximations made in our paper amount to using
for the ion-laser interaction in a q-analog harmonic oscillator trap, the
operator $F_{q}=exp{-(|\epsilon|^2}/2)}exp{i\epsilon A^{\dagger}}exp{i\epsilon
A}$, which is analogous to the corresponding operator for ion in a harmonic
oscillator trap that is $F=exp{-(|\epsilon|^2 /2)}exp{i\epsilon a^{\dagger
}}exp{i\epsilon a}$. In our article we do not claim to have diagonalized the
operator, $F_q = exp{i \epsilon (A^{\dagger}+A)}$, for which the basis states
|g,m> and |e,m> are not analytic vectors.


title: Small Violations of Statistics

abstract:
  There are two motivations to consider statistics that are neither Bose nor
Fermi: (1) to extend the framework of quantum theory and of quantum field
theory, and (2) to provide a quantitative measure of possible violations of
statistics. After reviewing tests of statistics for various particles, and
types of statistics that are neither Bose nor Fermi, I discuss quons, particles
characterized by the parameter $q$, which permit a smooth interpolation between
Bose and Fermi statistics; $q=1$ gives bosons, $q=-1$ gives fermions. The new
result of this talk is work by Robert C. Hilborn and myself that gives a
heuristic argument for an extension of conservation of statistics to quons with
trilinear couplings of the form $\bar{f}fb$, where $f$ is fermion-like and $b$
is boson-like. We showed that $q_f^2=q_b$. In particular, we related the bound
on $q_{\gamma}$ for photons to the bound on $q_e$ for electrons, allowing the
very precise bound for electrons to be carried over to photons. An extension of
our argument suggests that all particles are fermions or bosons to high
precision.


title: Noise in Grover's Quantum Search Algorithm

abstract:
  Grover's quantum algorithm improves any classical search algorithm. We show
how random Gaussian noise at each step of the algorithm can be modelled easily
because of the exact recursion formulas available for computing the quantum
amplitude in Grover's algorithm. We study the algorithm's intrinsic robustness
when no quantum correction codes are used, and evaluate how much noise the
algorithm can bear with, in terms of the size of the phone book and a desired
probability of finding the correct result. The algorithm loses efficiency when
noise is added, but does not slow down. We also study the maximal noise under
which the iterated quantum algorithm is just as slow as the classical
algorithm. In all cases, the width of the allowed noise scales with the size of
the phone book as N^-2/3.


title:
The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum
  Computer

abstract:
  A quantum computer can efficiently find the order of an element in a group,
factors of composite integers, discrete logarithms, stabilisers in Abelian
groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already
known how to phrase the first four problems as the estimation of eigenvalues of
certain unitary operators. Here we show how the solution to the more general
Abelian `hidden subgroup problem' can also be described and analysed as such.
We then point out how certain instances of these problems can be solved with
only one control qubit, or `flying qubits', instead of entire registers of
control qubits.


title: Decoherence - Fluctuation Relation and Measurement Noise

abstract:
  We discuss fluctuations in the measurement process and how these fluctuations
are related to the dissipational parameter characterising quantum damping or
decoherence. On the example of the measuring current of the variable-barrier or
QPC problem we show there is an extra noise or fluctuation connected with the
possible different outcomes of a measurement. This noise has an enhanced short
time component which could be interpreted as due to ``telegraph noise'' or
``wavefunction collapses''. Furthermore the parameter giving the the strength
of this noise is related to the parameter giving the rate of damping or
decoherence.


title:
The Dirac Oscillator. A relativistic version of the Jaynes--Cummings
  model

abstract:
  The dynamics of wave packets in a relativistic Dirac oscillator is compared
to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the
Dirac oscillator produces the entanglement of the spin with the orbital motion
similar to what is observed in the model of quantum optics. The collapses and
revivals of the spin which result extend to a relativistic theory our previous
findings on nonrelativistic oscillator where they were known under the name of
`spin-orbit pendulum'. There are important relativistic effects (lack of
periodicity, zitterbewegung, negative energy states). Many of them disappear
after a Foldy-Wouthuysen transformation.

categories: quant-ph math-ph math.MP physics.atom-ph


title:
Postselected versus nonpostselected quantum teleportation using
  parametric down-conversion

abstract:
  We study the experimental realisation of quantum teleportation as performed
by Bouwmeester {\em et al}. [Nature {\bf 390}, 575 (1997)] and the adjustments
to it suggested by Braunstein and Kimble [Nature {\bf 394}, 841 (1998)]. These
suggestions include the employment of a detector cascade and a relative
slow-down of one of the two down-converters. We show that coincidences between
photon-pairs from parametric down-conversion automatically probe the
non-Poissonian structure of these sources. Furthermore, we find that detector
cascading is of limited use, and that modifying the relative strengths of the
down-conversion efficiencies will increase the time of the experiment to the
order of weeks. Our analysis therefore points to the benefits of single-photon
detectors in non-post-selected type experiments, a technology currently
requiring roughly $6^{\circ}$K operating conditions.


title:
Quantum searching's underlying SU(2) structure and its quantum
  decoherence effects

abstract:
  The search operation for a marked state by means of Grover's quantum
searching algorithm is shown to be an element of group SU(2) which acts on a
2-dimensional space spanned by the marked state and the unmarked collective
state. Based on this underlying structure, those exact bounds of the steps in
various quantum search algorithms are obtained in a quite concise way. This
reformulation of the quantum searching algorithm also enables a detailed
analysis of the decoherence effects caused by its coupling with an environment.
It turns out that the environment will not only make the quantum search invalid
in case of complete decoherence, where the probability of finding the marked
state is unchanged, but also it may make the quantum search algorithm worse
than expected: It will decrease this probability when the environment shows its
quantum feature.


title: A Path Intergal Approach to Current

abstract:
  Discontinuous initial wave functions or wave functions with discontintuous
derivative and with bounded support arise in a natural way in various
situations in physics, in particular in measurement theory. The propagation of
such initial wave functions is not well described by the Schr\"odinger current
which vanishes on the boundary of the support of the wave function. This
propagation gives rise to a uni-directional current at the boundary of the
support. We use path integrals to define current and uni-directional current
and give a direct derivation of the expression for current from the path
integral formulation for both diffusion and quantum mechanics. Furthermore, we
give an explicit asymptotic expression for the short time propagation of
initial wave function with compact support for both the cases of discontinuous
derivative and discontinuous wave function. We show that in the former case the
probability propagated across the boundary of the support in time $\Delta t$ is
$O(\Delta t^{3/2})$ and the initial uni-directional current is $O(\Delta
t^{1/2})$. This recovers the Zeno effect for continuous detection of a particle
in a given domain. For the latter case the probability propagated across the
boundary of the support in time $\Delta t$ is $O(\Delta t^{1/2})$ and the
initial uni-directional current is $O(\Delta t^{-1/2})$. This is an anti-Zeno
effect. However, the probability propagated across a point located at a finite
distance from the boundary of the support is $O(\Delta t)$. This gives a decay
law.


title: Motion of a Relativistic Particle and the Vacuum

abstract:
  A vacuum medium model is advanced. The motion of a relativistic particle in
relation to its interaction with the medium is discussed. It is predicted that
elementary excitations of the vacuum, called "inertons," should exist. The
equations of the particle path in Euclidean space are derived. The motion is
marked by the relations basic for quantum mechanics: $E=h\nu$ and $Mv = h/
\lambda$ (here, $\lambda$ is the amplitude of spatial oscillations of the
particle along the trajectory, i.e., the interval at which the velocity of the
particle is periodically altered from $v$ to 0 and then from 0 to $v$; $\nu$ is
the frequency of these oscillations). Analysis is performed on the transition
to wave mechanics where $\lambda$ manifests itself as the de Broglie wavelength
and $\nu$ is the distinctive frequency of the "particle-wave". A prerequisite
for the wave solution to be Lorentz-invariant is treated. A hypothesis for a
plausible hydrodynamic description of the relativistic particle motion is
covered.


title: On oscillatorlike developments and further improvements in squeezing

abstract:
  A recent proposal of new sets of squeezed states is seen as a particular case
of a general context admitting realistic physical Hamiltonians. Such
improvements reveal themselves helpful in the study of associated squeezing
effects. Coherence is also considered.


title: Subdynamics theory in the functional approach to quantum mechanics

abstract:
  The formalism of subdynamics is extended to the functional approach of
quantum systems, and used for the Friedrichs model, in which diagonal
singularities in states and observables are included. We compute in this
approach the generalized eigenvectors and eigenvalues of the Liouvulle-Von
Newmann operator, using an iterative scheme. As complex generalized eigenvalues
are obtained, the decay rates of unstable modes are included in the spectral
decomposition.


title: Scattering and intrinsic irreversibility

abstract:
  The formalism of quantum systems with diagonal singularities is applied to
describe scattering processes. Well defined states are obtained for infinite
time, which are related to a ''weak form'' of intrinsic irreversibility. Real
and complex generalized spectral decompositions of the Liouville-Von Neumann
superoperator are computed. The physical meaning of ''Gamov states'' is
discussed.


title: Some remarks on time, uncertainty, and spin

abstract:
  Some observations are made about energy-time uncertainty and spin in the
context of trajectories as in Faraggi-Matone or Floyd.


title: The ultimate quantum limit to the linewidth of lasers

abstract:
  The standard quantum limit to the linewidth of a laser for which the gain
medium can be adiabatically eliminated is $\ell_{0}=\kappa/2\bar{n}$. Here
$\kappa$ is the intensity damping rate and $\bar{n}$ the mean photon number.
This contains equal contributions from the loss and gain processes, so that
simple arguments which attribute the linewidth wholly to phase noise from
spontaneous gain are wrong. I show that an {\em unstimulated} gain process
actually introduces no phase noise, so that the ultimate quantum limit to the
laser linewidth comes from the loss alone and is equal to $\ell_{ult}=
\kappa/4\bar{n}$. I investigate a number of physical gain mechanisms which
attempt to achieve gain without phase noise: a linear atom-field coupling with
finite interaction time; a nonlinear atom-field coupling; and adiabatic photon
transfer using a counterintuitive pulse sequence. The first at best reaches the
standard limit $\ell_{0}$, the second reaches $3/4 \ell_{0}$, while the third
reaches the ultimate limit of $\ell_{ult} = 1/2 \ell_{0}$.


title:
Quantum Entanglement and the Maximum Entropy States from the Jaynes
  Principle

abstract:
  We show that the Jaynes principle is indeed a proper inference scheme when
applied to compound systems and will correctly produce the entangled maximum
entropy states compatible with appropriate data. This is accomplished by
including the dispersion of the entanglement along with its mean value as
constraints and an application of the uncertainty principle. We also construct
a "thermodynamic-like" description of the entanglement arising out of the
maximum entropy principle.


title: A General Type of a Coherent States with Thermal Effects

abstract:
  Within the framework of thermofield dynamics, we construct a thermalized
coherent thermal state, which is a general type of the coherent state with the
thermal effects and can be presumably produced experimentally. The wavefunction
and the density matrix element in the coordinate repersentation are calculated,
and furthermore we give the probability densities, average values and variances
of the position, momentum and particle number, which in special cases are
consistent with those in the literature. All calculations are performed in the
coordinate representation.


title: Quantum Entangled Supercorrelated States in the Jaynes-Cummings Model

abstract:
  The regions of independent quantum states, maximally classically correlated
states, and purely quantum entangled (supercorrelated) states described in a
recent formulation of quantum information theory by Cerf and Adami are explored
here numerically in the parameter space of the well-known exactly soluable
Jaynes-Cummings model for equilibrium and nonequilibrium time-dependent
ensembles.


title:
The Casimir Problem of Spherical Dielectrics: A Solution in Terms of
  Quantum Statistical Mechanics

abstract:
  The Casimir energy for a compact dielectric sphere is considered in a novel
way, using the quantum statistical method introduced by H\oye - Stell and
others. Dilute media are assumed. It turns out that this method is a very
powerful one: we are actually able to derive an expression for the Casimir
energy that contains also the negative part resulting from the attractive van
der Waals forces between the molecules. It is precisely this part of the
Casimir energy that has turned out to be so difficult to extract from the
formalism when using the conventional field theoretical methods for a
continuous medium. Assuming a frequency cutoff, our results are in agreement
with those recently obtained by Barton [J. Phys. A: Math. Gen. 32(1999)525].


title: Localizing the Relativistic Electron

abstract:
  A causally well-behaved solution of the localization problem for the free
electron is given, with natural space-time transformation properties, in terms
of Dirac's position operator. It is shown that, although this operator does not
represent an observable in the usual sense, and has no positive-energy
(generalized) eigenstates, the associated 4-vector density is observable, and
can be localized arbitrarily precisely about any point in space, at any instant
of time, using only positive-energy states. A suitable spin operator can be
diagonalized at the same time.


title: On hybrid dynamics of the Copenhagen dichotomic world

abstract:
  In the Copenhagen viewpoint, part of the world is quantized and the
complementary part remains classical. From a formal dynamic aspect, standard
theory is incomplete since it does never account for the so-called
'back-reaction' of quantized systems on classical systems except for the highly
idealized system-detector interaction. To resolve this formal issue, a certain
'hybrid dynamics' can be constructed to account for the generic interaction
between classical and quantized parts. Hybrid dynamics incorporates standard
quantum theory, including collapse of the wave function during system-detector
interaction. Measurable predictions are robust against shifting the
classical-quantum boundary (von Neumann-cut).


title: Stochastic Wave-function Simulation of Two-time Correlation Functions

abstract:
  We propose an optimized algorithm for the numerical simulation of two-time
correlation functions by means of stochastic wave functions. As a first
application, we investigate the two-time correlation function of a nonlinear
optical parametric oscillator.


title:
Internal Time Superoperator for Quantum Systems with Diagonal
  Singularity

abstract:
  We generalize the concepts of Internal Time Superoperator, its associated non
unitary similarity transformations and Liapounov variables, to quantum systems
with diagonal singularity, and we give a constructive proof of the existence of
these superoperators for systems with purely diagonal Hamiltonian having
uniform absolutely continuous spectrum on the interval from zero to infinity.


title:
Tunneling Proximity Resonances: Interplay between Symmetry and
  Dissipation

abstract:
  We report the first observation of bound-state proximity resonances in
coupled dielectric resonators. The proximity resonances arise from the combined
action of symmetry and dissipation. We argue that the large ratio between the
widths is a distinctive signature of the multidimensional nature of the system.
Our experiments shed light on the properties of 2D tunneling in the presence of
a dissipative environment.


title: Anomalies in nonrelativistic quantum mechanics

abstract:
  It is shown that if a potential in a nonrelativistic system of Fermi
particles has a sufficiently strong singularity, anomalies (nonzero values of
quantities formally equal to zero) will probably appear. For different types of
singularities (in paticular, for the Coulomb potential), anomalies associated
with the energy and total number of particles in the system are calculated.
These anomalies may be beneficial in deriving a semiclassical description of
electron- nuclear systems.


title: Rotation Eigenvectors and Spin 1/2

abstract:
  It is an easily deduced fact that any four-component spin 1/2 state for a
massive particle is a linear combination of pairs of two-component simultaneous
rotation eigenstates, where `simultaneous' means the eigenspinors of a given
pair share the same eigenvalue. The new work here constructs the reverse: Given
pairs of simultaneous rotation eigenvectors, the properties of these pairs
contains relationships that are equivalent to spin 1/2 single particle
equations. Thus the needed aspects of space-time symmetry can be produced as
special cases of more general properties already present in the rotation group.
The exercise exploits the flexibility of the rotation group in three dimensions
to deduce relativistic quantities in four dimensions.


title: Cooling of a mirror by radiation pressure

abstract:
  We describe an experiment in which a mirror is cooled by the radiation
pressure of light. A high-finesse optical cavity with a mirror coated on a
mechanical resonator is used as an optomechanical sensor of the Brownian motion
of the mirror. A feedback mechanism controls this motion via the radiation
pressure of a laser beam reflected on the mirror. We have observed either a
cooling or a heating of the mirror, depending on the gain of the feedback loop.


title:
The Meaning of Elements of Reality and Quantum Counterfactuals -- Reply
  to Kastner

abstract:
  This paper is the answer to the paper by Kastner [Found. Phys., to be
published, quant-ph/9807037] in which she continued the criticism of the
counterfactual usage of the Aharonov-Bergman-Lebowitz rule in the framework of
the time-symmetrized quantum theory, in particular, by analyzing the three-box
``paradox''. It is argued that the criticism is not sound. Paradoxical features
of the three-box example has been explained. It is explained that the elements
of reality in the framework of time-symmetrized quantum theory are
counterfactual statements and, therefore, even conflicting elements of reality
can be associated with a single particle. It is shown how such
``counterfactual'' elements of reality can be useful in the analysis of a
physical experiment (the three-box example). The validity of Kastner's
application of the consistent histories approach to the time-symmetrized
counterfactuals is questioned.


title: Adiabatic population transfer via multiple intermediate states

abstract:
  This paper discusses a generalization of stimulated Raman adiabatic passage
(STIRAP) in which the single intermediate state is replaced by $N$ intermediate
states. Each of these states is connected to the initial state $\state{i}$ with
a coupling proportional to the pump pulse and to the final state $\state{f}$
with a coupling proportional to the Stokes pulse, thus forming a parallel
multi-$\Lambda$ system. It is shown that the dark (trapped) state exists only
when the ratio between each pump coupling and the respective Stokes coupling is
the same for all intermediate states. We derive the conditions for existence of
a more general adiabatic-transfer state which includes transient contributions
from the intermediate states but still transfers the population from state
$\state{i}$ to state $\state{f}$ in the adiabatic limit. We present various
numerical examples for success and failure of multi-$\Lambda$ STIRAP which
illustrate the analytic predictions. Our results suggest that in the general
case of arbitrary couplings, it is most appropriate to tune the pump and Stokes
lasers either just below or just above all intermediate states.


title:
Topological Expansion and Exponential Asymptotics in 1D Quantum
  Mechanics

abstract:
  Borel summable semiclassical expansions in 1D quantum mechanics are
considered. These are the Borel summable expansions of fundamental solutions
and of quantities constructed with their help. An expansion, called
topological,is constructed for the corresponding Borel functions. Its main
property is to order the singularity structure of the Borel plane in a
hierarchical way by an increasing complexity of this structure starting from
the analytic one. This allows us to study the Borel plane singularity structure
in a systematic way. Examples of such structures are considered for linear,
harmonic and anharmonic potentials. Together with the best approximation
provided by the semiclassical series the exponentially small contribution
completing the approximation are considered. A natural method of constructing
such an exponential asymptotics relied on the Borel plane singularity
structures provided by the topological expansion is developed. The method is
used to form the semiclassical series including exponential contributions for
the energy levels of the anharmonic oscillator.


title:
Many-body system with a four-parameter family of point interactions in
  one dimension

abstract:
  We consider a four-parameter family of point interactions in one dimension.
This family is a generalization of the usual $\delta$-function potential. We
examine a system consisting of many particles of equal masses that are
interacting pairwise through such a generalized point interaction. We follow
McGuire who obtained exact solutions for the system when the interaction is the
$\delta$-function potential. We find exact bound states with the four-parameter
family. For the scattering problem, however, we have not been so successful.
This is because, as we point out, the condition of no diffraction that is
crucial in McGuire's method is not satisfied except when the four-parameter
family is essentially reduced to the $\delta$-function potential.


title: Fault-Tolerant Quantum Computation with Local Gates

abstract:
  I discuss how to perform fault-tolerant quantum computation with concatenated
codes using local gates in small numbers of dimensions. I show that a threshold
result still exists in three, two, or one dimensions when
next-to-nearest-neighbor gates are available, and present explicit
constructions. In two or three dimensions, I also show how nearest-neighbor
gates can give a threshold result. In all cases, I simply demonstrate that a
threshold exists, and do not attempt to optimize the error correction circuit
or determine the exact value of the threshold. The additional overhead due to
the fault-tolerance in both space and time is polylogarithmic in the error rate
per logical gate.


title: About Heisenberg Uncertainty Relation (by E.Schrodinger)

abstract:
  The original Schrodinger's paper is translated and annotated in honour of the
70-th anniversary of his Uncertainty Relation [published also in: Bulg. Journal
of Physics,vol.26,no.5/6 (1999) pp.193-203]. In the annotation it is shown that
the Uncertainty Relation can be written in a complete compact canonical form.


title: Classical model for bulk-ensemble NMR quantum computation

abstract:
  We present a classical model for bulk-ensemble NMR quantum computation: the
quantum state of the NMR sample is described by a probability distribution over
the orientations of classical tops, and quantum gates are described by
classical transition probabilities. All NMR quantum computing experiments
performed so far with three quantum bits can be accounted for in this classical
model. After a few entangling gates, the classical model suffers an exponential
decrease of the measured signal, whereas there is no corresponding decrease in
the quantum description. We suggest that for small numbers of quantum bits, the
quantum nature of NMR quantum computation lies in the ability to avoid an
exponential signal decrease.


title: Berry phase from a quantum Zeno effect

abstract:
  We exhibit a specific implementation of the creation of geometrical phase
through the state-space evolution generated by the dynamic quantum Zeno effect.
That is, a system is guided through a closed loop in Hilbert space by means a
sequence of closely spaced projections leading to a phase difference with
respect to the original state. Our goal is the proposal of a specific
experimental setup in which this phase could be created and observed. To this
end we study the case of neutron spin, examine the practical aspects of
realizing the "projections," and estimate the difference between the idealized
projections and the experimental implementation.


title: Quantum Time Evolution in Terms of Nonredundant Expectation Values

abstract:
  Each scheme of state reconstruction comes down to parametrize the state of a
quantum system by expectation values or probabilities directly measurable in an
experiment. It is argued that the time evolution of these quantities provides
an unambiguous description of the quantal dynamics. This is shown explicitly
for a single spin s, using a quorum of expectation values which contains no
redundant information. The quantum mechanical time evolution of the system is
rephrased in terms of a closed set of linear first-order differential equations
coupling (2s+1)^2 expectation values. This `realization' of the dynamical law
refers neither to the wavefunction of the system nor to its statistical
operator.


title: Progress in a Many-Minds Interpretation of Quantum Theory

abstract:
  In a series of papers, a many-minds interpretation of quantum theory has been
developed. The aim in these papers is to present an explicit mathematical
formalism which constitutes a complete theory compatible with relativistic
quantum field theory. In this paper, which could also serve as an introduction
to the earlier papers, three issues are discussed. First, a significant, but
fairly straightforward, revision in some of the technical details is proposed.
This is used as an opportunity to introduce the formalism. Then the
probabilistic structure of the theory is revised, and it is proposed that the
experience of an individual observer can be modelled as the experience of
observing a particular, identified, discrete stochastic process. Finally, it is
argued that the formalism can be modified to give a physics in which no
constants are required. Instead, `constants' have to be determined by
observation, and are fixed only to the extent to which they have been observed.


title: Squeezing as an irreducible resource

abstract:
  We show that squeezing is an irreducible resource which remains invariant
under transformations by linear optical elements. In particular, we give a
decomposition of any optical circuit with linear input-output relations into a
linear multiport interferometer followed by a unique set of single mode
squeezers and then another multiport interferometer. Using this decomposition
we derive a no-go theorem for superpositions of macroscopically distinct states
from single-photon detection. Further, we demonstrate the equivalence between
several schemes for randomly creating polarization-entangled states. Finally,
we derive minimal quantum optical circuits for ideal quantum non-demolition
coupling of quadrature-phase amplitudes.


title: Interference and Distinguishability in Quantum Mechanics

abstract:
  Quantitative measures are introduced for the indistinguishability $U$ of two
quantum states in a given measurement and the amount of interference $I$
observable in this measurement. It is shown that these measures obey an
inequality $U\geq I$ which can be seen as an exact formulation of Bohr's claim
that one cannot distinguish between two possible paths of a particle while
maintaining an interference phenomenon. This formulation is applied to a
neutron interferometer experiment of Badurek e.a. It is shown that the
formulation is stronger than an argument based on an uncertainty relation for
phase and photon number considered by these authors.


title: Observational Consequences of Many-Worlds Quantum Theory

abstract:
  Contrary to an oft-made claim, there can be observational distinctions (say
for the expansion of the universe or the cosmological constant) between
"single-history" quantum theories and "many-worlds" quantum theories. The
distinctions occur when the number of observers is not uniquely predicted by
the theory. In single-history theories, each history is weighted simply by its
quantum-mechanical probability, but in many-worlds theories in which random
observations are considered, there should also be the weighting by the numbers
or amounts of observations occurring in each history.


title: Optimal Decompositions of Barely Separable States

abstract:
  Two families of bipartite mixed quantum states are studied for which it is
proved that the number of members in the optimal-decomposition ensemble --- the
ensemble realizing the entanglement of formation --- is greater than the rank
of the mixed state. We find examples for which the number of states in this
optimal ensemble can be larger than the rank by an arbitrarily large factor. In
one case the proof relies on the fact that the partial transpose of the mixed
state has zero eigenvalues; in the other case the result arises from the
properties of product bases that are completable only by embedding in a larger
Hilbert space.


title: Prolegomena to a non-equilibrium quantum statistical mechanics

abstract:
  We suggest that the framework of quantum information theory, which has been
developing rapidly in recent years due to intense activity in quantum
computation and quantum communication, is a reasonable starting point to study
non-equilibrium quantum statistical phenomena. As an application, we discuss
the non-equilibrium quantum thermodynamics of black hole formation and
evaporation.


title:
Multiple parameter structure of Mielnik's isospectrality in unbroken
  SUSYQM

abstract:
  Within unbroken SUSYQM and for zero factorization energy, I present an
iterative generalization of Mielnik's isospectral method by employing a
Schroedinger true zero mode in the first-step general Riccati solution and
imposing the physical condition of normalization at each iterative step. This
procedure leads to a well-defined multiple-parameter structure within Mielnik's
construction for both zero modes and potentials


title: Sonoluminescence and the QED vacuum

abstract:
  In this talk I shall describe an extension of the quantum-vacuum approach to
sonoluminescence proposed several years ago by J.Schwinger. We shall first
consider a model calculation based on Bogolubov coefficients relating the QED
vacuum in the presence of an expanded bubble to that in the presence of a
collapsed bubble. In this way we shall derive an estimate for the spectrum and
total energy emitted. This latter will be shown to be proportional to the
volume of space over which the refractive index changes, as Schwinger
predicted. After this preliminary check we shall deal with the physical
constraints that any viable dynamical model for SL has to satisfy in order to
fit the experimental data. We shall emphasize the importance of the timescale
of the change in refractive index. This discussion will led us to propose a
somewhat different version of dynamical Casimir effect in which the change in
volume of the bubble is no longer the only source for the change in the
refractive index.


title:
New possibilities for supersymmetry breakdown in quantum mechanics and
  second order irreducible Darboux transformations

abstract:
  New types of irreducible second order Darboux transformations for the one
dimensional Schroedinger equation are described. The main feature of such
transformations is that the transformation functions have the eigenvalues
grater then the ground state energy of the initial (or reference) Hamiltonian.
When such a transformation is presented as a chain of two first order
transformations, an intermediate potential is singular and therefore
intermediate Hamiltonian can not be Hermitian while the final potential is
regular and the final Hamiltonian is Hermitian. Second derivative
supersymmetric quantum mechanical model based on a transformation of this kind
exhibits properties inherent to models with exact and broken supersymmetry at
once.


title: Quantum computing with neutral atoms

abstract:
  We develop a method to entangle neutral atoms using cold controlled
collisions. We analyze this method in two particular set-ups: optical lattices
and magnetic micro-traps. Both offer the possibility of performing certain
multi-particle operations in parallel. Using this fact, we show how to
implement efficient quantum error correction and schemes for fault-tolerant
computing.


title: Holonomic Quantum Computation

abstract:
  We show that the notion of generalized Berry phase i.e., non-abelian
holonomy, can be used for enabling quantum computation. The computational space
is realized by a $n$-fold degenerate eigenspace of a family of Hamiltonians
parametrized by a manifold $\cal M$. The point of $\cal M$ represents classical
configuration of control fields and, for multi-partite systems, couplings
between subsystem. Adiabatic loops in the control $\cal M$ induce non trivial
unitary transformations on the computational space. For a generic system it is
shown that this mechanism allows for universal quantum computation by composing
a generic pair of loops in $\cal M.$


title:
Canonical Transformations and the Hamilton-Jacobi Theory in Quantum
  Mechanics

abstract:
  Canonical transformations using the idea of quantum generating functions are
applied to construct a quantum Hamilton-Jacobi theory, based on the analogy
with the classical case. An operator and a c-number forms of the time-dependent
quantum Hamilton-Jacobi equation are derived and used to find dynamical
solutions of quantum problems. The phase-space picture of quantum mechanics is
discussed in connection with the present theory.


title: Sonoluminescence as a QED vacuum effect. I: The Physical Scenario

abstract:
  Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of changes in the properties of the
quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased
in terms of changes in the Casimir Energy: changes in the distribution of
zero-point energies and has recently been the subject of considerable
controversy. The present paper further develops this quantum-vacuum approach to
sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum
states in the presence of a homogeneous medium of changing dielectric constant.
In this way we derive an estimate for the spectrum, number of photons, and
total energy emitted. We emphasize the importance of rapid spatio-temporal
changes in refractive indices, and the delicate sensitivity of the emitted
radiation to the precise dependence of the refractive index as a function of
wavenumber, pressure, temperature, and noble gas admixture. Although the
physics of the dynamical Casimir effect is a universal phenomenon of QED,
specific experimental features are encoded in the condensed matter physics
controlling the details of the refractive index. This calculation places rather
tight constraints on the possibility of using the dynamical Casimir effect as
an explanation for sonoluminescence, and we are hopeful that this scenario will
soon be amenable to direct experimental probes. In a companion paper we discuss
the technical complications due to finite-size effects, but for reasons of
clarity in this paper we confine attention to bulk effects.


title:
Monotonicity Properties of Certain Measures over the Two-Level Quantum
  Systems

abstract:
  We demonstrate --- using the case of the two-dimensional quantum systems ---
that the "natural measure on the space of density matrices describing
N-dimensional quantum systems" proposed by Zyczkowski et al (quant-ph/9804024)
does not belong to the class of normalized volume elements of monotone metrics
on the quantum systems. Such metrics possess the statistically important
property of being decreasing under stochastic mappings (coarse-grainings). We
do note that the proposed natural measure (and certain evident variations upon
it) exhibit quite specific monotonicity properties, but not of the form
required for membership in the class.


title: Spontaneous decay of an excited atom in an absorbing dielectric

abstract:
  Starting from the quantized version of Maxwell's equations for the
electromagnetic field in an arbitrary linear Kramers-Kronig dielectric,
spontaneous decay of the excited state of a two-level atom embedded in a
dispersive and absorbing medium is studied and the decay rate is calculated.
The calculations are performed for both the (Clausius-Mosotti) virtual cavity
model and the (Glauber-Lewenstein) real cavity model. It is shown that owing to
nonradiative decay associated with absorption the rate of spontaneous decay
sensitively depends on the cavity radius when the atomic transition frequency
approaches an absorption band of the medium. Only when the effect of absorption
is fully disregarded, then the familiar local-field correction factors are
recovered.


title: Nonlocality in Nonlinear Quantum Mechanics

abstract:
  A general method for testing essential nonlocality of nonlinear modifications
of quantum mechanics is presented and applied to show the inconsistency of I.
Bialynicki-Birula's and J. Mycielski's nonlinear quantum theory.


title: Nonclassical correlations in damped quantum solitons

abstract:
  Using cumulant expansion in Gaussian approximation, the internal quantum
statistics of damped soliton-like pulses in Kerr media are studied numerically,
considering both narrow and finite bandwidth spectral pulse components. It is
shown that the sub-Poissonian statistics can be enhanced, under certain
circumstances, by absorption, which damps out some destructive interferences.
Further, it is shown that both the photon-number correlation and the
correlation of the photon-number variance between different pulse components
can be highly nonclassical even for an absorbing fiber. Optimum frequency
windows are determined in order to realize strong nonclassical behavior, which
offers novel possibilities of using solitons in optical fibers as a source of
nonclassically correlated light beams.


title: Sonoluminescence: Two-photon correlations as a test of thermality

abstract:
  In this Letter we propose a fundamental test for probing the thermal nature
of the spectrum emitted by sonoluminescence. We show that two-photon
correlations can in principle discriminate between real thermal light and the
quasi-thermal squeezed-state photons typical of models based on the dynamic
Casimir effect. Two-photon correlations provide a powerful experimental test
for various classes of sonoluminescence models.


title:
Quantum-Classical Correspondence: Controlling Quantum Transport by State
  Synthesis in Ion Traps

abstract:
  A procedure to enhance the quantum--classical correspondence even in
situations far from the classical limit is proposed. It is based on controlling
the quantum transport between classical regions using the capability to
synthesize arbitrary motional states in ion traps. Quantum barriers and
passages to transport can be created selecting the relevant frequencies. This
technique is then applied to stabilize the quantum motion onto classical
structures or alter the dynamical tunneling in nonintegrable systems.


title: Deviations from exponential law and Van Hove's "\lambda^2 t" limit

abstract:
  The deviations from a purely exponential behavior in a decay process are
analyzed in relation to Van Hove's "\lambda^2 t" limiting procedure. Our
attention is focused on the effects that arise when the coupling constant is
small but nonvanishing. We first consider a simple model (two-level atom in
interaction with the electromagnetic field), then gradually extend our analysis
to a more general framework. We estimate all deviations from exponential
behavior at leading orders in the coupling constant.


title: Quantum information and precision measurement

abstract:
  We describe some applications of quantum information theory to the analysis
of quantum limits on measurement sensitivity. A measurement of a weak force
acting on a quantum system is a determination of a classical parameter
appearing in the master equation that governs the evolution of the system;
limitations on measurement accuracy arise because it is not possible to
distinguish perfectly among the different possible values of this parameter.
Tools developed in the study of quantum information and computation can be
exploited to improve the precision of physics experiments; examples include
superdense coding, fast database search, and the quantum Fourier transform.


title: Quantum information and physics: some future directions

abstract:
  I consider some promising future directions for quantum information theory
that could influence the development of 21st century physics. Advances in the
theory of the distinguishability of superoperators may lead to new strategies
for improving the precision of quantum-limited measurements. A better grasp of
the properties of multi-partite quantum entanglement may lead to deeper
understanding of strongly-coupled dynamics in quantum many-body systems,
quantum field theory, and quantum gravity.


title: Entanglement-Assisted Classical Capacity of Noisy Quantum Channels

abstract:
  Prior entanglement between sender and receiver, which exactly doubles the
classical capacity of a noiseless quantum channel, can increase the classical
capacity of some noisy quantum channels by an arbitrarily large constant factor
depending on the channel, relative to the best known classical capacity
achievable without entanglement. The enhancement factor is greatest for very
noisy channels, with positive classical capacity but zero quantum capacity.
Although such quantum channels can be simulated classically, no violation of
causality is implied, because the simulation requires at least as much forward
classical communication as the entanglement-assisted classical capacity of the
channel being simulated. We obtain exact expressions for the
entanglement-assisted capacity of depolarizing and erasure channels in d
dimensions.


title:
Unifying Approach to Software and Hardware Design for Scientific
  Calculations

abstract:
  A unifying approach to software and hardware design generated by ideas of
Idempotent Mathematics is discussed. The so-called idempotent correspondence
principle for algorithms, programs and hardware units is described. A software
project based on this approach is presented.
  Key words: universal algorithms, idempotent calculus, software design,
hardware design, object oriented programming


title:
Nondigital implementation of the arithmetic of real numbers by means of
  quantum computer media

abstract:
  In the framework of a model for quantum computer media, a nondigital
implementation of the arithmetic of the real numbers is described. For this
model, an elementary storage "cell" is an ensemble of qubits (quantum bits). It
is found that to store an arbitrary real number it is sufficient to use four of
these ensembles and the arithmetic operations can be implemented by fixed
quantum circuits.


title:
Generalized Adiabatic Product Expansion: A nonperturbative method of
  solving time-dependent Schroedinger equation

abstract:
  We outline a method based on successive canonical transformations which
yields a product expansion for the evolution operator of a general (possibly
non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion
involves a finite number of terms, and our method gives the exact solution of
the corresponding time-dependent Schroedinger equation. We apply this method to
study the dynamics of a general nondegenerate two-level quantum system, a
time-dependent classical harmonic oscillator, and a degenerate system
consisting of a spin 1 particle interacting with a time-dependent electric
field E(t) through the Stark Hamiltonian H=\lambda [J.E(t)]^2.


title:
Non-classical properties and algebraic characteristics of negative
  binomial states in quantized radiation fields

abstract:
  We study the nonclassical properties and algebraic characteristics of the
negative binomial states introduced by Barnett recently. The ladder operator
formalism and displacement operator formalism of the negative binomial states
are found and the algebra involved turns out to be the SU(1,1) Lie algebra via
the generalized Holstein-Primarkoff realization. These states are essentially
Peremolov's SU(1,1) coherent states. We reveal their connection with the
geometric states and find that they are excited geometric states. As
intermediate states, they interpolate between the number states and geometric
states. We also point out that they can be recognized as the nonlinear coherent
states. Their nonclassical properties, such as sub-Poissonian distribution and
squeezing effect are discussed. The quasiprobability distributions in phase
space, namely the Q and Wigner functions, are studied in detail. We also
propose two methods of generation of the negative binomial states.


title:
Teleportation of a Zero-and One-photon Running Wave State by Projection
  Synthesis

abstract:
  We show how to teleport a running wave superposition of zero- and one-photon
field state through the projection synthesis technique. The fidelity of the
scheme is computed taking into account the noise introduced by dissipation and
the efficiency of the detectors. These error sources have been introduced
through a single general relationship between input and output operators.


title:
Implications of Form Invariance to the Structure of Nonextensive
  Entropies

abstract:
  The form invariance of the statement of the maximum entropy principle and the
metric structure in quantum density matrix theory, when generalized to
nonextensive situations, is shown here to determine the structure of the
nonextensive entropies. This limits the range of the nonextensivity parameter
to so as to preserve the concavity of the entropies. The Tsallis entropy is
thereby found to be appropriately renormalized.


title:
Numerical computation of one-photon mazer resonances for arbitrary field
  modes

abstract:
  We present a novel approach for solving numerically one-dimensional
scattering problems and apply it for computing the emission probability of an
ultracold atom interacting with an arbitrary field mode of a high-$Q$ cavity.
Our method is efficient, stable and succeeds when other numerical integration
methods fail. It also replaces and improves advantageously the WKB
approximation. The cases of sinusoidal, $\mathrm{sech}^2$ and Gaussian field
modes are studied and compared. Divergences with previous works, where WKB was
used, are found.


title:
Ultra-Slow Light and Enhanced Nonlinear Optical Effects in a Coherently
  Driven Hot Atomic Gas

abstract:
  We report the observation of small group velocities of order 90 meters per
second, and large group delays of greater than 0.26 ms, in an optically dense
hot rubidium gas (~360 K). Media of this kind yield strong nonlinear
interactions between very weak optical fields, and very sharp spectral
features. The result is in agreement with previous studies on nonlinear
spectroscopy of dense coherent media.


title: Enhancement of Magneto-Optic Effects via Large Atomic Coherence

abstract:
  We utilize the generation of large atomic coherence to enhance the resonant
nonlinear magneto-optic effect by several orders of magnitude, thereby
eliminating power broadening and improving the fundamental signal-to-noise
ratio. A proof-of-principle experiment is carried out in a dense vapor of Rb
atoms. Detailed numerical calculations are in good agreement with the
experimental results. Applications such as optical magnetometry or the search
for violations of parity and time reversal symmetry are feasible.


title:
Squashed States of Light: Theory and Applications to Quantum
  Spectroscopy

abstract:
  Using a feedback loop it is possible to reduce the fluctuations in one
quadrature of an in-loop field without increasing the fluctuations in the
other. This effect has been known for a long time, and has recently been called
``squashing'' [B.C. Buchler et al., Optics Letters {\bf 24}, 259 (1999)], as
opposed to the ``squeezing'' of a free field in which the conjugate
fluctuations are increased. In this paper I present a general theory of
squashing, including simultaneous squashing of both quadratures and
simultaneous squeezing and squashing. I show that a two-level atom coupled to
the in-loop light feels the effect of the fluctuations as calculated by the
theory. In the ideal limit of light squeezed in one quadrature and squashed in
the other, the atomic decay can be completely suppressed.


title: Parametric Self-Oscillation via Resonantly Enhanced Multiwave Mixing

abstract:
  We demonstrate an efficient nonlinear process in which Stokes and anti-Stokes
components are generated spontaneously in a Raman-like, near resonant media
driven by low power counter-propagating fields. Oscillation of this kind does
not require optical cavity and can be viewed as a spontaneous formation of
atomic coherence grating.


title: The second-order electron self-energy in hydrogen-like ions

abstract:
  A calculation of the simplest part of the second-order electron self-energy
(loop after loop irreducible contribution) for hydrogen-like ions with nuclear
charge numbers $3 \leq Z \leq 92$ is presented. This serves as a test for the
more complicated second-order self-energy parts (loop inside loop and crossed
loop contributions) for heavy one-electron ions. Our results are in strong
disagreement with recent calculations of Mallampalli and Sapirstein for low $Z$
values but are compatible with the two known terms of the analytical
$Z\alpha$-expansion.


title: Coherent States and the Reconstruction of Pure Spin States

abstract:
  Coherent states provide an appealing method to reconstruct efficiently a pure
state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to
measure (4s+1) expectations of projection operators on appropriate coherent
states in the unknown state. These measurements are compatible with a finite
number of states which can be distinguished, in the generic case, by measuring
one more probability. In addition, the present technique shows that the zeroes
of a Husimi distribution do have an operational meaning: they can be identified
directly by measurements with a Stern-Gerlach apparatus. This result comes down
to saying that it is possible to resolve experimentally structures in quantum
phase-space which are smaller than hbar.


title: Quantum Information is physical too

abstract:
  We discuss the physical nature of quantum information, in particular
focussing on tasks that are achievable by some physical realizations of qubits
but not by others.


title: Practical quantum key distribution over a 48-km optical fiber network

abstract:
  The secure distribution of the secret random bit sequences known as "key"
material, is an essential precursor to their use for the encryption and
decryption of confidential communications. Quantum cryptography is a new
technique for secure key distribution with single-photon transmissions:
Heisenberg's uncertainty principle ensures that an adversary can neither
successfully tap the key transmissions, nor evade detection (eavesdropping
raises the key error rate above a threshold value). We have developed
experimental quantum cryptography systems based on the transmission of
non-orthogonal photon states to generate shared key material over
multi-kilometer optical fiber paths and over line-of-sight links. In both
cases, key material is built up using the transmission of a single-photon per
bit of an initial secret random sequence. A quantum-mechanically random subset
of this sequence is identified, becoming the key material after a data
reconciliation stage with the sender. Here we report the most recent results of
our optical fiber experiment in which we have performed quantum key
distribution over a 48-km optical fiber network at Los Alamos using photon
interference states with the B92 and BB84 quantum key distribution protocols.


title: Speedup of iterated quantum search by parallel performance

abstract:
  Given a sequence $f_1 (x_1), f_2 (x_1, x_2), ..., f_k (x_1, ..., x_k)$ of
Boolean functions, each of which $f_i$ takes the value 1 in a single point of
the form $x_1^0, x_2^0, ..., x_i^0, i=1,2,..., k$. A length of all $x_i^0$ is
$n, N=2^n$. It is shown how to find $x_k^0 (k\geq 2)$ using
\frac{k\pi\sqrt{N}}{4\sqrt{2}}$ simultaneous evaluations of functions of the
form $f_i, f_{i+1}$ with an error probability of order $k/\sqrt{N}$ which is
$\sqrt{2}$ times as fast as by the $k$ sequential applications of Grover
algorithm for the quantum search. Evolutions of amplitudes in parallel quantum
computations are approximated by systems of linear differential equations. Some
advantage of simultaneous evaluations of all $f_1 ,... f_k$ are discussed.


title: The Weyl representation on the torus

abstract:
  We construct reflection and translation operators on the Hilbert space
corresponding to the torus by projecting them from the plane. These operators
are shown to have the same group properties as their analogue on the plane. The
decomposition of operators in the basis of reflections corresponds to the Weyl
or center representation, conjugate to the chord representation which is based
on quantized translations. Thus, the symbol of any operator on the torus is
derived as the projection of the symbol on the plane. The group properties
allow us to derive the product law for an arbitrary number of operators in a
simple form. The analogy between the center and the chord representations on
the torus to those on the plane is then exploited to treat Hamiltonian systems
defined on the torus and to formulate a path integral representation of the
evolution operator. We derive its semiclassical approximation.


title: Delayed choice for entanglement swapping

abstract:
  Two observers (Alice and Bob) independently prepare two sets of singlets.
They test one particle of each singlet along an arbitrarily chosen direction
and send the other particle to a third observer, Eve. At a later time, Eve
performs joint tests on pairs of particles (one from Alice and one from Bob).
According to Eve's choice of test and to her results, Alice and Bob can sort
into subsets the samples that they have already tested, and they can verify
that each subset behaves as if it consisted of entangled pairs of distant
particles, that have never communicated in the past, even indirectly via other
particles.


title: Anomalous Acceleration Effects for Neutrons

abstract:
  Comparing the Dirac Hamiltonians for a neutron subjected to either a
Schwartzchild gravitational field or a uniform acceleration, we observe that
the difference between the two is precisely the sort that might be eliminated
by the introduction of a new quantum number. The origin of this quantum number
lies in the noncommutation of an acceleration with the quark operators that
constitute the neutron. We show that the term containing the new quantum number
only acts on very long length scales. Furthermore, the symmetries of an
acceleration prevent the effects of this term from being periodic.


title: The Faraday Quantum Clock and Non-local Photon Pair Correlations

abstract:
  We study the use of the Faraday effect as a quantum clock for measuring
traversal times of evanescent photons through magneto-refractive structures.
The Faraday effect acts both as a phase-shifter and as a filter for circular
polarizations. Only measurements based on the Faraday phase-shift properties
are relevant to the traversal time measurements. The Faraday polarization
filtering may cause the loss of non-local (Einstein-Podolsky-Rosen) two-photon
correlations, but this loss can be avoided without sacrificing the clock
accuracy. We show that a mechanism of destructive interference between
consecutive paths is responsible for superluminal traversal times measured by
the clock.


title: Effects of motion in cavity QED

abstract:
  We consider effects of motion in cavity quantum electrodynamics experiments
where single cold atoms can now be observed inside the cavity for many Rabi
cycles. We discuss the timescales involved in the problem and the need for good
control of the atomic motion, particularly the heating due to exchange of
excitation between the atom and the cavity, in order to realize nearly unitary
dynamics of the internal atomic states and the cavity mode which is required
for several schemes of current interest such as quantum computing. Using a
simple model we establish ultimate effects of the external atomic degrees of
freedom on the action of quantum gates. The perfomance of the gate is
characterized by a measure based on the entanglement fidelity and the motional
excitation caused by the action of the gate is calculated. We find that schemes
which rely on adiabatic passage, and are not therefore critically dependent on
laser pulse areas, are very much more robust against interaction with the
external degrees of freedom of atoms in the quantum gate.


title:
Between Schroedinger and Hermite: Supersymmetric pair of q-deformed
  non-local operators

abstract:
  A simple version of the q-deformed calculus is used to generate a pair of
q-nonlocal, second-order difference operators by means of deformed counterparts
of Darboux intertwining operators for zero factorization energy. These deformed
non-local operators may be considered as supersymmetric partners and their
structure contains contributions originating in both the Hermite operator and
the quantum harmonic oscillator operator. There are also extra $\pm x$
contributions. The undeformed limit, in which all q-nonlocalities wash out,
corresponds to the usual supersymmetric pair of quantum mechanical harmonic
oscillator Hamiltonians. The more general case of negative factorization energy
is briefly discussed as well


title: Testing of quantum phase in matter wave optics

abstract:
  Various phase concepts may be treated as special cases of the maximum
likelihood estimation. For example the discrete Fourier estimation that
actually coincides with the operational phase of Noh, Fouge`res and Mandel is
obtained for continuous Gaussian signals with phase modulated mean.Since
signals in quantum theory are discrete, a prediction different from that given
by the Gaussian hypothesis should be obtained as the best fit assuming a
discrete Poissonian statistics of the signal. Although the Gaussian estimation
gives a satisfactory approximation for fitting the phase distribution of almost
any state the optimal phase estimation offers in certain cases a measurable
better performance. This has been demonstrated in neutron--optical experiment.


title:
State Vector Collapse Probabilities and Separability of Independent
  Systems in Hughston's Stochastic Extension of the Schr\"odinger Equation

abstract:
  We give a general proof that Hughston's stochastic extension of the
Schr\"odinger equation leads to state vector collapse to energy eigenstates,
with collapse probabilities given by the quantum mechanical probabilities
computed from the initial state. We also show that for a system composed of
independent subsystems, Hughston's equation separates into similar independent
equations for the each of the subsystems, correlated only through the common
Wiener process that drives the state reduction.


title: Generalized Quantum Search with Parallelism

abstract:
  We generalize Grover's unstructured quantum search algorithm to enable it to
use an arbitrary starting superposition and an arbitrary unitary matrix
simultaneously. We derive an exact formula for the probability of the
generalized Grover's algorithm succeeding after n iterations. We show that the
fully generalized formula reduces to the special cases considered by previous
authors. We then use the generalized formula to determine the optimal strategy
for using the unstructured quantum search algorithm. On average the optimal
strategy is about 12% better than the naive use of Grover's algorithm. The
speedup obtained is not dramatic but it illustrates that a hybrid use of
quantum computing and classical computing techniques can yield a performance
that is better than either alone. We extend the analysis to the case of a
society of k quantum searches acting in parallel. We derive an analytic formula
that connects the degree of parallelism with the optimal strategy for
k-parallel quantum search. We then derive the formula for the expected speed of
k-parallel quantum search.


title: A Computer Scientist's View of Life, the Universe, and Everything

abstract:
  Is the universe computable? If so, it may be much cheaper in terms of
information requirements to compute all computable universes instead of just
ours. I apply basic concepts of Kolmogorov complexity theory to the set of
possible universes, and chat about perceived and true randomness, life,
generalization, and learning in a given universe.

categories: quant-ph cs.CC cs.CY physics.comp-ph physics.pop-ph


title: New loophole for the EPR paradox

abstract:
  We exhibit a classical model free from any paradox which exactly simulates
the spin EPR test. We conclude that Bell's inequality violation is a strictly
classical phenomenon, contrary to a general belief.


title:
The Standard Model in Strong Fields: Electroweak Radiative Corrections
  for Highly Charged Ions

abstract:
  Electroweak radiative corrections to the matrix elements $<ns_{1/2}|{\hat
H}_{PNC}|n'p_{1/2}>$ are calculated for highly charged hydrogenlike ions. These
matrix elements constitute the basis for the description of the most parity
nonconserving (PNC) processes in atomic physics. The operator ${\hat H}_{PNC}$
represents the parity nonconserving relativistic effective atomic Hamiltonian
at the tree level. The deviation of these calculations from the calculations
valid for the momentum transfer $q^{2}=0$ demonstrates the effect of the strong
field, characterized by the momentum transfer $q^{2}=m_{e}^{2}$ ($m_{e}$ is the
electron mass). This allows for a test of the Standard Model in the presence of
strong fields in experiments with highly charged ions.


title:
Reduction of optimum light power with Heisenberg-limited photon-counting
  noise in interferometric gravitational-wave detectors

abstract:
  We study how the behavior of quantum noise, presenting the fundamental limit
on the sensitivity of interferometric gravitational-wave detectors, depends on
properties of input states of light. We analyze the situation with specially
prepared nonclassical input states which reduce the photon-counting noise to
the Heisenberg limit. This results in a great reduction of the optimum light
power needed to achieve the standard quantum limit, compared to the usual
configuration.


title:
Inverted spectroscopy and interferometry for quantum-state
  reconstruction of systems with SU(2) symmetry

abstract:
  We consider how the conventional spectroscopic and interferometric schemes
can be rearranged to serve for reconstructing quantum states of physical
systems possessing SU(2) symmetry. The discussed systems include a collection
of two-level atoms, a two-mode quantized radiation field with a fixed total
number of photons, and a single laser-cooled ion in a two-dimensional harmonic
trap with a fixed total number of vibrational quanta. In the proposed
rearrangement, the standard spectroscopic and interferometric experiments are
inverted. Usually one measures an unknown frequency or phase shift using a
system prepared in a known quantum state. Our aim is just the inverse one,
i.e., to use a well-calibrated apparatus with known transformation parameters
to measure unknown quantum states.


title:
Time-of-arrival distribution for arbitrary potentials and Wigner's
  time-energy uncertainty relation

abstract:
  A realization of the concept of "crossing state" invoked, but not
implemented, by Wigner, allows to advance in two important aspects of the time
of arrival in quantum mechanics: (i) For free motion, we find that the
limitations described by Aharonov et al. in Phys. Rev. A 57, 4130 (1998) for
the time-of-arrival uncertainty at low energies for certain mesurement models
are in fact already present in the intrinsic time-of-arrival distribution of
Kijowski; (ii) We have also found a covariant generalization of this
distribution for arbitrary potentials and positions.


title: Optimal generalized quantum measurements for arbitrary spin systems

abstract:
  Positive operator valued measurements on a finite number of N identically
prepared systems of arbitrary spin J are discussed. Pure states are
characterized in terms of Bloch-like vectors restricted by a SU(2 J+1)
covariant constraint. This representation allows for a simple description of
the equations to be fulfilled by optimal measurements. We explicitly find the
minimal POVM for the N=2 case, a rigorous bound for N=3 and set up the analysis
for arbitrary N.


title: q-deformed dynamics of q-deformed oscillators

abstract:
  We show that an infinite set of q-deformed relevant operators close a partial
q-deformed Lie algebra under commutation with the Arik-Coon oscillator. The
dynamics is described by the multicommutator: [H,..., [H, O]...], that follows
a power law which leads to a dynamical scaling. We study the dynamics of the
Arik-Coon and anharmonic oscillators and analyze the role of q and the other
parameters in the evolution of both systems.


title:
Wigner functions, squeezing properties and slow decoherence of atomic
  Schrodinger cats

abstract:
  We consider a class of states in an ensemble of two-level atoms: a
superposition of two distinct atomic coherent states, which can be regarded as
atomic analogues of the states usually called Schrodinger cat states in quantum
optics. According to the relation of the constituents we define polar and
nonpolar cat states. The properties of these are investigated by the aid of the
spherical Wigner function. We show that nonpolar cat states generally exhibit
squeezing, the measure of which depends on the separation of the components of
the cat, and also on the number of the constituent atoms. By solving the master
equation for the polar cat state embedded in an external environment, we
determine the characteristic times of decoherence, dissipation and also the
characteristic time of a new parameter, the non-classicality of the state. This
latter one is introduced by the help of the Wigner function, which is used also
to visualize the process. The dependence of the characteristic times on the
number of atoms of the cat and on the temperature of the environment shows that
the decoherence of polar cat states is surprisingly slow.


title: Quantum theory of excess noise

abstract:
  We analyze the excess noise in the framework of the conventional quantum
theory of laser-like systems. Our calculation is conceptually simple and our
result also shows a correction to the semi-classical result derived earlier.


title: Quantum Langevin theory of excess noise

abstract:
  In an earlier work [P. J. Bardroff and S. Stenholm], we have derived a fully
quantum mechanical description of excess noise in strongly damped lasers. This
theory is used here to derive the corresponding quantum Langevin equations.
Taking the semi-classical limit of these we are able to regain the starting
point of Siegman's treatment of excess noise [Phys. Rev. A 39, 1253 (1989)].
Our results essentially constitute a quantum derivation of his theory and allow
some generalizations.


title: The Dynamic Effect of Quantum Decoherence

abstract:
  An effective force induced by spatially depending decoherence is predicted.
The phenomenon is illustrated by a simple model of a 1/2-spin particle
subjected to distributed unselective measurement of noncommuting spin
components.


title: Quantum state transfer between motion and light

abstract:
  We describe schemes for transferring quantum states between light fields and
the motion of a trapped atom. Coupling between the motion and the light is
achieved via Raman transitions driven by a laser field and the quantized field
of a high-finesse microscopic cavity mode. By cascading two such systems and
tailoring laser field pulses, we show that it is possible to transfer an
arbitrary motional state of one atom to a second atom at a spatially distant
site.


title: Maximum-likelihood algorithm for quantum tomography

abstract:
  Optical homodyne tomography is discussed in the context of classical image
processing. Analogies between these two fields are traced and used to formulate
an iterative numerical algorithm for reconstructing the Wigner function from
homodyne statistics.


title:
Tunnelling series in terms of perturbation theory for quantum spin
  systems

abstract:
  Considered is quantum tunnelling in anisotropic spin systems in a magnetic
field perpendicular to the anisotropy axis. In the domain of small field the
problem of calculating tunnelling splitting of energy levels is reduced to
constructing the perturbatio n series with degeneracy, the order of degeneracy
being proportional to a spin value. Partial summation of this series taking
into account ''dangerous terms'' with small denominators is performed and the
value of tunnelling splitting is calculated with allowance for the first
correction with respect to a magnetic field.


title:
Quantum stochastic models of two-level atoms and electromagnetic cross
  sections

abstract:
  Quantum stochastic differential equations have been used to describe the
dynamics of an atom interacting with the electromagnetic field via
absorption/emission processes. Here, by using the full quantum stochastic
Schroedinger equation proposed by Hudson and Parthasarathy fifteen years ago,
we show that such models can be generalized to include other processes into the
interaction. In the case of a two-level atom we construct a model in which the
interaction with the field is due either to absorption/emission processes
either to direct scattering processes, which simulate the interaction due to
virtual transitions to the levels which have been eliminated from the
description. To see the effects of the new terms, the total, elastic and
inelastic eloctromagnetic cross sections are studied. The new power spectrum is
compared with Mollow's results.


title: Probabilities to accept languages by quantum finite automata

abstract:
  We construct a hierarchy of regular languages such that the current language
in the hierarchy can be accepted by 1-way quantum finite automata with a
probability smaller than the corresponding probability for the preceding
language in the hierarchy. These probabilities converge to 1/2.


title:
Dressed-State Approach to Population Trapping in the Jaynes-Cummings
  Model

abstract:
  The phenomenon of atomic population trapping in the Jaynes-Cummings Model is
analysed from a dressed-state point of view. A general condition for the
occurrence of partial or total trapping from an arbitrary, pure initial
atom-field state is obtained in the form of a bound to the variation of the
atomic inversion. More generally, it is found that in the presence of initial
atomic or atom-field coherence the population dynamics is governed not by the
field's initial photon distribution, but by a `weighted dressedness'
distribution characterising the joint atom-field state. In particular,
individual revivals in the inversion can be analytically described to good
approximation in terms of that distribution, even in the limit of large
population trapping. This result is obtained through a generalisation of the
Poisson Summation Formula method for analytical description of revivals
developed by Fleischhauer and Schleich [Phys. Rev. A {\bf 47}, 4258 (1993)].


title: "Assisted cloning'' and "orthogonal-complementing" of an unknown state

abstract:
  We propose a protocol where one can exploit dual quantum and classical
channels to achieve perfect ``cloning'' and ``orthogonal-complementing'' of an
unknown state with a minimal assistance from a state preparer (without
revealing what the input state is). The first stage of the protocol requires
usual teleportation and in the second stage, the preparer disentangles the
left-over entangled states by a single particle measurement process and
communicates a number of classical bits (1-cbit per copy) to different parties
so that perfect copies and complement copies are produced. We discuss our
protocol for producing two copies and three copies (and complement copies)
using two and four particle entangled state and suggest how to generalise this
for N copies and complement copies using multiparticle entangled state.


title: Complementarity and the uncertainty relations

abstract:
  We formulate a general complementarity relation starting from any Hermitian
operator with discrete non-degenerate eigenvalues. We then elucidate the
relationship between quantum complementarity and the Heisenberg-Robertson's
uncertainty relation. We show that they are intimately connected. Finally we
exemplify the general theory with some specific suggested experiments.


title: Against Quantum Noise

abstract:
  This is a brief description of how to protect quantum states from dissipation
and decoherence that arise due to uncontrolled interactions with the
environment. We discuss recoherence and stabilisation of quantum states based
on two techniques known as "symmetrisation" and "quantum error correction". We
illustrate our considerations with the most popular quantum-optical model of
the system-environment interaction, commonly used to describe spontaneous
emission, and show the benefits of quantum error correction in this case.


title: Nonlocality of the Einstein-Podolsky-Rosen state in the phase space

abstract:
  We discuss violation of Bell inequalities by the regularized
Einstein-Podolsky-Rosen (EPR) state, which can be produced in a quantum optical
parametric down-conversion process. We propose an experimental photodetection
scheme to probe nonlocal quantum correlations exhibited by this state.
Furthermore, we show that the correlation functions measured in two versions of
the experiment are given directly by the Wigner function and the Q function of
the EPR state. Thus, the measurement of these two quasidistribution functions
yields a novel scheme for testing quantum nonlocality.


title:
Basic Quantum Theory and Measurement from the Viewpoint of Local Quantum
  Physics

abstract:
  Several aspects of the manifestation of the causality principle in LQP (local
quantum physics) are reviewed or presented. Particular emphasis is given to
those properties which are typical for LQP in the sense that they do go beyond
the structure of general quantum theory and even escape the Lagrangian
quantization methods of standard QFT. The most remarkable are those relating
causality to the modular Tomita-Takesaki theory, since they bring in the basic
concepts of antiparticles, charge superselections as well as internal and
external (geometric and hidden) symmetries.


title: Quantum theory of fluctuations in a cold damped accelerometer

abstract:
  We present a quantum network approach to real high sensitivity measurements.
Thermal and quantum fluctuations due to active as well as passive elements are
taken into account. The method is applied to the analysis of the capacitive
accelerometer using the cold damping technique, developed for fundamental
physics in space by ONERA and the ultimate limits of this instrument are
discussed. It is confirmed in this quantum analysis that the cold damping
technique allows one to control efficiently the test mass motion without
degrading the noise level.


title: Generation and Measurement of Nonclassical States by Quantum Fock Filter

abstract:
  We study a novel optical setup which is able to select a specific Fock
component from a generic input state. The device allows to synthesize number
states and superpositions of few number states, and to measure the photon
distribution and the density matrix of a generic input signal.


title: Noncausal Superluminal Nonlocal Signalling

abstract:
  We propose a thought experiment for classical superluminal signal
transmission based on the quantum nonlocal influence of photons on their
momentum entangled EPR twins. The signal sender measures either position or
momentum of particles in a pure ensemble of the entangled pairs, leaving their
twins as localized particles or plane waves. The signal receiver distinguishes
these outcomes interferometrically using a double slit interferometer modified
by a system of optical filters. Since the collapse of the wavefunction is
postulated to be instantaneous, this signal can be transmitted superluminally.
We show that the method circumvents the no-signalling theorem because the
receiver is able to modify the disentangled wavefunction before his
measurement. We propose a plan for the possible practical realization of a
superluminal quantum telegraph based on the thought experiment.


title:
Modifying the lifetime of an unstable system by an intense
  electromagnetic field

abstract:
  We study the temporal behavior of a three-level system (such as an atom or a
molecule), initially prepared in an excited state, bathed in a laser field
tuned at the transition frequency of the other level. We analyze the dependence
of the lifetime of the initial state on the intensity of the laser field. The
phenomenon we discuss is related to both electromagnetic induced transparency
and quantum Zeno effect.


title:
Arbitrary phase rotation of the marked state can not be used for
  Grover's quantum search algorithm

abstract:
  A misunderstanding that an arbitrary phase rotation of the marked state
together with the inversion about average operation in Grover's search
algorithm can be used to construct a (less efficient) quantum search algorithm
is cleared. The $\pi$ rotation of the phase of the marked state is not only the
choice for efficiency, but also vital in Grover's quantum search algorithm. The
results also show that Grover's quantum search algorithm is robust.


title: Unconditionally Secure Quantum Coin Tossing

abstract:
  In coin tossing two remote participants want to share a uniformly distributed
random bit. At the least in the quantum version, each participant test whether
or not the other has attempted to create a bias on this bit. It is requested
that, for b = 0,1, the probability that Alice gets bit b and pass the test is
smaller than 1/2 whatever she does, and similarly for Bob. If the bound 1/2
holds perfectly against any of the two participants, the task realised is
called an exact coin tossing. If the bound is actually $1/2 + \xi$ where the
bias $\xi$ vanishes when a security parameter m defined by the protocol
increases, the task realised is a (non exact) coin tossing. It is found here
that exact coin tossing is impossible. At the same time, an unconditionally
secure quantum protocol that realises a (non exact) coin tossing is proposed.
The protocol executes m biased quantum coin tossing procedures at the same
time. It executes the first round in each of these m procedures sequentially,
then the second rounds are executed, and so on until the end of the n
procedures. Each procedure requires 4n particles where $n \in O(\lg m)$. The
final bit x is the parity of the m random bits. The information about each of
these m bits is announced a little bit at a time which implies that the
principle used against bit commitment does not apply. The bias on x is smaller
than $1/m$. The result is discussed in the light of the impossibility result
for exact coin tossing.


title: Average-Case Quantum Query Complexity

abstract:
  We compare classical and quantum query complexities of total Boolean
functions. It is known that for worst-case complexity, the gap between quantum
and classical can be at most polynomial. We show that for average-case
complexity under the uniform distribution, quantum algorithms can be
exponentially faster than classical algorithms. Under non-uniform distributions
the gap can even be super-exponential. We also prove some general bounds for
average-case complexity and show that the average-case quantum complexity of
MAJORITY under the uniform distribution is nearly quadratically better than the
classical complexity.


title: Noise perturbations in the Brownian motion and quantum dynamics

abstract:
  The third Newton law for mean velocity fields is utilised to generate
anomalous (enhanced) or non-dispersive diffusion-type processes which, in
particular, can be interpreted as a probabilistic counterpart of the
Schr\"{o}dinger picture quantum dynamics.


title: Quantum mechanics and elements of reality

abstract:
  It is widely accepted that a Born probability of 1 is sufficient for the
existence of a corresponding element of reality. Recently Vaidman has extended
this idea to the ABL probabilities of the time-symmetrized version of quantum
mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have
objected to Vaidman's time-symmetrized elements of reality without casting
doubt on the widely accepted sufficiency condition for `ordinary' elements of
reality. In this paper I show that while the proper truth condition for a
quantum counterfactual is an ABL probability of 1, neither a Born probability
of 1 nor an ABL probability of 1 is sufficient for the existence of an element
of reality. The reason this is so is that the contingent properties of
quantum-mechanical systems are extrinsic. To obtain this result, I need to
discuss objective probabilities, retroactive causality, and the objectivity or
otherwise of the psychological arrow of time. One consequence of the extrinsic
nature of quantum-mechanical properties is that quantum mechanics presupposes
property-defining actual events (or states of affairs) and therefore cannot be
called upon to account for their occurrence (existence). Neither these events
nor the correlations between them are capable of explanation, the former
because they are causal primaries, the latter because they are fundamental:
there are no underlying causal processes. Causal connections are something we
project onto the statistical correlations, and this works only to the extent
that statistical variations can be ignored. There are nevertheless important
conclusions to be drawn from the quantum-mechanical correlations, such as the
spatial nonseparability of the world.


title: Berry phase due to quantum measurements

abstract:
  The usual, "static" version of the quantum Zeno effect consists in the
hindrance of the evolution of a quantum systems due to repeated measurements.
There is however a "dynamic" version of the same phenomenon, first discussed by
von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which
a system is forced to follow a given trajectory. A Berry phase appears if such
a trajectory is a closed loop in the projective Hilbert space. A specific
example involving neutron spin is considered and a similar situation with
photon polarization is investigated.


title: Classical and quantum mechanics of a particle on a rotating loop

abstract:
  The toy model of a particle on a vertical rotating circle in the presence of
uniform gravitational/ magnetic fields is explored in detail. After an analysis
of the classical mechanics of the problem we then discuss the quantum mechanics
from both exact and semi--classical standpoints. Exact solutions of the
Schrodinger equation are obtained in some cases by diverse methods. Instantons,
bounces are constructed and semi-classical, leading order tunneling
amplitudes/decay rates are written down. We also investigate qualitatively the
nature of small oscillations about the kink/bounce solutions. Finally, the
connections of these toy examples with field theoretic and statistical
mechanical models of relevance are pointed out.


title: Non-Exponential Decay for Polaron Model

abstract:
  A model of particle interacting with quantum field is considered. The model
includes as particular cases the polaron model and non-relativistic quantum
electrodynamics. We compute matrix elements of the evolution operator in the
stochastic approximation and show that depending on the state of the particle
one can get the non-exponential decay with the rate t^{-3/2}. In the process of
computation a new algebra of commutational relations that can be considered as
an operator deformation of quantum Boltzmann commutation relations is used.


title:
Transfer of coherence from atoms to mixed field states in a two-photon
  lossless micromaser

abstract:
  We propose a two-photon micromaser-based scheme for the generation of a
nonclassical state from a mixed state. We conclude that a faster, as well as a
higher degree of field purity is achieved in comparison to one-photon
processes. We investigate the statistical properties of the resulting field
states, for initial thermal and (phase-diffused) coherent states.
Quasiprobabilities are employed to characterize the state of the generated
fields.


title: Wigner function and coherence properties of cold and thermal neutrons

abstract:
  We analyze the coherence properties of a cold or a thermal neutron by
utilizing the Wigner quasidistribution function. We look in particular at a
recent experiment performed by Badurek {\em et al.}, in which a polarized
neutron crosses a magnetic field that is orthogonal to its spin, producing
highly non-classical states. The quantal coherence is extremely sensitive to
the field fluctuation at high neutron momenta. A "decoherence parameter" is
introduced in order to get quantitative estimates of the losses of coherence.


title:
Control of Decoherence and Relaxation by Frequency Modulation of Heat
  Bath

abstract:
  We demonstrate in a very general fashion, considerable slowing down of
decoherence and relaxation by fast frequency modulation of the system heat bath
coupling. The slowing occurs as the decoherence rates are now determined by the
spectral components of bath correlations which are shifted due to fast
modulation. We present several examples including the slowing down of the
heating of a trapped ion, where the system - bath interaction is not
necessarily Markovian.