title:
Reconstructing a pure state of a spin s through three Stern-Gerlach
  measurements

abstract:
  Consider a spin s prepared in a pure state. It is shown that, generically,
the moduli of the (2s+1) spin components along three directions in space
determine the state unambiguously. These probabilities are accessible
experimentally by means of a standard Stern-Gerlach apparatus. To reconstruct a
pure spin state is therefore possible on the basis of 3(2s+1) measured
intensities.


title: An Inversion Inequality for Potentials in Quantum Mechanics

abstract:
  We suppose: (1) that the ground-state eigenvalue E = F(v) of the Schroedinger
Hamiltonian H = -Delta + vf(x) in one dimension is known for all values of the
coupling v > 0; and (2) that the potential shape can be expressed in the form
f(x) = g(x^2), where g is monotone increasing and convex. The inversion
inequality f(x) <= fbar(1/(4x^2)) is established, in which the `kinetic
potential' fbar(s) is related to the energy function F(v) by the
transformation: fbar(s) = F'(v), s = F(v) - vF'(v) As an example f is
approximately reconstructed from the energy function F for the potential f(x) =
x^2 + 1/(1+x^2).


title: Coherent states on the circle

abstract:
  A careful study of the physical properties of a family of coherent states on
the circle, introduced some years ago by de Bi\`evre and Gonz\'alez in [DG 92],
is carried out. They were obtained from the Weyl-Heisenberg coherent states in
$L^2(\R)$ by means of the Weil-Brezin-Zak transformation, they are labeled by
the points of the cylinder $S^1 \times \R$, and they provide a realization of
$L^2(S^1)$ by entire functions (similar to the well-known Fock-Bargmann
construction). In particular, we compute the expectation values of the position
and momentum operators on the circle and we discuss the Heisenberg uncertainty
relation.


title:
Strictly isospectral SUSY potentials and the Riccati superposition
  principle

abstract:
  The connection of unbroken SUSY quantum mechanics in its strictly isospectral
form with the nonlinear Riccati superposition principle is pointed out


title: Sending Quantum Information with Gaussian States

abstract:
  Quantum information characteristics, such as quantum mutual information,
loss, noise and coherent information are explicitly calculated for Bosonic
attenuation/amplification channel with input Gaussian state. The coherent
information is shown to be negative for the values of the attenuation
coefficient $k<1/\sqrt{2}$.


title: Coding Theorems for Quantum Channels

abstract:
  The more than thirty years old issue of the (classical) information capacity
of quantum communication channels was dramatically clarified during the last
years, when a number of direct quantum coding theorems was discovered. The
present paper gives a self contained treatment of the subject, following as
much in parallel as possible with classical information theory and, on the
other side, stressing profound differences of the quantum case. An emphasis is
made on recent results, such as general quantum coding theorems including cases
of infinite (possibly continuous) alphabets and constrained inputs, reliability
function for pure state channels and quantum Gaussian channel. Several still
unsolved problems are briefly outlined.


title: Quantum identification system

abstract:
  A secure quantum identification system combining a classical identification
procedure and quantum key distribution is proposed. Each identification
sequence is always used just once and new sequences are ``refuelled'' from a
shared provably secret key transferred through the quantum channel. Two
identification protocols are devised. The first protocol can be applied when
legitimate users have an unjammable public channel at their disposal. The
deception probability is derived for the case of a noisy quantum channel. The
second protocol employs unconditionally secure authentication of information
sent over the public channel, and thus it can be applied even in the case when
an adversary is allowed to modify public communications. An experimental
realization of a quantum identification system is described.


title: Long-distance Bell-type tests using energy-time entangled photons

abstract:
  Long-distance Bell-type experiments are presented. The different experimental
challenges and their solutions in order to maintain the strong quantum
correlations between energy-time entangled photons over more than 10 km are
reported and the results analyzed from the point of view of tests of
fundamental physics as well as from the more applied side of quantum
communication, specially quantum key distribution. Tests using more than one
analyzer on each side are also presented.


title: Characteristic uncertainty relations

abstract:
  New uncertainty relations for n observables are established. The relations
take the invariant form of inequalities between the characteristic coefficients
of order r, r = 1,2,...,n, of the uncertainty matrix and the matrix of mean
commutators of the observables.
  It is shown that the second and the third order characteristic inequalities
for the three generators of SU(1,1) and SU(2) are minimized in the
corresponding group-related coherent states with maximal symmetry.


title: Two-particle scattering theory for anyons

abstract:
  We consider potential scattering theory of a nonrelativistic quantum
mechanical 2-particle system in R^2 with anyon statistics. Sufficient
conditions are given which guarantee the existence of wave operators and the
unitarity of the S-matrix. As examples the rotationally invariant potential
well and the delta-function potential are discussed in detail. In case of a
general rotationally invariant potential the angular momentum decomposition
leads to a theory of Jost functions. The anyon statistics parameter gives rise
to an interpolation for angular momenta analogous to the Regge trajectories for
complex angular momenta. Levinson's theorem is adapted to the present context.
In particular we find that in case of a zero energy resonance the statistics
parameter can be determined from the scattering phase.

categories: quant-ph cond-mat.mes-hall hep-th math-ph math.MP


title: Quantum Computation, Spectroscopy of Trapped Ions, and Schrodinger's Cat

abstract:
  We summarize efforts at NIST to implement quantum computation using trapped
ions, based on a scheme proposed by J.I. Cirac and P. Zoller (Innsbruck
University). The use of quantum logic to create entangled states, which can
maximize the quantum-limited signal-to-noise ratio in spectroscopy, is
discussed.


title: How fast can a quantum computer search?

abstract:
  This paper gives a simple proof of why a quantum computer, despite being in
all possible states simultaneously, needs at least 0.707 sqrt(N) queries to
retrieve a desired item from an unsorted list of items. The proof is refined to
show that a quantum computer would need at least 0.785 sqrt(N) queries. The
quantum search algorithm needs precisely this many queries.


title: Instantaneous Spreading and Einstein Causality in Quantum Theory

abstract:
  In nonrelativistic quantum mechanics the wave-function of a free particle
which initially is in a finite volume immediately spreads to infinity. In a
nonrelativistic theory this is of no concern, but we show that the same
instantaneous spreading can occur in relativistic quantum theory and that
transition probabilities in widely separated systems may instantaneously become
nonzero. We discuss how this affects Einstein causality.


title:
Few-body approach to diffraction of small helium clusters by
  nanostructures

abstract:
  We use few-body methods to investigate the diffraction of weakly bound
systems by a transmission grating. For helium dimers, He$_2$, we obtain
explicit expressions for the transition amplitude in the elastic channel.


title: Planck Scale to Hubble Scale

abstract:
  Within the context of the usual semi classical investigation of Planck scale
Schwarzchild Black Holes, as in Quantum Gravity, and later attempts at a full
Quantum Mechanical description in terms of a Kerr-Newman metric including the
spinorial behaviour, we attempt to present a formulation that extends from the
Planck scale to the Hubble scale. In the process the so called large number
coincidences as also the hitherto inexplicable relations between the pion mass
and the Hubble Constant, pointed out by Weinberg, turn out to be natural
consequences in a consistent description.


title: A Combinatorial Bit Bang Leading to Quaternions

abstract:
  This paper describes in detail how (discrete) quaternions - ie. the abstract
structure of 3-D space - emerge from, first, the Void, and thence from
primitive combinatorial structures, using only the exclusion and co-occurrence
of otherwise unspecified events. We show how this computational view
supplements and provides an interpretation for the mathematical structures, and
derive quark structure. The build-up is emergently hierarchical, compatible
with both quantum mechanics and relativity, and can be extended upwards to the
macroscopic. The mathematics is that of Clifford algebras emplaced in the
homology-cohomology structure pioneered by Kron. Interestingly, the ideas
presented here were originally developed by the author to resolve fundamental
limitations of existing AI paradigms. As such, the approach can be used for
learning, planning, vision, NLP, pattern recognition; and as well, for
modelling, simulation, and implementation of complex systems, eg. biological.


title:
Pulsed energy-time entangled twin-photon source for quantum
  communication

abstract:
  A pulsed source of energy-time entangled photon pairs pumped by a standard
laser diode is proposed and demonstrated. The basic states can be distinguished
by their time of arrival. This greatly simplifies the realization of 2-photon
quantum cryptography, Bell state analyzers, quantum teleportation, dense
coding, entanglement swapping, GHZ-states sources, etc. Moreover the
entanglement is well protected during photon propagation in telecom optical
fibers, opening the door to few-photon applications of quantum communication
over long distances.


title: Number-phase-squeezed few-photon state generated from squeezed atoms

abstract:
  This paper develops a method of manipulating the squeezed atom state to
generate a few-photon state whose phase or photon-number fluctuations are
prescribed at our disposal. The squeezed atom state is a collective atomic
state whose quantum fluctuations in population difference or collective dipole
are smaller than those of the coherent atom state. It is shown that the
squeezed atom state can be generated by the interaction of atoms with a
coherent state of the electromagnetic field, and that it can be used as a
tunable source of squeezed radiation. A variety of squeezed states, including
the photon-number squeezed state and the phase squeezed state, can be produced
by manipulating the atomic state. This is owing to the fact that
quantum-statistical information of the atomic state is faithfully transferred
to that of the photon state. Possible experimental situations to implement our
theory are discussed.


title: Real-time tunneling

abstract:
  Starting with the equivalence of the rest energy of a particle to an amount
of the radiant energy characterized by a frequency, in addition to the usual
relativistic transformation rules leading to the wave-particle duality, we
investigate the case in which this frequency is an internal propery of the
particle. This kind of interpretation of the frequency is shown to be relevant
to the tunneling effect. The investigations in this direction yield (1) a
purely real time everywhere, (2) an anti-hermitian momentum operator, (3) a
corpuscular structure for the particle, and (4) all of the known theoretical
predictions about the tunneling effect.


title:
Macroscopically distinct quantum superposition states as a bosonic code
  for amplitude damping

abstract:
  We show how macroscopically distinct quantum superposition states
(Schroedinger cat states) may be used as logical qubit encodings for the
correction of spontaneous emission errors. Spontaneous emission causes a bit
flip error which is easily corrected by a standard error correction circuit.
The method works arbitrarily well as the distance between the amplitudes of the
superposed coherent states increases.


title:
Quantum Turing Machines: Local Transition, Preparation, Measurement, and
  Halting

abstract:
  Foundations of the theory of quantum Turing machines are investigated. The
protocol for the preparation and the measurement of quantum Turing machines is
discussed. The local transition functions are characterized for fully general
quantum Turing machines. A new halting protocol is proposed without augmenting
the halting qubit and is shown to work without spoiling the computation.


title: Quantum Cryptography with Imperfect Apparatus

abstract:
  Quantum key distribution, first proposed by Bennett and Brassard, provides a
possible key distribution scheme whose security depends only on the quantum
laws of physics. So far the protocol has been proved secure even under channel
noise and detector faults of the receiver, but is vulnerable if the photon
source used is imperfect. In this paper we propose and give a concrete design
for a new concept, {\it self-checking source}, which requires the manufacturer
of the photon source to provide certain tests; these tests are designed such
that, if passed, the source is guaranteed to be adequate for the security of
the quantum key distribution protocol, even though the testing devices may not
be built to the original specification. The main mathematical result is a
structural theorem which states that, for any state in a Hilbert space, if
certain EPR-type equations are satisfied, the state must be essentially the
orthogonal sum of EPR pairs.


title: The Fermi accelerator in atom optics

abstract:
  We study the classical and quantum dynamics of a Fermi accelerator realized
by an atom bouncing off a modulated atomic mirror. We find that in a window of
the modulation amplitude dynamical localization occurs in both position and
momentum. A recent experiment [A. Steane, P. Szriftgiser, P. Desbiolles, and J.
Dalibard, Phys. Rev. Lett. {\bf 74}, 4972 (1995)] shows that this system can be
implemented experimentally.


title: Wave packet tunneling

abstract:
  The tunneling of Gaussian wave packets has been investigated by numerically
solving the one-dimensional Schr\"odinger equation. The shape of wave packets
interacting with a square barrier has been monitored for various values of the
barrier width, height and initial width of the wave packet. Compared to the
case of free propagation, the maximum of a tunneled wave packet exhibits a
shift, which can be interpreted as an enhanced velocity during tunneling.


title:
Sensitivity of estimates of the volume of the set of separable states to
  the choice of "uniform" distributions

abstract: This paper has been withdrawn for the reasons mentioned in the Comments.


title: Lower Bounds for Attainable Fidelity in Entanglement Purification

abstract:
  We derive lower bounds for the attainable fidelity of standard entanglement
purification protocols when local operations and measurements are subjected to
errors. We introduce an error parameter which measures the distance between the
ideal completely positive map describing a purification step and the one in the
presence of errors. We derive non--linear maps for a lower bound of the
fidelity at each purification step in terms of this parameter.


title:
Thermalized Displaced and Squeezed Number States in Coordinate
  Representation

abstract:
  Within the framework of thermofield dynamics, the wavefunctions of the
thermalized displaced number and squeezed number states are given in the
coordinate representation. Furthermore, the time evolution of these
wavefunctions is considered by introducing a thermal coordinate representation,
and we also calculate the corresponding probability densities, average values
and variances of position coordinate, which are consistent with results in the
literature.


title: The effective Hamiltonian of the Pound-Overhauser controlled-NOT gate

abstract:
  In NMR-based quantum computing, it is known that the controlled-NOT gate can
be implemented by applying a low-power, monochromatic radio-frequency field to
one peak of a doublet in a weakly-coupled two-spin system. This is known in NMR
spectroscopy as Pound-Overhauser double resonance. The ``transition''
Hamiltonian that has been associated with this procedure is however only an
approximation, which ignores off-resonance effects and does not correctly
predict the associated phase factors. In this paper, the exact effective
Hamiltonian for evolution of the spins' state in a rotating frame is derived,
both under irradiation of a single peak (on-transition) as well as between the
peaks of the doublet (on-resonance). The accuracy of these effective
Hamiltonians is validated by comparing the observable product operator
components of the density matrix obtained by simulation to those obtained by
fitting the corresponding experiments. It is further shown how both the
on-transition and on-resonance fields can be used to implement the
controlled-NOT gate exactly up to conditional phases, and analytic expressions
for these phases are derived. In Appendices, the on-resonance Hamiltonian is
analytically diagonalized, and proofs are given that, in the weak-coupling
approximation, off-resonance effects can be neglected whenever the
radio-frequency field power is small compared to the difference in resonance
frequencies of the two spins.


title: Coherent polychotomous waves from an attractive well

abstract:
  A novel effect of a wave packet scattering off an attractive one- dimensional
well is found numerically and analytically. For a wave packet narrower than the
width of the well, the scattering proceeds through a quasi-bound state of
almost zero energy. The wave reflected from the well is a polychotomous
(multiple peak) monochromatic and coherent train. The transmitted wave is a
spreading smooth wave packet. The effect is strong for low average speeds of
the packet, and it disappears for wide packets.


title:
Quantum mechanics of an electron in a homogeneous magnetic field and a
  singular magnetic flux tube

abstract:
  The eigenvalue problem of the Hamiltonian of an electron confined to a plane
and subjected to a perpendicular time-independent magnetic field which is the
sum of a homogeneous field and an additional field contributed by a singular
flux tube, i.e. of zero width, is investigated. Since both a direct approach
based on distribution-valued operators and a limit process starting from a
non-singular flux tube, i.e. of finite size, fail, an alternative method is
applied leading to consistent results. An essential feature is quantum
mechanical supersymmetry at g=2 which imposes, by proper representation, the
correct choice of "boundary conditions". The corresponding representation of
the Hilbert space in coordinate space differs from the usual space of
square-integrable 2-spinors, entailing other unusual properties. The analysis
is extended to $g\ne 2$ so that supersymmetry is explicitly broken. Finally,
the singular Aharonov-Bohm system with the same amount of singular flux is
analysed by making use of the fact that the Hilbert space must be the same.


title: Measurability and Computability

abstract:
  The conceptual relation between the measurability of quantum mechanical
observables and the computability of numerical functions is re-examined. A new
formulation is given for the notion of measurability with finite precision in
order to reconcile the conflict alleged by M. A. Nielsen [Phys. Rev. Lett. 79,
2915 (1997)] that the measurability of a certain observable contradicts the
Church-Turing thesis. It is argued that any function computable by a quantum
algorithm is a recursive function obeying the Church-Turing thesis, whereas any
observable can be measured in principle.


title: High-order nonlinearities in the motion of a trapped atom

abstract:
  We study the counterpart to the multi-photon down conversion in the quantised
motion of a trapped atom. The Lamb-Dicke approximation leads to a divergence of
the mean motional excitation in a finite interaction time for k-quantum down
conversions with k>=3, analogous to the situation in the parametric
approximation of nonlinear optics. We show that, in contrast to the Lamb-Dicke
approximation, the correct treatment of the overlap of the atomic
center-of-mass wave function and the driving laser waves leads to a proper
dynamics without any divergence problem. That is, the wavy nature of both
matter and light is an important physical property which cannot be neglected
for describing the motional dynamics of a trapped atom, even for small
Lamb-Dicke parameters.


title: Governing dynamics by squeezing in a system of cold trapped ions

abstract:
  We consider a system of laser-cooled ions in a linear harmonic trap and study
the phenomenon of squeezing exchange between their internal and motional
degrees of freedom. An interesting relation between the quantum noise reduction
(squeezing) and the dynamical evolution is found when the internal and motional
subsystems are prepared in properly squeezed (intelligent) states.
Specifically, the evolution of the system is fully governed by the relative
strengths of spectroscopic and motional squeezing, including the phenomenon of
total cancellation of the interaction when the initial squeezing parameters are
equal.


title:
Collective effects in the collapse-revival phenomenon and squeezing in
  the Dicke model

abstract:
  Resonant interaction of a collection of two-level atoms with a single-mode
coherent cavity field is considered in the framework of the Dicke model. We
focus on the role of collective atomic effects in the phenomenon of collapses
and revivals of the Rabi oscillations. It is shown that the behavior of the
system strongly depends on the initial atomic state. In the case of the initial
half-excited Dicke state we account for a number of interesting phenomena. The
correlations between the atoms result in a suppression of the revival
amplitude, and the revival time is halved, compared to the uncorrelated
fully-excited and ground states. The phenomenon of squeezing of the radiation
field in the atom-field interaction is also discussed. For the initial
fully-excited and ground atomic states, the field is squeezed on the short-time
scale, and squeezing can be enhanced by increasing the number of atoms. Some
empirical formulas are found which describe the behavior of the system in
excellent agreement with numerical results. For the half-excited Dicke state,
the field can be strongly squeezed on the long-time scale in the case of two
atoms. This kind of squeezing is enhanced by increasing the intensity of the
initial coherent field and is of the same nature as revival-time squeezing in
the Jaynes-Cummings model. The appearance of this long-time squeezing can be
explained using the factorization approximation for semiclassical atomic
states.


title:
Phase-space formulation of quantum mechanics and quantum state
  reconstruction for physical systems with Lie-group symmetries

abstract:
  We present a detailed discussion of a general theory of phase-space
distributions, introduced recently by the authors [J. Phys. A {\bf 31}, L9
(1998)]. This theory provides a unified phase-space formulation of quantum
mechanics for physical systems possessing Lie-group symmetries. The concept of
generalized coherent states and the method of harmonic analysis are used to
construct explicitly a family of phase-space functions which are postulated to
satisfy the Stratonovich-Weyl correspondence with a generalized traciality
condition. The symbol calculus for the phase-space functions is given by means
of the generalized twisted product. The phase-space formalism is used to study
the problem of the reconstruction of quantum states. In particular, we consider
the reconstruction method based on measurements of displaced projectors, which
comprises a number of recently proposed quantum-optical schemes and is also
related to the standard methods of signal processing. A general group-theoretic
description of this method is developed using the technique of harmonic
expansions on the phase space.


title: Quantile Motion and Tunneling

abstract:
  The concepts of quantile position, trajectory, and velocity are defined. For
a tunneling quantum mechanical wave packet, it is proved that its quantile
position always stays behind that of a free wave packet with the same initial
parameters. In quantum mechanics the quantile trajectories are mathematically
identical to Bohm's trajectories. A generalization to three dimensions is
given.


title: Efficient fault-tolerant quantum computing

abstract:
  Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order $10^{-5}$, is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.


title: An Optimization for Qubiter

abstract:
  In a previous paper, we described a computer program called Qubiter which can
decompose an arbitrary unitary matrix into elementary operations of the type
used in quantum computation. In this paper, we describe a method of reducing
the number of elementary operations in such decompositions.


title: Short survey of Darboux transformations

abstract:
  A selective chronological survey of Darboux transformations as related to
supersymmetric quantum mechanics, intertwining operators and inverse scattering
techniques is presented. Short comments are appended to each quotation and
basic concepts are explained in order to provide a useful primer


title: Quantum error avoiding codes versus quantum error correcting codes

abstract:
  A general theory of quantum error avoiding codes is established, and new
light is shed on the relation between quantum error avoiding and correcting
codes. Quantum error avoiding codes are found to be a special type of highly
degenerate quantum error correcting codes. A combination of the ideas of
correcting and avoiding quantum errors may yield better codes. We give a
practical example.


title: Decoherence control in quantum information processing: simple models

abstract:
  We explore a strategy for protecting the evolution of a qubit against the
effects of environmental noise based on the application of controlled
time-dependent perturbations. In the case of a purely decohering coupling, an
explicit sequence of control operations is designed, able to average out the
decoherence of the qubit with high efficiency. We argue that, in principle, the
effects of arbitrary qubit-environment interactions can be removed through
suitable decoupling perturbations acting on the system dynamics over time
scales comparable to the correlation time of the environment.


title:
Limitations on the superposition principle: superselection rules in
  non-relativistic quantum mechanics

abstract:
  The superposition principle is a very basic ingredient of quantum theory.
What may come as a surprise to many students, and even to many practitioners of
the quantum craft, is tha superposition has limitations imposed by certain
requirements of the theory. The discussion of such limitations arising from the
so-called superselection rules is the main purpose of this paper. Some of their
principal consequences are also discussed. The univalence, mass and particle
number superselection rules of non-relativistic quantum mechanics are also
derived using rather simple methods.


title: A classical ontology for quantum phenomena

abstract:
  Quantum mechanics states that a particle emitted at point (x_1,t_1) and
detected at point (x_2,t_2) does not travel along a definite path between the
two points. This conclusion arises essentially from the analysis of the
two-slit experiment, which implicitly assumes (as in the demonstration of the
EPR paradox) that a property we will call Independence Property holds. This
paper shows that this assumption is not indispensable. Abandoning the
assumption allows to develop an ontology where particle motion is described by
classical paths and quantum phenomena are interpreted as a manifestation of a
contingent law, i.e., of a law deriving from the boundary conditions of the
universe, such as the second law of thermodynamics. The paper also proposes an
equation having a typical quantum-like structure to represent the contingent
laws of the universe.


title: Microscopic Foundation of Nonextensive Statistics

abstract:
  Combination of the Liouville equation with the q-averaged energy $U_q =
<H>_q$ leads to a microscopic framework for nonextensive q-thermodynamics. The
resulting von Neumann equation is nonlinear: $i\dot\rho=[H,\rho^q]$. In spite
of its nonlinearity the dynamics is consistent with linear quantum mechanics of
pure states. The free energy $F_q=U_q-TS_q$ is a stability function for the
dynamics. This implies that q-equilibrium states are dynamically stable. The
(microscopic) evolution of $\rho$ is reversible for any q, but for $q\neq 1$
the corresponding macroscopic dynamics is irreversible.


title: Sturmian Basis Functions for the Harmonic Oscillator

abstract:
  We define Sturmian basis functions for the harmonic oscillator and
investigate whether recent insights into Sturmians for Coulomb-like potentials
can be extended to this important potential. We also treat many body problems
such as coupling to a bath of harmonic oscillators. Comments on coupled
oscillators and time-dependent potentials are also made.
  It is argued that the Sturmian method amounts to a non-perturbative
calculation of the energy levels, but the limitations of the method is also
pointed out, and the cause of this limitation is found to be related to the
divergence of the potential. Thus the divergent nature of the anharmonic
potential leads to the Sturmian method being less acurate than in the Coulomb
case. We discuss how modified anharmonic oscillator potentials, which are well
behaved at infinity, leads to a rapidly converging Sturmian approximation.


title: On Bell measurements for teleportation

abstract:
  In this paper we investigate the possibility to make complete Bell
measurements on a product Hilbert space of two two-level bosonic systems. We
restrict our tools to linear elements, like beam splitters and phase shifters,
delay lines and electronically switched linear elements, photo-detectors, and
auxiliary bosons. As a result we show that with these tools a never failing
Bell measurement is impossible.


title: Symmetrizing Evolutions

abstract:
  We introduce quantum procedures for making $\cal G$-invariant the dynamics of
an arbitrary quantum system S, where $\cal G$ is a finite group acting on the
space state of S. Several applications of this idea are discussed. In
particular when S is a N-qubit quantum computer interacting with its
environment and $\cal G$ the symmetric group of qubit permutations, the
resulting effective dynamics admits noiseless subspaces. Moreover it is shown
that the recently introduced iterated-pulses schemes for reducing decoherence
in quantum computers fit in this general framework. The noise-inducing
component of the Hamiltonian is filtered out by the symmetrization procedure
just due to its transformation properties.


title: Reconstruction of spin states and its conceptual implications

abstract:
  State reconstruction for quantum spins is reviewed. Emphasis is on
non-tomographic approaches which are based on measurements performed with a
Stern-Gerlach apparatus. Two consequences of successfully implemented state
reconstruction are pointed out. First, it allows one to determine
experimentally the expectation value of an arbitrary operator without a device
measuring it. Second, state reconstruction suggests a reformulation of
Schroedinger's equation in terms of expectation values only, without explicit
reference to a wave function or a density operator.


title:
The assumptions underlying the consistent-amplitude approach to quantum
  theory

abstract:
  In this note I expand further on the main assumptions leading to the
consistent-amplitude approach to quantum theory and I offer a reply to Jerry
Finkelstein's recent comment (quant-ph/9809017) concerning my argument for the
linearity of quantum mechanics (Phys. Rev. A57, 1572 (1998)).


title:
Interacting Dark Resonances: Interference Effects Induced by Coherently
  Altered Quantum Superpositions

abstract:
  We predict the possibility of sharp, high-contrast resonances in the optical
response of a broad class of systems, wherein interference effects are
generated by coherent perturbation or interaction of dark states. The
properties of these resonances can be manipulated to design a desired atomic
response.


title: Stochastic Conservation Laws?

abstract:
  We examine conservation laws, typically the conservation of linear momentum,
in the light of a recent successful formulation of fermions as Kerr-Newman type
Black Holes, which are created fluctuationally from a background Zero Point
Field. We conclude that these conservation laws are to be taken in the spirit
of thermodynamic laws.


title: Nonstandard introduction to squeezing of the electromagnetic field

abstract:
  This article contains a review of an alternative theory of squeezing, based
entirely on the wave function description of the squeezed states. Quantum field
theoretic approach is used to describe the squeezing of the electromagnetic
field in its most complete form that takes into account temporal and spatial
characteristics of the squeezed state. An analog of the Wigner function for the
full electromagnetic field is introduced and expressed in terms of second order
correlation functions. The field-theoretic approach enables one to study the
propagation of the ``squeezing wave'' in space-time. A simple example of weak
squeezing, that allows for all calculations to be done analytically, is
discussed in detail.


title: Third Newton Law in the Mean and Perturbations of Noise

abstract:
  We analyze an isothermal Brownian motion of particle ensembles in the
Smoluchowski approximation.
  Contrary to standard procedures, the environmental recoil effects associated
with locally induced heat flows are not completely disregarded. The main
technical tool in the study of such weakly-out-of equilibrium systems is a
consequent exploitation of the Hamilton-Jacobi equation. The third Newton law
in the mean is utilised to generate diffusion-type processes which are either
anomalous (enhanced), or generically non-dispersive.


title: Dynamical Decoupling of Open Quantum Systems

abstract:
  We propose a novel dynamical method for beating decoherence and dissipation
in open quantum systems. We demonstrate the possibility of filtering out the
effects of unwanted (not necessarily known) system-environment interactions and
show that the noise-suppression procedure can be combined with the capability
of retaining control over the effective dynamical evolution of the open quantum
system. Implications for quantum information processing are discussed.


title: PT-Symmetric Quantum Mechanics

abstract:
  This paper proposes to broaden the canonical formulation of quantum
mechanics. Ordinarily, one imposes the condition $H^\dagger=H$ on the
Hamiltonian, where $\dagger$ represents the mathematical operation of complex
conjugation and matrix transposition. This conventional Hermiticity condition
is sufficient to ensure that the Hamiltonian $H$ has a real spectrum. However,
replacing this mathematical condition by the weaker and more physical
requirement $H^\ddag=H$, where $\ddag$ represents combined parity reflection
and time reversal ${\cal PT}$, one obtains new classes of complex Hamiltonians
whose spectra are still real and positive. This generalization of Hermiticity
is investigated using a complex deformation $H=p^2+x^2(ix)^\epsilon$ of the
harmonic oscillator Hamiltonian, where $\epsilon$ is a real parameter. The
system exhibits two phases: When $\epsilon\geq0$, the energy spectrum of $H$ is
real and positive as a consequence of ${\cal PT}$ symmetry. However, when
$-1<\epsilon<0$, the spectrum contains an infinite number of complex
eigenvalues and a finite number of real, positive eigenvalues because ${\cal
PT}$ symmetry is spontaneously broken. The phase transition that occurs at
$\epsilon=0$ manifests itself in both the quantum-mechanical system and the
underlying classical system. Similar qualitative features are exhibited by
complex deformations of other standard real Hamiltonians
$H=p^2+x^{2N}(ix)^\epsilon$ with $N$ integer and $\epsilon>-N$; each of these
complex Hamiltonians exhibits a phase transition at $\epsilon=0$. These ${\cal
PT}$-symmetric theories may be viewed as analytic continuations of conventional
theories from real to complex phase space.


title: Towards new understanding of nuclear rotation

abstract:
  Properties of time evolution of wave packets built up from rotator
eigenstates are discussed. The mechanism of perfect cloning of the initial wave
packet for "circular states" at fractional revival times is explained. The
smooth transition from "circular" to "linear" through intermediate "elliptic"
is described. Example of time evolution of a nuclear wave packet created in
Coulomb excitation mechanism is presented.


title:
Finite-dimensional Schwinger basis, deformed symmetries, Wigner
  function, and an algebraic approach to quantum phase

abstract:
  Schwinger's finite (D) dimensional periodic Hilbert space representations are
studied on the toroidal lattice ${\ee Z}_{D} \times {\ee Z}_{D}$ with specific
emphasis on the deformed oscillator subalgebras and the generalized
representations of the Wigner function. These subalgebras are shown to be
admissible endowed with the non-negative norm of Hilbert space vectors. Hence,
they provide the desired canonical basis for the algebraic formulation of the
quantum phase problem. Certain equivalence classes in the space of labels are
identified within each subalgebra, and connections with area-preserving
canonical transformations are examined. The generalized representations of the
Wigner function are examined in the finite-dimensional cyclic Schwinger basis.
These representations are shown to conform to all fundamental conditions of the
generalized phase space Wigner distribution. As a specific application of the
Schwinger basis, the number-phase unitary operator pair in ${\ee Z}_{D} \times
{\ee Z}_{D}$ is studied and, based on the admissibility of the underlying
q-oscillator subalgebra, an {\it algebraic} approach to the unitary quantum
phase operator is established. This being the focus of this work, connections
with the Susskind-Glogower- Carruthers-Nieto phase operator formalism as well
as standard action-angle Wigner function formalisms are examined in the
infinite-period limit. The concept of continuously shifted Fock basis is
introduced to facilitate the Fock space representations of the Wigner function.


title: NP problem in quantum algorithm

abstract:
  In complexity theory, there exists a famous unsolved problem whether NP can
be P or not. In this paper, we discuss this aspect in SAT (satisfiability)
problem, and it is shown that the SAT can be solved in plynomial time by means
of quantum algorithm.


title: Guiding Neutral Atoms with a Wire

abstract:
  We demonstrate guiding of cold neutral atoms along a current carrying wire.
Atoms either move in Kepler-like orbits around the wire or are guided in a
potential tube on the side of the wire which is created by applying an
additional homogeneous bias field. These atom guides are very versatile and
promising for applications in atom optics.


title: Quantum Wires and Quantum Dots for Neutral Atoms

abstract:
  By placing changeable nanofabricated structures (wires, dots, etc.) on an
atom mirror one can design guiding and trapping potentials for atoms. These
potentials are similar to the electrostatic potentials which trap and guide
electrons in semiconductor quantum devices like quantum wires and quantum dots.
This technique will allow the fabrication of nanoscale atom optical devices.


title: A rigorous treatment of distillable entanglement

abstract:
  The notion of distillable entanglement is one of the fundamental concepts of
quantum information theory. Unfortunately, there is an apparent mismatch
between the intuitive and rigorous definitions of distillable entanglement. To
be precise, the existing rigorous definitions impose the constraint that the
distilation protocol produce an output of constant dimension. It is therefore
conceivable that this unnecessary constraint might have led to underestimation
of the true distillable entanglement. We give a new definition of distillable
entanglement which removes this constraint, but could conceivably overestimate
the true value. Since the definitions turn out to be equivalent, neither
underestimation nor overestimation is possible, and both definitions are
arguably correct


title:
Gardiner's phonon for Bose-Einstein Condensation: A physical realization
  of the $q$-deformed Boson

abstract:
  The Gardiner's phonon presented for a particle-number conserving
approximation method to describe the dynamics of Bose-Einstein Condesation
(BEC) (C.W. Gardiner, Phys. Rev. A 56, 1414 (1997)) is shown to be a physical
realization of the $q$-deformed boson, which was abstractly developed in
quantum group theory. On this observation, the coherent output of BEC atoms
driven by a radio frequency (r.f) field is analyzed in the viewpoint of a
$q$-deformed Fock space. It is illustrated that the $q$-deformation of bosonic
commutation relation corresponds to the non-ideal BEC with the finite particle
number $N$ of condensated atoms. Up to order 1/N, the coherent output state of
the untrapped atoms minimizes the uncertainty relation like a coherent state
does in the ideal case of BEC that $N$ approaches infinity or $q=1-2/N$
approaches one.


title:
Quantum Dynamics of Topological Singularities: Feynman's Influence
  Functional Approach

abstract:
  Starting from the microscopic theory of Bardeen-Cooper-Schrieffer (BCS) for
the fermionic superfluids, we show that the vortex dynamics can be followed
naturally by extending Feynman's influence functional approach to incorporate
the transverse force.
  There is a striking mutual independence of the transverse and longitudinal
influences:
  The former has the topological origin and is insensitive to details, while
the latter corresponds to the well-known damping kernel depending on details.


title:
Concatenating Decoherence Free Subspaces with Quantum Error Correcting
  Codes

abstract:
  An operator sum representation is derived for a decoherence-free subspace
(DFS) and used to (i) show that DFSs are the class of quantum error correcting
codes (QECCs) with fixed, unitary recovery operators, and (ii) find explicit
representations for the Kraus operators of collective decoherence. We
demonstrate how this can be used to construct a concatenated DFS-QECC code
which protects against collective decoherence perturbed by independent
decoherence. The code yields an error threshold which depends only on the
perturbing independent decoherence rate.


title: An improved bound on distillable entanglement

abstract:
  The best bound known on 2-locally distillable entanglement is that of Vedral
and Plenio, involving a certain measure of entanglement based on relative
entropy. It turns out that a related argument can be used to give an even
stronger bound; we give this bound, and examine some of its properties. In
particular, and in contrast to the earlier bounds, the new bound is not
additive in general. We give an example of a state for which the bound fails to
be additive, as well as a number of states for which the bound is additive.


title: Poisson-Lie Structures and Quantisation with Constraints

abstract:
  We develop here a simple quantisation formalism that make use of Lie algebra
properties of the Poisson bracket. When the brackets $\{H,\phi_i\}$ and
$\{\phi_i,\phi_j\}$, where $H$ is the Hamiltonian and $\phi_i$ are primary and
secondary constraints, can be expressed as functions of $H$ and $\phi_i$
themselves, the Poisson bracket defines a Poisson-Lie structure. When this
algebra has a finite dimension a system of first order partial differential
equations is established whose solutions are the observables of the theory. The
method is illustrated with a few examples.


title: Influence Action and decoherence of hydrodynamic modes

abstract:
  We derive an influence action for the heat diffusion equation and from its
spectral dependence show that long wavelength hydrodynamic modes are most
readily decohered. The result is independent of the details of the microscopic
dynamics, and follows from general principles alone.


title: Ambiguities of arrival-time distributions in quantum theory

abstract:
  We consider the definition that might be given to the time at which a
particle arrives at a given place, both in standard quantum theory and also in
Bohmian mechanics. We discuss an ambiguity that arises in the standard theory
in three, but not in one, spatial dimension.


title: Flow Equations for the Henon-Heiles Hamiltonian

abstract:
  The Henon-Heiles Hamiltonian was introduced in 1964 as a mathematical model
to describe the chaotic motion of stars in a galaxy. By canonically
transforming the classical Hamiltonian to a Birkhoff-Gustavson normalform Delos
and Swimm obtained a discrete quantum mechanical energy spectrum. The aim of
the present work is to first quantize the classical Hamiltonian and to then
diagonalize it using different variants of flow equations, a method of
continuous unitary transformations introduced by Wegner in 1994. The results of
the diagonalization via flow equations are comparable to those obtained by the
classical transformation. In the case of commensurate frequencies the
transformation turns out to be less lengthy. In addition, the dynamics of the
quantum mechanical system are analyzed on the basis of the transformed
observables.


title:
Radiative atom-atom interactions in optically dense media: Quantum
  corrections to the Lorentz-Lorenz formula

abstract:
  Generalized single-atom Maxwell-Bloch equations for optically dense media are
derived taking into account non-cooperative radiative atom-atom interactions.
Applying a Gaussian approximation and formally eliminating the degrees of
freedom of the quantized radiation field and of all but a probe atom leads to
an effective time-evolution operator for the probe atom. The mean coherent
amplitude of the local field seen by the atom is shown to be given by the
classical Lorentz-Lorenz relation. The second-order correlations of the field
lead to terms that describe relaxation or pump processes and level shifts due
to multiple scattering or reabsorption of spontaneously emitted photons. In the
Markov limit a nonlinear and nonlocal single-atom density matrix equation is
derived. To illustrate the effects of the quantum corrections we discuss
amplified spontaneous emission and radiation trapping in a dense ensemble of
initially inverted two-level atoms and the effects of radiative interactions on
intrinsic optical bistability in coherently driven systems.


title:
Floquet-Markov description of the parametrically driven, dissipative
  harmonic quantum oscillator

abstract:
  Using the parametrically driven harmonic oscillator as a working example, we
study two different Markovian approaches to the quantum dynamics of a
periodically driven system with dissipation. In the simpler approach, the
driving enters the master equation for the reduced density operator only in the
Hamiltonian term. An improved master equation is achieved by treating the
entire driven system within the Floquet formalism and coupling it to the
reservoir as a whole. The different ensuing evolution equations are compared in
various representations, particularly as Fokker-Planck equations for the Wigner
function. On all levels of approximation, these evolution equations retain the
periodicity of the driving, so that their solutions have Floquet form and
represent eigenfunctions of a non-unitary propagator over a single period of
the driving. We discuss asymptotic states in the long-time limit as well as the
conservative and the high-temperature limits. Numerical results obtained within
the different Markov approximations are compared with the exact path-integral
solution. The application of the improved Floquet-Markov scheme becomes
increasingly important when considering stronger driving and lower
temperatures.


title:
Long-time dynamics of spontaneous parametric down-conversion and quantum
  limitations of conversion efficiency

abstract:
  We analyze the long-time quantum dynamics of degenerate parametric
down-conversion from an initial sub-harmonic vacuum (spontaenous
down-conversion). Standard linearization of the Heisenberg equations of motions
fails in this case, since it is based on an expansion around an unstable
classical solution and neglects pump depletion. Introducing a mean-field
approximation we find a periodic exchange of energy between the pump and
subharmonic mode goverened by an anharmonic pendulum equation. From this
equation the optimum interaction time or crystal length for maximum conversion
can be determined. A numerical integration of the 2-mode Schr"odinger equation
using a dynamically optimized basis of displaced and squeezed number states
verifies the characteristic times predicted by the mean-field approximation. In
contrast to semiclassical and mean-field predictions it is found that quantum
fluctuations of the pump mode lead to a substantial limitation of the
efficiency of parametric down-conversion.


title: A posteriori teleportation

abstract:
  The article by Bouwmeester et al. on experimental quantum teleportation
constitutes an important advance in the burgeoning field of quantum
information. The experiment was motivated by the proposal of Bennett et al. in
which an unknown quantum state is `teleported' by Alice to Bob. As illustrated
in Fig. 1, in the implementation of this procedure, by Bouwmeester et al., an
input quantum state is `disembodied' into quantum and classical components, as
in the original protocol. However, in contrast to the original scheme,
Bouwmeester et al.'s procedure necessarily destroys the state at Bob's
receiving terminal, so a `teleported' state can never emerge as a freely
propagating state for subsequent examination or exploitation. In fact,
teleportation is achieved only as a postdiction.


title: From Stochastic Differential Equations to Quantum Field Theory

abstract:
  Covariant stochastic partial (pseudo-)differential equations are studied in
any dimension. In particular a large class of covariant interacting local
quantum fields obeying the Morchio-Strocchi system of axioms for indefinite
quantum field theory is constructed by solving the analysed equations. The
associated random cosurface models are discussed and some elementary properties
of them are outlined.


title: Ultra-bright source of polarization-entangled photons

abstract:
  Using the process of spontaneous parametric down conversion in a novel
two-crystal geometry, one can generate a source of polarization-entangled
photon pairs which is orders of magnitude brighter than previous sources. We
have measured a high level of entanglement between photons emitted over a
relatively large collection angle, and over a 10-nm bandwidth. As a
demonstration of the source intensity, we obtained a 242-$\sigma$ violation of
Bell's inequalities in less than three minutes.


title: Classical and quantum signatures of competing chi(2) nonlinearities

abstract:
  We report the first observation of the quantum effects of competing
$\chi^{(2)}$ nonlinearities. We also report new classical signatures of
competition, namely clamping of the second harmonic power and production of
nondegenerate frequencies in the visible. Theory is presented that describes
the observations as resulting from competition between various $\chi^{(2)}$
upconversion and downconversion processes. We show that competition imposes
hitherto unsuspected limits to both power generation and squeezing. The
observed signatures are expected to be significant effects in practical
systems.


title:
Internal Time Peculiarities as a Cause of Bifurcations Arising in
  Classical Trajectory Problem and Quantum Chaos Creation in Three-Body System

abstract:
  A new formulation of the theory of quantum mechanical multichannel scattering
for three-body collinear systems is proposed. It is shown, that in this simple
case the principle of quantum determinism in the general case breaks down and
we have a micro-irreversible quantum mechanics. The first principle
calculations of the quantum chaos (wave chaos) were pursued on the example of
an elementary chemical reaction Li+(FH)->(LiFH)*->(LiF)+H.


title: Classical Trajectories for two Ring-Shaped Potentials

abstract:
  This paper deals with the classical trajectories for two super-integrable
systems: a system known in quantum chemistry as the Hartmann system and a
system of potential use in quantum chemistry and nuclear physics. Both systems
correspond to ring-shaped potentials. They admit two maximally super-integrable
systems as limiting cases, viz, the isotropic harmonic oscillator system and
the Coulomb-Kepler system in three dimensions. The planarity of the
trajectories is studied in a systematic way. In general, the trajectories are
quasi-periodic rather than periodic. A constraint condition allows to pass from
quasi-periodic motions to periodic ones. When written in a quantum mechanical
context, this constraint condition leads to new accidental degeneracies for the
two systems studied.


title: A posteriori teleportation ?

abstract:
  Braunstein and Kimble observe correctly that, in the Innsbruck experiment,
Nature 390, 575 (1997), one does not always observe a teleported photon
conditioned on a coincidence recording at the Bell-state analyser. However,
when a teleported photon appears, it has all the properties required by the
teleportation protocol.


title: Two qubit copying machine for economical quantum eavesdropping

abstract:
  We study the mapping which occurs when a single qubit in an arbitrary state
interacts with another qubit in a given, fixed state resulting in some unitary
transformation on the two qubit system which, in effect, makes two copies of
the first qubit. The general problem of the quality of the resulting copies is
discussed using a special representation, a generalization of the usual Schmidt
decomposition, of an arbitrary two-dimensional subspace of a tensor product of
two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can
reproduce the results of any two qubit copying machine of this type. A simple
stochastic generalization (using a ``classical'' random signal) of the copying
machine is also considered. These copying machines provide simple embodiments
of previously proposed optimal eavesdropping schemes for the BB84 and B92
quantum cryptography protocols.


title: An atom optics experiment to investigate faster-than-light tunneling

abstract:
  We describe a series of atom optics experiments underway at Toronto for
investigating tunnelling interaction times of various sorts. We begin by
discussing some outstanding issues and confusions related to the question of
whether or not superluminal tunnelling can be construed as true
faster-than-light ``signal propagation,'' a question which we answer in the
negative. We then argue that atom optics is an arena ideally suited for
addressing a variety of remaining questions about how, where, and for how long
a particle interacts with a tunnel barrier. We present recent results on a
modified ``delta-kick cooling'' scheme which we have used to prepare Rubidium
atoms with one-dimensional de Broglie wavelengths on the order of an optical
wavelength, along with simulations showing that from these temperatures, we
will be able to use acousto-optically modulated dipole-force barriers to
velocity-select ultracold atom samples ideal for future tunnelling experiments.


title: Maximal violation of Bell's inequality in the case of real experiments

abstract:
  Einstein's locality is invoked to derive a correlation inequality. In the
case of ideal experiments, this inequality is equivalent to Bell's original
inequality of 1965 which, as is well known, is violated by a maximum factor of
1.5. The crucial point is that even in the case of real experiments where
polarizers and detectors are non-ideal, the present inequality is violated by a
factor of 1.5, whereas previous inequalities such as Clauser-Horne-Shimony-Holt
inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a
factor of $\sqrt 2$. The larger magnitude of violation can be of importance for
the experimental test of locality. Moreover, the supplementary assumption used
to derive this inequality is weaker than Garuccio-Rapisarda assumption. Thus an
experiment based on this inequality refutes a larger family of hidden variable
theories than an experiment based on Garuccio-Rapisarda inequality.


title: Quantum phase space distributions in thermofield dynamics

abstract:
  It is shown that the the quantum phase space distributions corresponding to a
density operator $\rho$ can be expressed, in thermofield dynamics, as overlaps
between the state $\mid \rho >$ and "thermal" coherent states. The usefulness
of this approach is brought out in the context of a master equation describing
a nonlinear oscillator for which exact expressions for the quantum phase
distributions for an arbitrary initial condition are derived.


title:
The Scalar Curvature of the Bures Metric on the Space of Density
  Matrices

abstract:
  The Riemannian Bures metric on the space of (normalized) complex positive
matrices is used for parameter estimation of mixed quantum states based on
repeated measurements just as the Fisher information in classical statistics.
It appears also in the concept of purifications of mixed states in quantum
physics. Here we determine its scalar curvature and Ricci tensor and prove a
lower bound for the curvature on the submanifold of trace one matrices. This
bound is achieved for the maximally mixed state, a further hint for the quantum
statistical meaning of the scalar curvature.


title: Creation of entangled states of distant atoms by interference

abstract:
  We propose a scheme to create distant entangled atomic states. It is based on
driving two (or more) atoms with a weak laser pulse, so that the probability
that two atoms are excited is negligible. If the subsequent spontaneous
emission is detected, the entangled state is created. We have developed a model
to analyze the fidelity of the resulting state as a function of the dimensions
and location of the detector, and the motional properties of the atoms.


title:
Changes in Floquet state structure at avoided crossings: delocalization
  and harmonic generation

abstract:
  Avoided crossings are common in the quasienergy spectra of strongly driven
nonlinear quantum wells. In this paper we examine the sinusoidally driven
particle in a square potential well to show that avoided crossings can alter
the structure of Floquet states in this system. Two types of avoided crossings
are identified: on type leads only to temporary changes (as a function of
driving field strength) in Floquet state structure while the second type can
lead to permanent delocalization of the Floquet states. Radiation spectra from
these latter states show significant increase in high harmonic generation as
the system passes through the avoided crossing.


title: Topics in Quantum Measurement and Quantum Noise

abstract:
  In this thesis we consider primarily the dynamics of quantum systems
subjected to continuous observation. In the Schr\"{o}dinger picture the
evolution of a continuously monitored quantum system, referred to as a `quantum
trajectory', may be described by a stochastic equation for the state vector. We
present a method of deriving explicit evolution operators for linear quantum
trajectories, and apply this to a number of physical examples of varying
mathematical complexity.
  In the Heisenberg picture evolution resulting from continuous observation may
be described by quantum Langevin equations. We use this method to examine the
noise spectrum that results from a continuous observation of the position of a
moving mirror, and examine the possibility of detecting the noise resulting
from the quantum back-action of the measurement.
  In addition to the work on continuous measurement theory, we also consider
the problem of reconstructing the state of a quantum system from a set of
measurements. We present a scheme for determining the state of a single cavity
mode from the photon statistics measured both before and after an interaction
with one or two two-level atoms.


title: Consistent Histories and Quantum Delayed Choice

abstract:
  John Wheeler devised a gedanken experiment in which a piece of apparatus can
be altered just before the arrival of particle, and this ``delayed choice''
can, seemingly, alter the quantum state of the particle at a much earlier time,
long before the choice is made.
  A slightly different gedanken experiment, which exhibits the same conceptual
difficulty, is analyzed using the techniques of consistent history quantum
theory. The idea that the future influences the past disappears when proper
account is taken of the diversity of possible quantum descriptions of the
world, and their mutual compatibility or incompatibility.


title:
An Inherently Quantum Computation Paradigm: NP-complete=P Under the
  Hypothetical Notion of Continuous Uncomplete von Neumann Measurement

abstract:
  The topical quantum computation paradigm is a transposition of the Turing
machine into the quantum framework. Implementations based on this paradigm have
limitations as to the number of: qubits, computation steps, efficient quantum
algorithms (found so far). A new exclusively quantum paradigm (with no
classical counterpart) is propounded, based on the speculative notion of
continuous uncomplete von Neumann measurement. Under such a notion, NP-complete
is equal to P. This can provide a mathematical framework for the search of
implementable paradigms, possibly exploiting particle statistics.


title: Cumulant expansion for studying damped quantum solitons

abstract:
  The quantum statistics of damped optical solitons is studied using
cumulant-expansion techniques. The effect of absorption is described in terms
of ordinary Markovian relaxation theory, by coupling the optical field to a
continuum of reservoir modes. After introduction of local bosonic field
operators and spatial discretization pseudo-Fokker-Planck equations for
multidimensional s-parameterized phase-space functions are derived. These
partial differential equations are equivalent to an infinite set of ordinary
differential equations for the cumulants of the phase-space functions.
Introducing an appropriate truncation condition, the resulting finite set of
cumulant evolution equations can be solved numerically. Solutions are presented
in Gaussian approximation and the quantum noise is calculated, with special
emphasis on squeezing and the recently measured spectral photon-number
correlations [Spaelter et al., Phys. Rev. Lett. 81, 786 (1998)].


title: A Beable Interpretation of the Continuous Spontaneous Localization Model

abstract:
  We extend the beable interpretation, due to Bell, to the continuous
spontaneous localization model (CSL). Results obtained by Vink are generalized
to the modified Schrodinger equation of Ghirardi, Pearle and Rimini (GPR),
which allows a beable interpretation for position and momentum.


title: Quantum noise reduction in singly resonant optical devices

abstract:
  Quantum noise in a model of singly resonant frequency doubling including
phase mismatch and driving in the harmonic mode is analyzed. The general
formulae about the fixed points and their stability as well as the squeezing
spectra calculated linearizing around such points are given. The use of a
nonlinear normalization allows to disentangle in the spectra the dynamic
response of the system from the contributions of the various noisy inputs. A
general ``reference'' model for one-mode systems is developed in which the
dynamic aspects of the problem are not contaminated by static contributions
from the noisy inputs. The physical insight gained permits the elaboration of
general criteria to optimize the noise suppression performance. With respect to
the squeezing in the fundamental mode the optimum working point is located near
the first turning point of the dispersive bistability induced by cascading of
the second order nonlinear response. The nonlinearities induced by conventional
crystals appear enough to reach it being the squeezing ultimately limited by
the escape efficiency of the cavity. In the case of the harmonic mode both,
finite phase mismatch and/or harmonic mode driving allow for an optimum dynamic
response of the system something not possible in the standard phase matched
Second Harmonic Generation. The squeezing is then limited by the losses in the
harmonic mode, allowing for very high degrees of squeezing because of the
non-resonant nature of the mode. This opens the possibility of very high
performances using artificial materials with resonantly enhanced
nonlinearities. It is also shown how it is possible to substantially increase
the noise reduction and at the same time to more than double the output power
for parameters corresponding to reported experiments.


title: Improvement of quantum key distribution protocols

abstract:
  The security of the previous quantum key distribution protocols, which is
guaranteed by the nature of physics law, is based on the legitimate users.
However, the impersonation of Alice or Bob by eavesdropper, in practice. will
be existed in a large probability. In this paper an improvement scheme for the
security quantum key is proposed.


title: Stochastic Phase Space Localization for a Single Particle

abstract:
  We propose a feedback scheme to control the vibrational motion of a single
trapped particle based on indirect measurements of its position. It results the
possibility of a motional phase space uncertainty contraction, correponding to
cool the particle close to the motional ground state.


title: Nonlinear von Neumann-type equations: Darboux invariance and spectra

abstract:
  Generalized Euler-Arnold-von Neumann density matrix equations can be solved
by a binary Darboux transformation given here in a new form:
$\rho[1]=e^{P\ln(\mu/\nu)}\rho e^{-P\ln(\mu/\nu)}$ where $P=P^2$ is explicitly
constructed in terms of conjugated Lax pairs, and $\mu$, $\nu$ are complex. As
a result spectra of $\rho$ and $\rho[1]$ are identical. Transformations
allowing to shift and rescale spectrum of a solution are introduced, and a
class of stationary seed solutions is discussed.


title:
Geometrical properties of intelligent spin states and time evolution of
  coherent states

abstract:
  We remind the properties of the intelligent (and quasi-intelligent) spin
states introduced by Aragone et al. We use these states to construct families
of coherent wave packets on the sphere and we sketch the time evolution of
these wave packets for a rigid body molecule.

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


title: Mixed state dense coding and its relation to entanglement measures

abstract:
  Ideal dense coding protocols allow one to use prior maximal entanglement to
send two bits of classical information by the physical transfer of a single
encoded qubit. We investigate the case when the prior entanglement is not
maximal and the initial state of the entangled pair of qubits being used for
the dense coding is a mixed state. We find upper and lower bounds on the
capability to do dense coding in terms of the various measures of entanglement
and in terms of the average mutual distinguishability of the signal states.


title: A priori Probabilities of Separable Quantum States

abstract:
  Zyczkowski, Horodecki, Sanpera, and Lewenstein (ZHSL) recently proposed a
``natural measure'' on the N-dimensional quantum systems (quant-ph/9804024),
but expressed surprise when it led them to conclude that for N = 2 x 2,
disentangled (separable) systems are more probable (0.632) in nature than
entangled ones. We contend, however, that ZHSL's (rejected) intuition has, in
fact, a sound theoretical basis, and that the a priori probability of
disentangled 2 x 2 systems should more properly be viewed as (considerably)
less than 0.5. We arrive at this conclusion in two quite distinct ways, the
first based on classical and the second, quantum considerations. Both
approaches, however, replace (in whole or part) the ZHSL (product) measure by
ones based on the volume elements of monotone metrics, which in the classical
case amounts to adopting the Jeffreys' prior of Bayesian theory. Only the
quantum-theoretic analysis (which yields the smallest probabilities of
disentanglement) uses the minimum number of parameters possible, N^2 - 1, as
opposed to N^2 + N - 1 (although this "over-parameterization", as recently
indicated by Byrd, should be avoidable). However, despite substantial
computation, we are not able to obtain precise estimates of these
probabilities, and the need for additional (possibly supercomputer) analyses is
indicated (particularly so, for higher-dimensional quantum systems, such as the
2 x 3 we also study here).


title: Quantum Observables associated with Einstein Localisation

abstract:
  The description of relativistic effects requires a preliminary definition of
events localised in space-time while the clocks used for time definition and
the fields used in synchronisation or localisation procedures are necessarily
quantum systems.
  We outline an algebraic framework where basic requirements of quantum theory
and relativity are consistently dealt with. This approach which may be termed
as a `quantum relativity' is built on the algebra of symmetries. It contains
the definition of quantum observables associated with Einstein localisation in
space-time as well as the evaluation of their commutation relations including
the energy-time relation. These commutators also describe the relativistic
shifts undergone under frame transformations, not only for inertial frames but
also for uniformly accelerated frames. The quantum redshift laws differ from
their classical counterparts while still obeying universal metric properties.
  The paper presents this approach in terms closely connected to the seminal
Einstein conception of localisation in space-time and refers to already
published papers for more technical developments.


title:
Quantum superpositions and definite perceptions:envisaging new feasible
  experimental tests

abstract:
  We call attention on the fact that recent unprecedented technological
achievements, in particular in the field of quantum optics, seem to open the
way to new experimental tests which might be relevant both for the foundational
problems of quantum mechanics as well as for investigating the perceptual
processes.


title: Many Time Interpretation Of the Quantum Measurement Process

abstract:
  Many Time Interpretation (MTI) proposes that each stochastic "quantum jump"
("reduction") concerning each single object (of an ensemble) represents a
consequence of a (stochastic) choice (change) of Time. Therefore, each single
object experiences its own (local), stochastically chosen Time, which is as
real for it, as the macroscopic Time is real in classical physics. Therefore,
instead of the "indeterminism" with regard to the macroscopic Time, MTI
proposes "determinism", but with regard to the set(s) of (stochastically
chosen) local Times. Within an axiomatization, which includes the composite
system "single object+apparatus+environment, MTI leads to : (i) Recognizing the
amplification process as the fundamental "part" of the measurement process,
(ii) Nonvalidity of the Schrodinger equation concerning the "whole", O+A+E,
which makes the "state reduction process" unnecessary and unphysical, (iii)
Natural deducibility of the macroscopic irreversibility, and (iv)
Nonequivalence of MTI with any existing measurement theory, or interpretation.
Thus, within MTI, the measurement problem reduces basically onto the search for
quantum effect, which would allow forthe local, stochastic change of Time.


title: Comment on "Neutron Interferometric Observation of Noncyclic Phase"

abstract:
  A critique of a recent experiment [Wagh et.al., Phys.Rev.Lett.81, 1992 (7 Sep
1998)] to measure the noncyclic phase associated with a precessing neutron spin
in a neutron interferometer, as given by the Pancharatnam criterion, is
presented. It is pointed out that since the experiment measures, not the
noncyclic phase itself, but a quantity derived from it, it misses the most
interesting feature of such a phase, namely the different sign associated with
states lying in the upper and the lower hemispheres, a feature originating in
the existence of a phase singularity. Such effects have earlier been predicted
and seen in optical interference experiments using polarization of light as the
spinor [Bhandari, Phys.Rep.281, 1 (Mar 1997)].


title: Superluminal Signals: Causal Loop Paradoxes Revisited

abstract:
  Recent results demonstrating superluminal group velocities and tachyonic
dispersion relations reopen the question of superluminal signals and causal
loop paradoxes. The sense in which superluminal signals are permitted is
explained in terms of pulse reshaping, and the self-consistent behavior which
prevents causal loop paradoxes is illustrated by an explicit example.


title: Just Two Nonorthogonal Quantum States

abstract:
  From the perspective of quantum information theory, a system so simple as one
restricted to just two nonorthogonal states can be surprisingly rich in
physics. In this paper, we explore the extent of this statement through a
review of three topics: (1) ``nonlocality without entanglement'' as exhibited
in binary quantum communication channels, (2) the tradeoff between information
gain and state disturbance for two prescribed states, and (3) the quantitative
clonability of those states. Each topic in its own way quantifies the extent to
which two states are ``quantum'' with respect to each other, i.e., the extent
to which the two together violate some classical precept. It is suggested that
even toy examples such as these hold some promise for shedding light on the
foundations of quantum theory.


title: Intertwining relations of non-stationary Schr\"odinger operators

abstract:
  General first- and higher-order intertwining relations between non-stationary
one-dimensional Schr\"odinger operators are introduced. For the first-order
case it is shown that the intertwining relations imply some hidden symmetry
which in turn results in a $R$-separation of variables. The Fokker-Planck and
diffusion equation are briefly considered. Second-order intertwining operators
are also discussed within a general approach. However, due to its complicated
structure only particular solutions are given in some detail.


title:
Exact quantum states of a general time-dependent quadratic system from
  classical action

abstract:
  A generalization of driven harmonic oscillator with time-dependent mass and
frequency, by adding total time-derivative terms to the Lagrangian, is
considered. The generalization which gives a general quadratic Hamiltonian
system does not change the classical equation of motion. Based on the
observation by Feynman and Hibbs, the propagators (kernels) of the systems are
calculated from the classical action, in terms of solutions of the classical
equation of motion: two homogeneous and one particular solutions. The kernels
are then used to find wave functions which satisfy the Schr\"{o}dinger
equation. One of the wave functions is shown to be that of a Gaussian pure
state. In every case considered, we prove that the kernel does not depend on
the way of choosing the classical solutions, while the wave functions depend on
the choice. The generalization which gives a rather complicated quadratic
Hamiltonian is simply interpreted as acting an unitary transformation to the
driven harmonic oscillator system in the Hamiltonian formulation.


title: Observation of three-photon Greenberger-Horne-Zeilinger entanglement

abstract:
  We present the experimental observation of polarization entanglement for
three spatially separated photons. Such states of more than two entangled
particles, known as GHZ states, play a crucial role in fundamental tests of
quantum mechanics versus local realism and in many quantum information and
quantum computation schemes. Our experimental arrangement is such that we start
with two pairs of entangled photons and register one photon in a way that any
information as to which pair it belongs to is erased. The registered events at
the detectors for the remaining three photons then exhibit the desired GHZ
correlations.


title: A Phase in a Coherent State Wave Function - Is It Always Irrelevant?

abstract:
  We point out that harmonic oscillator coherent states, in coordinate
representation, require particular phase factor, in order to represent
classical time evolution properly. The presence of such a phase is clearly
stated only in a minority of scientific sources discussing properties of
coherent states.


title: Quantizing Constrained Systems: New Perspectives

abstract:
  We consider quantum mechanics on constrained surfaces which have
non-Euclidean metrics and variable Gaussian curvature. The old controversy
about the ambiguities involving terms in the Hamiltonian of order hbar^2
multiplying the Gaussian curvature is addressed. We set out to clarify the
matter by considering constraints to be the limits of large restoring forces as
the constraint coordinates deviate from their constrained values. We find
additional ambiguous terms of order hbar^2 involving freedom in the
constraining potentials, demonstrating that the classical constrained
Hamiltonian or Lagrangian cannot uniquely specify the quantization: the
ambiguity of directly quantizing a constrained system is inherently
unresolvable. However, there is never any problem with a physical quantum
system, which cannot have infinite constraint forces and always fluctuates
around the mean constraint values. The issue is addressed from the perspectives
of adiabatic approximations in quantum mechanics, Feynman path integrals, and
semiclassically in terms of adiabatic actions.


title:
Quantum Maxwell-Bloch equations for spontaneous emission in optical
  semiconductor devices

abstract:
  We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous
optical semiconductor devices taking into account the quantum noise effects
which cause spontaneous emission and amplified spontaneous emission. Analytical
expressions derived from the QMBE are presented for the spontaneous emission
factor beta and the far field pattern of amplified spontaneous emission in
broad area quantum well lasers.


title: Quantum computation with ions in thermal motion

abstract:
  We propose an implementation of quantum logic gates via virtual vibrational
excitations in an ion trap quantum computer. Transition paths involving
unpopulated, vibrational states interfere destructively to eliminate the
dependence of rates and revolution frequencies on vibrational quantum numbers.
As a consequence quantum computation becomes feasible with ions whos vibrations
are strongly coupled to a thermal reservoir.


title: Multi-particle entanglement of hot trapped ions

abstract:
  We propose an efficient method to produce multi-particle entangled states of
ions in an ion trap for which a wide range of interesting effects and
applications have been suggested. Our preparation scheme exploits the
collective vibrational motion of the ions, but it works in such a way that this
motion need not be fully controlled in the experiment. The ions may, e.g., be
in thermal motion and exchange mechanical energy with a surrounding heat bath
without detrimental effects on the internal state preparation. Our scheme does
not require access to the individual ions in the trap.


title:
Do dynamical reduction models imply that arithmetic does not apply to
  ordinary macroscopic objects?

abstract:
  We analyze a recent paper in which an alleged devastating criticism to the so
called GRW proposal to account for the objectification of the properties of
macroscopic systems has been presented and we show that the author has not
taken into account the precise implications of the GRW theory. This fact makes
his conclusions basically wrong. We also perform a survey of measurement theory
aimed to better focus the physical and the conceptual aspects of the so-called
macro-objectification problem.


title: Error free quantum communication through noisy channels

abstract:
  We suggest a method to perform a quantum logic gate between distant qubits by
off-resonant field-atom dispersive interactions. The scheme we present is shown
to work ideally even in the presence of errors in the photon channels used for
communication. The stability against errors arises from the paradoxical
situation that the transmitted photons carry no information about the state of
the qubits. In contrast to a previous proposal for ideal communication [Phys.
Rev. Lett. 78, 4293 (1997)] our proposal only involves single atoms in the
sending and receiving devices.


title: Coherent State Path Integrals at (Nearly) 40

abstract:
  Coherent states can be used for diverse applications in quantum physics
including the construction of coherent state path integrals. Most definitions
make use of a lattice regularization; however, recent definitions employ a
continuous-time regularization that may involve a Wiener measure concentrated
on continuous phase space paths. The introduction of constraints is both
natural and economical in coherent state path integrals involving only the
dynamical and Lagrange multiplier variables. A preliminary indication of how
these procedures may possibly be applied to quantum gravity is briefly
discussed.


title: Coherent States for Discrete Spectrum Dynamics

abstract:
  Coherent states for general systems with discrete spectrum, such as the bound
states of the hydrogen atom, are discussed. The states in question satisfy: (1)
continuity of labeling, (2) resolution of unity, (3) temporal stability, and
(4) an action identity. This set of reasonable physical requirements uniquely
specify coherent states for the (bound state portion of the) hydrogen atom.


title: Semiclassical Series at Finite Temperature

abstract:
  We derive the semiclassical series for the partition function of a
one-dimensional quantum-mechanical system consisting of a particle in a
single-well potential. We do this by applying the method of steepest descent to
the path-integral representation of the partition function, and we present a
systematic procedure to generate the terms of the series using the minima of
the Euclidean action as the only input. For the particular case of a quartic
anharmonic oscillator, we compute the first two terms of the series, and
investigate their high and low temperature limits. We also exhibit the
nonperturbative character of the terms, as each corresponds to sums over
infinite subsets of perturbative graphs. We illustrate the power of such
resummations by extracting from the first term an accurate nonperturbative
estimate of the ground-state energy of the system and a curve for the specific
heat. We conclude by pointing out possible extensions of our results which
include field theories with spherically symmetric classical solutions.


title:
Controlling atom-atom interaction at ultralow temperatures by dc
  electric fields

abstract:
  We propose a physical mechanism for tuning the atom-atom interaction strength
at ultra-low temperatures. In the presence of a dc electric field the
interatomic potential is changed due to the effective dipole-dipole interaction
between the polarized atoms. Detailed multi-channel scattering calculations
reveal features never before discussed for ultra-cold atomic collisions. We
demonstrate that optimal control of the effective atom-atom interactions can be
achieved under reasonable laboratory conditions. Implications of this research
on the physics of atomic Bose-Einstein condensation (BEC) and on the pursuit
for atomic degenerate fermion gases will be discussed.


title:
Control of dynamical localization by an additional quantum degree of
  freedom

abstract:
  We identify a new parameter that controls the localization length in a driven
quantum system. This parameter results from an additional quantum degree of
freedom. The center-of-mass motion of a two-level ion stored in a Paul trap and
interacting with a standing wave laser field exhibits this phenomenon. We also
discuss the influence of spontaneous emission.


title: Field Purification in the intensity-dependent Jaynes-Cummings model

abstract:
  We have found that, in the intensity-dependent Jaynes-Cummings model, a field
initially prepared in a statistical mixture of two coherent states, $|\alpha>$
and $|-\alpha>$, evolves toward a pure state. We have also shown that an
even-coherent state turns periodically a into rotated odd-coherent state during
the evolution.


title:
On exact solutions of Maxwell-Bloch system for two-level medium with
  degeneracy

abstract:
  Maxwell-Bloch system describing the resonant propagation of electromagnetic
pulses in both two-level media with degeneracy in angle moment projection and
three-level media with equal oscillator forces is considered. The inhomogeneous
broadening of energy levels is accounted. Binary Darboux Transformation
generating the solutions of the system is constructed. Pulses corresponding to
the transition between levels with largest population difference are shown to
be stable. The solution describing the propargation of pulses in the medium
exited by the periodic wave is obtained. The hierarchy of infinitesimal
symmetries is obtained by means of Darboux transformation.


title: Shifts on a finite qubit string: A class of quantum baker's maps

abstract:
  We present two complementary ways in which Saraceno's symmetric version of
the quantum baker's map can be written as a shift map on a string of quantum
bits. One of these representations leads naturally to a family of quantizations
of the baker's map.


title:
Cavity-induced coherence effects in spontaneous emission from
  pre-Selection of polarization

abstract:
  Spontaneous emission can create coherences in a multilevel atom having close
lying levels, subject to the condition that the atomic dipole matrix elements
are non-orthogonal. This condition is rarely met in atomic systems. We report
the possibility of bypassing this condition and thereby creating coherences by
letting the atom with orthogonal dipoles to interact with the vacuum of a
pre-selected polarized cavity mode rather than the free space vacuum. We derive
a master equation for the reduced density operator of a model four level atomic
system, and obtain its analytical solution to describe the interference
effects. We report the quantum beat structure in the populations.


title:
Mesoscopic superpositions of states - approach to classicality and
  diagonalization in coherent state basis

abstract:
  I consider the interaction of a superposition of mesoscopic coherent states
and its approach to a mixed state as a result of a suitably controlled
environment. I show how the presence of a gain medium in a cavity can lead to
diagonalization in coherent state basis in contrast to the standard model of
decoherence. I further show how the new model of decoherence can lead to the
generation of $s$ ordered quasi distributions.


title: On Superluminal motions in photon and particle tunnelings

abstract:
  It is shown that the Hartman-Fletcher effect is valid for all the known
expressions of the mean tunnelling time, in various nonrelativistic approaches,
for the case of finite width barriers without absorption. Then, we show that
the same effect is not valid for the tunnelling time mean-square fluctuations.
On the basis of the Hartman-Fletcher effect and the known analogy between
photon and nonrelativistic-particle tunnelling, one can explain the
Superluminal group-velocities observed in various photon tunnelling experiments
(without violation of the so-called "Einstein causality").


title: The temperature of the quantum vacuum

abstract:
  We propose that the quantum vacuum may be considered as a gas of virtual
photons which carry a non-vanishing linear momentum as well as a non-vanishing
energy. We study, in particular, the Casimir effect in order to show that these
virtual photons should satisfy a Fermi-Dirac statistics, which implies a
non-zero temperature of the vacuum state.


title: Projective plane and planar quantum codes

abstract:
  Cellulations of the projective plane RP^2 define single qubit topological
quantum error correcting codes since there is a unique essential cycle in
H_1(RP^2;Z_2). We construct three of the smallest such codes, show they are
inequivalent, and identify one of them as Shor's original 9 qubit repetition
code. We observe that Shor's code can be constructed in a planar domain and
generalize to planar constructions of higher genus codes for multiple qubits.


title:
Exact Solutions to the Schr\"{o}dinger Equation for the potential
  $V(r)=a r^2+b r^{-4}+c r^{-6}$ in 2D

abstract:
  Making use of an ${\it ansatz}$ for the eigenfunctions, we obtain an exact
closed form solution to the non-relativistic Schr\"{o}dinger equation with the
anharmonic potential, $V(r)=a r^2+b r^{-4}+c r^{-6}$ in two dimensions, where
the parameters of the potential $a, b, c$ satisfy some constraints.


title: About optimal measurements in quantum hypothesizes testing

abstract:
  We consider the problem of a state determination for a two-level quantum
system which can be in one of two nonorthogonal mixed states. It is proved that
for the two independent identical systems the optimal combined measurement
(which considers the pair as one system) cannot be less optimal than the
corresponding sequential one (local measurements, accompanying by transfer of
classical information). The case of equality is achieved only when the mixed
states have the same eigenvalues or the same eigenvectors. Further, we consider
a case then the two systems are entangled: measurement of one system induces a
reduction of the another one's state. The conclusion about optimal character of
combined measurement takes place again, and conditions where the
above-mentioned methods coincide are derived.


title:
Bell's theorem, quantum mechanical non-locality and atomic cascade
  photons

abstract:
  Bell's theorem of 1965 is a proof that all realistic interpretations of
quantum mechanics must be non-local. Bell's theorem consists of two parts:
first a correlation inequality is derived that must be satisfied by all local
realistic theories; second it is demonstrated that quantum mechanical
probabilities violate this inequality in certain cases. In the case of ideal
experiments, Bell's theorem has been proven. However, in the case of real
experiments where polarizers and detectors are non-ideal, the theorem has not
yet been proven since the proof always requires some arbitrary and {\em ad hoc}
supplementary assumptions. In this paper, we state a new and rather weak
supplementary assumption for the ensemble of photons that emerge from the
polarizers, and we show that the conjunction of Einstein's locality with this
assumption leads to validity of an inequality that is violated by a factor as
large as 1.5 in the case of real experiments. Moreover, the present
supplementary assumption is considerably weaker and more general than Clauser,
Horne, Shimony, Holt supplementary assumption.


title: Topological phases and circulating states of Bose-Einstein condensates

abstract:
  We show that the quantum topological effect predicted by Aharonov and Casher
(AC effect) [Phys. Rev. Lett. 53, 319 (1984)] may be used to create circulating
states of magnetically trapped atomic Bose-Einstein condensates (BEC). A simple
experimental setup is suggested based on a multiply connected geometry such as
a toroidal trap or a magnetic trap pinched by a blue-detuned laser. We give
numerical estimates of such effects within the current atomic BEC experiments,
and point out some interesting properties of the associated quantized
circulating states.


title: Backward Causation and the EPR Paradox

abstract:
  Backward causation in which future events affect the past is formalized in a
way consistent with Special Relativity and shown to restore locality to
nonrelativistic quantum mechanics. It can explain the correlations of the EPR
paradox without using hidden variables. It also restores time-symmetry to
microphysics. Quantum Mechanics has the right properties to allow for backward
causation. The new model is probably untestable experimentally but it has
profound philosophical implications concerning reality.


title:
On the spectrum of a Hamiltonian defined on su_q(2) and quantum optical
  models

abstract:
  Analytical expressions are given for the eigenvalues and eigenvectors of a
Hamiltonian with su_q(2) dynamical symmetry. The relevance of such an operator
in Quantum Optics is discussed. As an application, the ground state energy in
the Dicke model is studied through su_q(2) perturbation theory.


title: Tunneling Ionization Rates from Arbitrary Potential Wells

abstract:
  We present a practical numerical technique for calculating tunneling
ionization rates from arbitrary 1-D potential wells in the presence of a linear
external potential by determining the widths of the resonances in the spectral
density, rho(E), adiabatically connected to the field-free bound states. While
this technique applies to more general external potentials, we focus on the
ionization of electrons from atoms and molecules by DC electric fields, as this
has an important and immediate impact on the understanding of the multiphoton
ionization of molecules in strong laser fields.


title:
The problem of equilibration and the computation of correlation
  functions on a quantum computer

abstract:
  We address the question of how a quantum computer can be used to simulate
experiments on quantum systems in thermal equilibrium. We present two
approaches for the preparation of the equilibrium state on a quantum computer.
For both approaches, we show that the output state of the algorithm, after long
enough time, is the desired equilibrium. We present a numerical analysis of one
of these approaches for small systems. We show how equilibrium
(time)-correlation functions can be efficiently estimated on a quantum
computer, given a preparation of the equilibrium state. The quantum algorithms
that we present are hard to simulate on a classical computer. This indicates
that they could provide an exponential speedup over what can be achieved with a
classical device.


title:
Non-Abelian Geometric Phase, Floquet Theory, and Periodic Dynamical
  Invariants

abstract:
  For a periodic Hamiltonian, periodic dynamical invariants may be used to
obtain non-degenerate cyclic states. This observation is generalized to the
degenerate cyclic states, and the relation between the periodic dynamical
invariants and the Floquet decompositions of the time-evolution operator is
elucidated. In particular, a necessary condition for the occurrence of cyclic
non-adiabatic non-Abelian geometrical phase is derived. Degenerate cyclic
states are obtained for a magnetic dipole interacting with a precessing
magnetic field.


title: A small 1-way quantum finite automaton

abstract:
  We study 1-way quantum finite automata (QFAs) and compare them with their
classical counterparts. We show that 1-way QFAs can be very space efficient. We
construct a 1-way QFAs that are quadratically smaller than any equivalent
deterministic finite automata and give the correct answer with a large
probability by recognizing the languages in a two letter alphabet "the number
of the letters a and the number of the letters b are divisible by n".


title: Reasoning about Grover's Quantum Search Algorithm using Probabilistic wp

abstract:
  Grover's search algorithm is designed to be executed on a quantum mechanical
computer. In this paper, the probabilistic wp-calculus is used to model and
reason about Grover's algorithm. It is demonstrated that the calculus provides
a rigorous programming notation for modelling this and other quantum algorithms
and that it also provides a systematic framework of analysing such algorithms.


title: Coin Tossing is Strictly Weaker Than Bit Commitment

abstract:
  We define cryptographic assumptions applicable to two mistrustful parties who
each control two or more separate secure sites between which special relativity
guarantees a time lapse in communication. We show that, under these
assumptions, unconditionally secure coin tossing can be carried out by
exchanges of classical information. We show also, following Mayers, Lo and
Chau, that unconditionally secure bit commitment cannot be carried out by
finitely many exchanges of classical or quantum information. Finally we show
that, under standard cryptographic assumptions, coin tossing is strictly weaker
than bit commitment. That is, no secure classical or quantum bit commitment
protocol can be built from a finite number of invocations of a secure coin
tossing black box together with finitely many additional information exchanges.


title: Unconditionally Secure Bit Commitment

abstract:
  We describe a new classical bit commitment protocol based on cryptographic
constraints imposed by special relativity. The protocol is unconditionally
secure against classical or quantum attacks. It evades the no-go results of
Mayers, Lo and Chau by requiring from Alice a sequence of communications,
including a post-revelation verification, each of which is guaranteed to be
independent of its predecessor.


title:
A rigorous path-integral formula for quantum-spin dynamics via planar
  Brownian motion

abstract:
  Adapting ideas of Daubechies and Klauder we derive a continuum path-integral
formula for the time evolution generated by a spin Hamiltonian. For this
purpose we identify the finite-dimensional spin Hilbert space with the
ground-state eigenspace of a suitable Sch\"odinger operator on
$L^2({\mathbb{R}}^2)$, the Hilbert space of square-integrable functions on the
Euclidean plane ${\mathbb{R}}^2$, and employ the Feynman-Kac-It\^o formula.