title: Experimental demonstration of quantum correlations over more than 10 km

abstract:
  Energy and time entangled photons at a wavelength of 1310 nm are produced by
parametric downconversion in a KNbO3 crystal and are sent into all-fiber
interferometers using a telecom fiber network. The two interferometers of this
Franson-type test of the Bell-inequality are located 10.9 km apart from one
another. Two-photon fringe visibilities of up to 81.6 % are obtained. These
strong nonlocal correlations support the nonlocal predictions of quantum
mechanics and provide evidence that entanglement between photons can be
maintained over long distances.


title: Separability and entanglement of composite quantum systems

abstract:
  We provide a constructive algorithm to find the best separable approximation
to an arbitrary density matrix of a composite quantum system of finite
dimensions. The method leads to a condition of separability and to a measure of
entanglement.


title: Ermakov approach for the one-dimensional Helmholtz Hamiltonian

abstract:
  For the one-dimensional Helmholtz equation we write the corresponding
time-dependent Helmholtz Hamiltonian in order to study it as an Ermakov problem
and derive geometrical angles and phases in this context


title: Macroscopic Coherence for a Trapped Electron

abstract:
  We investigate the possibility of generating quantum macroscopic coherence
phenomena by means of relativistic effects on a trapped electron.


title:
Quantum control of atomic systems by time resolved homodyne detection
  and feedback

abstract:
  We investigate the possibilities of preserving and manipulating the coherence
of atomic two-level systems by ideal projective homodyne detection and
feedback. For this purpose, the photon emission process is described on time
scales much shorter than the lifetime of the excited state using a model based
on Wigner-Weisskopf theory. The backaction of this emission process is
analytically described as a quantum diffusion of the Bloch vector. It is shown
that the evolution of the atomic wavefunction can be controlled completely
using the results of homodyne detection. This allows the stabilization of a
known quantum state or the creation of coherent states by a feedback mechanism.
However, the feedback mechanism can never compensate the dissipative effects of
quantum fluctuations even though the coherent state of the system is known at
all times.


title: Quantum Disentanglement and Computation

abstract:
  Entanglement is essential for quantum computation. However, disentanglement
is also necessary. It can be achieved without the need of classical operations
(measurements). Two examples are analyzed: the discrete Fourier transform and
error correcting codes.


title: Phase Coherence in Quantum Brownian Motion

abstract:
  The quantum theory of Brownian motion is discussed in the Schwinger version
wherein the notion of a coordinate moving forward in time $x(t)$ is replaced by
two coordinates, $x_+(t)$ moving forward in time and $x_-(t)$ moving backward
in time. The role of the doubling of the degrees of freedom is illustrated for
the case of electron beam two slit diffraction experiments. Interference is
computed with and without dissipation (described by a thermal bath). The notion
of a dissipative interference phase, closely analogous to the Aharonov-Bohm
magnetic field induced phase, is explored.


title: Continuous Error Correction

abstract:
  We propose a new approach to study the evolution of a quantum state that is
encoded in a system which is continuously subject to the operations required to
implement a quantum error correcting code. In the limit of continuous error
correction we introduce a Markovian master equation that includes the effects
of: a) Hamiltonian evolution, b) errors caused by the interaction with an
environment and c) error-correcting operations. The master equation is formally
presented for all stabilizer codes and its solution is analyzed for the
simplest such code.


title:
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by
  Impurities

abstract:
  A one-dimensional discrete Stark Hamiltonian with a continuous electric field
is constructed by extension theory methods. In absence of the impurities the
model is proved to be exactly solvable, the spectrum is shown to be simple,
continuous, filling the real axis; the eigenfunctions, the resolvent and the
spectral measure are constructed explicitly. For this (unperturbed) system the
resonance spectrum is shown to be empty. The model considering impurity in a
single node is also constructed using the operator extension theory methods.
The spectral analysis is performed and the dispersion equation for the
resolvent singularities is obtained. The resonance spectrum is shown to contain
infinite discrete set of resonances. One-to-one correspondence of the
constructed Hamiltonian to some Lee-Friedrichs model is established.


title:
Where and why the generalized Hamilton-Jacobi representation describes
  microstates of the Schr\"odinger wave function

abstract:
  A generalized Hamilton-Jacobi representation describes microstates of the
Schr\"odinger wave function for bound states. At the very points that boundary
values are applied to the bound state Schr\"odinger wave function, the
generalized Hamilton-Jacobi equation for quantum mechanics exhibits a nodal
singularity. For initial value problems, the two representations are
equivalent.


title: Born's principle and Action-Reaction problem

abstract:
  In a recent paper, A.Valentini tried to obtain Born's principle as a result
of a subquantum heat death, using classical H-theorem and the definition of a
proper quantum H-theorem within the framwork of Bohm's theory. In this paper,
we shall show the possibility of solving the problem of action-reaction
asymmetry present in Bohm's theory by modifying Valentini's procedure. However,
we get his main result too.


title: Approximate Consistency and Prediction Algorithms in Quantum Mechanics

abstract:
  This dissertation investigates questions arising in the consistent histories
formulation of the quantum mechanics of closed systems. Various criteria for
approximate consistency are analysed. The connection between the
Dowker-Halliwell criterion and sphere packing problems is shown and used to
prove several new bounds on the violation of probability sum rules. The quantum
Zeno effect is also analysed within the consistent histories formalism and used
to demonstrate some of the difficulties involved in discussing approximate
consistency. The complications associated with null histories and infinite sets
are briefly discussed.
  The possibility of using the properties of the Schmidt decomposition to
define an algorithm which selects a single, physically natural, consistent set
for pure initial density matrices is investigated. The problems that arise are
explained, and different possible algorithms discussed. Their properties are
analysed with the aid of simple models. A set of computer programs is described
which apply the algorithms to more complicated examples.
  Another algorithm is proposed that selects the consistent set (formed using
Schmidt projections) with the highest Shannon information. This is applied to a
simple model and shown to produce physically sensible histories. The theory is
capable of unconditional probabilistic prediction for closed quantum systems,
and is strong enough to be falsifiable. Ideas on applying the theory to more
complicated examples are discussed.


title: Decoherence for phase-sensitive relaxation

abstract:
  The linear and quadratic interactions of an impurity vibrational mode coupled
with a heat bath are investigated with a non-Markovian equation of motion for
the reduced density matrix valid for the initial, intermediate and kinetic
stages of relaxation. The evolution of the superpositional states is considered
for all cases.


title: Nonlinear Quantum Mechanics and Locality

abstract:
  It is shown that, in order to avoid unacceptable nonlocal effects, the free
parameters of the general Doebner-Goldin equation have to be chosen such that
this nonlinear Schr\"odinger equation becomes Galilean covariant.


title: Time and the Mind/Body Problem: A Quantum Perspective

abstract:
  The Semiotic Interpretation (SI) of QM pushes further the Von Neumann point
of view that `experience only makes statements of this type: an observer has
made a certain observation; and never any like this: a physical quantity has a
certain value.' The supposition that the observables of a system `possess'
objective values is purely idealistic. According to the SI view, the state-
vector collapse cannot result from the Schroedinger evolution of a system (even
with its environment), but only from the empirical production of a mathematical
symbol, irreducible to the quantum level. The production of a symbol always
takes some time. Thus the state-vector collapse cannot be instantaneous
(Schneider 1994), a specific prediction of the present model.
  From this interpretation of Quantum Mechanics, the appearances of the body
are the result of state-vector collapses of several types, i.e. the production
of different kinds of symbols. In fact the universe of symbols is very rich: a
symbol can have a conceptual `value' (like in physics and then give rise to a
measurement), or other qualitative values (like in many human behaviors). In
the latter case, the Semiotic Interpretation of QM gives a way to understand
how a mental representation can modify the state of the body.


title: Brooding over Pion Lasers

abstract:
  Brooding over pions, wave packets and Bose-Einstein correlations, we present
a recently obtained analytical solution to a pion laser model, which may
describe the final state of pions in high energy heavy ion collisions.


title: Quantum chaos in an ion trap: the delta-kicked harmonic oscillator

abstract:
  We propose an experimental configuration, within an ion trap, by which a
quantum mechanical delta-kicked harmonic oscillator could be realized, and
investigated. We show how to directly measure the sensitivity of the ion motion
to small variations in the external parameters.


title:
Ionization Probabilities through ultra-intense Fields in the extreme
  Limit

abstract:
  We continue our investigation concerning the question of whether atomic bound
states begin to stabilize in the ultra-intense field limit. The pulses
considered are essentially arbitrary, but we distinguish between three
situations. First the total classical momentum transfer is non-vanishing,
second not both the total classical momentum transfer and the total classical
displacement are vanishing together with the requirement that the potential has
a finite number of bound states and third both the total classical momentum
transfer and the total classical displacement are vanishing. For the first two
cases we rigorously prove, that the ionization probability tends to one when
the amplitude of the pulse tends to infinity and the pulse shape remains fixed.
In the third case the limit is strictly smaller than one. This case is also
related to the high frequency limit considered by Gavrila et al.


title: Strict Bounds on Franson Inequality

abstract:
  An inequality, recently proposed by Franson [Phys. Rev. A 54, 3808 (1996)] is
analyzed and improved. The inequality connects the change of the expectation
value of an observable with the uncertainty of this observable. A strict bound
on the ratio between these two quantities is obtained.


title:
Collapse and revival of ultracold atoms in a microwave cavity and of
  photons in parametric down-conversion

abstract:
  We present a new theoretical method to study a trapped gas of bosonic
two-level atoms interacting with a single mode of a microwave cavity. This
interaction is described by a trilinear Hamiltonian which is formally
completely equivalent to the one describing parametric down-conversion in
quantum optics. A system of differential equations describing the evolution,
including the long-time behaviour, of not only the mean value but also the
variance of the number of excited atoms is derived and solved analytically. For
different initial states the mean number of excited atoms exhibits periodically
reappearing dips, with an accompanying peak in the variance, or fractional
collapses and revivals. Closed expressions for the period and the revival time
are obtained.


title: Preparation of Nonclassical States in Cavities with a Moving Mirror

abstract:
  We describe how a quantum system composed of a cavity field interacting with
a movable mirror can be utilized to generate a large variety of nonclassical
states of both the cavity field and the mirror. First we consider state
preparation of the cavity field. The system dynamics will prepare a single mode
of the cavity field in a multicomponent Schr\"{o}dinger cat state, in a similar
manner to that in a Kerr medium. In addition, when two or more cavity modes
interact with the mirror, they may be prepared in an entangled state which may
be regarded as a multimode generalisation of even and odd coherent states. We
show also that near-number states of a single mode may be prepared by
performing a measurement of the position of the mirror. Secondly we consider
state preparation of the mirror, and show that this macroscopic object may be
placed in a Scr\"{o}dinger cat state by a quadrature measurement of the light
field. In addition we examine the effect of the damping of the motion of the
mirror on the field states inside the cavity, and compare this with the effect
of cavity field damping.


title: On Quantum Mechanical Aspects of Microtubules

abstract:
  We discuss possible quantum mechanical aspects of MicroTubules (MT), based on
recent developments in quantum physics.We focus on potential mechanisms for
`energy-loss-free' transport along the microtubules, which could be considered
as realizations of Fr\"ohlich's ideas on the r\^ole of solitons for
superconductivity and/or biological matter. By representing the MT arrangements
as cavities,we present a novel scenario on the formation of macroscopic (or
mesoscopic) quantum-coherent states, as a result of the
(quantum-electromagnetic) interactions of the MT dimers with the surrounding
molecules of the ordered water in the interior of the MT cylinders. We suggest
specific experiments to test the above-conjectured quantum nature of the
microtubular arrangements inside the cell. These experiments are similar in
nature to those in atomic physics, used in the detection of the Rabi-Vacuum
coupling between coherent cavity modes and atoms. Our conjecture is that a
similar Rabi-Vacuum-splitting phenomenon occurs in the MT case.


title: A Multiparticle Generalization of Entanglement Swapping

abstract:
  We generalize the procedure of entanglement swapping to obtain a scheme for
manipulating entanglement in multiparticle systems. We describe how this scheme
allows to establish multiparticle entanglement between particles belonging to
distant users in a communication network through a prior distribution of
singlets followed by only local measurements. We show that this scheme can be
regarded as a method of generating entangled states of many particles and
compare it with existing schemes using simple quantum computational networks.
We highlight the practical advantages of using a series of entanglement
swappings during the distribution of entangled particles between two parties.
Applications of multiparticle entangled states in cryptographic conferencing
and in reading messages from more than one source through a single measurement
are also described.


title: Quantum Database Searching by a Single Query

abstract:
  In this paper we give a quantum mechanical algorithm that can search a
database by a single query, when the number of solutions is more than a
quarter. It utilizes modified Grover operator of arbitrary phase.


title: Two-mode squeezed states in high energy physics

abstract:
  We discuss the possibility to observe hadron modification in hot and dense
matter via the correlation of identical particles. We find that a modification
of hadronic masses in medium leads to two-mode squeezing which signals itself
in a back-to-back correlations of hadrons. This effect leads to a signal of a
shift of $\phi$-meson mass.


title:
Reflection time and the Goos-H\"anchen effect for reflection by a
  semi-infinite rectangular barrier

abstract:
  The reflection time, during which a particle is in the classically forbidden
region, is described by the trajectory representation for reflection by a
semi-infinite rectangular barrier. The Schr\"odinger wave function has
microstates for such reflection. The reflection time is a function of the
microstate. For oblique reflection, the Goos-H\"anchen displacement is also a
function of the microstate. For a square well duct, we develop a proposed test
where consistent overdetermination of the trajectory by a redundant set of
observed constants of the motion would be beyond the Copenhagen interpretation.


title: Engineering two-mode interactions in ion traps

abstract:
  We describe how two vibrational degrees of freedom of a single trapped ion
can be coupled through the action of suitably-chosen laser excitation. We
concentrate on a two-dimensional ion trap with dissimilar vibrational
frequencies in the x- and y-directions of motion, and derive from first
principles a variety of quantized two-mode couplings, concentrating on a linear
coupling which takes excitations from one mode to another. We demonstrate how
this can result in a state rotation, in which it is possible to transfer the
motional state of the ion from say the x-direction to the y-direction without
prior knowledge of that motional state.


title: Wave packet dynamics with Bose-Einstein condensates

abstract:
  We study wave packet dynamics of a Bose condensate in a periodically shaken
trap. Dichotomy, that is, dynamic splitting of the condensate, and dynamic
stabilization are analyzed in analogy with similar phenomena in the domain of
atoms in strong laser fields.


title: Coherent states for the hydrogen atom

abstract:
  We construct wave packets for the hydrogen atom labelled by the classical
action-angle variables with the following properties. i) The time evolution is
exactly given by classical evolution of the angle variables. (The angle
variable corresponding to the position on the orbit is now non-compact and we
do not get exactly the same state after one period. However the gross features
do not change. In particular the wave packet remains peaked around the labels.)
ii) Resolution of identity using this overcomplete set involves exactly the
classical phase space measure. iii) Semi-classical limit is related to
Bohr-Sommerfield quantization. iv) They are almost minimum uncertainty wave
packets in position and momentum.


title: Continuous stochastic Schrodinger equations and localization

abstract:
  The set of continuous norm-preserving stochastic Schrodinger equations
associated with the Lindblad master equation is introduced. This set is used to
describe the localization properties of the state vector toward eigenstates of
the environment operator. Particular focus is placed on determining the
stochastic equation which exhibits the highest rate of localization for wide
open systems. An equation having such a property is proposed in the case of a
single non-hermitian environment operator. This result is relevant to numerical
simulations of quantum trajectories where localization properties are used to
reduce the number of basis states needed to represent the system state, and
thereby increase the speed of calculation.


title: The Discovery of Squeezed States - In 1927

abstract:
  I first review a) the flowering of coherent states in the 1960's, yet b) the
discovery of coherent states in 1926, and c) the flowering of squeezed states
in the 1970's and 1980's. Then, with the background of the excitement over the
then new quantum mechanics, I describe d) the discovery of squeezed states in
1927.


title: Fidelity for displaced squeezed states and the oscillator semigroup

abstract:
  The fidelity for two displaced squeezed thermal states is computed using the
fact that the corresponding density operators belong to the oscillator
semigroup.


title: Output of a pulsed atom laser

abstract:
  We study the output properties of a pulsed atom laser consisting of an
interacting Bose-Einstein condensate (BEC) in a magnetic trap and an additional
rf field transferring atoms to an untrapped Zeeman sublevel. For weak output
coupling we calculate the dynamics of the decaying condensate population, of
its chemical potential and the velocity of the output atoms analytically.


title:
Reduction criterion of separability and limits for a class of protocols
  of entanglement distillation

abstract:
  We analyse the problem of distillation of entanglement of mixed states in
higher dimensional compound systems. Employing the positive maps method [M.
Horodecki et al., Phys. Lett. A 223 1 (1996)] we introduce and analyse a
criterion of separability which relates the structures of the total density
matrix and its reductions. We show that any state violating the criterion can
be distilled by suitable generalization of the two-qubit protocol which
distills any inseparable two-qubit state. Conversely, all the states which can
be distilled by such a protocol must violate the criterion. The proof involves
construction of the family of states which are invariant under transformation
$\varrho\to U\otimes U^*\varrho U^\dagger\otimes U^{*\dagger}$ where $U$ is a
unitary transformation and star denotes complex conjugation. The states are
related to the depolarizing channel generalized to non-binary case.


title: Quantum Algorithms Revisited

abstract:
  Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. A common pattern underpinning quantum algorithms can be
identified when quantum computation is viewed as multi-particle interference.
We use this approach to review (and improve) some of the existing quantum
algorithms and to show how they are related to different instances of quantum
phase estimation. We provide an explicit algorithm for generating any
prescribed interference pattern with an arbitrary precision.


title: Exponential Moments of Canonical Phase: Homodyne Measurements

abstract:
  A method for direct sampling of the exponential moments of canonical phase
from the data recorded in balanced homodyne detection is presented. Analytical
expressions for the sampling functions are shown which are valid for arbitrary
states. A numerical simulation illustrates the applicability of the method and
compares it with the direct measurement of phase by means of double homodyning.


title:
Photon adding and subtracting and Schroedinger-cat generation in
  conditional output measurement on a beam splitter

abstract:
  The problem of photon adding and subtracting is studied, using conditional
output measurement on a beam splitter. It is shown that for various classes of
states the corresponding photon-added and -subtracted states can be prepared.
Analytical results are presented, with special emphasis on photon-added and
-subtracted squeezed vacuum states, which are found to represent two different
types of Schroedinger-cat-like states. Effects of realistic photocounting and
Fock-state preparation are discussed.


title:
Quantum Entanglement and the Communication Complexity of the Inner
  Product Function

abstract:
  We consider the communication complexity of the binary inner product function
in a variation of the two-party scenario where the parties have an a priori
supply of particles in an entangled quantum state. We prove linear lower bounds
for both exact protocols, as well as for protocols that determine the answer
with bounded-error probability. Our proofs employ a novel kind of "quantum"
reduction from a quantum information theory problem to the problem of computing
the inner product. The communication required for the former problem can then
be bounded by an application of Holevo's theorem. We also give a specific
example of a probabilistic scenario where entanglement reduces the
communication complexity of the inner product function by one bit.


title: Analytical Models for Valence Fermions in Isotropic Traps

abstract:
  For isotropic confining Ioffe-Pritchard or TOP potentials, a valence fermion
trapped with a closed core of other fermions can be described by an analytical
effective one-particle model with a physical eigenspectrum. Related
constructions exist for Paul and Penning traps. The analytical models arise
from quantum-mechanical supersymmetry.


title:
Space, time, parallelism and noise requirements for reliable quantum
  computing

abstract:
  Quantum error correction methods use processing power to combat noise. The
noise level which can be tolerated in a fault-tolerant method is therefore a
function of the computational resources available, especially the size of
computer and degree of parallelism. I present an analysis of error correction
with block codes, made fault-tolerant through the use of prepared ancilla
blocks. The preparation and verification of the ancillas is described in
detail. It is shown that the ancillas need only be verified against a small set
of errors. This, combined with previously known advantages, makes this `ancilla
factory' the best method to apply error correction, whether in concatenated or
block coding. I then consider the resources required to achieve $2 \times
10^{10}$ computational steps reliably in a computer of 2150 logical qubits,
finding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with
smaller overheads than the $7^L$-bit concatenated code. The scaling is such
that block codes remain the better choice for all computations one is likely to
contemplate.


title: Quantum Computing

abstract:
  The subject of quantum computing brings together ideas from classical
information theory, computer science, and quantum physics. This review aims to
summarise not just quantum computing, but the whole subject of quantum
information theory. It turns out that information theory and quantum mechanics
fit together very well. In order to explain their relationship, the review
begins with an introduction to classical information theory and computer
science, including Shannon's theorem, error correcting codes, Turing machines
and computational complexity. The principles of quantum mechanics are then
outlined, and the EPR experiment described. The EPR-Bell correlations, and
quantum entanglement in general, form the essential new ingredient which
distinguishes quantum from classical information theory, and, arguably, quantum
from classical physics. Basic quantum information ideas are described,
including key distribution, teleportation, data compression, quantum error
correction, the universal quantum computer and quantum algorithms. The common
theme of all these ideas is the use of quantum entanglement as a computational
resource. Experimental methods for small quantum processors are briefly
sketched, concentrating on ion traps, high Q cavities, and NMR. The review
concludes with an outline of the main features of quantum information physics,
and avenues for future research.


title: Quantum-Controlled Few-Photon State Generated by Squeezed Atoms

abstract:
  General principles and experimental schemes for generating a desired
few-photon state from an aggregate of squeezed atoms are presented.
Quantum-statistical information of the collective atomic dipole is found to be
faithfully transferred to the photon state even in a few-photon regime. The
controllability of few-photon states is shown to increase with increasing the
number of squeezed atoms.


title: Quantum anti-Zeno effect

abstract:
  Prevention of a quantum system's time evolution by repetitive, frequent
measurements of the system's state has been called the quantum Zeno effect (or
paradox). Here we investigate theoretically and numerically the effect of
repeated measurements on the quantum dynamics of the multilevel systems that
exhibit the quantum localization of the classical chaos. The analysis is based
on the wave function and Schroedinger equation, without introduction of the
density matrix. We show how the quantum Zeno effect in simple few-level systems
can be recovered and understood by formal modeling the measurement effect on
the dynamics by randomizing the phases of the measured states. Further the
similar analysis is extended to investigate of the dynamics of multilevel
systems driven by an intense external force and affected by frequent
measurement. We show that frequent measurements of such quantum systems results
in the delocalization of the quantum suppression of the classical chaos. This
result is the opposite of the quantum Zeno effect. The phenomenon of
delocalization of the quantum suppression and restoration of the classical-like
time evolution of these quasiclassical systems, owing to repetitive frequent
measurements, can therefore be called the 'quantum anti-Zeno effect'. From this
analysis we furthermore conclude that frequently or continuously observable
quasiclassical systems evolve basically in a classical manner.


title: Three-Body Halos in Two Dimensions

abstract:
  A method to study weakly bound three-body quantum systems in two dimensions
is formulated in coordinate space for short-range potentials. Occurrences of
spatially extended structures (halos) are investigated. Borromean systems are
shown to exist in two dimensions for a certain class of potentials. An
extensive numerical investigation shows that a weakly bound two-body state
gives rise to two weakly bound three-body states, a reminiscence of the Efimov
effect in three dimensions. The properties of these two states in the weak
binding limit turn out to be universal.
  PACS number(s): 03.65.Ge, 21.45.+v, 31.15.Ja, 02.60Nm


title:
Which causality? Differences between the trajectory and Copenhagen
  analyses of an impulsive perturbation

abstract:
  The trajectory and Copenhagen representations render different predictions
for impulse perturbations. The different predictions are due to the different
roles that causality plays in the trajectory and Copenhagen interpretations. We
investigate a small perturbing impulse acting on the ground state of an
infinitely deep square well. For the two representations, the first-order
perturbation calculations for the temporal change in energy differ. This
temporal change in energy for the trajectory representation is dependent upon
the microstate of the wave function. We show that even under Copenhagen
epistemology, the two representations predict different theoretical results.


title: Coherent-state quantization of constrained fermion systems

abstract:
  The quantization of systems with first- and second-class constraints within
the coherent-state path-integral approach is extended to quantum systems with
fermionic degrees of freedom. As in the bosonic case the importance of
path-integral measures for Lagrange multipliers, which in this case are in
general expected to be elements of a Grassmann algebra, is emphasized. Several
examples with first- and second-class constraints are discussed.


title: Choice of Consistent Family, and Quantum Incompatibility

abstract:
  In consistent history quantum theory, a description of the time development
of a quantum system requires choosing a framework or consistent family, and
then calculating probabilities for the different histories which it contains.
It is argued that the framework is chosen by the physicist constructing a
description of a quantum system on the basis of questions he wishes to address,
in a manner analogous to choosing a coarse graining of the phase space in
classical statistical mechanics. The choice of framework is not determined by
some law of nature, though it is limited by quantum incompatibility, a concept
which is discussed using a two-dimensional Hilbert space (spin half particle).
Thus certain questions of physical interest can only be addressed using
frameworks in which they make (quantum mechanical) sense. The physicist's
choice does not influence reality, nor does the presence of choices render the
theory subjective. On the contrary, predictions of the theory can, in
principle, be verified by experimental measurements. These considerations are
used to address various criticisms and possible misunderstandings of the
consistent history approach, including its predictive power, whether it
requires a new logic, whether it can be interpreted realistically, the nature
of ``quasiclassicality'', and the possibility of ``contrary'' inferences.


title: Complete positivity of nonlinear evolution: A case study

abstract:
  Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.

categories: quant-ph chao-dyn funct-an hep-th math.FA nlin.CD


title:
Fluorescence into flat and structured radiation continua: An atomic
  density matrix without a master equation

abstract:
  We investigate an atomic $\Lambda$-system with one transition coupled to a
laser field and a flat continuum of vacuum modes and the other transition
coupled to field modes near the edge of a photonic band gap. The system
requires simultaneous treatment of Markovian and non-Markovian dissipation
processes, but the photonic band gap continuum can not be eliminated within a
density matrix treatment. Instead we propose a formalism based on Monte-Carlo
wavefunctions, and we present results relevant to an experimental
characterization of a structured continuum.


title: Quantum control by compensation of quantum fluctuations

abstract:
  We show that the influence of quantum fluctuations in the electromagnetic
field vacuum on a two level atom can be measured and consequently compensated
by balanced homodyne detection and a coherent feedback field. This compensation
suppresses the decoherence associated with spontaneous emission for a specific
state of the atomic system allowing complete control of the coherent state of
the system.


title: Purifying two-bit quantum gates and joint measurements in cavity QED

abstract:
  Using a cavity QED setup we show how to implement a particular joint
measurement on two atoms in a fault tolerant way. Based on this scheme, we
illustrate how to realize quantum communication over a noisy channel when local
operations are subject to errors. We also present a scheme to perform and
purify a universal two-bit gate.


title: Strong Field Ionization in Arbitrary Laser Polarizations

abstract:
  We present a numerical method for investigating the non-perturbative quantum
mechanical interaction of light with atoms in two dimensions, without a basis
expansion. This enables us to investigate intense laser-atom interactions with
light of arbitrary polarization without approximation. Results are presented
for the dependence of ionization and high harmonic generation on ellipticity
seen in recent experiments. Strong evidence of stabilization in circular
polarization is found.


title: Feynman Integrals with Absorbing Boundaries

abstract:
  We propose a formulation of an absorbing boundary for a quantum particle. The
formulation is based on a Feynman-type integral over trajectories that are
confined to the non-absorbing region. Trajectories that reach the absorbing
wall are discounted from the population of the surviving trajectories with a
certain weighting factor. Under the assumption that absorbed trajectories do
not interfere with the surviving trajectories, we obtain a time dependent
absorption law. Two examples are worked out.


title: SWKB for the Angular Momentum

abstract:
  In this paper we solve the eigenvalue problem of the angular momentum
operator by using the supersymmetric semiclassical quantum mechanics (SWKB),
and show that it gives the correct quantization already at the leading order.


title: On the Convergence of the WKB Series for the Angular Momentum Operator

abstract:
  In this paper we prove a recent conjecture [Robnik M and Salasnich L 1997 J.
Phys. A: Math. Gen. 30 1719] about the convergence of the WKB series for the
angular momentum operator. We demonstrate that the WKB algorithm for the
angular momentum gives the exact quantization formula if all orders are summed.


title:
Moments of the Wigner Distribution and a Generalized Uncertainty
  Principle

abstract:
  The nonnegativity of the density operator of a state is faithfully coded in
its Wigner distribution, and this places constraints on the moments of the
Wigner distribution. These constraints are presented in a canonically invariant
form which is both concise and explicit. Since the conventional uncertainty
principle is such a constraint on the first and second moments, our result
constitutes a generalization of the same to all orders. Possible application in
quantum state reconstruction using optical homodyne tomography is noted.


title:
Nonclassicality and the concept of local constraints on the photon
  number distribution

abstract:
  We exploit results from the classical Stieltjes moment problem to bring out
the totality of all the information regarding phase insensitive nonclassicality
of a state as captured by the photon number distribution p_n. Central to our
approach is the realization that n !p_n constitutes the sequence of moments of
a (quasi) probability distribution, notwithstanding the fact that p_n can by
itself be regarded as a probability distribution. This leads to classicality
restrictions on p_n that are local in n involving p_n's for only a small number
of consecutive n's, enabling a critical examination of the conjecture that
oscillation in p_n is a signature of nonclassicality.


title: Homodyne measurement of exponential phase moments

abstract:
  It is shown that the exponential moments of the canonical phase can be
directly sampled from the data recorded in balanced homodyne detection.
Analytical expressions for the sampling functions are derived, which are valid
for arbitrary states and bridge the gap between quantum and classical phase.
The reconstruction of the canonical phase distribution from the experimentally
determined exponential moments is discussed.


title: Nonlinear quantum state transformation of spin-1/2

abstract:
  A non-linear quantum state transformation is presented. The transformation,
which operates on pairs of spin-1/2, can be used to distinguish optimally
between two non-orthogonal states. Similar transformations applied locally on
each component of an entangled pair of spin-1/2 can be used to transform a
mixed nonlocal state into a quasi-pure maximally entangled singlet state. In
both cases the transformation makes use of the basic building block of the
quantum computer, namely the quantum-XOR gate.


title: Extension of the Barut-Girardello Coherent State and Path Integral II

abstract:
  We have constructed the coherent state of $U(N,1)$, which is an extension of
the Barut-Girardello (BG) coherent state of $SU(1,1)$, in our previous paper.
However there is a restriction that the eigenvalue of the Casimir operator is
natural number. In this paper we construct the coherent state in the analytic
representation to overcome this restriction. Next we show that the measure of
the BG coherent state is not the symplectic induced measure.


title: Dissipative dynamics in a quantum register

abstract:
  A model for a quantum register dissipatively coupled with a bosonic thermal
bath is studied. The register consists of $N$ qubits (i.e. spin ${1/2}$ degrees
of freedom), the bath is described by $N_b$ bosonic modes. The register-bath
coupling is chosen in such a way that the total number of excitations is
conserved. The Hilbert space splits allowing the study of the dynamics
separately in each sector. Assuming that the coupling with the bath is the same
for all qubits, the excitation sectors have a further decomposition according
the irreducible representations of the $su(2)$ spin algebra. The stability
against environment-generated noise of the information encoded in a quantum
state of the register depends on its $su(2)$ symmetry content. At zero
temperature we find that states belonging to the vacuum symmetry sector have
for long time vanishing fidelity, whereas each lowest spin vector is decoupled
from the bath and therefore is decoherence free. Numerical results are shown in
the one-excitation space in the case qubit-dependent bath-system coupling.


title: Quantum Measurement Back-Reaction and Induced Toplogical Phases

abstract:
  It is shown that a topological vector-potential (Berry phase) is induced by
the act of measuring angular momentum in a direction defined by a reference
particle. This vector potential appears as a consequence of the back-reaction
due to the quantum measurement.


title:
Explanation of the violation of Bell's inequality by maintaining
  Einstein separability

abstract:
  A new interpretation offers a consistent conceptual basis for nonrelativistic
quantum mechanics. The violation of Bell's inequality is explained by
maintaining realism, inductive inference and Einstein separability.


title:
On the solution of the EPR paradox and the explanation of the violation
  of Bell's inequality

abstract:
  A new interpretation offers a consistent conceptual basis for nonrelativistic
quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the
violation of Bell's inequality is explained by maintaining realism, inductive
inference and Einstein separability.


title: Coding Theorems for Quantum Communication Channels

abstract:
  The more than thirty years old issue of the information capacity of quantum
communication channels was dramatically clarified during the last period, when
a number of direct quantum coding theorems was discovered. To considerable
extent this progress is due to an interplay between the quantum communication
theory and quantum information ideas related to more recent development in
quantum computing. It is remarkable, however, that many probabilistic tools
underlying the treatment of quantum case have their roots, and in some cases
direct prototypes, in classical Shannon's theory. This paper presents an
outline of some basic ideas and results in that direction.


title: Factoring and Fourier Transformation with a Mach-Zehnder Interferometer

abstract:
  The scheme of Clauser and Dowling (Phys. Rev. A 53, 4587 (1996)) for
factoring $N$ by means of an N-slit interference experiment is translated into
an experiment with a single Mach-Zehnder interferometer. With dispersive phase
shifters the ratio of the coherence length to wavelength limits the numbers
that can be factored. A conservative estimate permits $N \approx 10^7$. It is
furthermore shown, that sine and cosine Fourier coefficients of a real periodic
function can be obtained with such an interferometer.


title: Experiment on Interaction-Free Measurement in Neutron Interferometry

abstract:
  A neutron interferometric test of interaction-free detection of the presence
of an absorbing object in one arm of a neutron interferometer has been
performed. Despite deviations from the ideal performance characteristics of a
Mach-Zehnder interferometer it could be shown that information is obtained
without interaction.


title:
Equivalence of the grand canonical partition functions of particles with
  different statistics

abstract:
  It is shown that the grand partition function of an ideal Bose system with
single particle spectrum $\epsilon_i = (2n+k+3/2)\hbar\omega$ is identical to
that of a system of particles with single particle energy $\epsilon_i
=(n+1/2)\hbar\omega$ and obeying a particular kind of statistics based on the
permutation group.


title: The Los Alamos Trapped Ion Quantum Computer Experiment

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


title: Is the Deformation Parameter in q-Rotor Model Really Phenomenological ?

abstract:
  We cast the $q$-rotor in the framework of Barnett-Pegg theory for rotation
angle, whose underlying algebra is $SU_q(2)$. A new method to fix the
deformation parameter from the theory is suggested. We test our ideas by
fitting rotational spectra in deformed even-even and superdeformed nuclei. The
results are in good agreement with the previous phenomenological applications
of $q$-rotor model.


title: Nonlocal looking equations can make nonlinear quantum dynamics local

abstract:
  A general method for extending a non-dissipative nonlinear Schr\"odinger and
Liouville-von Neumann 1-particle dynamics to an arbitrary number of particles
is described. It is shown at a general level that the dynamics so obtained is
completely separable, which is the strongest condition one can impose on
dynamics of composite systems. It requires that for all initial states
(entangled or not) a subsystem not only cannot be influenced by any action
undertaken by an observer in a separated system (strong separability), but
additionally that the self-consistency condition $Tr_2\circ
\phi^t_{1+2}=\phi^t_{1}\circ Tr_2$ is fulfilled. It is shown that a correct
extension to $N$ particles involves integro-differential equations which, in
spite of their nonlocal appearance, make the theory fully local. As a
consequence a much larger class of nonlinearities satisfying the complete
separability condition is allowed than has been assumed so far. In particular
all nonlinearities of the form $F(|\psi(x)|)$ are acceptable. This shows that
the locality condition does not single out logarithmic or 1-homeogeneous
nonlinearities.


title: How to visualize a quantum transition of a single atom

abstract:
  The previously proposed visualization of Rabi oscillations of a single atom
by a continuous fuzzy measurement of energy is specified for the case of a
single transition between levels caused by a $\pi$-pulse of a driving field. An
analysis in the framework of the restricted-path-integral approach (which
reduces effectively to a Schr\"odinger equation with a complex Hamiltonian)
shows that the measurement gives a reliable information about the system
evolution, but the probability of the transition becomes less than unity. In
addition an experimental setup is proposed for continuous monitoring the state
of an atom by observation of electrons scattered by it. It is shown how this
setup realizes a continuous fuzzy measurement of the atom energy.


title: Models of Quantum Turing machines

abstract:
  Quantum Turing machines are discussed and reviewed in this paper. Most of the
paper is concerned with processes defined by a step operator $T$ that is used
to construct a Hamiltonian $H$ according to Feynman's prescription. Differences
between these models and the models of Deutsch are discussed and reviewed. It
is emphasized that the models with $H$ constructed from $T$ include fully
quantum mechanical processes that take computation basis states into linear
superpositions of these states. The requirement that $T$ be distinct path
generating is reviewed. The advantage of this requirement is that
Schr\"{o}dinger evolution under $H$ is one dimensional along distinct finite or
infinite paths of nonoverlapping states in some basis $B_{T}$. It is emphasized
that $B_{T}$ can be arbitrarily complex with extreme entanglements between
states of component systems. The new aspect of quantum Turing machines
introduced here is the emphasis on the structure of graphs obtained when the
states in the $B_{T}$ paths are expanded as linear superpositions of states in
a reference basis such as the computation basis $B_{C}$. Examples are discussed
that illustrate the main points of the paper. For one example the graph
structures of the paths in $B_{T}$ expanded as states in $B_{C}$ include finite
stage binary trees and concatenated finite stage binary trees with or without
terminal infinite binary trees. Other examples are discussed in which the graph
structures correspond to interferometers and iterations of interferometers.


title: Atom optical elements for Bose condensates

abstract:
  A simple model for atom optical elements for Bose condensate of trapped,
dilute alkali atomns is proposed and numerical simulations are presented to
illustrate its characteristics. We demonstrate ways of focusing and splitting
the condensate by modifying experimentally adjustable parameters. We show that
there are at least two ways of implementing atom optical elements: one may
modulate the interatomic scattering length in space, or alternatively, use a
sinusoidal, externally applied potential.


title: Unusual light spectra from a two-level atom in squeezed vacuum

abstract:
  We investigate the interaction of an atom with a multi-channel squeezed
vacuum. It turns out that the light coming out in a particular channel can have
anomalous spectral properties, among them asymmetry of the spectrum, absence of
the central peak as well as central hole burning for particular parameters. As
an example plane-wave squeezing is considered. In this case the above phenomena
can occur for the light spectra in certain directions. In the total spectrum
these phenomena are washed out.


title:
Nuclear magnetic resonance spectroscopy: An experimentally accessible
  paradigm for quantum computing

abstract:
  We present experimental results which demonstrate that nuclear magnetic
resonance spectroscopy is capable of efficiently emulating many of the
capabilities of quantum computers, including unitary evolution and coherent
superpositions, but without attendant wave-function collapse. Specifically, we
have: (1) Implemented the quantum XOR gate in two different ways, one using
Pound-Overhauser double resonance, and the other using a spin-coherence double
resonance pulse sequence; (2) Demonstrated that the square root of the
Pound-Overhauser XOR corresponds to a conditional rotation, thus obtaining a
universal set of gates; (3) Devised a spin-coherence implementation of the
Toffoli gate, and confirmed that it transforms the equilibrium state of a
four-spin system as expected; (4) Used standard gradient-pulse techniques in
NMR to equalize all but one of the populations in a two-spin system, so
obtaining the pseudo-pure state that corresponds to |00>; (5) Validated that
one can identify which basic pseudo-pure state is present by transforming it
into one-spin superpositions, whose associated spectra jointly characterize the
state; (6) Applied the spin-coherence XOR gate to a one-spin superposition to
create an entangled state, and confirmed its existence by detecting the
associated double-quantum coherence via gradient-echo methods.


title: Classical and quantum measurements of position

abstract:
  We study the dynamics of classical and quantum systems undergoing a
continuous measurement of position by schematizing the measurement apparatus
with an infinite set of harmonic oscillators at finite temperature linearly
coupled to the measured system. Selective and nonselective measurement
processes are then introduced according to a selection of or an average over
all possible initial configurations of the measurement apparatus. At quantum
level, the selective processes are described by a nonlinear stochastic
Schr\"odinger equation whose solutions evolve into properly defined coherent
states in the case of linear systems. For arbitrary measured systems, classical
behavior is always recovered in the macroscopic limit.


title: Quantum Zeno Effect with the Feynman-Mensky Path-Integral Approach

abstract:
  A model for quantum Zeno effect based upon an effective Schr\"odinger
equation originated by the path-integral approach is developed and applied to a
two-level system simultaneously stimulated by a resonant perturbation. It is
shown that inhibition of stimulated transitions between the two levels appears
as a consequence of the influence of the meter whenever measurements of energy,
either continuous or pulsed, are performed at quantum level of sensitivity. The
generality of this approach allows to qualitatively understand the inhibition
of spontaneous transitions as the decay of unstable particles, originally
presented as a paradox of quantum measurement theory.


title: Quantum Phenomenology with the Path Integral Approach

abstract:
  A quantum measurement model based upon restricted path-integrals allows us to
study measurements of generalized position in various one-dimensional systems
of phenomenological interest. After a general overview of the method we discuss
the cases of a harmonic oscillator, a bistable potential and two coupled
systems, briefly illustrating their applications.


title: Optimal Monitoring of Position in Nonlinear Quantum Systems

abstract:
  We discuss a model of repeated measurements of position in a quantum system
which is monitored for a finite amount of time with a finite instrumental
error. In this framework we recover the optimum monitoring of a harmonic
oscillator proposed in the case of an instantaneous collapse of the
wavefunction into an infinite-accuracy measurement result. We also establish
numerically the existence of an optimal measurement strategy in the case of a
nonlinear system. This optimal strategy is completely defined by the spectral
properties of the nonlinear system.


title: Continuous Quantum Monitoring of Position of Nonlinear Oscillators

abstract:
  Application of the path-integral approach to continuous measurements leads to
effective Lagrangians or Hamiltonians in which the effect of the measurement is
taken into account through an imaginary term. We apply these considerations to
nonlinear oscillators with use of numerical computations to evaluate quantum
limitations for monitoring position in such a class of systems.


title: EPR correlations and EPW distributions revisited

abstract:
  It is shown that Bell's proof of violation of local realism in phase space is
incorrect. Using Bell's approach, a violation can be derived also for
nonnegative Wigner distributions. The error is found to lie in the use of an
unnormalizable Wigner function.


title: Trembling cavities in the canonical approach

abstract:
  We present a canonical formalism facilitating investigations of the dynamical
Casimir effect by means of a response theory approach. We consider a massless
scalar field confined inside of an arbitaray domain $G(t)$, which undergoes
small displacements for a certain period of time. Under rather general
conditions a formula for the number of created particles per mode is derived.
The pertubative approach reveals the occurance of two generic processes
contributing to the particle production: the squeezing of the vacuum by
changing the shape and an acceleration effect due to motion af the boundaries.
The method is applied to the configuration of moving mirror(s). Some properties
as well as the relation to local Green function methods are discussed.
PACS-numbers: 12.20; 42.50; 03.70.+k; 42.65.Vh Keywords: Dynamical Casimir
effect; Moving mirrors; Cavity quantum field theory; Vibrating boundary;


title: Trajectory-coherent states for the Caldirola - Kanai Hamiltonian

abstract:
  In this paper we construct the trajectory-coherent states for the Caldirola -
Kanai Hamiltonian. We investigate the properties of this states.


title: Jaynes principle versus entanglement

abstract:
  We show, by explicit examples, that the Jaynes inference scheme based on
maximization of entropy can produce inseparable states even if there exists a
separable state compatible with the measured data. It can lead to problems with
processing of entanglement. The difficulty vanishes when one uses inference
scheme based on minimization of entanglement.


title:
The Hydrogen Atom in Combined Electric and Magnetic Fields with
  Arbitrary Mutual Orientations

abstract:
  For the hydrogen atom in combined magnetic and electric fields we investigate
the dependence of the quantum spectra, classical dynamics, and statistical
distributions of energy levels on the mutual orientation of the two external
fields. Resonance energies and oscillator strengths are obtained by exact
diagonalization of the Hamiltonian in a complete basis set, even far above the
ionization threshold. At high excitation energies around the Stark saddle point
the eigenenergies exhibit strong level repulsions when the angle between the
fields is varied. The large avoided crossings occur between states with the
same approximately conserved principal quantum number, n, and this
intramanifold mixing of states cannot be explained, not even qualitatively, by
conventional perturbation theory. However, it is well reproduced by an extended
perturbation theory which takes into account all couplings between the angular
momentum and Runge-Lenz vector. The large avoided crossings are interpreted as
a quantum manifestation of classical intramanifold chaos. This interpretation
is supported by both classical Poincar\'e surfaces of section, which reveal a
mixed regular-chaotic intramanifold dynamics, and the statistical analysis of
nearest-neighbor-spacing


title:
Different realizations of tomographic principle in quantum state
  measurement

abstract:
  We establish a general principle for the tomographic approach to quantum
state reconstruction, till now based on a simple rotation transformation in the
phase space, which allows us to consider other types of transformations. Then,
we will present different realizations of the principle in specific examples.


title: Interference effects in f-deformed fields

abstract:
  We show how the introduction of an algeabric field deformation affects the
interference phenomena. We also give a physical interpretation of the developed
theory.


title: Maximally Robust Unravelings of Quantum Master Equations

abstract:
  The stationary solution \rho of a quantum master equation can be represented
as an ensemble of pure states in a continuous infinity of ways. An ensemble
which is physically realizable through monitoring the system's environment we
call an `unraveling'. The survival probability S(t) of an unraveling is the
average probability for each of its elements to be unchanged a time t after
cessation of monitoring. The maximally robust unraveling is the one for which
S(t) remains greater than the largest eigenvalue of \rho for the longest time.
The optical parametric oscillator is a soluble example.


title: Supersymmetry of a Nonstationary Pauli Equation

abstract:
  The supersymmetry of the electron in both the nonstationary magnetic and
electric fields in a two-dimensional case is studied. The supercharges which
are the integrals of motion and their algebra are established. Using the
obtained algebra the solutions of nonstationary Pauli equation are generated.


title: The wave packet - a universal quantum object

abstract:
  We summarize the theoretical description of wave packets on molecular energy
levels. We review the various quantum mechanical effects which can be studied
and the models that can be verified on this system. This justifies our claim
that the wave packet constitutes a universal quantum object.


title: Decoherence in localized photon emission

abstract:
  The spatiotemporal dynamics of photon emission into a non-local farfield
channel and two local nearfield channels from a pair of coupled two level
systems is analysed using a model for emission based on Wigner-Weisskopf
theory. The local quantum beats can be observed in the two nearfield channels.
However, the presence of the farfield causes decoherence in the quantum beats
even if only photon emissions into the near field channels are considered.


title: Quantum gravity and the problem of measurement

abstract:
  We discuss some arguments in favour of the proposal that the quantum
correlations contained in the pure state-vector evolving according to
Schoedinger equation can be eliminated by the action of multiply connected
wormholes during measurement. We devise a procedure to obtain a proper master
equation which governes the changes of the reduced density matrix of matter
fields interacting with doubly connected wormholes. It is shown that this
master equation predicts an appropriate damping of the off-diagonal
correlations contained in the state vector.


title:
Supersymmetric one-parameter strict isospectrality for the attractive
  delta potentials

abstract:
  The Schr\"odinger equation with attractive delta potential has been
previously studied in the supersymmetric quantum mechanical approach by a
number of authors, but they all used only the particular superpotential
solution. Here, we introduce a one-parameter family of strictly isospectral
attractive delta function potentials, which is based on the general
superpotential (general Riccati) solution, we study the problem in some detail
and suggest possible applications


title: Adiabatic Decoherence

abstract:
  We study a general quantum system interacting with environment modeled by the
bosonic heat bath of Caldeira and Leggett type. General interaction
Hamiltonians are considered that commute with the system's Hamiltonian so that
there is no energy exchange between the system and bath. We argue that this
model provides an appropriate description of adiabatic quantum decoherence,
i.e., loss of entanglement on time scales short compared to those of thermal
relaxation processes associated with energy exchange with the bath. The
interaction Hamiltonian is then proportional to a conserved "pointer
observable." Calculation of the elements of the reduced density matrix of the
system is carried out exactly, and time-dependence of decoherence is
identified, similar to recent results for related models. Our key finding is
that the decoherence process is controlled by spectral properties of the
interaction rather than system's Hamiltonian.


title:
Supersymmetric Construction of Exactly Solvable Potentials and
  Non-Linear Algebras

abstract:
  Using algebraic tools of supersymmetric quantum mechanics we construct
classes of conditionally exactly solvable potentials being the supersymmetric
partners of the linear or radial harmonic oscillator. With the help of the
raising and lowering operators of these harmonic oscillators and the SUSY
operators we construct ladder operators for these new conditionally solvable
systems. It is found that these ladder operators together with the Hamilton
operator form a non-linear algebra which is of quadratic and cubic type for the
SUSY partners of the linear and radial harmonic oscillator, respectively.

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


title: Dephasing due to Which Path Detector

abstract:
  We study dephasing of electrons induced by a which path detector and thus
verify Bohr's complementarity principle for fermions. We utilize a double path
interferometer with two slits, with one slit being replaced by a coherent
quantum dot (QD). A short one dimensional channel, in the form of a quantum
point contact (QPC), in close proximity to the QD, serves as a which path
detector. We find that by varying the properties of the QPC detector we affect
the visibility of the interference, inducing thus dephasing. We develop a
simple model to explain the dephasing due to the nearby detector and find good
agreement with the experiment.


title: Quantum self-induced transparency in frequency gap media

abstract:
  We study quantum effects of light propagation through an extended absorbing
system of two-level atoms placed within a frequency gap medium (FGM). Apart
from ordinary solitons and single particle impurity band states, the
many-particle spectrum of the system contains massive pairs of confined gap
excitations and their bound complexes - gap solitons. In addition,
``composite'' solitons are predicted as bound states of ordinary and gap
solitons. Quantum gap and composite solitons propagate without dissipation, and
should be associated with self-induced transparency pulses in a FGM.


title: Incoherent dynamics in neutron-matter interaction

abstract:
  Coherent and incoherent neutron-matter interaction is studied inside a
recently introduced approach to subdynamics of a macrosystem. The equation
describing the interaction is of the Lindblad type and using the Fermi
pseudopotential we show that the commutator term is an optical potential
leading to well-known relations in neutron optics. The other terms, usually
ignored in optical descriptions and linked to the dynamic structure function of
the medium, give an incoherent contribution to the dynamics, which keeps
diffuse scattering and attenuation of the coherent beam into account, thus
warranting fulfilment of the optical theorem. The relevance of this analysis to
experiments in neutron interferometry is briefly discussed.


title: NMR GHZ

abstract:
  We describe the creation of a Greenberger-Horne-Zeilinger (GHZ) state of the
form |000>+|111> (three maximally entangled quantum bits) using Nuclear
Magnetic Resonance (NMR). We have successfully carried out the experiment using
the proton and carbon spins of trichloroethylene, and confirmed the result
using state tomography. We have thus extended the space of entangled quantum
states explored systematically to three quantum bits, an essential step for
quantum computation.


title: Causality and Nonlocality as Axioms for Quantum Mechanics

abstract:
  Quantum mechanics permits nonlocality - both nonlocal correlations and
nonlocal equations of motion - while respecting relativistic causality. Is
quantum mechanics the unique theory that reconciles nonlocality and causality?
We consider two models, going beyond quantum mechanics, of nonlocality:
"superquantum" correlations, and nonlocal "jamming" of correlations. These
models are consistent with some definitions of nonlocality and causality.


title: Are there Floquet Quanta?

abstract:
  The Zeldovich hypothesis is revised and the meaning of quasi energy spectra
is discussed. The observation of Floquet resonance for microobjects in quickly
oscillating external fields might bring a new information about the time scale
of hypothetical quantum jumps.


title: Squeezed States and Helmholtz Spectra

abstract:
  The 'classical interpretation' of the wave function psi(x) reveals an
interesting operational aspect of the Helmholtz spectra. It is shown that the
traditional Sturm-Liouville problem contains the simplest key to predict the
squeezing effect for charged particle states.


title: Entanglement of Formation of an Arbitrary State of Two Qubits

abstract:
  The entanglement of a pure state of a pair of quantum systems is defined as
the entropy of either member of the pair. The entanglement of formation of a
mixed state is defined as the minimum average entanglement of an ensemble of
pure states that represents the given mixed state. An earlier paper [Phys. Rev.
Lett. 78, 5022 (1997)] conjectured an explicit formula for the entanglement of
formation of a pair of binary quantum objects (qubits) as a function of their
density matrix, and proved the formula to be true for a special class of mixed
states. The present paper extends the proof to arbitrary states of this system
and shows how to construct entanglement-minimizing pure-state decompositions.


title:
Necessary and Sufficient Classicality Conditions on Photon Number
  Distributions

abstract:
  We exploit results on the classical Stieltjes moment problem to obtain
completely explicit necessary and sufficient conditions for the photon number
distribution p(n) of a radiation field mode to be classical. These conditions
are given in two forms - respectively local and global in the individual photon
number probabilities. Central to the first approach is the recognition of the
important fact that the quantities n!p(n) are moments of a quasiprobability
distribution, notwithstanding the fact that p(n)'s can by themselves be
considered as a probability distribution over the nonnegative integers. This
leads to local classicality conditions involving p(n)'s for only a small number
of values of n. This local approach enables us to present detailed quantitative
statements on the connection between nonclassicality and oscillations in the
photon number distribution. The second approach is in terms of the traditional
factorial moments of p(n). Equivalence of the two approaches is established.


title: Measurement of Time-of-Arrival in Quantum Mechanics

abstract:
  It is argued that the time-of-arrival cannot be precisely defined and
measured in quantum mechanics. By constructing explicit toy models of a
measurement, we show that for a free particle it cannot be measured more
accurately then $\Delta t_A \sim 1/E_k$, where $E_k$ is the initial kinetic
energy of the particle. With a better accuracy, particles reflect off the
measuring device, and the resulting probability distribution becomes distorted.
It is shown that a time-of-arrival operator cannot exist, and that approximate
time-of-arrival operators do not correspond to the measurements considered
here.


title: The Interpretation of Quantum Mechanics: Many Worlds or Many Words?

abstract:
  As cutting-edge experiments display ever more extreme forms of non-classical
behavior, the prevailing view on the interpretation of quantum mechanics
appears to be gradually changing. A (highly unscientific) poll taken at the
1997 UMBC quantum mechanics workshop gave the once all-dominant Copenhagen
interpretation less than half of the votes. The Many Worlds interpretation
(MWI) scored second, comfortably ahead of the Consistent Histories and Bohm
interpretations. It is argued that since all the above-mentioned approaches to
nonrelativistic quantum mechanics give identical cookbook prescriptions for how
to calculate things in practice, practical-minded experimentalists, who have
traditionally adopted the ``shut-up-and-calculate interpretation'', typically
show little interest in whether cozy classical concepts are in fact real in
some untestable metaphysical sense or merely the way we subjectively perceive a
mathematically simpler world where the Schrodinger equation describes
everything - and that they are therefore becoming less bothered by a profusion
of worlds than by a profusion of words.
  Common objections to the MWI are discussed. It is argued that when
environment-induced decoherence is taken into account, the experimental
predictions of the MWI are identical to those of the Copenhagen interpretation
except for an experiment involving a Byzantine form of ``quantum suicide''.
This makes the choice between them purely a matter of taste, roughly equivalent
to whether one believes mathematical language or human language to be more
fundamental.


title: Decoherence and Dissipation in Quantum Two-State Systems

abstract:
  The Brownian dynamics of the density operator for a quantum system
interacting with a classical heat bath is described using a stochastic,
non-linear Liouville equation obtained from a variational principle. The
environment's degrees of freedom are simulated by classical harmonic
oscillators, while the dynamical variables of the quantum system are two
non-hermitian "square root operators" defined by a Gauss-like decomposition of
the density operator. The rate of the noise-induced transitions is expressed as
a function of the environmental spectral density, and is discussed for the case
of the white noise and blackbody radiation. The result is compared with the
rate determined by a quantum environment, calculated by partial tracing in the
whole Hilbert space. The time-dependence of the von Neumann entropy and of the
dissipated energy is obtained numerically for a system of two quantum states.
These are the ground and first excited state of the center of mass vibrations
for an ion confined in a harmonic trap.


title: A Comment on "Semiquantum Chaos"

abstract:
  The identification of the particle creation and distruction operators is
discussed.


title:
Realizing Discontinuous Wave Functions with Renormalized Short-Range
  Potentials

abstract:
  It is shown that a potential consisting of three Dirac's delta functions on
the line with disappearing distances can give rise to the discontinuity in wave
functions with the proper renormalization of the delta function strength. This
can be used as a building block, along with the usual Dirac's delta, to
construct the most general three-parameter family of point interactions, which
allow both discontinuity and asymmetry of the wave function, as the zero-size
limit of self-adjoint local operators in one-dimensional quantum mechanics.
Experimental realization of the Neumann boundary is discussed.
  KEYWORDS: point interaction, self-adjoint extension, $\delta'$ potential,
wave function discontinuity, Neumann boundary
  PACS Nos: 3.65.-w, 11.10.Gh, 68.65+g


title:
Gauge Transformations in Quantum Mechanics and the Unification of
  Nonlinear Schr\"odinger Equations

abstract:
  Beginning with ordinary quantum mechanics for spinless particles, together
with the hypothesis that all experimental measurements consist of positional
measurements at different times, we characterize directly a class of nonlinear
quantum theories physically equivalent to linear quantum mechanics through
nonlinear gauge transformations. We show that under two physically-motivated
assumptions, these transformations are uniquely determined: they are exactly
the group of time-dependent, nonlinear gauge transformations introduced
previously for a family of nonlinear Schr\"odinger equations. The general
equation in this family, including terms considered by Kostin, by
Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent
coefficients, can be obtained from the linear Schr\"odinger equation through
gauge transformation and a subsequent process we call gauge generalization. We
thus unify, on fundamental grounds, a rather diverse set of nonlinear
time-evolutions in quantum mechanics.


title: Probability distribution of arrival times in quantum mechanics

abstract:
  In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)]
we introduced a self-adjoint operator $\hat {{\cal T}}(X)$ whose eigenstates
can be used to define consistently a probability distribution of the time of
arrival at a given spatial point. In the present work we show that the
probability distribution previously proposed can be well understood on
classical grounds in the sense that it is given by the expectation value of a
certain positive definite operator $\hat J^{(+)}(X)$ which is nothing but a
straightforward quantum version of the modulus of the classical current. For
quantum states highly localized in momentum space about a certain momentum $p_0
\neq 0$, the expectation value of $\hat J^{(+)}(X)$ becomes indistinguishable
from the quantum probability current. This fact may provide a justification for
the common practice of using the latter quantity as a probability distribution
of arrival times.


title: Berry's phase for large spins in external fields

abstract:
  It is shown that even for large spins $J$ the fundamental difference between
integer and half-integer spins persists. In a quasi-classical description this
difference enters via Berry's connection. This general phenomenon is derived
and illustrated for large spins confined to a plane by crystalline electric
fields. Physical realizations are rare-earth Nickel Borocarbides. Magnetic
moments for half-integer spin
  (Dy$^{3+}$, $J=15/2$) and magnetic susceptibilities for integer spin
(Ho$^{3+}$, $J=8$) are calculated. Experiments are proposed to furnish evidence
for the predicted fundamental difference.


title:
Supersymmetry of the Nonstationary Schr\"odinger equation and
  Time-Dependent Exactly Solvable Quantum Models

abstract:
  New exactly solvable quantum models are obtained with the help of the
supersymmetric extencion of the nonstationary Schr/"odinger equation.


title: Time Dependent Supersymmetry in Quantum Mechanics

abstract:
  The well-known supersymmetric constructions such as Witten's supersymmetric
quantum mechanics, Spiridonov-Rubakov parasupersymmetric quantum mechanics, and
higher-derivative SUSY of Andrianov et al. are extended to the nonstationary
Schr\"odinger equation. All these constructions are based on the time-dependent
Darboux transformation. The superalgebra over the conventional Lie algebra is
constructed. Examples of time-dependent exactly solvable potentials are given.


title:
Supersymmetry and Supercoherent States of a Nonrelativistic Free
  Particle

abstract:
  Coordinate atypical representation of the orthosymplectic superalgebra
osp(2/2) in a Hilbert superspace of square integrable functions constructed in
a special way is given. The quantum nonrelativistic free particle Hamiltonian
is an element of this superalgebra which turns out to be a dynamical
superalgebra for this system. The supercoherent states, defined by means of a
supergroup displacement operator, are explicitly constructed. These are the
coordinate representation of the known atypical abstract super group $OSp(2/2)$
coherent states. We interpret obtained results from the classical mechanics
viewpoint as a model of classical particle which is immovable in the even
sector of the phase superspace and is in rectilinear movement (in the
appropriate coordinate system) in its odd sector.


title: Measurement and state preparation via ion trap quantum computing

abstract:
  We investigate in detail the effects of a QND vibrational number measurement
made on single ions in a recently proposed measurement scheme for the
vibrational state of a register of ions in a linear rf trap [C. D'Helon and
G.J. Milburn, Phys. Rev. A 54, 5141 (1996)]. The performance of a measurement
shows some interesting patterns which are closely related to searching.


title:
A Bell inequality which can be used to test locality more simply than
  Clauser-Horne inequality and which is violated by a larger magnitude of
  violation than Clauser-Horne-Shimony-Holt inequality

abstract:
  A correlation inequality is derived from local realism and a supplementary
assumption. Unlike Clauser-Horne (CH) inequality [or Clauser-Horne-Shimony-Holt
(CHSH) inequality] which is violated by quantum mechanics by a factor of $\sqrt
2$, this inequality is violated by a factor of 1.5. Thus the magnitude of
violation of this inequality is approximately 20.7% larger than the magnitude
of violation of previous inequalities. Moreover, unlike CH (or CHSH) inequality
which requires the measurement of five detection probabilities, the present
inequality requires the measurement of only two detection probabilities. This
inequality can therefore be used to test locality more simply than CH or CHSH
inequality.


title: On (non)linear Quantum Mechanics

abstract:
  We review a possible framework for (non)linear quantum theories, into which
linear quantum mechanics fits as well, and discuss the notion of
``equivalence'' in this setting. Finally, we draw the attention to persisting
severe problems of nonlinear quantum theories.


title: Logical Reversibility and Physical Reversibility in Quantum Measurement

abstract:
  A quantum measurement is logically reversible if the premeasurement density
operator of the measured system can be calculated from the postmeasurement
density operator and from the outcome of the measurement. This paper analyzes
why many quantum measurements are logically irreversible, shows how to make
them logically reversible, and discusses reversing measurement that returns the
postmeasurement state to the premeasurement state by another measurement
(physical reversibility). Reversing measurement and unitarily reversible
quantum operation are compared from the viewpoint of error correction in
quantum computation.


title:
Interference phenomena in the photon production between two oscillating
  walls

abstract:
  We study the photon production in a 1D cavity whose left and right walls
oscillate with the frequency $\Omega_{L} $ and $\Omega_{R} $, respectively. For
$\Omega_{L} \neq \Omega_{R}, $ the number of generated photons by the
parametric resonance is the sum of the photon numbers produced when the left
and the right wall oscillates separately. But for $\Omega_{L} = \Omega_{R} $,
the interference term proportional to $\cos \phi $ is found additionally, where
$\phi $ is the phase difference between two oscillations of the walls.


title: Proposed experimental tests of the Bell-Kochen-Specker theorem

abstract:
  For a two-particle two-state system, sets of compatible propositions exist
for which quantum mechanics and noncontextual hidden-variable theories make
conflicting predictions for every individual system whatever its quantum state.
This permits a simple all-or-nothing state-independent experimental
verification of the Bell-Kochen-Specker theorem.


title: The Quantum Canonical Ensemble

abstract:
  The phase space of quantum mechanics can be viewed as the complex projective
space endowed with a Kaehlerian structure given by the Fubini-Study metric and
an associated symplectic form. We can then interpret the Schrodinger equation
as generating a Hamiltonian dynamics. Based upon the geometric structure of the
quantum phase space we introduce the corresponding natural microcanonical and
canonical ensembles. The resulting density matrix for the canonical ensemble
differs from density matrix of the conventional approach. As an illustration,
the results are applied to the case of a spin one-half particle in a heat bath
with an applied magnetic field.


title: Upper Bounds on the Size of Quantum Codes

abstract:
  Several upper bounds on the size of quantum codes are derived using the
linear programming approach. These bounds are strengthened for the linear
quantum codes.


title: Exact Evolution Operator on Non-compact Group Manifolds

abstract:
  Free quantal motion on group manifolds is considered. The Hamiltonian is
given by the Laplace -- Beltrami operator on the group manifold, and the
purpose is to get the (Feynman's) evolution kernel. The spectral expansion,
which produced a series of the representation characters for the evolution
kernel in the compact case, does not exist for non-compact group, where the
spectrum is not bounded. In this work real analytical groups are investigated,
some of which are of interest for physics. An integral representation for the
evolution operator is obtained in terms of the Green function, i.e. the
solution to the Helmholz equation on the group manifold. The alternative series
expressions for the evolution operator are reconstructed from the same integral
representation, the spectral expansion (when exists) and the sum over classical
paths. For non-compact groups, the latter can be interpreted as the (exact)
semi-classical approximation, like in the compact case. The explicit form of
the evolution operator is obtained for a number of non-compact groups.


title: On the selection of preferred consistent sets

abstract:
  The theme of this paper is the multiplicity of the consistent sets appearing
in the consistent histories approach to quantum mechanics. We propose one
criterion for choosing preferred families among them: that the physically
realizable quasiclassical domain ought to be one corresponding to classical
histories. We examine the way classical mechanics arises as a particular window
and the important role played by the canonical group and the Hamiltonian. We
finally discuss possible implications of our having a selection criterion
generally and of our criterion in particular.


title: The Hydrogen Atom as an Entangled Electron-Proton System

abstract:
  We illustrate the description of correlated subsystems by studying the simple
two-body Hydrogen atom. We study the entanglement of the electron and proton
coordinates in the exact analytical solution. This entanglement, which we
quantify in the framework of the density matrix formalism, describes
correlations in the electron-proton motion.


title: Making An Empty Promise With A Quantum Computer

abstract:
  Alice has made a decision in her mind. While she does not want to reveal it
to Bob at this moment, she would like to convince Bob that she is committed to
this particular decision and that she cannot change it at a later time. Is
there a way for Alice to get Bob's trust? Until recently, researchers had
believed that the above task can be performed with the help of quantum
mechanics. And the security of the quantum scheme lies on the uncertainty
principle. Nevertheless, such optimism was recently shattered by Mayers and by
us, who found that Alice can always change her mind if she has a quantum
computer. Here, we survey this dramatic development and its implications on the
security of other quantum cryptographic schemes.


title: An open systems approach to calculating time dependent spectra

abstract:
  A new method to calculate the spectrum using cascaded open systems and master
equations is presented. The method uses two state analyzer atoms which are
coupled to the system of interest, whose spectrum of radiation is read from the
excitation of these analyzer atoms. The ordinary definitions of a spectrum uses
two-time averages and Fourier-transforms. The present method uses only one-time
averages. The method can be used to calculate time dependent as well as
stationary spectra.


title: The quantum effects in the undulator of infinite length

abstract:
  The first order quantum correction to the power of spontaneous radiation of
electrons in an arbitrary two-component periodic magnetic field was obtained.
The phenomenon of selfpolarization of the spin of electrons in a process of
spontaneous radiation was also studied. By electron's motion in a spiral
magnetic undulator, the quantitative characteristics of selfpolarization (the
polarization degree and the relaxation time) are different from corresponding
ones in synchrotron radiation. The limiting cases of near-axis and
ultrarelativistic approximation were considered.


title:
Quantum mechanics and elements of reality inferred from joint
  measurements

abstract:
  The Einstein-Podolsky-Rosen argument on quantum mechanics incompleteness is
formulated in terms of elements of reality inferred from joint (as opposed to
alternative) measurements, in two examples involving entangled states of three
spin-1/2 particles. The same states allow us to obtain proofs of the
incompatibility between quantum mechanics and elements of reality.


title:
Comment on ``Experimental demonstration of the violation of local
  realism without Bell inequalities'' by Torgerson et al

abstract:
  We exhibit a local-hidden-variable model in agreement with the results of the
two-photon coincidence experiment made by Torgerson et al. [Phys. Lett. A 204
(1995) 323]. The existence of any such model shows that the experiment does not
exclude local realism.


title: Quantum privacy and quantum coherence

abstract:
  We derive a simple relation between a quantum channel's capacity to convey
coherent (quantum) information and its usefulness for quantum cryptography.


title: Against Measurement? -- On the Concept of Information

abstract:
  In his last article "Against `Measurement'" J. S. Bell sums up his well known
critique of the problem of explaining the measurement process within the
framework of quantum theory. In this article I will discuss the measurement
process by analysing the concept of measurement from the epistemological point
of view and I will argue against Bell that it belongs to the preconditions of
experience to necessarily end up with a "reduction of the wavefunction". I will
consider the "chain of reduction" in detail -- from pure states of S&A (system
S and measuring apparatus A) via different kinds of mixtures to pure states of
A(S). It turns out that decoherence is not sufficient to explain reduction, but
that this can be done in terms of the concept of information within a
transcendental approach.


title: Quantum conditional operator and a criterion for separability

abstract:
  We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
$\Gamma:\rho \to (Tr \rho) - \rho$, where $\rho$ is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
$\Gamma$ reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
$2\times 2$ and $2\times 3$ systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.


title:
Comment on: Preserving Coherence in Quantum Computation by Pairing
  Quantum Bits

abstract:
  We argue that several claims of paper Phys. Rev. Lett 79, 1953 (1997), by
Lu-Ming Duan and Guang-Can Guo, are questionable. In particular we stress that
the environmental noise considered by the authors belongs to a very special
class


title:
Incompatible and contradictory retrodictions in the history approach to
  quantum mechanics

abstract:
  We illustrate two simple spin examples which show that in the consistent
histories approach to quantum mechanics one can retrodict with certainty
incompatible or contradictory propositions corresponding to non-orthogonal or,
respectively, orthogonal projections. V.2 vs. V1: The example previously quoted
as "d'Espagnat's example" is now properly quoted as "Griffiths' example". A
reference to a previous work by Aharonov and Vaidman is added.


title: The WKB Approximation without Divergences

abstract:
  In this paper, the WKB approximation to the scattering problem is developed
without the divergences which usually appear at the classical turning points. A
detailed procedure of complexification is shown to generate results identical
to the usual WKB prescription but without the cumbersome connection formulas.


title:
Spectral Properties of the Two-Dimensional Laplacian with a Finite
  Number of Point Interactions

abstract:
  We discuss spectral properties of the Laplacian with multiple ($N$) point
interactions in two-dimensional bounded regions. A mathematically sound
formulation for the problem is given within the framework of the self-adjoint
extension of a symmetric (Hermitian) operator in functional analysis. The
eigenvalues of this system are obtained as the poles of a transition matrix
which has size $N$. Closely examining a generic behavior of the eigenvalues of
the transition matrix as a function of the energy, we deduce the general
condition under which point interactions have a substantial effect on
statistical properties of the spectrum.

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


title: Wave Chaos in Quantum Pseudointegrable Billiards

abstract:
  We clarify from a general perspective, the condition for the appearance of
chaotic energy spectrum in quantum pseudointegrable billiards with a point
scatterer inside.


title: Higher Order Modification of the Schroedinger Equation

abstract:
  We modify the Schr\"{o}dinger equation in a way that preserves its main
properties but makes use of higher order derivative terms. Although the
modification represents an analogy to the Doebner-Goldin modification, it can
differ from it quite distinctively. A particular model of this modification
including derivatives up to the fourth order is examined in greater detail. We
observe that a special variant of this model partially retains the linear
superposition principle for the wave packets of standard quantum mechanics
remain solutions to it. It is a peculiarity of this variant that a periodic
structure emerges naturally from its equations. As a result, a free particle,
in addition to a plane wave solution, can possess band solutions. It is argued
that this can give rise to well-focused particle trajectories. Owing to this
peculiarity, when interpreted outside quantum theory, the equations of this
modification could also be used to model pattern formation phenomena.


title: Relativistically Extended Modification of the Schroedinger Equation

abstract:
  We propose a nonlinear modification of the Schr\"{o}dinger equation that
possesses the main properties of this equation such as the Galilean invariance,
the weak separability of composite systems, and the homogeneity in the wave
function. The modification is derived from the relativistic relation between
the energy and momentum of free particle and, as such, it is the best
relativistic extension of the Schr\"{o}dinger equation that preserves the
properties in question. The only change it effectively entails in the
Schr\"{o}dinger equation involves the conserved probability current. It is
pointed out that it partially retains the linear superposition principle and
that it can be used to model the process of decoherence.


title:
Extension of the Staruszkiewicz Modification of the Schroedinger
  Equation

abstract:
  We present an extension of Staruszkiewicz's modification of the
Schr\"{o}dinger equation which preserves its main and unique feature: in the
natural system of units the modification terms do not contain any dimensional
constants. The extension, similarly as the original, is formulated in a
three-dimensional space and derives from a Galilean invariant Lagrangian. It is
pointed out that this model of nonlinearity violates the separability of
compound systems in the fundamentalist approach to this issue. In its general
form, this modification does not admit stationary states for all potentials for
which such states exist in linear quantum mechanics. This is, however, possible
for a suitable choice of its free parameters. It is only in the original
Staruszkiewicz modification that the energy of these states remains unchanged,
which marks the uniqueness of this variant of the modification.


title: Nonlinear Phase Modification of the Schroedinger Equation

abstract:
  A nonlinear modification of the Schr\"{o}dinger equation is proposed in which
the Lagrangian density for the Schr\"{o}dinger equation is extended by terms
polynomial in $\Delta^{m}\ln (\Psi^{*}/{\Psi})$ multiplied by $\Psi^{*}{\Psi}$.
This introduces a homogeneous nonlinearity in a Galilean invariant manner
through the phase $S$ rather than the amplitude $R$ of the wave function $\Psi
=R\exp (iS)$. From this general scheme we choose the simplest minimal model
defined in some reasonable way. The model in question offers the simplest way
to modify the Bohm formulation of quantum mechanics so as to allow a leading
phase contribution to the quantum potential and a leading quantum contribution
to the probability current removing asymmetries present in Bohm's original
formulation. It preserves most of physically relevant properties of the
Schr\"{o}dinger equation including stationary states of quantum-mechanical
systems. It can be thought of as the simplest model of nonlinear quantum
mechanics of extended objects among other such models that also emerge within
the general scheme proposed. The extensions of this model to $n$ particles and
the question of separability of compound systems are studied. It is noted that
there exists a weakly separable extension in addition to a strongly separable
one. The place of the general modification scheme in a broader spectrum of
nonlinear modifications of the Schr\"{o}dinger equation is discussed. It is
pointed out that the models it gives rise to have a unique definition of energy
in that the field-theoretical energy functional coincides with the
quantum-mechanical one. It is found that the Lagrangian for its simplest
variant represents the Lagrangian for a restricted version of the
Doebner-Goldin modification of this equation.


title: Is an Electromagnetic Extension of the Schroedinger Equation Possible?

abstract:
  The idea of equivalence of the free electromagnetic phase and
quantum-mechanical one is investigated in an attempt to seek modifications of
Schr\"{o}dinger's equation that could realize it. It is assumed that physically
valid realizations are compatibile with the U(1)-gauge and Galilean invariance.
It is shown that such extensions of the Schr\"{o}dinger equation do not exist,
which also means that despite their apparent similarity the quantum-mechanical
phase is essentially different from the electromagnetic one.


title:
A Nonlinear $sl(2)$ Dynamics and New Quasiclassical Solutions for a
  Class of Quantum Coupled Systems

abstract:
  Hamiltonians of a wide-spread class of strongly coupled quantum system models
are expressed as nonlinear functions of $sl(2)$ generators. It enables us to
use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states
(GCS) for solving both spectral and evolution tasks. In such a manner, using
standard variational schemes with $sl(2)$ GCS as trial functions we find new
analytical expressions for energy spectra and non-linear evolution equations
for cluster dynamics variables in mean-field approximations which are beyond
quasi-harmonic ones obtained earlier. General results are illustrated on
certain concrete models of quantum optics and laser physics.


title:
Experimental Realization of Teleporting an Unknown Pure Quantum State
  via Dual Classical and Einstein-Podolski-Rosen Channels

abstract:
  We report on a quantum optical experimental implementation of teleportation
of unknown pure quantum states. This realizes all the nonlocal aspects of the
original scheme proposed by Bennett et al. and is equivalent to it up to a
local operation. We exhibit results for the teleportation of a linearly
polarized state and of an elliptically polarized state. We show that the
experimental results cannot be explained in terms of a classical channel alone.


title: Reply to the comment "quant-ph/9710002"

abstract:
  In the comment, Zanardi and Rasetti argue that several claims in our recent
letter (Phys. Rev. Lett. 79, 1953, 1997) are questionable. The reply shows
these claims remain true.