title: A brief review on the impossibility of quantum bit commitment

abstract:
  The desire to obtain an unconditionally secure bit commitment protocol in
quantum cryptography was expressed for the first time thirteen years ago. Bit
commitment is sufficient in quantum cryptography to realize a variety of
applications with unconditional security. In 1993, a quantum bit commitment
protocol was proposed together with a security proof. However, a basic flaw in
the protocol was discovered by Mayers in 1995 and subsequently by Lo and Chau.
Later the result was generalized by Mayers who showed that unconditionally
secure bit commitment is impossible. A brief review on quantum bit commitment
which focuses on the general impossibility theorem and on recent attempts to
bypass this result is provided.


title: All bound states of NO_2 (J=0)

abstract:
  We calculated all 2967 even and odd bound states of the adiabatic ground
state of NO_2, using a modification of the ab initio potential energy surface
of Leonardi et al. [J. Chem. Phys. 105, 9051 (1996)]. The calculation was
performed by harmonic inversion of the Chebyshev correlation function generated
by a DVR Hamiltonian in Radau coordinates. The relative error for the computed
eigenenergies is $10^{-4}$ or better. Near the dissociation threshold the
density of states is about 0.3cm$^{-1}$. Statistical analysis of the states
shows some interesting structure of the rigidity parameter $\Delta_3$ as a
function of energy.


title: Quantum Relational Databases

abstract:
  The approach given by Grover can be generalised to set an upper complexity
limit to the basic operations of relational algebra on a quantum computer.
Except in special cases where indices can be used on a classical machine, the
quantum upper complexity limit is lower than the classical one.


title:
Ordered Products, $W_{\infty}$-Algebra, and Two-Variable,
  Definite-Parity, Orthogonal Polynomials

abstract:
  It has been shown that the Cartan subalgebra of $W_{\infty}$- algebra is the
space of the two-variable, definite-parity polynomials. Explicit expressions of
these polynomials, and their basic properties are presented. Also has been
shown that they carry the infinite dimensional irreducible representation of
the $su(1,1)$ algebra having the spectrum bounded from below. A realization of
this algebra in terms of difference operators is also obtained. For particular
values of the ordering parameter $s$ they are identified with the classical
orthogonal polynomials of a discrete variable, such as the Meixner,
Meixner-Pollaczek, and Askey-Wilson polynomials. With respect to variable $s$
they satisfy a second order eigenvalue equation of hypergeometric type. Exact
scattering states with zero energy for a family of potentials are expressed in
terms of these polynomials. It has been put forward that it is the
\.{I}n\"{o}n\"{u}-Wigner contraction and its inverse that form bridge between
the difference and differential calculus.


title:
Quantum communication and the creation of maximally entangled pairs of
  atoms over a noisy channel

abstract:
  We show how to create maximally entangled EPR pairs between spatially distant
atoms, each of them inside a high-Q optical cavity, by sending photons through
a general, noisy channel, such as a standard optical fiber. An error correction
scheme that uses few auxiliary atoms in each cavity effectively eliminates
photoabsorption and other transmission errors. This realizes the `absorption
free channel.' A concatenation protocol using the absorption free channel
allows for quantum communication with single qubits over distances much larger
than the coherence length of the channel.


title:
Quantum singular oscillator as a model of two-ion trap: an amplification
  of transition probabilities due to small time variations of the binding
  potential

abstract:
  Following the paper by M. Combescure [Ann. Phys. (NY) 204, 113 (1990)], we
apply the quantum singular time dependent oscillator model to describe the
relative one dimensional motion of two ions in a trap. We argue that the model
can be justified for low energy excited states with the quantum numbers $n\ll
n_{max}\sim 100$, provided that the dimensionless constant characterizing the
strength of the repulsive potential is large enough, $g_*\sim 10^5$. Time
dependent Gaussian-like wave packets generalizing odd coherent states of the
harmonic oscillator, and excitation number eigenstates are constructed. We show
that the relative motion of the ions, in contradistinction to its center of
mass counterpart, is extremely sensitive to the time dependence of the binding
harmonic potential, since the large value of $g_*$ results in a significant
amplification of the transition probabilities between energy eigenstate even
for slow time variations of the frequency.


title: Quantum Convolutional Error Correcting Codes

abstract:
  I report two general methods to construct quantum convolutional codes for
$N$-state quantum systems. Using these general methods, I construct a quantum
convolutional code of rate 1/4, which can correct one quantum error for every
eight consecutive quantum registers.


title: The Role of dimensionality in the stability of a confined Bose gas

abstract:
  We study analytically the ground-state stability of a Bose-Einstein
condensate (BEC) confined in an harmonic trap with repulsive or attractive
zero-range interaction by minimizing the energy functional of the system. In
the case of repulsive interaction the BEC mean radius grows by increasing the
number of bosons, instead in the case of attractive interaction the BEC mean
radius decreases by increasing the number of bosons: to zero if the system is
one-dimensional and to a minimum radius, with a maximum number of bosons, if
the system is three-dimensional.


title:
Random motion of quantum reactive harmonic oscillator. Thermodynamics of
  Vacuum of Asymptotic Subspace

abstract:
  The system of oscillator interacting with vacuum is considered as a problem
of random motion of quantum reactive harmonic oscillator (QRHO). It is
formulated in terms of a wave functional regarded as complex probability
process in the extended space. This wave functional obeys some stochastic
differential equation (SDE). Based on the nonlinear Langevin type SDE of second
order, introduced in the functional space R{W(t)}, the variables in original
equation are separated. The general measure in the space R{W(t)} of the
Fokker-Plank type is obtained and expression for total wave function (wave
mixture) of random QRHO is constructed as functional expansion over the
stochastic basis set. The pertinent transition matrix S_br is constructed. For
Wiener type measure W(t) of functional space the exact representation for
''vacuum-vacuum'' transition probability is obtained. The thermodynamics of
vacuum is described in detail for the asymptotic space R1_as. The exact values
for Energy, shift and expansion of ground state of oscillator and its Entropy
are calculated.


title: Direct and indirect strategies for phase measurement

abstract:
  Recently, Torgerson and Mandel [Phys. Rev. Lett. 76, 3939 (1996)] have
reported a disagreement between two schemes for measuring the phase difference
of a pair of optical fields. We analyze these schemes and derive their
associated phase-difference probability distributions, including both their
strong and weak field limits. Our calculation confirms the main point of
Torgerson and Mandel of the non-uniqueness of an operational definition of the
phase distribution. We further discuss the role of postselection of data and
argue that it cannot meaningfully improve the sensitivity.


title: Reversible Mapping for Tree Structured Quantum Computation

abstract:
  A hierarchical, reversible mapping between levels of tree structured
computation, applicable for structuring the Quantum Computation algorithm for
NP-complete problem is presented. It is proven that confining the state of a
quantum computer to a subspace of the available Hilbert space, where states are
consistent with the problem constraints, can be done in polynomial time. The
proposed mapping, together with the method of state reduction can be
potentially used for solving NP-complete problems in polynomial time.


title: Multi-access channels in quantum information theory

abstract:
  The multi-access channels in quantum information theory are considered.
Classical messages from independent sources, which are represented as some
quantum states, are transported by a channel to one address. The messages can
interact with each other and with external environment. After statement of
problem and proving some general results we investigate physically important
case when information is transported by states of electromagnetic field.
One-way communication by noisy quantum channels is also considered.


title:
Limits for compression of quantum information carried by ensembles of
  mixed states

abstract:
  We consider the problem of compression of the quantum information carried by
ensemble of mixed states. We prove that for arbitrary coding schemes the least
number of qubits needed to convey the signal states asymptotically faithfully
is bounded from below by the Holevo function
$S(\varrho)-\sum_ip_iS(\varrho_i)$. We also show that a compression protocol
can be composed with another one, provided that the latter offers perfect
transmission. Such a compound protocol is applied to the case of binary source.
It is conjectured to reach the obtained bound. Finally, we point out that in
the case of mixed signal states there could be a difference between the maximal
compression rates at the coding schemes which are ``blind'' to the signal and
the ones which assume the knowledge about the identities of the signal states.


title: Nonlocality and Bohr's Reply to EPR

abstract:
  David Mermin's recent paper with the same title as this one makes it clear
that his claim to have found a gap in my reasoning rests on his claim that my
argument violates a criterion for meaningfulness of counterfactual statements
that I myself had set down. I set down no such requirement. But I am willing to
accept it as a conservative sufficient condition. This already entails, within
my proof, that nature must have a deep structure that extends beyond what
actually occurs. It imposes, without appeal to the notion of determinism or
hidden variables, constraints connecting, at the macroscopic level, what did
occur to what would have occurred if certain quantum choices had gone
differently. All the statements in the proof have natural meanings within the
context of an examination of that deep structure.


title: A Solution to the Quantum Measurement Problem

abstract:
  A new formulation of quantum mechanics is developed which does not require
the concept of the wave-particle duality. Rather than assigning probabilities
to outcomes, probabilities are instead assigned to entire fine-grained
histories. The formulation is fully relativistic and applicable to
multi-particle systems. It shall be shown that this new formulation makes the
same experimental predictions as quantum field theory, but without having to
rely upon the notion of a system evolving in a superposition of quantum states
until collapsed by an observation. It is thus free from the problem of deciding
what exactly constitutes an observation (the measurement problem) and may
therefore be applied just as readily to the macroscopic world as to the
microscopic.


title:
Hilbert Space or Gelfand Triplet - Time Symmetric or Time Asymmetric
  Quantum Mechanics

abstract:
  Intrinsic microphysical irreversibility is the time asymmetry observed in
exponentially decaying states. It is described by the semigroup generated by
the Hamiltonian $\QTR{it}{H}$ of the quantum physical system, not by the
semigroup generated by a Liouvillian $\QTR{it}{L}$ which describes the
irreversibility due to the influence of an external reservoir or measurement
apparatus. The semigroup time evolution generated by $\QTR{it}{H}$ is
impossible in the Hilbert Space (HS) theory, which allows only time symmetric
boundary conditions and an unitary group time evolution. This leads to problems
with decay probabilities in the HS theory. To overcome these and other problems
(non-existence of Dirac kets) caused by the Lebesgue integrals of the HS, one
extends the HS to a Gel'fand triplet, which contains not only Dirac kets, but
also generalized eigenvectors of the self-adjoint $\QTR{it}{H}$ with complex
eigenvalues ($E_R-i\Gamma /2$) and a Breit-Wigner energy distribution. These
Gamow states $\psi ^G$ have a time asymmetric exponential evolution. One can
derive the decay probability of the Gamow state into the decay products
described by $\Lambda $ from the basic formula of quantum mechanics
$\QTR{cal}{P}(t)=Tr(|\psi ^G> < \psi ^G|\Lambda)$, which in HS quantum
mechanics is identically zero. From this result one derives the decay rate
$\QTR{group}{\dot c}(t)$ and all the standard relations between
$\QTR{group}{\dot c}(0)$, $\Gamma $ and the lifetime $\tau_R$ used in the
phenomenology of resonance scattering and decay. In the Born approximation one
obtains Dirac's Golden Rule.


title: Change of Variable as Borel Resummation of Semiclassical Series

abstract:
  It is shown that a change of variable in 1-dim Schroedinger equation applied
to the Borel summable fundamental solutions [Giller] is equivalent to Borel
resummation of the fundamental solutions multiplied by suitably chosen
$\hbar$-dependent constant. This explains why change of variable can improve
JWKB formulae [Giller, Milczarski]. It is shown also that a change of variable
alone cannot provide us with the exact JWKB formulae.


title: Computing Local Invariants of Qubit Systems

abstract:
  We investigate means to describe the non-local properties of quantum systems
and to test if two quantum systems are locally equivalent. For this we consider
quantum systems that consist of several subsystems, especially multiple qubits.
We compute invariant polynomials, i. e., polynomial functions of the entries of
the density operator which are invariant under local unitary operations.
  As an example, we consider a system of two qubits. We compute the Molien
series for the corresponding representation which gives information about the
number of linearly independent invariants. Furthermore, we present a set of
polynomials which generate all invariants (at least) up to degree 23. Finally,
the use of invariants to check whether two density operators are locally
equivalent is demonstrated.


title: Rectangular Well as Perturbation

abstract:
  We discuss a finite rectangular well as a perturbation for the infinite one
with a depth $\lambda^2$ of the former as a perturbation parameter. In
particular we consider a behaviour of energy levels in the well as functions of
complex $\lambda$. It is found that all the levels of the same parity are
defined on infinitely sheeted Riemann surfaces which topological structures are
described in details. These structures differ considerably from those found in
models investigated earlier. It is shown that perturbation series for all the
levels converge what is in contrast with the known results of Bender and Wu.
The last property is shown to hold also for the finite rectangular well with
Dirac delta barier as a perturbation considered earlier by Ushveridze.


title: Cryptographic Distinguishability Measures for Quantum Mechanical States

abstract:
  This paper, mostly expository in nature, surveys four measures of
distinguishability for quantum-mechanical states. This is done from the point
of view of the cryptographer with a particular eye on applications in quantum
cryptography. Each of the measures considered is rooted in an analogous
classical measure of distinguishability for probability distributions: namely,
the probability of an identification error, the Kolmogorov distance, the
Bhattacharyya coefficient, and the Shannon distinguishability (as defined
through mutual information). These measures have a long history of use in
statistical pattern recognition and classical cryptography. We obtain several
inequalities that relate the quantum distinguishability measures to each other,
one of which may be crucial for proving the security of quantum cryptographic
key distribution. In another vein, these measures and their connecting
inequalities are used to define a single notion of cryptographic exponential
indistinguishability for two families of quantum states. This is a tool that
may prove useful in the analysis of various quantum cryptographic protocols.


title: Reply to Unruh

abstract:
  William Unruh has suggested (quant-ph/9710032) that a certain counterfactual
statement in my recent nonlocality proof should be re-interpreted in a way that
would block the proof. I give reason's why that statement should not be
re-interpreted.


title: Quantum and classical descriptions of a measuring apparatus

abstract:
  A measuring apparatus is described by quantum mechanics while it interacts
with the quantum system under observation, and then it must be given a
classical description so that the result of the measurement appears as
objective reality. Alternatively, the apparatus may always be treated by
quantum mechanics, and be measured by a second apparatus which has such a dual
description. This article examines whether these two different descriptions are
mutually consistent. It is shown that if the dynamical variable used in the
first apparatus is represented by an operator of the Weyl-Wigner type (for
example, if it is a linear coordinate), then the conversion from quantum to
classical terminology does not affect the final result. However, if the first
apparatus encodes the measurement in a different type of operator (e.g., the
phase operator), the two methods of calculation may give different results.


title: Multi-Particle Entanglement Purification Protocols

abstract:
  Purification schemes for multi-particle entangled states cannot be treated as
straightforward extensions of those for two particles because of the lack of
symmetry they possess. We propose purification protocols for a wide range of
mixed entangled states of many particles. These are useful for understanding
entanglement, and will be of practical significance in multi-user cryptographic
schemes or distributed quantum computation and communication. We show that
operating locally on multi-particle entangled states directly is more efficient
than relying on two-particle purification.


title:
Note on the stability of a confined Bose gas: Comment on
  quant-ph/9712030 by L. Salasnich

abstract:
  We demonstrate analytically that a Bose-Einstein condensate confined in a
harmonic trap with zero-range attractive interparticle interactions is unstable
if there is more than 1 boson. Replacing the zero-range interaction by a
short-range attractive interaction lifts the instability, and leads to a
pronounced clustering, by which the particles leak out of the condensate.


title: Quantum Mechanics is Either Non-Linear Or Non-Introspective

abstract:
  The measurement conundrum seems to have plagued quantum mechanics for so long
that impressions of an inconsistency amongst its axioms have spawned.
  A demonstration that such purported inconsistency is fictitious may then be
in order and is presented here.
  An exclusion principle of sorts emerges, stating that quantum mechanics
cannot be simultaneously linear and introspective (self-observing).


title: Fault-tolerant quantum computation

abstract:
  The discovery of quantum error correction has greatly improved the long-term
prospects for quantum computing technology. Encoded quantum information can be
protected from errors that arise due to uncontrolled interactions with the
environment, or due to imperfect implementations of quantum logical operations.
Recovery from errors can work effectively even if occasional mistakes occur
during the recovery procedure. Furthermore, encoded quantum information can be
processed without serious propagation of errors. In principle, an arbitrarily
long quantum computation can be performed reliably, provided that the average
probability of error per gate is less than a certain critical value, the
accuracy threshold. It may be possible to incorporate intrinsic fault tolerance
into the design of quantum computing hardware, perhaps by invoking topological
Aharonov-Bohm interactions to process quantum information.


title: Relativistic Nonlocality in experiments with successive impacts

abstract:
  Relativistic Nonlocality is applied to experiments in which one of the
photons impacts successively at two beam-splitters. It is discussed whether a
time series with 2 non-before impacts can be produced with beam-splitters at
rest, and such an experiment may allow us to decide between Quantum Mechanics
(QM) and Relativistic Nonlocality (RNL).


title: The zeropoint field - no longer a ghost

abstract:
  We develop a local realist analysis of parametric down conversion, based on
the recognition that the pump field, instead of down converting spontaneously,
does so through its nonlinear coupling with a real zeropoint, or "vacuum"
electromagnetic field. The theory leads tothe prediction of a new phenomenon -
that, in addition to the main down-conversion rainbow, there is a satellite
rainbow, whose intensity is about 3 per cent of the main one. Confirmation of
this prediction will call seriously into question the current description of
the light field in terms of photons.
  The present article extends the analysis of its predecessors (this archive,
numbers 9711029 and 9712001) to take account of the pump's polarization>


title: Quantum Computer Can Not Speed Up Iterated Applications of a Black Box

abstract:
  Let a classical algorithm be determined by sequential applications of a black
box performing one step of this algorithm. If we consider this black box as an
oracle which gives a value F(a) for any query a, we can compute T sequential
applications of F on a classical computer relative to this oracle in time T.
  It is proved that if T=O(2^{n/7}), where n is the length of input, then the
result of T sequential applications of F can not be computed on quantum
computer with oracle for F for all possible F faster than in time \Omega (T).
This means that there is no general method of quantum speeding up of classical
algorithms provided in such a general method a classical algorithm is regarded
as iterated applications of a given black box.
  For an arbitrary time complexity T a lower bound for the time of quantum
simulation was found to be \Omega (T^{1/2}).


title:
Quantum mechanics of lattice gas automata. II. Boundary conditions and
  other inhomogeneities

abstract:
  We continue our analysis of the physics of quantum lattice gas automata
(QLGA). Previous work has been restricted to periodic or infinite lattices;
simulation of more realistic physical situations requires finite sizes and
non-periodic boundary conditions. Furthermore, envisioning a QLGA as a
nanoscale computer architecture motivates consideration of inhomogeneities in
the `substrate'; this translates into inhomogeneities in the local evolution
rules. Concentrating on the one particle sector of the model, we determine the
various boundary conditions and rule inhomogeneities which are consistent with
unitary global evolution. We analyze the reflection of plane waves from
boundaries, simulate wave packet refraction across inhomogeneities, and
conclude by discussing the extension of these results to multiple particles.


title: A diakoptic approach to quantum computation

abstract:
  In the diakoptic approach, mechanisms are divided into simpler parts
interconnected in some standard way (say by a "mechanical connection''). We
explore the possibility of applying this approach to quantum mechanisms: the
specialties of the quantum domain seem to yield a richer result. First parts
are made independent of each other by assuming that connections are removed.
The overall state would thus become a superposition of tensor products of the
eigenstates of the independent parts. Connections are restored by projecting
off all the tensor products which violate them. This would be performed by
particle statistics, under a special interpretation thereof. The NP-complete
problem of testing the satisfiability of a Boolean network is approached in
this way. The diakoptic approach appears to be able of taming the quantum whole
without clipping its richness.


title: Cryptography, Quantum Computation and Trapped Ions

abstract:
  The significance of quantum computation for cryptography is discussed.
Following a brief survey of the requirements for quantum computational
hardware, an overview of the ion trap quantum computation project at Los Alamos
is presented. The physical limitations to quantum computation with trapped ions
are analyzed and an assessment of the computational potential of the technology
is made.


title:
Ladder proof of nonlocality without inequalities and without
  probabilities

abstract:
  The ladder proof of nonlocality without inequalities for two spin half
particles proposed by Hardy et al. (Phys. Rev. Lett. 79 (1997) 2755) works only
for nonmaximally entangled states and goes through for 50% of pairs at the
most. A similar ladder proof for two spin-1 particles in a maximally entangled
state is presented. In its simplest form, the proof goes through for 17% of
pairs. An extended version works for 100% of pairs. The proof can be extended
to any maximally entangled state of two spin-s particles (with s equal or
greater than 1).


title: A new approximation scheme in quantum mechanics

abstract:
  An approximation method which combines the perturbation theory with the
variational calculation is constructed for quantum mechanical problems. Using
the anharmonic oscillator and the He atom as examples, we show that the present
method provides an efficient scheme in estimating both the ground and the
excited states. We also discuss the limitations of the present method.


title: New Perturbation Theory for Nonstationary Anharmonic Oscillator

abstract:
  The new perturbation theory for the problem of nonstationary anharmonic
oscillator with polynomial nonstationary perturbation is proposed. As a zero
order approximation the exact wave function of harmonic oscillator with
variable frequency in external field is used. Based on some intrinsic
properties of unperturbed wave function the variational-iterational method is
proposed, that make it possible to correct both the amplitude and the phase of
wave function. As an application the first order correction are proposed both
for wave function and S-matrix elements for asymmetric perturbation potential
of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude
''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail
depending on perturbation parameter $\lambda $ (including strong coupling
region $% \lambda $ $\sim 1$) and one-dimensional refraction coefficient $\rho
$.


title: Towards the Born-Weyl Quantization of Fields

abstract:
  Elements of the quantization in field theory based on the covariant
polymomentum Hamiltonian formalism (the De Donder-Weyl theory), a possibility
of which was originally discussed in 1934 by Born and Weyl, are developed. The
approach is based on a recently proposed graded Poisson bracket on differential
forms in field theory (see e.g. hep-th/9709229). A covariant analogue of the
Schr\"odinger equation for a hypercomplex wave function on the space of field
and space-time variables is put forward. It is shown to lead to the De
Donder-Weyl Hamilton-Jacobi equations in quasiclassical limit. A possible
relation to the functional Schr\"odinger picture in quantum field theory is
outlined.


title:
Reply to a Comment on "the Role of Dimensionality in the Stability of a
  Confined Condensed Bose Gas"

abstract:
  As pointed out by the authors of the comment quant-ph/9712046, in our paper
quant-ph/9712030 we studied in detail the metastability of a Bose-Einstein
Condensate (BEC) confined in an harmonic trap with zero-range interaction. As
well known, the BEC with attractive zero-range interaction is not stable but
can be metastable. In our paper we analyzed the role of dimensionality for the
metastability of the BEC with attractive and repulsive interaction.


title:
Expressing the operations of quantum computing in multiparticle
  geometric algebra

abstract:
  We show how the basic operations of quantum computing can be expressed and
manipulated in a clear and concise fashion using a multiparticle version of
geometric (aka Clifford) algebra. This algebra encompasses the product operator
formalism of NMR spectroscopy, and hence its notation leads directly to
implementations of these operations via NMR pulse sequences.


title: Quantum Theory and Spacelike Measurements

abstract:
  Experimentally observed violations of Bell inequalities rule out local
realistic theories. Consequently, the quantum state vector becomes a strong
candidate for providing an objective picture of reality. However, such an
ontological view of quantum theory faces difficulties when spacelike
measurements on entangled states have to be described, because time ordering of
spacelike events can change under Lorentz-Poincar\'e transformations. In the
present paper it is shown that a necessary condition for consistency is to
require state vector reduction on the backward light-cone. A fresh approach to
the quantum measurement problem appears feasible within such a framework.


title: Does Schrodinger's Cat Know Something That Schrodinger Does Not Know?

abstract:
  Macroscopic objects appear to have definite positions. In a many-worlds
interpretation of quantum theory, this appearance is an illusion; the correct
view is the "view from outside" in which even macroscopic objects are in
general in a superposition of different positions. In the Bohm model, objects
really are in definite positions. This additional aspect of reality is
accessible only from the "inside"; thus in the Bohm model the view from inside
can be more correct than is the view from outside.


title: Quantum cloning without signaling

abstract:
  Perfect Quantum Cloning Machines (QCM) would allow to use quantum nonlocality
for arbitrary fast signaling. However perfect QCM cannot exist. We derive a
bound on the fidelity of QCM compatible with the no-signaling constraint. This
bound equals the fidelity of the Bu\v{z}ek-Hillery QCM.


title: Free-space quantum key distribution

abstract:
  A working free-space quantum key distribution (QKD) system has been developed
and tested over a 205-m indoor optical path at Los Alamos National Laboratory
under fluorescent lighting conditions. Results show that free-space QKD can
provide secure real-time key distribution between parties who have a need to
communicate secretly.


title: Realization of a collective decoding of codeword states

abstract:
  This was also extended from the previous article quant-ph/9705043, especially
in a realization of the decoding process.


title:
Quantum-state synthesis of multi-mode bosonic fields: Preparation of
  arbitrary states of 2-D vibrational motion of trapped ions

abstract:
  We present a universal algorithm for an efficient deterministic preparation
of an arbitrary two--mode bosonic state. In particular, we discuss in detail
preparation of entangled states of a two-dimensional vibrational motion of a
trapped ion via a sequence of laser stimulated Raman transitions. Our formalism
can be generalized for multi-mode bosonic fields. We examine stability of our
algorithm with respect to a technical noise.


title: Universal optimal cloning of qubits and quantum registers

abstract:
  We review our recent work on the universal (i.e. input state independent)
optimal quantum copying (cloning) of qubits. We present unitary transformations
which describe the optimal cloning of a qubit and we present the corresponding
quantum logical network. We also present network for an optimal quantum copying
``machine'' (transformation) which produces N+1 identical copies from the
original qubit. Here again the quality (fidelity) of the copies does not depend
on the state of the original and is only a function of the number of copies, N.
In addition, we present the machine which universaly and optimally clones
states of quantum objects in arbitrary-dimensional Hilbert spaces. In
particular, we discuss universal cloning of quantum registers.


title: Large moments in external fields of cubic group symmetry

abstract:
  We predict that large moments $J$, placed into a crystal field with the cubic
point symmetry group, differ by their spectrum and magnetic properties. E. g.,
properties of the odd-integer moments are different from those of the
even-integer. The effect is due to Berry's phases gained by the moment, when it
tunnels between minima of the external field. Two cases of the group $O$ are
classified, namely, 6- and 8-fold coordinations. The spectrum and degeneration
of energy levels depend on a remainder $\{J/n\}$, where the divisor $n=4$ and 3
for 6-fold and 8-fold coordination respectively. %High symmetry results in a
finite magnetic moment for half-integer %and some integer moments, for example
odd $J$ at 6-fold coordination. Large moments in the cubic environment can be
realized by diluted alloys ${R}_{1-x}{R}_{x}'$Sb, where R=Lu, La, and R$'$=Tb,
Dy, Ho, Er.


title: Yet another comment on "Nonlocal character of quantum theory"

abstract:
  There has been considerable discussion of the claim by Stapp [Am. J. Phys.
65, 300 (1997)] that quantum theory is incompatible with locality. In this note
I analyze the meaning of some of the statements used in this discussion.


title: Quantum channels showing superadditivity in capacity

abstract:
  This was significantly extended from the previous article
quant-ph/9705043,especially in an information theoretic aspect, by adding new
results.


title: Extending the quantal adiabatic theorem: Geometry of noncyclic motion

abstract:
  We show that a noncyclic phase of geometric origin has to be included in the
approximate adiabatic wave function. The adiabatic noncyclic geometric phase
for systems exhibiting a conical intersection as well as for an Aharonov-Bohm
situation is worked out in detail. A spin-1/2 experiment to measure the
adiabatic noncyclic geometric phase is discussed. We also analyze some
misconceptions in the literature and textbooks concerning noncyclic geometric
phases.


title: Quantum Entanglement and the Nonexistence of Superluminal Signals

abstract:
  This paper shows that ordinary quantum mechanics is not consistent with the
superluminal transmission of classical information.


title:
Canonical equivalence of quantum systems, multimode squeezed states and
  Robertson relation

abstract:
  It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum
systems can be related by means of time-dependent canonical transformations
(CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides
with the invariance group of H(t). Quadratic Hamiltonians can be diagonalized
by means of linear time-dependent CT. The diagonalization can be explicitly
carried out in the case of stationary and some nonstationary quadratic H.
Linear CT can diagonalize the uncertainty matrix \sigma(\rho) for canonical
variables p_k, q_j in any state \rho, i.e., \sigma(\rho) is symplectically
congruent to a diagonal uncertainty matrix. For multimode squeezed canonical
coherent states (CCS) and squeezed Fock states with equal photon numbers in
each mode \sigma is symplectic itself. It is proved that the multimode
Robertson uncertainty relation is minimized only in squeezed CCS.


title:
Annihilators of Irreducible Modules and Kinematical Constraints of Pair
  Operators

abstract:
  The kinematical constraints of pair operators in nuclear collective motion,
pointed out by Yamamura and identified by Nishiyama as relations between so(2n)
generators, are recognized as equations satisfied by second-degree annihilators
(deduced in previous work) of irreducible so(2n)-modules. The recursion
relations for Nishiyama's tensors and their dependence on the parity of the
tensor degree are explained. An explanation is also given for the recursion
relation for the sp(2n) tensors pointed out by Hwa and Nuyts. The statements
for the algebras so(2n) and sp(2n) are proved simultaneously.


title: Center of the charged particle orbit for any linear gauge

abstract:
  In the case of a constant uniform magnetic field it can be assumed, without
the loss of generality, that the vector potential (the gauge) is a linear
function of position, i.e. it could be considered as a three-dimensional real
matrix or, more generally in an n-dimensional space, as a tensor A of the rank
two. The magnetic tensor H is obtained from A by antisymmetrization, i.e.
H=A-A^T. It is shown that the transpose of A plays a special role, since it
determines the operator of the orbit center of a charged particle moving in an
external magnetic field H. Moreover, this movement can be considered as a
combination of N<=n independent cyclotronic movements in orthogonal planes
(cyclotron orbits) with quantized energies, whereas in other n-2N dimensions
the particle is completely free with a continuous energy spectrum. The proposed
approach enables introduction of the four-dimensional space-time and, after
some generalizations, non-linear gauges.

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


title:
Clones and other interferance effects in the evolution of angular
  momentum coherent states

abstract:
  The aim of this article is to present the interference effects which occur
during the time evolution of simple angular wave packets (WP) which can be
associated to a diatomic rigid molecule (heteronuclear) or to a quantum rigid
body with axial symmetry like a molecule or a nucleus. The time evolution is
understood entirely within the frame of fractional revivals discovered by
Averbukh and Perelman since the energy spectrum is exactly quadratic. Our
objectives are to study how these interference effects differ when there is a
change of the initial WP. For this purpose we introduce a two parameter set of
angular momentum coherent states. From one hand this set emerge quite naturally
from the three dimensional coherent states of the harmonic oscillator, from
another hand this set is shown to be buit from intelligent spin states.We have
also compared our coherent states to some previously constructed using boson
representation of angular momentum. The time evolution of coherent states for
symmetric top is also discussed.

categories: quant-ph math-ph math.MP nucl-th physics.atom-ph physics.chem-ph


title:
Symmetry as a source of hidden coherent structures in quantum physics:
  general outlook and examples

abstract:
  A general algebraic approach, incorporating both invariance groups and
dynamic symmetry algebras, is developed to reveal hidden coherent structures
(closed complexes and configurations) in quantum many-body physics models due
to symmetries of their Hamiltonians $H$. Its general ideas are manifested on
some recent new examples: 1) G-invariant bi-photons and a related
SU(2)-invariant treatment of unpolarized light; 2) quasi-spin clusters in
nonlinear models of quantum optics; 3) construction of composite particles and
(para)fields from G-invariant clusters due to internal symmetries.


title: The Electromagnetic Coupling in Kemmer-Duffin-Petiau Theory

abstract:
  We analyse the electromagnetic coupling in the Kemmer-Duffin-Petiau (KDP)
equation. Since the KDP--equation which describes spin-0 and spin-1 bosons is
of Dirac-type, we examine some analogies and differences from the Dirac
equation. The main difference to the Dirac equation is that the KDP equation
contains redundant components. We will show that as a result certain
interaction terms in the Hamilton form of the KDP equation do not have a
physical meaning and will not affect the calculation of physical observables.
We point out that a second order KDP equation derived by Kemmer as an analogy
to the second order Dirac equation is of limited physical applicability as (i)
it belongs to a class of second order equations which can be derived from the
original KDP equation and (ii) it lacks a back-transformation which would allow
one to obtain solutions of the KDP equation out of solutions of the second
order equation. We therefore suggest a different higher order equation which,
as far as the solutions for the wave functions are concerned, is equivalent to
the orginal first order KDP wave equation.


title: Quasi-Exactly Solvable Potentials with Two Known Eigenstates

abstract:
  A new supersymmetry method for the generation of the quasi-exactly solvable
(QES) potentials with two known eigenstates is proposed. Using this method we
obtained new QES potentials for which we found in explicit form the energy
levels and wave functions of the ground state and first excited state.


title: Security of Quantum Key Distribution Against All Collective Attacks

abstract:
  Security of quantum key distribution against sophisticated attacks is among
the most important issues in quantum information theory. In this work we prove
security against a very important class of attacks called collective attacks
(under a compatible noise model) which use quantum memories and gates, and
which are directed against the final key. Although attacks stronger than the
collective attacks can exist in principle, no explicit example was found and it
is conjectured that security against collective attacks implies also security
against any attack.


title: Quantum-state control in optical lattices

abstract:
  We study the means to prepare and coherently manipulate atomic wave packets
in optical lattices, with particular emphasis on alkali atoms in the
far-detuned limit. We derive a general, basis independent expression for the
lattice operator, and show that its off-diagonal elements can be tailored to
couple the vibrational manifolds of separate magnetic sublevels. Using these
couplings one can evolve the state of a trapped atom in a quantum coherent
fashion, and prepare pure quantum states by resolved-sideband Raman cooling. We
explore the use of atoms bound in optical lattices to study quantum tunneling
and the generation of macroscopic superposition states in a double-well
potential. Far-off-resonance optical potentials lend themselves particularly
well to reservoir engineering via well controlled fluctuations in the
potential, making the atom/lattice system attractive for the study of
decoherence and the connection between classical and quantum physics.


title: Quantum inseparability as local pseudomixture

abstract:
  We show how to decompose any density matrix of the simplest binary composite
systems, whether separable or not, in terms of only product vectors. We
determine for all cases the minimal number of product vectors needed for such a
decomposition. Separable states correspond to mixing from one to four pure
product states. Inseparable states can be described as pseudomixtures of four
or five pure product states, and can be made separable by mixing them with one
or two pure product states.


title:
Resolved-sideband Raman cooling to the ground state of an optical
  lattice

abstract:
  We trap neutral Cs atoms in a two-dimensional optical lattice and cool them
close to the zero-point of motion by resolved-sideband Raman cooling. Sideband
cooling occurs via transitions between the vibrational manifolds associated
with a pair of magnetic sublevels and the required Raman coupling is provided
by the lattice potential itself. We obtain mean vibrational excitations
\bar{n}_x \approx \bar{n}_y \approx 0.01, corresponding to a population \sim
98% in the vibrational ground state. Atoms in the ground state of an optical
lattice provide a new system in which to explore quantum state control and
subrecoil laser cooling


title: Phase space caustics in multi-component systems

abstract:
  As examples of quantum-"classical" coupling systems, multi-component systems
are studied by semiclassical evaluations of the Feynman kernels in the
coherent-state representation. From the observation of the phase space caustics
due to the presence of the internal degree of freedom (IDF), two phenomena are
explained in terms of the semiclassical theory: (1) The quantum oscillations of
the IDF induce quantum interference patterns in the Hushimi representation; (2)
Chaotic dynamics destroys the coherence of the quantum oscillations.


title:
Implementation of a Quantum Algorithm to Solve Deutsch's Problem on a
  Nuclear Magnetic Resonance Quantum Computer

abstract:
  We demonstrate the use of an NMR quantum computer based on the pyrimidine
base cytosine, and the implementation of a quantum algorithm to solve Deutsch's
problem.


title:
Reply on the ``Comment on `Loss-error compensation in quantum- state
  measurements' ''

abstract:
  The authors of the Comment [G. M. D'Ariano and C. Macchiavello to be
published in Phys. Rev. A, quant-ph/9701009] tried to reestablish a 0.5
efficiency bound for loss compensation in optical homodyne tomography. In our
reply we demonstrate that neither does such a rigorous bound exist nor is the
bound required for ruling out the state reconstruction of an individual system
[G. M. D'Ariano and H. P. Yuen, Phys. Rev. Lett. 76, 2832 (1996)].


title: Coherent states for a quantum particle on a circle

abstract:
  The coherent states for the quantum particle on the circle are introduced.
The Bargmann representation within the actual treatment provides the
representation of the algebra $[\hat J,U]=U$, where $U$ is unitary, which is a
direct consequence of the Heisenberg algebra $[\hat \phi, \hat J]=i$, but it is
more adequate for the study of the circlular motion.


title: Antibunching of distorted optical wave packets at a beam splitter

abstract:
  Interference of single-photon wave packets at a beam splitter usually leads
to an anticorrelation of the light intensity in the two output ports of the
beam splitter. The effect may be regarded as ``bunching'' of the photons at the
beam splitter and has widely been interpreted as a result of quantum mechanical
interference between the probability amplitudes of indistinguishable bosonic
particles. Here we show that when the wave packets are sufficiently distorted,
then the opposite behaviour is observed, i.e., simultaneous clicks of the
photodetectors in the two output ports are favoured, which may be regarded as
``antibunching'' of the photons at the beam splitter.


title: Borel Summable Solutions to 1D Schr\"odinger Equation

abstract:
  It is shown that so called fundamental solutions the semiclassical expansions
of which have been established earlier to be Borel summable to the solutions
themselves appear also to be the unique solutions to the 1D Schr\"odinger
equation having this property. Namely, it is shown in this paper that for the
polynomial potentials the Borel function defined by the fundamental solutions
can be considered as the canonical one. The latter means that any Borel
summable solution can be obtained by the Borel transformation of this unique
canonical Borel function multiplied by some $\hbar$-dependent and Borel
summable constant. This justify the exceptional role the fundamental solutions
play in 1D quantum mechanics and completes the relevant semiclassical theory
relied on the Borel resummation technique and developed in our other papers.


title:
On Stapp-Unruh-Mermin Discussion on Quantum Nonlocality: Quantum Jumps
  and Relativity

abstract:
  We argue that the participants of the discussion have overlooked an essential
circumstance, in view of which Stapp's fifth proposition fails. The
circumstance is that though $L$ and $R$ measurements, being causally separated,
are not invariantly time ordered, quantum-jump hypersurfaces associated with
the measurements are causelikewise ordered. Stapp's fifth proposition is true
iff $L$ hypersurface precedes $R$ one; but within the limits of special
relativity, it is impossible to determine the causelike order of those
hypersurfaces. The entire Stapp's construct is revised.


title:
Exact Green's functions for delta-function potentials and
  renormalization in quantum mechanics

abstract:
  We present a simple recipe to construct the Green's function associated with
a Hamiltonian of the form H=H_0+V, where H_0 is a Hamiltonian for which the
associated Green's function is known and V is a delta-function potential. We
apply this result to the case in which H_0 is the Hamiltonian of a free
particle in D dimensions. Field theoretic concepts such as regularization,
renormalization, dimensional transmutation and triviality are introduced
naturally in order to deal with an infinity which shows up in the formal
expression of the Green's function for D>1.


title: Minimum Inaccuracy for Traversal-Time

abstract:
  Using various model clocks it has been shown that the time-of-arrival cannot
be measured more accurately than 1/E where E is the kinetic energy of a free
particle. However, this result has never been proved. In this paper, we show
that a violation of the above limitation for the transit-time, implies a
violation of the Heisenberg uncertainty relation.


title: Quantum radiation in external background fields

abstract:
  A canonical formalism is presented which allows for investigations of quantum
radiation induced by localized, smooth disturbances of classical background
fields by means of a perturbation theory approach. For massless,
non-selfinteracting quantum fields at zero temperature we demonstrate that the
low-energy part of the spectrum of created particles exhibits a non-thermal
character. Applied to QED in varying dielectrics the response theory approach
facilitates to study two distinct processes contributing to the production of
photons: the squeezing effect due to space-time varying properties of the
medium and of the velocity effect due to its motion. The generalization of this
approach to finite temperatures as well as the relation to sonoluminescence is
indicated.


title:
Solving in the quantum computer every classical NP problem in polynomial
  time

abstract:
  This paper has been withdrawn by the author due to a crucial error in eq.59.
I apologize for the inconveniences.


title: Experimental realization of a quantum algorithm

abstract:
  Nuclear magnetic resonance techniques are used to realize a quantum algorithm
experimentally. The algorithm allows a simple NMR quantum computer to determine
global properties of an unknown function requiring fewer function ``calls''
than is possible using a classical computer.


title:
Another Way to Perform the Quantum Fourier Transform in Linear Parallel
  Time

abstract: This paper has been withdrawn.


title: Standard Quantum Limits for broadband position measurement

abstract:
  I utilize the Caves-Milburn model for continuous position measurements to
formulate a broadband version of the Standard Quantum Limit (SQL) for
monitoring the position of a free mass, and illustrate the use of Kalman
filtering to recover the SQL for estimating a weak classical force that acts on
a quantum-mechanical test particle under continuous observation. These
derivations are intended to clarify the interpretation of SQL's in the context
of continuous quantum measurement.


title:
Remarks concerning an Entropy-like Quantity $S_q$ especially for Quantum
  Systems with a Particle Picture; Model with pure Point Spectra

abstract:
  For quantum mechanical systems an entropy-like quantity $S_q$ is defined.
$S_q$ can differ from the usually defined entropy $S$ and $S_q$ may increase
with time for an isolated system. The essential condition for the difference
between $S$ and $S_q$ is the assumption that the set {\bf A} of observables
which can be represented by a measurement is a proper subset of the set of
selfadjoint operators. The underlying idea is made visible in the case of
particle systems with non-trivial scattering. The model-character of the
reasoning comes from the fact that continuous spectra are replaced by
point-spectra. So it seems evident, that no direct connection exists between
$S_q$ and the Sinai-Kolmogorov-Entropy at least in this model with pure
point-spectra.


title:
Nonlinear quantum mechanics implies polynomial-time solution for
  NP-complete and #P problems

abstract:
  If quantum states exhibit small nonlinearities during time evolution, then
quantum computers can be used to solve NP-complete problems in polynomial time.
We provide algorithms that solve NP-complete and #P oracle problems by
exploiting nonlinear quantum logic gates. It is argued that virtually any
deterministic nonlinear quantum theory will include such gates, and the method
is explicitly demonstrated using the Weinberg model of nonlinear quantum
mechanics.


title:
Linear quantum trajectories: Applications to continuous projection
  measurements

abstract:
  We present a method for obtaining evolution operators for linear quantum
trajectories. We apply this to a number of physical examples of varying
mathematical complexity, in which the quantum trajectories describe the
continuous projection measurement of physical observables. Using this method we
calculate the average conditional uncertainty for the measured observables,
being a central quantity of interest in these measurement processes.


title: The time of arrival concept in quantum mechanics

abstract:
  The concept and the formalization of the arrival time in quantum mechanics
are discussed. Different approaches based on trajectories, quantization rules,
time operators, phase space techniques, renewal equations or operational
procedures are reviewed or proposed. Open questions and loose ends are pointed
out.


title:
A dynamic model of atoms: structure, internal interactions and photon
  emissions of hydrogen

abstract:
  The standard solution of the Schroedinger equation for the hydrogen atom is
analyzed. Comparing with the recently established internal properties of
electrons it is found, that these solutions cannot be seen as physically valid
states of the electron wave. The paper therefore proposes a new model of
hydrogen based on internal properties of electrons. The ground state of the
hydrogen system (T=0) is an inertial aggregation within the atomic shell, the
calculation yields an atomic radius of 0.330 nm. Electron proton interaction
within the atom are treated with a causal and deterministic model, the
resonance frequency of the hydrogen system of $ 6.57 \times 10^{15} Hz $ is
referred to elastic deformations of its nucleus, resonance levels are a result
of boundary conditions for radial electron waves and photon interactions due to
nuclear oscillations. Spectral emissions of excited atoms can be referred to a
decay of the state of motion of the coupled electron-proton system. The
framework developed is essentially deterministic, microphysical processes
analyzed are referred to material characteristics of particles involved.
Statistical effects are referred to interactions with the atomic environment,
the results derived are compatible with the second and third principle of
thermodynamics.


title: Non-linear properties of strongly pumped lasers

abstract:
  Bloch equations for the atomic population and the polarization/coherence and
the equation of motion for the photon number in a laser are solved in steady
state as a function of the pump rate. Two level atom and two modes of three
levels atom are investigated. Close to threshold the usual linear dependence of
the intensity on the pump rate in found for all cases. However, far above
threshold strongly nonlinear dependence is encountered. In the cases for which
the pump connects the lower lasing state to one of the excited states the
character of the non-linearity differs crucially from the cases when the pump
in not related directly to the lower lasing state. Non-monotonic dependence of
laser intensity upon the pump rate is predicted. Detailed discussion of the
nonlinear behavior is presented, including saturation and depletion effects.


title: The Born and Markov approximations for atom lasers

abstract:
  We discuss the use of the Born and Markov approximations in describing the
dynamics of an atom laser. In particular, we investigate the applicability of
the quantum optical Born-Markov master equation for describing output coupling.
We derive conditions based on the atomic reservoir, and atom dispersion
relations for when the Born-Markov approximations are valid and discuss
parameter regimes where these approximations fail in our atom laser model.
Differences between the standard optical laser model and the atom laser are due
to a combination of factors, including the parameter regimes in which a typical
atom laser would operate, the different reservoir state which is appropriate
for atoms, and the different dispersion relations between atoms and photons. We
present results based on an exact method in the regimes in which the
Born-Markov approximation fails. The exact solutions in some experimentally
relavent parameter regimes give non-exponential loss of atoms from a cavity.


title: Stability of Three- and Four-Body Coulomb Systems

abstract:
  We discuss the stability of three- and four-particle system interacting by
pure Coulomb interactions, as a function of the masses and charges of the
particles. We present a certain number of general properties which allow to
answer a certain number of questions without or with less numerical
calculations.


title: Quantum back-action of optical observations on Bose condensates

abstract:
  Impressive pictures of moving Bose-Einstein condensates have been taken using
phase-contrast imaging M. R. Andrews et al., Science 273, 84 (1996). We
calculate the quantum backaction of this measurement technique. We find that
phase-contrast imaging is not a quantum nondemolition measurement of the atomic
density. Instead, the condensate gets gradually depleted at a rate that is
proportional to the light intensity and to the inverse cube of the optical wave
length. The fewer atoms are condensed the higher is the required intensity to
see a picture, and, consequently, the higher is the induced backaction. To
describe the quantum physics of phase-contrast imaging we put forward a new
approach to quantum-optical propagation. We develop an effective field theory
of paraxial optics in a fully quantized atomic medium.


title: Cold atoms: A new medium for quantum optics

abstract:
  Laser-cooled and trapped cesium atoms have been used as a nonlinear medium in
a nearly resonant cavity. A study of the semiclassical dynamics of the system
was performed, showing bistability and instabilities. In the quantum domain,
squeezing in a probe beam having interacted with this system was demonstrated.


title: Atomic number fluctuations in a falling cold atom cloud

abstract:
  We evaluate the effective number of atoms in experiments where a probe laser
beam with a Gaussian profile passes through an atomic medium consisting of a
cold atom cloud released from a magneto-optical trap. Considering the case
where the initial distribution is a Gaussian function of position and velocity,
we give a quantitative description of the time variation of the effective atom
number while the cloud is exploding and falling. We discuss the two cases where
the effective number is defined from the linear and nonlinear phase shifts,
respectively. We also evaluate the fluctuations of the effective atom number by
calculating their correlation functions and the associated noise spectra.
Finally we estimate the effect of these fluctuations on experiments where the
probe beam passes through a cavity containing the atomic cloud.


title: Squeezing with cold atoms

abstract:
  Cold atoms from a magneto-optic trap have been used as a nonlinear medium in
a nearly resonant cavity. Squeezing in a probe beam passing through the cavity
was demonstrated. The measured noise reduction is 40% for free atoms and 20%
for weakly trapped atoms.


title: Transverse effects on squeezing with atoms

abstract:
  We evaluate the squeezing of a probe beam with a transverse Gaussian profile
interacting with an ensemble of two-level atoms in a cavity. We use the linear
input-output formalism where the effect of atoms is described by susceptibility
and noise functions. The transverse structure is accounted for by averaging
atomic functions over the intensity profile. The results of the plane-wave and
Gaussian-wave theories are compared. When large squeezing is predicted we find
the prediction of the plane-wave model not to be reliable outside the Kerr
domain. We give an estimate of the squeezing degradation due to the Gaussian
transverse structure.


title: Transverse-mode coupling in a Kerr medium

abstract:
  We analyze nonlinear transverse mode coupling in a Kerr medium placed in an
optical cavity and its influence on bistability and different kinds of quantum
noise reduction. Even for an input beam that is perfectly matched to a cavity
mode, the nonlinear coupling produces an excess noise in the fluctuations of
the output beam. Intensity squeezing seems to be particularly robust with
respect to mode coupling, while quadrature squeezing is more sensitive.
However, it is possible to find a mode the quadrature squeezing of which is not
affected by the coupling.


title: Optical nonlinear dynamics with cold atoms in a cavity

abstract:
  This paper presents the nonlinear dynamics of laser cooled and trapped cesium
atoms placed inside an optical cavity and interacting with a probe light beam
slightly detuned from the 6S1/2(F=4) to 6P3/2(F=5) transition. The system
exhibits very strong bistability and instabilities. The origin of the latter is
found to be a competition between optical pumping and non-linearities due to
saturation of the optical transition.


title: The Casimir force for passive mirrors

abstract:
  We show that the Casimir force between mirrors with arbitrary frequency
dependent reflectivities obeys bounds due to causality and passivity
properties. The force is always smaller than the Casimir force between two
perfectly reflecting mirrors. For narrow-band mirrors in particular, the force
is found to decrease with the mirrors bandwidth.


title: Comments on Unruh's Paper

abstract:
  Unruh has commented upon my recent proof that certain predictions of quantum
theory are incompatible with the assertion that no influence of any kind acts
backward in time in any Lorentz frame. Unruh fails to make a necessary
distinction between statements that assert the existence of values, and
statements that assert the existence merely of correlations between possible
values. Consequently his argument fails to show that my proof involves a tacit
or hidden reality assumption that is alien to quantum theory.


title: What is quantum mechanics trying to tell us?

abstract:
  I explore whether it is possible to make sense of the quantum mechanical
description of physical reality by taking the proper subject of physics to be
correlation and only correlation, and by separating the problem of
understanding the nature of quantum mechanics from the hard problem of
understanding the nature of objective probability in individual systems, and
the even harder problem of understanding the nature of conscious awareness. The
resulting perspective on quantum mechanics is supported by some elementary but
insufficiently emphasized theorems. Whether or not it is adequate as a new
Weltanschauung, this point of view toward quantum mechanics provides a
different perspective from which to teach the subject or explain its peculiar
character to people in other fields.


title: A Parity-Conserving Canonical Quantization for the Baker's Map

abstract:
  We present here a complete description of the quantization of the baker's
map. The method we use is quite different from that used in Balazs and Voros
[BV] and Saraceno [S]. We use as the quantum algebra of observables the
operators generated by {exp(2 Pi ix),exp (2 Pi ip)} and construct a unitary
propagator such that as Planck's constant tends to zero,the classical dynamics
is returned. For Planck's constant satisfying the integrality condition 1/N
with N even, and for periodic boundary conditions for the wave functions on the
torus, we show that the dynamics can be reduced to the dynamics on an
N-dimensional Hilbert space, and the unitary N by N matrix propagator is the
same as given in [BV] except for a small correction of order Planck's constant.
This correction is is shown to preserve the symmetry x->1-x and p->1-p of the
classical map for periodic boundary conditions.


title: Statistical uncertainty in quantum optical photodetection measurements

abstract:
  We present a complete statistical analysis of quantum optical measurement
schemes based on photodetection. Statistical distributions of quantum
observables determined from a finite number of experimental runs are
characterized with the help of the generating function, which we derive using
the exact statistical description of raw experimental outcomes. We use the
developed formalism to point out that the statistical uncertainty results in
substantial limitations of the determined information on the quantum state:
though a family of observables characterizing the quantum state can be safely
evaluated from experimental data, its further use to obtain the expectation
value of some operators generates exploding statistical errors. These issues
are discussed using the example of phase-insensitive measurements of a single
light mode. We study reconstruction of the photon number distribution from
photon counting and random phase homodyne detection. We show that utilization
of the reconstructed distribution to evaluate a simple well-behaved observable,
namely the parity operator, encounters difficulties due to accumulation of
statistical errors. As the parity operator yields the Wigner function at the
phase space origin, this example also demonstrates that transformation between
various experimentally determined representations of the quantum state is a
quite delicate matter.


title:
First International Conference on Unconventional Models of Computation
  UMC'98. An Unconventional Review

abstract:
  Review of the First International Conference on Unconventional Models of
Computation UMC'98, Auckland, New Zealand, 5-9 January, 1998


title:
Does Quantum Mechanics imply influences acting backward in time in
  impact series experiments?

abstract:
  A real two-particle experiment is proposed in which one of the particles
undergoes two successive impacts on beam-splitters. It is shown that the
standard quantum mechanical superposition principle implies the possibility of
influences acting backward in time ("retrocausation"), in striking contrast
with the principle of causality. It is argued that nonlocality and
retrocausation are not necessarily entangled.


title:
Comment on ``Quantum Entanglement and the Nonexistence of Superluminal
  Signals''

abstract:
  We argue that the claim given in quant-ph/9801014 is untenable. The fallacy
in the proof is a misinterpretation of the no-cloning theorem, which does not
allow quantum jumps, specifically measurements.


title:
A quantum-mechanical study of optical regenerators based on
  nonlinear-loop mirrors

abstract:
  We present a quantum-mechanical analysis of a nonlinear interferometer that
achieves optical switching via cross-phase modulation resulting from the Kerr
effect. We show how it performs as a very precise optical regenerator, highly
improving the transmitted bit-error rate in the presence of loss.


title: Phenomenological damping in trapped atomic Bose-Einstein condensates

abstract:
  The method of phenomenological damping developed by Pitaevskii for
superfluidity near the $\lambda$ point is simulated numerically for the case of
a dilute, alkali, inhomogeneous Bose-condensed gas near absolute zero. We study
several features of this method in describing the damping of excitations in a
Bose-Einstein condensate. In addition, we show that the method may be employed
to obtain numerically accurate ground states for a variety of trap potentials.


title: Noise, errors and information in quantum amplification

abstract:
  We analyze and compare the characterization of a quantum device in terms of
noise, transmitted bit-error-rate (BER) and mutual information, showing how the
noise description is meaningful only for Gaussian channels. After reviewing the
description of a quantum communication channel, we study the insertion of an
amplifier. We focus attention on the case of direct detection, where the linear
amplifier has a 3 decibels noise figure, which is usually considered an
unsurpassable limit, referred to as the standard quantum limit (SQL). Both
noise and BER could be reduced using an ideal amplifier, which is feasible in
principle. However, just a reduction of noise beyond the SQL does not generally
correspond to an improvement of the BER or of the mutual information. This is
the case of a laser amplifier, where saturation can greatly reduce the noise
figure, although there is no corresponding improvement of the BER. Such
mechanism is illustrated on the basis of Monte Carlo simulations.


title:
Generalized Grover Search Algorithm for Arbitrary Initial Amplitude
  Distribution

abstract:
  Grover's algorithm for quantum searching of a database is generalized to deal
with arbitrary initial amplitude distributions. First order linear difference
equations are found for the time evolution of the amplitudes of the r marked
and N-r unmarked states. These equations are solved exactly. An expression for
the optimal measurement time T \sim O(\sqrt{N/r}) is derived which is shown to
depend only on the initial average amplitudes of the marked and unmarked
states. A bound on the probability of measuring a marked state is derived,
which depends only on the standard deviation of the initial amplitude
distributions of the marked or unmarked states.


title: A two-step optimized measurement for the phase-shift

abstract:
  A two-step detection strategy is suggested for the precise measurement of the
optical phase-shift. In the first step an unsharp, however, unbiased joint
measurement of the phase and photon number is performed by heterodyning the
signal field. Information coming from this step is then used for suitable
squeezing of the probe mode to obtain a sharp phase distribution. Application
to squeezed states leads to a phase sensitivity scaling as $\Delta\phi\simeq
N^{-1}$ relative to the total number of photons impinged into the apparatus.
Numerical simulations of the whole detection strategy are also also presented.


title: Quantum Binary Decision for Driven Harmonic Oscillator

abstract:
  We address the problem of determining whether or not a harmonic oscillator
has been perturbed by an external force. Quantum detection and estimation
theory has been used in devising optimum measurement schemes. Detection
probability has been evaluated for different initial state preparations of
oscillator. The corresponding lower bounds on minimum detectable perturbation
intensity has been evaluated and a general bound for random phase perturbation
has been also induced.


title:
Mixed-state entanglement and distillation: is there a ``bound''
  entanglement in nature?

abstract:
  It is shown that if a mixed state can be distilled to the singlet form, it
must violate partial transposition criterion [A. Peres, Phys. Rev. Lett. 76,
1413 (1996)]. It implies that there are two qualitatively different types of
entanglement: ``free'' entanglement which is distillable, and ``bound''
entanglement which cannot be brought to the singlet form useful for quantum
communication purposes. Possible physical meaning of the result is discussed.


title: Hypersurface Bohm-Dirac models

abstract:
  We define a class of Lorentz invariant Bohmian quantum models for N entangled
but noninteracting Dirac particles. Lorentz invariance is achieved for these
models through the incorporation of an additional dynamical space-time
structure provided by a foliation of space-time. These models can be regarded
as the extension of Bohm's model for N Dirac particles, corresponding to the
foliation into the equal-time hyperplanes for a distinguished Lorentz frame, to
more general foliations. As with Bohm's model, there exists for these models an
equivariant measure on the leaves of the foliation. This makes possible a
simple statistical analysis of position correlations analogous to the
equilibrium analysis for (the nonrelativistic) Bohmian mechanics.


title: Relativity of Motion in Vacuum

abstract:
  The existence of vacuum fluctuations leads to reconsider the question of
relativity of motion. The present article is devoted to this aim with a main
line which can be formulated as follows: ``The principle of relativity of
motion is directly related to symmetries of quantum vacuum''. Keeping close to
this statement, we discuss the controversial relation between vacuum and
motion. We introduce the question of relativity of motion in its historical
development before coming to the results obtained more recently.


title: Quantum Langevin Equations and Stability

abstract:
  Different quantum Langevin equations obtained by coupling a particle to a
field are examined. Instabilities or violations of causality affect the motion
of a point charge linearly coupled to the electromagnetic field. In contrast,
coupling a scatterer with a reflection cut-off to radiation pressure leads to
stable and causal motions. The radiative reaction force exerted on a scatterer,
and hence its quasistatic mass, depend on the field state. Explicit expressions
for a particle scattering a thermal field in a two dimensional space-time are
given.


title: Quantum Fluctuations of Mass for a Mirror in Vacuum

abstract:
  A mirror in vacuum is coupled to fluctuating quantum fields. As a result, its
energy-momentum and mass fluctuate. We compute the correlation spectra of force
and mass fluctuations for a mirror at rest in vacuum (of a scalar field in a
two-dimensional space-time). The obtained expressions agree with a mass
correction equal to a vacuum energy stored by the mirror. We introduce a
Lagrangian model which consistently describes a scalar field coupled to a
scatterer, with inertial mass being a quantum variable.


title: Gravitational Quantum Limit for Length Measurements

abstract:
  We discuss a limit for sensitivity of length measurements which is due to the
effect of vacuum fluctuations of gravitational field. This limit is associated
with irreducible quantum fluctuations of geodesic distances and it is
characterized by a noise spectrum with an order of magnitude mainly determined
by Planck length. The gravitational vacuum fluctuations may (in an analysis
restricted to questions of principle and when the measurement strategy is
optimized) dominate fluctuations added by the measurement apparatus if
macroscopic masses, i.e. masses larger than Planck mass, are used.


title: Quantum Reference Frames and Relativistic Time Operator

abstract:
  Aharonov-Kaufherr model of quantum space-time which accounts Reference Frames
(RF) quantum effects is considered in Relativistic Quantum Mechanics framework.
For RF connected with some macroscopic object its free quantum motion - wave
packet smearing results in additional uncertainty of test particle coordinate.
Due to the same effects the use of Galilean or Lorentz transformations for this
RFs becomes incorrect and the special quantum space-time transformations are
introduced.
  In particular for any RF the proper time becomes the operator in other RF.
This time operator calculated solving relativistic Heisenberg equations for
some quantum clocks models.
  Generalized Klein- Gordon equation proposed which depends on both the
particle and RF masses.


title: Non-local properties of multi-particle density matrices

abstract:
  As far as entanglement is concerned, two density matrices of $n$ particles
are equivalent if they are on the same orbit of the group of local unitary
transformations, $U(d_1)\times...\times U(d_n)$ (where the Hilbert space of
particle $r$ has dimension $d_r$). We show that for $n$ greater than or equal
to two, the number of independent parameters needed to specify an $n$-particle
density matrix up to equivalence is $\Pi_r d_r^2 - \sum_r d_r^2 + n - 1$. For
$n$ spin-${1\over 2}$ particles we also show how to characterise generic
orbits, both by giving an explicit parametrisation of the orbits and by finding
a finite set of polynomial invariants which separate the orbits.


title: Squeezed States of a Particle in Magnetic Field

abstract:
  For a charged particle in a homogeneous magnetic field, we construct
stationary squeezed states which are eigenfunctions of the Hamiltonian and the
non-Hermitian operator $\hat{X}_{\Phi} = \hat{X} \cos \Phi + \hat{Y} \sin
\Phi$, $\hat{X}$ and $\hat{Y}$ being the coordinates of the Larmor circle
center and $\Phi$ is a complex parameter. In the family of the squeezed states,
the quantum uncertainty in the Larmor circle position is minimal. The wave
functions of the squeezed states in the coordinate representation are found and
their properties are discussed. Also, for arbitrary gauge of the vector
potential we derive the symmetry operators of translations and rotations.


title: Energy Ambiguity in Nonlinear Quantum Mechanics

abstract:
  We observe that in nonlinear quantum mechanics, unlike in the linear theory,
there exists, in general, a difference between the energy functional defined
within the Lagrangian formulation as an appropriate conserved component of the
canonical energy-momentum tensor and the energy functional defined as the
expectation value of the corresponding nonlinear Hamiltonian operator. Some
examples of such ambiguity are presented for a particularly simple model and
some known modifications. However, we point out that there exist a class of
nonlinear modifications of the Schr\"{o}dinger equation where this difference
does not occur, which makes them more consistent in a manner similar to that of
the linear Schr\"{o}dinger equation. It is found that necessary but not
sufficient a condition for such modifications is the homogeneity of the
modified Schr\"{o}dinger equation or its underlying Lagrangian density which is
assumed to be ``bilinear'' in the wave function in some rather general sense.
Yet, it is only for a particular form of this density that the ambiguity in
question does not arise. A salient feature of this form is the presence of
phase functionals. The present paper thus introduces a new class of
modifications characterized by this desirable and rare property.


title: Long beating wavelength in the Schwarz-Hora effect

abstract:
  Thirty years ago, H.Schwarz has attempted to modulate an electron beam with
optical frequency. When a 50-keV electron beam crossed a thin crystalline
dielectric film illuminated with laser light, electrons produced the
electron-diffraction pattern not only at a fluorescent target but also at a
nonfluorescent target. In the latter case the pattern was of the same color as
the laser light (the Schwarz-Hora effect). This effect was discussed
extensively in the early 1970s. However, since 1972 no reports on the results
of further attempts to repeat those experiments in other groups have appeared,
while the failures of the initial such attempts have been explained by Schwarz.
The analysis of the literature shows there are several unresolved up to now
contradictions between the theory and the Schwarz experiments. In this work we
consider the interpretation of the long-wavelength spatial beating of the
Schwarz-Hora radiation. A more accurate expression for the spatial period has
been obtained, taking into account the mode structure of the laser field within
the dielectric film. It is shown that the discrepancy of more than 10% between
the experimental and theoretical results for the spatial period cannot be
reduced by using the existing quantum models that consider a collimated
electron beam.


title: Schroedinger's interpolation problem and its probabilistic solutions

abstract:
  Probablistic solutions of the so called Schr\"{o}dinger boundary data problem
provide for a unique Markovian interpolation between any two strictly positive
probability densities designed to form the input-output statistics data for a
certain dynamical process taking place in a finite-time interval. The key
problem is to select the jointly continuous in all variables positive semigroup
kernel, appropriate for the phenomenological (physical) situation.


title: Schroedinger's interpolation problem through Feynman-Kac kernels

abstract:
  We discuss the so-called Schr{\"o}dinger problem of deducing the microscopic
(basically stochastic) evolution that is consistent with given positive
boundary probability densities for a process covering a finite fixed time
interval. The sought for dynamics may preserve the probability measure or
induce its evolution, and is known to be uniquely reproducible, if the Markov
property is required. Feynman-Kac type kernels are the principal ingredients of
the solution and determine the transition probability density of the
corresponding stochastic process. The result applies to a large variety of
nonequilibrium statistical physics and quantum situations.


title:
Natural boundaries for the Smoluchowski equation and affiliated
  diffusion processes

abstract:
  The Schr\"{o}dinger problem of deducing the microscopic dynamics from the
input-output statistics data is known to admit a solution in terms of Markov
diffusions. The uniqueness of solution is found linked to the natural
boundaries respected by the underlying random motion. By choosing a reference
Smoluchowski diffusion process, we automatically fix the Feynman-Kac potential
and the field of local accelerations it induces. We generate the family of
affiliated diffusions with the same local dynamics, but different inaccessible
boundaries on finite, semi-infinite and infinite domains. For each diffusion
process a unique Feynman-Kac kernel is obtained by the constrained (Dirichlet
boundary data) Wiener path integration.As a by-product of the discussion, we
give an overview of the problem of inaccessible boundaries for the diffusion
and bring together (sometimes viewed from unexpected angles) results which are
little known, and dispersed in publications from scarcely communicating areas
of mathematics and physics.


title:
Remarks on unsharp quantum observables, objectification, and modal
  interpretations

abstract:
  This paper addresses the question whether a variant of a modal interpretation
is conceivable that could accommodate property ascriptions associated with
nonorthogonal resolutions of the unity and nonorthogonal families of relative
states as they occur in imperfect or genuinely unsharp measurements. I will
review a recent formulation of the quantum measurement problem in the form of
an insolubility theorem that incorporates the case of unsharp object
observables as well as certain types of unsharp pointers. In addition to
demonstrating the necessity for some modification of quantum mechanics, this
allows me to specify the logical position of the modal interpretations as a
resolution to the measurement problem and to indicate why I think their current
versions are not yet capable of dealing adequately with unsharp quantum
observables. The technical tools that will have been explained along this line
of reasoning will finally serve to make precise the notion of (unsharp) value
ascription that I would find desirable for a modal interpretation to ascertain.


title: Fault-Tolerant Quantum Computation with Higher-Dimensional Systems

abstract:
  Instead of a quantum computer where the fundamental units are 2-dimensional
qubits, we can consider a quantum computer made up of d-dimensional systems.
There is a straightforward generalization of the class of stabilizer codes to
d-dimensional systems, and I will discuss the theory of fault-tolerant
computation using such codes. I prove that universal fault-tolerant computation
is possible with any higher-dimensional stabilizer code for prime d.


title: Chaos Induced by Quantization

abstract:
  In this paper, we show that two-dimensional billiards with point interactions
inside exhibit a chaotic nature in the microscopic world, although their
classical counterpart is non-chaotic. After deriving the transition matrix of
the system by using the self-adjoint extension theory of functional analysis,
we deduce the general condition for the appearance of chaos. The prediction is
confirmed by numerically examining the statistical properties of energy
spectrum of rectangular billiards with multiple point interactions inside. The
dependence of the level statistics on the strength as well as the number of the
scatterers is displayed.
  KEYWORDS: wave chaos, quantum mechanics, pseudointegrable billiard, point
interaction, functional analysis


title: Quantum Convolutional Error Correction Codes

abstract:
  I report two general methods to construct quantum convolutional codes for
quantum registers with internal $N$ states. Using one of these methods, I
construct a quantum convolutional code of rate 1/4 which is able to correct one
general quantum error for every eight consecutive quantum registers.


title:
Unified Treatment of EPR and Bell Arguments in Algebraic Quantum Field
  Theory

abstract:
  A conjecture concerning vacuum correlations in axiomatic quantum field theory
is proved. It is shown that this result can be applied both in the context of
EPR-type experiments and Bell-type experiments.


title: Can `unsharp objectification' solve the quantum measurement problem?

abstract:
  The quantum measurement problem is formulated in the form of an insolubility
theorem that states the impossibility of obtaining, for all available object
preparations, a mixture of states of the compound object and apparatus system
that would represent definite pointer positions. A proof is given that
comprises arbitrary object observables, whether sharp or unsharp, and besides
sharp pointer observables a certain class of unsharp pointers, namely, those
allowing for the property of pointer value definiteness. A recent result of H.
Stein is applied to allow for the possibility that a given measurement may not
be applicable to all possible object states but only to a subset of them. The
question is raised whether the statement of the insolubility theorem remains
true for genuinely unsharp observables. This gives rise to a precise notion of
unsharp objectification.


title:
Unified treatment of the Coulomb and harmonic oscillator potentials in
  $D$ dimensions

abstract:
  Quantum mechanical models and practical calculations often rely on some
exactly solvable models like the Coulomb and the harmonic oscillator
potentials. The $D$ dimensional generalized Coulomb potential contains these
potentials as limiting cases, thus it establishes a continuous link between the
Coulomb and harmonic oscillator potentials in various dimensions. We present
results which are necessary for the utilization of this potential as a model
and practical reference problem for quantum mechanical calculations. We define
a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate
the Green's operator on this basis and also present an SU(1,1) algebra
associated with it. We formulate the problem for the one-dimensional case too,
and point out that the complications arising due to the singularity of the
one-dimensional Coulomb problem can be avoided with the use of the generalized
Coulomb potential.


title: Generalized Quantum Control-Not Gate in Two-Spin Ising System

abstract:
  The physical implementation of the quantum Control-Not gate for a two-spin
system is investigated numerically. The concept of a generalized quantum
Control-Not gate, with arbitrary phase shift, is introduced. It is shown that a
resonant $\pi$-pulse provides a simple example of a generalized quantum
Control-Not gate.


title:
Universal property of the information entropy in atoms, nuclei and
  atomic clusters

abstract:
  The position- and momentum-space information entropies of the electron
distributions of atomic clusters are calculated using a Woods-Saxon single
particle potential. The same entropies are also calculated for nuclear
distributions according to the Skyrme parametrization of the nuclear mean
field. It turns out that a similar functional form S=a+b ln N for the entropy
as function of the number of particles N holds approximately for atoms, nuclei
and atomic clusters. It is conjectured that this is a universal property of a
many-fermion system in a mean field. It is also seen that there is an analogy
of our expression for S to Boltzmann's thermodynamic entropy S=k ln W.


title:
Quantum Entangled States and Quasiclassical Dynamics in Macroscopic Spin
  Systems

abstract:
  When dealing with macroscopic objects one usually observes quasiclassical
phenomena, which can be described in terms of quasiclassical (or classical)
equations of motion. Recent development of the theory of quantum computation is
based on implementation of the entangled states which do not have a classical
analogy. Using a simple example of a paramagnetic spin system we show that the
entangled states can be detected in standard macroscopic experiments as a sharp
deviation from quasiclassical motion.


title:
Dynamics of a Quantum Control-Not Gate for an Ensemble of Four-Spin
  Molecules at Room Temperature

abstract:
  We investigate numerically a single-pulse implementation of a quantum
Control-Not (CN) gate for an ensemble of Ising spin systems at room
temperature. For an ensemble of four-spin ``molecules'' we simulate the
time-evolution of the density matrix, for both digital and superpositional
initial conditions. Our numerical calculations confirm the feasibility of
implementation of quantum CN gate in this system at finite temperature, using
electromagnetic $\pi$-pulse.


title:
Path Integral Approach to the Dynamic Casimir Effect with Fluctuating
  Boundaries

abstract:
  A path integral formulation is developed for the dynamic Casimir effect. It
allows us to study arbitrary deformations in space and time of the perfectly
reflecting (conducting) boundaries of a cavity. The mechanical response of the
intervening vacuum is calculated to linear order in the frequency-wavevector
plane, using which a plethora of interesting phenomena can be studied. For a
single corrugated plate we find a correction to mass at low frequencies, and an
effective shear viscosity at high frequencies that are both anisotropic. The
anisotropy is set by the wavevector of the corrugation. For two plates, the
mass renormalization is modified by a function of the ratio between the
separation of the plates and the wave-length of corrugations. The dissipation
rate is not modified for frequencies below the lowest optical mode of the
cavity, and there is a resonant dissipation for all frequencies greater than
that. In this regime, a divergence in the response function implies that such
high frequency deformation modes of the cavity can not be excited by any
macroscopic external forces. This phenomenon is intimately related to resonant
particle creation. For particular examples of two corrugated plates that are
stationary, or moving uniformly in the lateral directions, Josephson-like
effects are observed. For capillary waves on the surface of mercury a
renormalization to surface tension, and sound velocity is obtained.


title: Experimental Quantum Error Correction

abstract:
  Quantum error correction is required to compensate for the fragility of the
state of a quantum computer. We report the first experimental implementations
of quantum error correction and confirm the expected state stabilization. In
NMR computing, however, a net improvement in the signal-to-noise would require
very high polarization. The experiment implemented the 3-bit code for phase
errors in liquid state state NMR.


title:
Volume Elements of Monotone Metrics on the n x n Density Matrices as
  Densities-of-States for Thermodynamic Purposes. II

abstract:
  We derive explicit expressions for the volume elements of both the minimal
and maximal monotone metrics over the (n^{2} - 1)-dimensional convex set of n x
n density matrices for the cases n = 3 and 4. We make further progress for the
specific n = 3 maximal-monotone case, by taking the limit of a certain ratio of
integration results, obtained using an orthogonal set of eight coordinates. By
doing so, we find remarkably simple marginal probability distributions based on
the corresponding volume element, which we then use for thermodynamic purposes.
We, thus, find a spin-1 analogue of the Langevin function. In the fully general
n = 4 situation, however, we are impeded in making similar progress by the
inability to diagonalize a 3 x 3 Hermitian matrix and thereby obtain an
orthogonal set of coordinates to use in the requisite integrations.


title:
``Incerto tempore, incertisque loci'': Can we compute the exact time at
  which a quantum measurement happens?

abstract:
  Without addressing the measurement problem (i.e. what causes the wave
function to ``collapse'', or to ``branch'', or a history to become realized, or
a property to actualize), I discuss the problem of the timing of the quantum
measurement: assuming that in an appropriate sense a measurement happens, when
precisely does it happen? This question can be posed within most
interpretations of quantum mechanics. By introducing the operator M, which
measures whether or not the quantum measurement has happened, I suggest that,
contrary to what is often claimed, quantum mechanics does provide a precise
answer to this question, although a somewhat surprising one.


title: Comparing the strengths of various Bell inequalities

abstract:
  This paper has been withdrawn because it is superseded by quant-ph/9905084
"Bayesian analysis of Bell inequalities.


title:
On the Concept of Quantum State Reduction: Inconsistency of the Orthodox
  View

abstract:
  The argument is re-examined that the program of deriving the rule of state
reduction from the Schroedinger equation holding for the object-apparatus
composite system falls into a vicious circle or an infinite regress called the
von Neumann chain. It is shown that this argument suffers from a serious
physical inconsistency concerning the causality between the reading of the
outcome and the state reduction. A consistent argument which accomplishes the
above program without falling into the circular argument is presented.


title:
Homodyne measurement of exponential phase moments for quantum-phase
  reconstruction

abstract:
  We directly sample the exponential moments of the canonical phase for various
quantum states from the homodyne output. The method enables us to study the
phase properties experimentally, without making the detour via reconstructing
the density matrix or the Wigner function and calculating the phase statistics
from them. In particular, combing the measurement with a measurement of the
photon-number variance, we verify fundamental number-phase uncertainty.


title: Transitions in quantum networks

abstract:
  We consider transitions in quantum networks analogous to those in the
two-dimensional Ising model. We show that for a network of active components
the transition is between the quantum and the classical behaviour of the
network, and the critical amplification coincides with the fundamental quantum
cloning limit.


title: Unconditional security in Quantum Cryptography

abstract:
  Basic techniques to prove the unconditional security of quantum cryptography
are described. They are applied to a quantum key distribution protocol proposed
by Bennett and Brassard in 1984. The proof considers a practical variation on
the protocol in which the channel is noisy and photons may be lost during the
transmission. The initial coding into the channel must be perfect (i.e.,
exactly as described in the protocol). No restriction is imposed on the
detector used at the receiving side of the channel, except that whether or not
the received system is detected must be independent of the basis used to
measure this system.


title: Uncertainty, non-locality and Bell's inequality

abstract:
  We derive a Bell-like inequality involving all correlations in local
observables with uncertainty free states and show that the inequality is
violated in quantum mechanics for EPR and GHZ states. If the uncertainties are
allowed in local observables then the statistical predictions of hidden
variable theory is well respected in quantum world. We argue that the
uncertainties play a key role in understanding the non-locality issues in
quantum world. Thus we can not rule out the possibility that a local, realistic
hidden variable theory with statistical uncertainties in the observables might
reproduce all the results of quantum theory.


title: Spontaneous emission of non-dispersive Rydberg wave packets

abstract:
  Non dispersive electronic Rydberg wave packets may be created in atoms
illuminated by a microwave field of circular polarization. We discuss the
spontaneous emission from such states and show that the elastic incoherent
component (occuring at the frequency of the driving field) dominates the
spectrum in the semiclassical limit, contrary to earlier predictions. We
calculate the frequencies of single photon emissions and the associated rates
in the "harmonic approximation", i.e. when the wave packet has approximately a
Gaussian shape. The results agree well with exact quantum mechanical
calculations, which validates the analytical approach.


title: Analogue Quantum Computers for Data Analysis

abstract:
  Analogue computers use continuous properties of physical system for modeling.
In the paper is described possibility of modeling by analogue quantum computers
for some model of data analysis. It is analogue associative memory and a formal
neural network. A particularity of the models is combination of continuous
internal processes with discrete set of output states. The modeling of the
system by classical analogue computers was offered long times ago, but now it
is not very effectively in comparison with modern digital computers. The
application of quantum analogue modelling looks quite possible for modern level
of technology and it may be more effective than digital one, because number of
element may be about Avogadro number (N=6.0E23).


title:
On decoherence in quantum algorithm via dynamic models for quantum
  measurement

abstract:
  The possible effect of environment on the efficiency of a quantum algorithm
is considered explicitely. It is illustrated through the example of Shor's
prime factorization algorithm that this effect may be disastrous. The influence
of environment on quantum computation is probed on the basis of its analogy to
the problem of wave function collapse in quantum measurement.Techniques from
the Hepp-Colemen approach and its generalization are used to deal with
decoherence problems in quantum computation including dynamic mechanism of
decoherence, quantum error avoiding tricks and calculation of decoherence time.