title: Quantum limitations on superluminal propagation

abstract:
  Unstable systems such as media with inverted atomic population have been
shown to allow the propagation of analytic wavepackets with group velocity
faster than that of light, without violating causality. We illuminate the
important role played by unstable modes in this propagation, and show that the
quantum fluctuations of these modes, and their unitary time evolution, impose
severe restrictions on the observation of superluminal phenomena.


title: Observability of relative phases of macroscopic quantum states

abstract:
  After a measurement, to observe the relative phases of macroscopically
distinguishable states we have to ``undo'' a quantum measurement. We generalise
an earlier model of Peres from two state to N-state quantum system undergoing
measurement process and discuss the issue of observing relative phases of
different branches. We derive an inequality which is satisfied by the relative
phases of macroscopically distinguishable states and consequently any desired
relative phases can not be observed in interference setups. The principle of
macroscopic complementarity is invoked that might be at ease with the
macroscopic world. We illustrate the idea of limit on phase observability in
Stern-Gerlach measurements and the implications are discussed.


title: Phase transitions in open quantum systems

abstract:
  We consider the behaviour of open quantum systems in dependence on the
coupling to one decay channel by introducing the coupling parameter $\alpha$
being proportional to the average degree of overlapping. Under critical
conditions, a reorganization of the spectrum takes place which creates a
bifurcation of the time scales with respect to the lifetimes of the resonance
states. We derive analytically the conditions under which the reorganization
process can be understood as a second-order phase transition and illustrate our
results by numerical investigations. The conditions are fulfilled e.g. for a
picket fence with equal coupling of the states to the continuum. Energy
dependencies within the system are included. We consider also the generic case
of an unfolded Gaussian Orthogonal Ensemble. In all these cases, the
reorganization of the spectrum occurs at the critical value $\alpha_{crit}$ of
the control parameter globally over the whole energy range of the spectrum. All
states act cooperatively.


title: Quantum tomography of mesoscopic superpositions of radiation states

abstract:
  We show the feasibility of a tomographic reconstruction of Schr\"{o}dinger
cat states generated according to the scheme proposed by S. Song, C.M. Caves
and B. Yurke [Phys. Rev. A 41, 5261 (1990)]. We present a technique that
tolerates realistic values for quantum efficiency at photodetectors. The
measurement can be achieved by a standard experimental setup.


title:
Recoil and momentum diffusion of an atom close to a vacuum-dielectric
  interface

abstract:
  We derive the quantum-mechanical master equation (generalized optical Bloch
equation) for an atom in the vicinity of a flat dielectric surface. This
equation gives access to the semiclassical radiation pressure force and the
atomic momentum diffusion tensor, that are expressed in terms of the vacuum
field correlation function (electromagnetic field susceptibility). It is
demonstrated that the atomic center-of-mass motion provides a nonlocal probe of
the electromagnetic vacuum fluctuations. We show in particular that in a
circularly polarized evanescent wave, the radiation pressure force experienced
by the atoms is not colinear with the evanescent wave's propagation vector. In
a linearly polarized evanescent wave, the recoil per fluorescence cycle leads
to a net magnetization for a Jg = 1/2 ground state atom.


title: Decoherence in the Dirac equation

abstract:
  A Dirac particle is represented by a unitarily evolving state vector in a
Hilbert space which factors as $H_{spin} \otimes H_{position}$. Motivated by
the similarity to simple models of decoherence consisting of a two state system
coupled to an environment, we investigate the occurence of decoherence in the
Dirac equation upon tracing over position. We conclude that the physics of this
mathematically exact model for decoherence is closely related to
Zitterbewegung.


title: On the volume of the set of mixed entangled states

abstract:
  A natural measure in the space of density matrices describing N-dimensional
quantum systems is proposed. We study the probability P that a quantum state
chosen randomly with respect to the natural measure is not entangled (is
separable). We find analytical lower and upper bounds for this quantity.
Numerical calculations give P = 0.632 for N=4 and P=0.384 for N=6, and indicate
that P decreases exponentially with N. Analysis of a conditional measure of
separability under the condition of fixed purity shows a clear dualism between
purity and separability: entanglement is typical for pure states, while
separability is connected with quantum mixtures. In particular, states of
sufficiently low purity are necessarily separable.


title: NP in BQP with Nonlinearity

abstract:
  If one modifies the laws of Quantum Mechanics to allow nonlinear evolution of
quantum states, this paper shows that NP-complete problems would be efficiently
solvable in polynomial time with bounded probability (NP in BQP). With that
(admittedly very unlikely) assumption, this is demonstrated by describing a
polynomially large network of quantum gates that solves the 3SAT problem with
bounded probability in polynomial time. As in a previous paper by Abrams and
Lloyd (but by a somewhat simpler argument), allowing nonlinearity in the laws
of Quantum Mechanics would prove the "weak Church-Turing thesis" to be false.
General Relativity is suggested as a possible mechanism to supply the necessary
nonlinearity.


title:
First-kind measurements, non-demolition measurements, and conservation
  laws

abstract:
  A general discussion is given for first-kind (FK) and quantum non-demolition
(QND) measurements. The general conditions for these measurements are derived,
including the most general one (called the weak condition), an intermediate
one, and the strongest one. The weak condition indicates that we can realize a
FK or QND measuring apparatus of wide classes of observables by allowing the
apparatus to have a finite response range. A recently-proposed QND
photodetector using an electron interferometer is an example of such apparatus.


title: Quantum Measurement and Fluctuations in Nanostructures

abstract:
  Measurement and fluctuations are closely related to each other in quantum
mechanics. This fact is explicitly demonstrated in the case of a quantum
non-demolition photodetector which is composed of a double quantum-wire
electron interferometer.


title: Quantum Optics in Dispersive and Absorptive Media

abstract:
  Using microscopic models in which both photons and excitons are treated as
microscopic degrees of freedom, we discuss polaritons of two cases: One is the
case when excitonic parameters are time dependent. The time dependence causes
creation of polaritons from a "false vacuum." % We present the creation spectra
of both % the lower- and upper-branch polaritons. It is shown that both the
creation sepctra and the creation efficiency are much different from the
results of the previous studies. The other is polaritons in absorptive and
inhomogeneous cavities. A polariton in such a system cannot be viewed as a back
and forth oscillation between a photon state and an exciton state.


title:
Photon-energy dissipation caused by an external electric circuit in
  "virtual" photo-excitation processes

abstract:
  We consider generation of an electrical pulse by an optical pulse in the
``virtual excitation'' regime. The electronic system, which is any
electro-optic material including a quantum well structure biased by a dc
electric field, is assumed to be coupled to an external circuit. It is found
that the photon frequency is subject to an extra red shift in addition to the
usual self-phase modulation, whereas the photon number is conserved. The Joule
energy consumed in the external circuit is supplied only from the extra red
shift.


title:
Exact boundary conditions at finite distance for the time-dependent
  Schrodinger equation

abstract:
  Exact boundary conditions at finite distance for the solutions of the
time-dependent Schrodinger equation are derived. A numerical scheme based on
Crank-Nicholson method is proposed to illustrate its applicability in several
examples.


title: Optimal distinction between non-orthogonal quantum states

abstract:
  Given a finite set of linearly independent quantum states, an observer who
examines a single quantum system may sometimes identify its state with
certainty. However, unless these quantum states are orthogonal, there is a
finite probability of failure. A complete solution is given to the problem of
optimal distinction of three states, having arbitrary prior probabilities and
arbitrary detection values. A generalization to more than three states is
outlined.


title: N-order Darboux transformation and a spectral problem on semiaxis

abstract:
  N-order Darboux transformation operator is defined on the basis of a general
notion of transformation operators. Factorisation properties of this operator
are studied. The Darboux transformation operator technique is applied to
construct and investigate potentials with bound states at arbitrary energies
for the spectral problem on semiaxis.


title: Decoherence of mesoscopic states of cavity fields

abstract:
  We show that two-atom correlation measurements of the type involved in a
recent experimental study of the evolution of a mesoscopic superposition state
prepared in a definite mode of a high-Q cavity can be used to determine the
eigenvalues of the reduced density matrix of the field, provided the assumed
dynamical conditions are actually fulfilled to experimental accuracy. These
conditions involve i) a purely dispersive coupling of the field to the Rydberg
atoms used to manipulate and to monitor the cavity field, and ii) the effective
absence of correlations in the ground state of the system consisting of the
cavity coupled to the ``reservoir'' which accounts for the decoherence and
damping processes. A microscopic calculation at zero temperature is performed
and compared to master equation results.


title: Some Notes on Parallel Quantum Computation

abstract:
  We exhibit some simple gadgets useful in designing shallow parallel circuits
for quantum algorithms. We prove that any quantum circuit composed entirely of
controlled-not gates or of diagonal gates can be parallelized to logarithmic
depth, while circuits composed of both cannot. Finally, while we note the
Quantum Fourier Transform can be parallelized to linear depth, we exhibit a
simple quantum circuit related to it that we believe cannot be parallelized to
less than linear depth, and therefore might be used to prove that QNC < QP.


title:
Winding up by a quench: vortices in the wake of rapid Bose-Einstein
  condensation

abstract:
  A second order phase transition induced by a rapid quench can lock out
topological defects with densities far exceeding their equilibrium expectation
values. We use quantum kinetic theory to show that this mechanism, originally
postulated in the cosmological context, and analysed so far only on the mean
field classical level, should allow spontaneous generation of vortex lines in
trapped Bose-Einstein condensates of simple topology, or of winding number in
toroidal condensates.


title: Quantum mutual entropy for Jaynes-Cummings model

abstract:
  The dynamics of an atom on the Jaynes-Cummings model has been studied by an
atomic inversion, von Neumann entropy and so on. In this letter, we will treat
the Jaynes-Cummings model as a problem in non-equilibrium statistical mechanics
and apply quantum mutual entropy to study the irreversible dynamics of a state
for the atom on this model.


title: Hamiltonian path integral quantization in polar coordinates

abstract:
  Using a scheme proposed earlier we set up Hamiltonian path integral
quantization for a particle in two dimensions in plane polar coordinates.This
scheme uses the classical Hamiltonian, without any $O(\hbar^2)$ terms, in the
polar varivables. We show that the propagator satisfies the correct
Schr\"{o}dinger equation.


title:
Simulating the Effect of Decoherence and Inaccuracies on a Quantum
  Computer

abstract:
  A Quantum Computer is a new type of computer which can solve problems such as
factoring and database search very efficiently. The usefulness of a quantum
computer is limited by the effect of two different types of errors, decoherence
and inaccuracies. In this paper we show the results of simulations of a quantum
computer which consider both decoherence and inaccuracies. We simulate circuits
which factor the numbers 15, 21, 35, and 57 as well as circuits which use
database search to solve the circuit satisfaction problem. Our simulations show
that the error rate per gate is on the order of 10^-6 for a trapped ion quantum
computer whose noise is kept below pi/4096 per gate and with a decoherence rate
of 10^-6. This is an important bound because previous studies have shown that a
quantum computer can factor more efficiently than a classical computer if the
error rate is of order 10^-6.


title: A Parallel Quantum Computer Simulator

abstract:
  A Quantum Computer is a new type of computer which can efficiently solve
complex problems such as prime factorization. A quantum computer threatens the
security of public key encryption systems because these systems rely on the
fact that prime factorization is computationally difficult. Errors limit the
effectiveness of quantum computers. Because of the exponential nature of
quantum com puters, simulating the effect of errors on them requires a vast
amount of processing and memory resources. In this paper we describe a parallel
simulator which accesses the feasibility of quantum computers. We also derive
and validate an analytical model of execution time for the simulator, which
shows that parallel quantum computer simulation is very scalable.


title: On the logic of quantum physics and the concept of the time

abstract:
  The logic--linguistic structure of quantum physics is analysed. The role of
formal systems and interpretations in the representation of nature is
investigated. The problems of decidability, completeness, and consistency can
affect quantum physics in different ways. Bohr's complementarity is of great
interest,because it is a contradictory proposition. We shall see that the
flowing of time prevents the birth of contradictions in nature, because it
makes a cut between two different, but complementary aspects of the reality.


title:
Reply to the Comment on "Resonant Spectra and the Time Evolution of the
  Survival and Nonescape Probabilities"

abstract:
  In our paper [Phys. Rev. Lett. 74, 337 (1995)], we derived an exact
expression for the survival and nonescape probabilities as an expansion in
terms of resonant states. It was shown that these quantities exhibit at long
times a different behavior. Although both decay as a power law, they have
different exponents. In this paper we show that, contrary to the claim in the
Comment of R. M. Cavalcanti (quant-ph/9704023), the nonescape probability decay
for long times as an inverse power law.


title:
Wave Functions and Energy Terms of the SCHR\"Odinger Equation with
  Two-Center Coulomb Plus Harmonic Oscillator Potential

abstract:
  Schr\"odinger equation for two center Coulomb plus harmonic oscillator
potential is solved by the method of ethalon equation at large intercenter
separations. Asymptotical expansions for energy term and wave function are
obtained in the analytical form.


title: Dense Quantum Coding and a Lower Bound for 1-way Quantum Automata

abstract:
  We consider the possibility of encoding m classical bits into much fewer n
quantum bits so that an arbitrary bit from the original m bits can be recovered
with a good probability, and we show that non-trivial quantum encodings exist
that have no classical counterparts. On the other hand, we show that quantum
encodings cannot be much more succint as compared to classical encodings, and
we provide a lower bound on such quantum encodings. Finally, using this lower
bound, we prove an exponential lower bound on the size of 1-way quantum finite
automata for a family of languages accepted by linear sized deterministic
finite automata.


title: Quantum Computing

abstract:
  The main features of quantum computing are described in the framework of spin
resonance methods. Stress is put on the fact that quantum computing is in
itself nothing but a re-interpretation (fruitful indeed) of well-known
concepts. The role of the two basic operations, one-spin rotation and
controlled-NOT gates, is analyzed, and some exercises are proposed.


title: Bell inequality, Bell states and maximally entangled states for n qubits

abstract:
  First, we present a Bell type inequality for n qubits, assuming that m out of
the n qubits are independent. Quantum mechanics violates this inequality by a
ratio that increases exponentially with m. Hence an experiment on n qubits
violating of this inequality sets a lower bound on the number m of entangled
qubits. Next, we propose a definition of maximally entangled states of n
qubits. For this purpose we study 5 different criteria. Four of these criteria
are found compatible. For any number n of qubits, they determine an orthogonal
basis consisting of maximally entangled states generalizing the Bell states.


title: On Generalized Super-Coherent States

abstract:
  A set of operators, the so-called k-fermion operators, that interpolate
between boson and fermion operators are introduced through the consideration of
an algebra arising from two non-commuting quon algebras. The deformation
parameters q and 1/q for these quon algebras are roots of unity with q to the
power k being equal to 1. The case k = 2 corresponds to fermions and the case k
going to infinity to bosons. Generalized coherent states (connected to the
k-fermionic states) and super-coherent states (involving a k-fermionic sector
and a purely bosonic sector) are investigated.


title: Quantum Information in a Distributed Apparatus

abstract:
  We investigate the information provided about a specified distributed
apparatus of n units in the measurement of a quantum state. It is shown that,
in contrast to such measurement of a classical state, which is bounded by log
(n+1) bits, the information in a quantum measurement is bounded by 3.7 x
n^(1/2) bits. This means that the use of quantum apparatus offers an
exponential advantage over classical apparatus.


title: The theory of heating of the quantum ground state of trapped ions

abstract:
  Using a displacement operator formalism, I analyse the depopulation of the
vibrational ground state of trapped ions. Two heating times, one characterizing
short time behaviour, the other long time behaviour are found. The short time
behaviour is analyzed both for single and multiple ions, and a formula for the
relative heating rates of different modes is derived. The possibility of
correction of heating via the quantum Zeno effect, and the exploitation of the
suppression of heating of higher modes to reduce errors in quantum computation
is considered.


title:
An Introduction to Coordinate-free Quantization and its Application to
  Constrained Systems

abstract:
  Canonical quantization entails using Cartesian coordinates, and Cartesian
coordinates exist only in flat spaces. This situation can either be questioned
or accepted. In this paper we offer a brief and introductory overview of how a
flat phase space metric can be incorporated into a covariant, coordinate-free
quantization procedure involving a continuous-time (Wiener measure)
regularization of traditional phase space path integrals. Additionally we show
how such procedures can be extended to incorporate systems with constraints and
illustrate that extension for special systems.


title: Reconstruction of photon distribution with positivity constraints

abstract:
  An iterative algorithm for reconstructing the photon distribution from the
random phase homodyne statistics is discussed. This method, derived from the
maximum-likelihood approach, yields a positive definite estimate for the photon
distribution with bounded statistical errors even if numerical compensation for
the detector imperfection is applied.


title:
Quantum Langevin equations for semiconductor light-emitting devices and
  the photon statistics at a low-injection level

abstract:
  From the microscopic quantum Langevin equations (QLEs) we derive the
effective semiconductor QLEs and the associated noise correlations which are
valid at a low-injection level and in real devices. Applying the semiconductor
QLEs to semiconductor light-emitting devices (LEDs), we obtain a new formula
for the Fano factor of photons which gives the photon-number statistics as a
function of the pump statistics and several parameters of LEDs. Key ingredients
are non-radiative processes, carrier-number dependence of the radiative and
non-radiative lifetimes, and multimodeness of LEDs. The formula is applicable
to the actual cases where the quantum efficiency $\eta$ differs from the
differential quantum efficiency $\eta_{d}$, whereas previous theories
implicitly assumed $\eta = \eta_{d}$. It is also applicable to the cases when
photons in each mode of the cavity are emitted and/or detected inhomogeneously.
When $\eta_{d} < \eta$ at a running point, in particular, our formula predicts
that even a Poissonian pump can produce sub-Poissonian light. This mechanism
for generation of sub-Poissonian light is completely different from those of
previous theories, which assumed sub-Poissonian statistics for the current
injected into the active layers of LEDs. Our results agree with recent
experiments. We also discuss frequency dependence of the photon statistics.


title: Darboux-integrable nonlinear Liouville-von Neumann equation

abstract:
  A new form of a binary Darboux transformation is used to generate analytical
solutions of a nonlinear Liouville-von Neumann equation. General theory is
illustrated by explicit examples.

categories: quant-ph math-ph math.MP nlin.SI solv-int


title: Quantum Nonlocality without Entanglement

abstract:
  We exhibit an orthogonal set of product states of two three-state particles
that nevertheless cannot be reliably distinguished by a pair of separated
observers ignorant of which of the states has been presented to them, even if
the observers are allowed any sequence of local operations and classical
communication between the separate observers. It is proved that there is a
finite gap between the mutual information obtainable by a joint measurement on
these states and a measurement in which only local actions are permitted. This
result implies the existence of separable superoperators that cannot be
implemented locally. A set of states are found involving three two-state
particles which also appear to be nonmeasurable locally. These and other
multipartite states are classified according to the entropy and entanglement
costs of preparing and measuring them by local operations.


title: The Functional Derivation of Master Equations

abstract:
  Master equations describe the quantum dynamics of open systems interacting
with an environment. They play an increasingly important role in understanding
the emergence of semiclassical behavior and the generation of entropy, both
being related to quantum decoherence. Presently we derive the exact master
equation for a homogeneous scalar Higgs or inflaton like field coupled to an
environment field represented by an infinite set of harmonic oscillators. Our
aim is to demonstrate a derivation directly from the path integral
representation of the density matrix propagator. Applications and
generalizations of this result are discussed.


title:
Casimir Force between a Dielectric Sphere and a Wall: A Model for
  Amplification of Vacuum Fluctuations

abstract:
  The interaction between a polarizable particle and a reflecting wall is
examined. A macroscopic approach is adopted in which the averaged force is
computed from the Maxwell stress tensor. The particular case of a perfectly
reflecting wall and a sphere with a dielectric function given by the Drude
model is examined in detail. It is found that the force can be expressed as the
sum of a monotonically decaying function of position and of an oscillatory
piece. At large separations, the oscillatory piece is the dominant
contribution, and is much larger than the Casimir-Polder interaction that
arises in the limit that the sphere is a perfect conductor. It is argued that
this enhancement of the force can be interpreted in terms of the frequency
spectrum of vacuum fluctuations. In the limit of a perfectly conducting sphere,
there are cancellations between different parts of the spectrum which no longer
occur as completely in the case of a sphere with frequency dependent
polarizability. Estimates of the magnitude of the oscillatory component of the
force suggest that it may be large enough to be observable.


title: Vacuum Energy Density near Fluctuating Boundaries

abstract:
  The imposition of boundary conditions upon a quantized field can lead to
singular energy densities on the boundary. We treat the boundaries as quantum
mechanical objects with a nonzero position uncertainty, and show that the
singular energy density is removed. This treatment also resolves a long
standing paradox concerning the total energy of the minimally coupled and
conformally coupled scalar fields.


title: Adiabatic Berry Phase and Hannay Angle for Open Paths

abstract:
  We obtain the adiabatic Berry phase by defining a generalised gauge potential
whose line integral gives the phase holonomy for arbitrary evolutions of
parameters. Keeping in mind that for classical integrable systems it is hardly
clear how to obtain open-path Hannay angle, we establish a connection between
the open-path Berry phase and Hannay angle by using the parametrised coherent
state approach. Using the semiclassical wavefunction we analyse the open-path
Berry phase and obtain the open-path Hannay angle. Further, by expressing the
adiabatic Berry phase in terms of the commutator of instantaneous projectors
with its differential and using Wigner representation of operators we obtain
the Poisson bracket between distribution function and its differential. This
enables us to talk about the classical limit of the phase holonomy which yields
the angle holonomy for open-paths. An operational definition of Hannay angle is
provided based on the idea of classical limit of quantum mechanical inner
product. A probable application of the open-path Berry phase and Hannay angle
to wave-packet revival phenomena is also pointed out.


title: Interaction-free measurement and forward scattering

abstract:
  Interaction-free measurement is shown to arise from the forward-scattered
wave accompanying absorption: a "quantum silhouette" of the absorber.
Accordingly, the process is not free of interaction. For a perfect absorber the
forward-scattered wave is locked both in amplitude and in phase. For an
imperfect one it has a nontrivial phase of dynamical origin (``colored
silhouette"), measurable by interferometry. Other examples of quantum
silhouettes, all controlled by unitarity, are briefly discussed.


title: Skirting Hidden-Variable No-Go Theorems

abstract:
  It is observed that the proofs of hidden-variable no-go theorems depend on
the `projection postulate,' which is seen to be contradictory with respect to
spin operators in directions orthogonal to the magnetic field direction. In
this light it is argued that it is less costly to abandon the projection
postulate than to abandon locality and this in turn renders Hidden-Variable
No-Go Theorems evadible. To buttress this point, a local realist model of the
EPR experiment which ignores the constraints of the projection postulate is
presented.


title: Scalable NMR Quantum Computation

abstract:
  Nuclear magnetic resonance offers an appealing prospect for implementation of
quantum computers, because of the long coherence times associated with nuclear
spins, and extensive laboratory experience in manipulating the spins with radio
frequency pulses. Existing proposals, however, suffer from a signal-to-noise
ratio that decays exponentially in the number of qubits in the quantum
computer. This places a severe limit on the size of the computations that can
be performed by such a computer; estimates of that limit are well within the
range in which a conventional computer taking exponentially more steps would
still be practical.
  We give an NMR implementation in which the signal-to-noise ratio depends only
on features of NMR technology, not the size of the computer. This provides a
means for NMR computation techniques to scale to sizes at which the exponential
speedup enables quantum computation to solve problems beyond the capabilities
of classical computers.


title: Evanescent Waves are Not Superluminal

abstract:
  It is demonstrated that an electromagnetic pulse, which is made to tunnel
trough a barrier, would not be photo-detected before an identical pulse, which
travels the same distance in vacuum.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics. II.
  Equations of motion and observables

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. Its evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
  In the second part of this investigation we derive several forms of the
bundle (analogue of the) Schr\"odinger equation governing the time evolution of
state sections. We prove that up to a constant the matrix-bundle Hamiltonian,
entering in the bundle analogue of the matrix form of the conventional
Schr\"odinger equation, coincides with the matrix of coefficients of the
evolution transport. This allows to interpret the Hamiltonian as a gauge field.
Here we also apply the bundle approach to the description of observables. It is
shown that to any observable there corresponds a unique Hermitian bundle
morphism (along paths) and vice versa.


title: Reply to Aharonov and Anandan's "Meaning of the Density Matrix"

abstract:
  Aharonov and Anandan's claim that the notion of ``proper mixture'' is
improper is shown to be unjustified. The point is made that if a purely
operationalist standpoint is taken the three difficulties these authors
describe relatively to the conventional interpretation of density matrices in
fact vanish. It is noted that nevertheless it is very difficult for us to do
without any form of realism, in particular when the quantum measurement problem
is considered, and it is stressed that the proper mixture notion comes in
precisely at this level. The more general question of the real bearing of
Aharonov and Anandan's ideas on the interpretation of quantum mechanics problem
is considered.


title:
Probabilistic cloning and identification of linearly independent quantum
  states

abstract:
  We construct a probabilistic quantum cloning machine by a general
unitary-reduction operation. With a postselection of the measurement results,
the machine yields faithful copies of the input states. It is shown that the
states secretly chosen from a certain set $\$=\left\{\left| \Psi_1\right>
,\left| \Psi_2\right> ,... ,\left| \Psi_n\right> \right\} $ can be
probabilistically cloned if and only if $% \left| \Psi_1\right>$, $\left|
\Psi_2\right>$, $... ,$ and $\left| \Psi_n\right>$ are linearly-independent. We
derive the best possible cloning efficiencies. Probabilistic cloning has close
connection with the problem of identification of a set of states, which is a
type of $n+1$ outcome measurement on $n$ linearly independent states. The
optimal efficiencies for this type of measurement are obtained.


title: Efficient quantum computing on low temperature spin ensembles

abstract:
  A new scheme is proposed which will permit electron spin resonance pulse
techniques to be used to realize a quantum computer with a 100 qbits, or more.
The computation is performed on effective pure states which correspond to
off-diagonal blocks of the density matrix. Described is a scheme which very
efficiently performs the preparation stage and which permits
``pseudo-projective measurement'' to be made on the output. With such
measurements all members of the ensemble remain coherent.


title:
The quantum query complexity of approximating the median and related
  statistics

abstract:
  Let X = (x_0,...,x_{n-1})$ be a sequence of n numbers. For \epsilon > 0, we
say that x_i is an \epsilon-approximate median if the number of elements
strictly less than x_i, and the number of elements strictly greater than x_i
are each less than (1+\epsilon)n/2. We consider the quantum query complexity of
computing an \epsilon-approximate median, given the sequence X as an oracle. We
prove a lower bound of \Omega(\min{{1/\epsilon},n}) queries for any quantum
algorithm that computes an \epsilon-approximate median with any constant
probability greater than 1/2. We also show how an \epsilon-approximate median
may be computed with O({1/\epsilon}\log({1\/\epsilon}) \log\log({1/\epsilon}))
oracle queries, which represents an improvement over an earlier algorithm due
to Grover. Thus, the lower bound we obtain is essentially optimal. The upper
and the lower bound both hold in the comparison tree model as well.
  Our lower bound result is an application of the polynomial paradigm recently
introduced to quantum complexity theory by Beals et al. The main ingredient in
the proof is a polynomial degree lower bound for real multilinear polynomials
that ``approximate'' symmetric partial boolean functions. The degree bound
extends a result of Paturi and also immediately yields lower bounds for the
problems of approximating the kth-smallest element, approximating the mean of a
sequence of numbers, and that of approximately counting the number of ones of a
boolean function. All bounds obtained come within polylogarithmic factors of
the optimal (as we show by presenting algorithms where no such optimal or near
optimal algorithms were known), thus demonstrating the power of the polynomial
method.


title: Supercoherent States of Calogero-Sutherland Oscillator

abstract:
  Supersymmetric quantum mechanical model of Calogero-Sutherlend singular
oscillator is constructed. Supercoherent states are defined with the help of
supergroup displacement operator. They are proper states of a fermionic
annihilation operator. Their coordinate and superholomorphic representations
are considered. The supermeasure on superunit disc which realizes the
resolution of the unity is calculated. The cases of exact and spontaneously
broken supersymmetry are treated separately. As an example the supersymmetric
partners of the input Hamiltonian expressed in terms of elementary functions
are given.


title:
1/N-expansion and nonclassical state generation in higher-order
  anharmonic oscillators

abstract: Paper is withdrawn


title: Timelike Nonseparability and Retrocausation

abstract:
  Renewed interest in the quantum zigzagging causality model is highlighted by
an ingenious proposal by Suarez (quant-ph/9801061) to test the timelike aspect
of nonseparability. Taking advantage of a work by Froehner I argue that the
Dirac representation of a state, has the Bayesian-like connotation of best
estimate given the Hilbert frame chosen. As a measurement perturbs
uncontrollably a system it is (Hoekzema's wording) a retroparation. My bet is
that Suarez' sources and sinks of paired particles operating inside the
coherence length of the laser beam will evidence retrocausation.


title:
Calculation of Planetary Precession from Quantum-corrected Newton's
  Gravitation Law

abstract:
  With consideration of quantization of space, we relate Newton's gravitation
with the Second Law of thermodynamics. This leads to a correction to its
original form, which takes into consideration the role of classical
measurement. Our calculation shows this corrected form of gravitation can give
explanation for planetary precession.


title: Coherent and incoherent chaotic tunneling near singlet-doublet crossings

abstract:
  In the spectrum of systems showing chaos-assisted tunneling, three-state
crossings are formed when a chaotic singlet intersects a tunnel doublet. We
study the dissipative quantum dynamics in the vicinity of such crossings. A
harmonically driven double well coupled to a bath serves as a model. Markov and
rotating-wave approximations are introduced with respect to the Floquet
spectrum of the time-dependent central system. The resulting master equation is
integrated numerically. We find various types of transient tunneling,
determined by the relation of the level width to the inherent energy scales of
the crossing. The decay of coherent tunneling can be significantly retarded or
accelerated. Modifications of the quantum asymptotic state by the crossing are
also studied. The comparison with a simple three-state model shows that in
contrast to the undamped case, the participation of states outside the crossing
cannot be neglected in the presence of dissipation.


title: On a Generalized D-Dimensional Oscillator: Interbasis Expansions

abstract:
  This article deals with nonrelativistic study of a D-dimensional
superintegrable system, which generalizes the ordinary isotropic oscillator
system. The coefficients for the expansion between the hyperspherical and
Cartesian bases (transition matrix), and vice-versa, are found in terms of the
SU(2) Clebsch--Gordan coefficients analytically continued to real values of
their arguments. The diagram method, which allow one to construct a transition
matrix for arbitrary dimension, is developed.


title:
Bohm`s Interpretation of Quantum Mechanics and the Reconstruction of the
  Probability Distribution

abstract:
  Within Bohm`s interpretation of quantum mechanics particles follow classical
trajectories that are determined by the full solution of the time dependent
Schroedinger equation. If this interpretation is consistent it must be possible
to determine the probability distribution at time t from the probability
distribution at time t=0 by using these trajectories. In this paper it is shown
that this is the case indeed.


title:
Dispersion of Klauder's temporally stable coherent states for the
  hydrogen atom

abstract:
  We study the dispersion of the "temporally stable" coherent states for the
hydrogen atom introduced by Klauder. These are states which under temporal
evolution by the hydrogen atom Hamiltonian retain their coherence properties.
We show that in the hydrogen atom such wave packets do not move
quasi-classically; i.e., they do not follow with no or little dispersion the
Keplerian orbits of the classical electron. The poor quantum-classical
correspondence does not improve in the semiclassical limit.


title: Entanglement in Quantum Information Theory

abstract:
  Quantum mechanics has many counter-intuitive consequences which contradict
our intuition which is based on classical physics. Here we discuss a special
aspect of quantum mechanics, namely the possibility of entanglement between two
or more particles. We will establish the basic properties of entanglement using
quantum state teleportation. These principles will then allow us to formulate
quantitative measures of entanglement. Finally we will show that the same
general principles can also be used to prove seemingly difficult questions
regarding entanglement dynamics very easily. This will be used to motivate the
hope that we can construct a thermodynamics of entanglement.


title: Hamiltonian Formalism in Quantum Mechanics

abstract:
  Heisenberg motion equations in Quantum mechanics can be put into the Hamilton
form. The difference between the commutator and its principal part, the Poisson
bracket, can be accounted for exactly. Canonical transformations in Quantum
mechanics are not, or at least not what they appear to be; their properties are
formulated in a series of Conjectures.


title: Purifying noisy entanglement requires collective measurements

abstract:
  Known entanglement purification protocols for mixed states use collective
measurements on several copies of the state in order to increase the
entanglement of some of them. We address the question of whether it is possible
to purify the entanglement of a state by processing each copy separately. While
this is possible for pure states, we show that this is impossible, in general,
for mixed states. The importance of this result both conceptually and for
experimental realization of purification is discussed. We also give explicit
invariants of an entangled state of two qubits under local actions and
classical communication.


title: The Initialization Problem in Quantum Computing

abstract:
  The problem of initializing phase in a quantum computing system is
considered. The initialization of phases is a problem when the system is
initially present in an entangled state and also in the application of the
quantum gate transformations since each gate will introduce phase uncertainty.
The accumulation of these random phases will reduce the effectiveness of the
recently proposed quantum computing schemes. The paper also presents general
observations on the nonlocal nature of quantum errors and the expected
performance of the proposed quantum error-correction codes that are based on
the assumption that the errors are either bit-flip or phase-flip or both. It is
argued that these codes cannot directly solve the initialization problem of
quantum computing.


title: Quantum Communication with Phantom Photons

abstract:
  We show that quantum information may be transferred between atoms in
different locations by using ``phantom photons'': the atoms are coupled through
electromagnetic fields, but the corresponding field modes do not have to be
fully populated. In the case where atoms are placed inside optical cavities,
errors in quantum information processing due to photon absorption inside the
cavity are diminished in this way. This effect persists up to intercavity
distances of about a meter for the current levels of cavity losses, and may be
useful for distributed quantum computing.


title:
Wigner transform and quantum-like corrections for charged-particle beam
  transport

abstract:
  It is shown that charged-particle beam transport in the paraxial
approximation can be effectively described with a quantum-like picture in
semiclassical approximation. In particular, the classical Liouville equation
can be suitably replaced by a von Neuman-like equation. Relevant remarks
concerning the standard classical description of the beam transport are given.


title: Wave function of a Brownian particle

abstract:
  Using the Caldirola-Kanai Hamiltonian, we study the time evolution of the
wave function of a particle whose classical motion is governed by the Langevin
equation. We show, in particular, that if the initial wave function is
Gaussian, then (i) it remains Gaussian for all times, (ii) its width grows,
approaching a finite value when t->infinity, and (iii) its center describes a
Brownian motion, and so the uncertainty in the position of the particle grows
without limit.


title:
Quantum Oracle Interrogation: Getting all information for almost half
  the price

abstract:
  Consider a quantum computer in combination with a binary oracle of domain
size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess
the whole content of the oracle (being an N bit string) with probability
greater than 95%. This contrasts the power of classical computers which would
require N calls to achieve the same task. From this result it follows that any
function with the N bits of the oracle as input can be calculated using
N/2+sqrt(N) queries if we allow a small probability of error. It is also shown
that this error probability can be made arbitrary small by using N/2+O(sqrt(N))
oracle queries.
  In the second part of the article `approximate interrogation' is considered.
This is when only a certain fraction of the N oracle bits are requested. Also
for this scenario does the quantum algorithm outperform the classical
protocols. An example is given where a quantum procedure with N/10 queries
returns a string of which 80% of the bits are correct. Any classical protocol
would need 6N/10 queries to establish such a correctness ratio.


title:
Classical properties of generalized coherent states: from phase-space
  dynamics to Bell's inequality

abstract:
  We review classical properties of harmonic-oscillator coherent states. Then
we discuss which of these classical properties are preserved under the
group-theoretic generalization of coherent states. We prove that the
generalized coherent states of quantum systems with Lie-group symmetries are
the unique Bell states, i.e., the pure quantum states preserving the
fundamental classical property of satisfying Bell's inequality upon splitting.


title: A New Approach to Locality and Causality

abstract:
  In the light of some recent results, it is argued that usual concepts of
causality and locality are approximations valid at scales greater than the
Compton wavelength and corresponding time scales. It follows that the "spooky"
non-locality of Quantum Mechanics is not really so and infact is perfectly
consistent with a recently discussed holistic model, which again is
corroborated by latest astrophysical and cosmological observations. This
approach also provides a rationale for the origin of the metric and points to,
what may be called a space time quantization which may be, ultimately,
fundamental.


title: The Chiral Oscillator and its Applications in Quantum Theory

abstract:
  The fundamental importance of the chiral oscillator is elaborated. Its
quantum invariants are computed. As an application the Zeeman effect is
analysed. We also show that the chiral oscillator is the most basic example of
a duality invariant model, simulating the effect of the familiar
electric-magnetic duality.


title: Toward a finite-dimensional formulation of Quantum Field Theory

abstract:
  Rules of quantization and equations of motion for a finite-dimensional
formulation of Quantum Field Theory are proposed which fulfill the following
properties: a) both the rules of quantization and the equations of motion are
covariant; b) the equations of evolution are second order in derivatives and
first order in derivatives of the space-time co-ordinates; and c) these rules
of quantization and equations of motion lead to the usual (canonical) rules of
quantization and the (Schr\"odinger) equation of motion of Quantum Mechanics in
the particular case of mechanical systems. We also comment briefly on further
steps to fully develop a satisfactory quantum field theory and the difficuties
which may be encountered when doing so.


title: The Piecewise Deterministic Process Associated to EEQT

abstract:
  In the framework of Event Enhanced Quantum Theory (EEQT) a probabilistic
construction of the piecewise deterministic process associated with a dynamical
semigroup is presented. The process generates sample histories of individual
systems quantums systems continuously coupled to classical measuring devices;
it gives a unique algorithm generating time series of pointer readings in real
experiments with quantum systems.


title: Critique of Protective Measurements

abstract:
  Recently proposed idea of "protective" measurement of a quantum state is
critically examined, and generalized. Earlier criticisms of the idea are
discussed and their relevance to the proposal assessed. Several constraints on
measuring apparatus required by "protective" measurements are discussed, with
emphasis on how they may restrict their experimental feasibility. Though
"protective" measurements result in an unchanged system state and a shift of
the pointer proportional to the expectation value of the measured observable in
the system state, the actual reading of the pointer position gives rise to
several subtleties. We propose several schemes for reading pointer position,
both when the apparatus is treated as a classical system as well as when its
quantum aspects are taken into account, that address these issues. The tiny
entanglement which is always present due to deviation from extreme adiabaticity
in realistic situations is argued to be the weakest aspect of the proposal.
Because of this, one can never perform a protective measurement on a single
quantum system with absolute certainty. This clearly precludes an ontological
status for the wave function. Several other conceptual issues are also
discussed.


title: Towards a Unified Description of the Fundamental Interactions

abstract:
  We consider a recent successful model of leptons as Kerr-Newman type Black
Holes in a Quantum Mechanical context. The model leads to a cosmology which
predicts an ever expanding accelerating universe with decreasing density and to
the conclusion that at Compton wavelength scales, electrons would exhibit low
dimensionality, both of which conclusions have been verified by several
independent experiments and observations very recently. In this preliminary
communication we indicate how the above model describes the quarks' fractional
charges, handedness and masses (as any fundamental theory should) and could
lead to a unified description of the four fundamental interactions.


title: Path Integral Quantization and Riemannian-Symplectic Manifolds

abstract:
  We develop a mathematically well-defined path integral formalism for general
symplectic manifolds. We argue that in order to make a path integral
quantization covariant under general coordinate transformations on the phase
space and involve a genuine functional measure that is both finite and
countably additive, the phase space manifold should be equipped with a
Riemannian structure (metric). A suitable method to calculate the metric is
also proposed.


title: A Rudimentary Quantum Compiler

abstract:
  We present a new algorithm for reducing an arbitrary unitary matrix into a
sequence of elementary operations (operations such as controlled-nots and qubit
rotations). Such a sequence of operations can be used to manipulate an array of
quantum bits (i.e., a quantum computer). We report on a C++ program called
"Qubiter" that implements our algorithm. Qubiter source code is publicly
available.


title: How to Compile A Quantum Bayesian Net

abstract:
  We show how to express the information contained in a Quantum Bayesian (QB)
net as a product of unitary matrices. If each of these unitary matrices is
expressed as a sequence of elementary operations (operations such as
controlled-nots and qubit rotations), then the result is a sequence of
operations that can be used to run a quantum computer. QB nets have been run
entirely on a classical computer, but one expects them to run faster on a
quantum computer.


title: Universal Quantum Information Compression

abstract:
  Suppose that a quantum source is known to have von Neumann entropy less than
or equal to S but is otherwise completely unspecified. We describe a method of
universal quantum data compression which will faithfully compress the quantum
information of any such source to S qubits per signal (in the limit of large
block lengths).


title: Logical Dissipation of Automata Implements - Dissipation of Computation

abstract:
  As revealed by discussions of principle on energy dissipation by computers,
logic imposes constraints on physical systems designed for a logical function.
We define a notion of logical dissipation for a finite automaton. We discuss
the constraints associated with physical implementation of automata and exhibit
the role played by modularity for testability. As a result, practical
computers, which are necessarily modular, dissipate proportionally to
computation time.


title: Optimal eavesdropping in quantum cryptography with six states

abstract:
  A generalization of the quantum cryptographic protocol by Bennett and
Brassard is discussed, using three conjugate bases, i.e. six states. By
calculating the optimal mutual information between sender and eavesdropper it
is shown that this scheme is safer against eavesdropping on single qubits than
the one based on two conjugate bases. We also address the question for a
connection between the maximal classical correlation in a generalized Bell
inequality and the intersection of mutual informations between sender/receiver
and sender/eavesdropper.


title: Quantum State Reconstruction From Incomplete Data

abstract:
  Knowing and guessing, these are two essential epistemological pillars in the
theory of quantum-mechanical measurement. As formulated quantum mechanics is a
statistical theory. In general, a priori unknown states can be completely
determined only when measurements on infinite ensembles of identically prepared
quantum systems are performed. But how one can estimate (guess) quantum state
when just incomplete data are available (known)? What is the most reliable
estimation based on a given measured data? What is the optimal measurement
providing only a finite number of identically prepared quantum objects are
available? These are some of the questions we address. We present several
schemes for a reconstruction of states of quantum systems from measured data:
(1) We show how the maximum entropy (MaxEnt) principle can be efficiently used
for an estimation of quantum states on incomplete observation levels. (2) We
show how Bayesian inference can be used for reconstruction of quantum states
when only a finite number of identically prepared systems are measured. (3) We
describe the optimal generalized measurement of a finite number of identically
prepared quantum systems which results in the estimation of a quantum state
with the highest fidelity.


title:
Quantum mechanical 'Backward in Time'? Comments, Answers, and the Causal
  Indistinguishability Condition

abstract:
  We discuss a number of comments on quant-ph/9801061, and propose to introduce
the concept of 'Causal Indistinguishability'. The incompatibility between
Quantum Mechanics and Nonlocal Causality appears to be unavoidable: upholding
of Quantum Mechanics by experiment would mean to live with influences backward
in time, just as we are now living with such faster than light.


title: Phase Information in Quantum Oracle Computing

abstract:
  Computational devices may be supplied with external sources of information
(oracles). Quantum oracles may transmit phase information which is available to
a quantum computer but not a classical computer. One consequence of this
observation is that there is an oracle which is of no assistance to a classical
computer but which allows a quantum computer to solve undecidable problems.
Thus useful relativized separations between quantum and classical complexity
classes must exclude the transmission of phase information from oracle to
computer.


title:
Sonoluminescence: Bogolubov coefficients for the QED vacuum of a
  time-dependent dielectric bubble

abstract:
  We extend Schwinger's ideas regarding sonoluminescence by explicitly
calculating the Bogolubov coefficients relating the QED vacuum states
associated with changes in a dielectric bubble. Sudden (non-adiabatic) changes
in the refractive index lead to an efficient production of real photons with a
broadband spectrum, and a high-frequency cutoff that arises from the asymptotic
behaviour of the dielectric constant.


title: Asymmetric quantum cloning machines in any dimension

abstract:
  A family of asymmetric cloning machines for $N$-dimensional quantum states is
introduced. These machines produce two imperfect copies of a single state that
emerge from two distinct Heisenberg channels. The tradeoff between the quality
of these copies is shown to result from a complementarity akin to Heisenberg
uncertainty principle. A no-cloning inequality is derived for isotropic
cloners: if $\pi_a$ and $\pi_b$ are the depolarizing fractions associated with
the two copies, the domain in $(\sqrt{\pi_a},\sqrt{\pi_b})$-space located
inside a particular ellipse representing close-to-perfect cloning is forbidden.
More generally, a no-cloning uncertainty relation is discussed, quantifying the
impossibility of copying imposed by quantum mechanics. Finally, an asymmetric
Pauli cloning machine is defined that makes two approximate copies of a quantum
bit, while the input-to-output operation underlying each copy is a (distinct)
Pauli channel. The class of symmetric Pauli cloning machines is shown to
provide an upper bound on the quantum capacity of the Pauli channel of
probabilities $p_x$, $p_y$ and $p_z$.


title:
Product rule for gauge invariant Weyl symbols and its application to the
  semiclassical description of guiding center motion

abstract:
  We derive a product rule for gauge invariant Weyl symbols which provides a
generalization of the well-known Moyal formula to the case of non-vanishing
electromagnetic fields. Applying our result to the guiding center problem we
expand the guiding center Hamiltonian into an asymptotic power series with
respect to both Planck's constant $\hbar$ and an adiabaticity parameter already
present in the classical theory. This expansion is used to determine the
influence of quantum mechanical effects on guiding center motion.


title: Bound states of a spin-1/2 charged particle in a magnetic flux tube

abstract:
  We study a spin-1/2 charged particle with gyromagnetic factor g>2 moving in a
plane threaded by a magnetic flux tube. We prove that, if the magnetic field
(i) has radial symmetry, (ii) has compact support and (iii) does not change
sign, there is at least one bound state for each angular momentum l in the
interval [0,v], where v (assumed positive) is the total magnetic flux in units
of the quantum of flux.


title:
Physical interpretation of stochastic Schroedinger equations in cavity
  QED

abstract:
  We propose physical interpretations for stochastic methods which have been
developed recently to describe the evolution of a quantum system interacting
with a reservoir. As opposed to the usual reduced density operator approach,
which refers to ensemble averages, these methods deal with the dynamics of
single realizations, and involve the solution of stochastic Schr\"odinger
equations. These procedures have been shown to be completely equivalent to the
master equation approach when ensemble averages are taken over many
realizations. We show that these techniques are not only convenient
mathematical tools for dissipative systems, but may actually correspond to
concrete physical processes, for any temperature of the reservoir. We consider
a mode of the electromagnetic field in a cavity interacting with a beam of two-
or three-level atoms, the field mode playing the role of a small system and the
atomic beam standing for a reservoir at finite temperature, the interaction
between them being given by the Jaynes-Cummings model. We show that the
evolution of the field states, under continuous monitoring of the state of the
atoms which leave the cavity, can be described in terms of either the Monte
Carlo Wave-Function (quantum jump) method or a stochastic Schr\"odinger
equation, depending on the system configuration. We also show that the Monte
Carlo Wave-Function approach leads, for finite temperatures, to localization
into jumping Fock states, while the diffusion equation method leads to
localization into states with a diffusing average photon number, which for
sufficiently small temperatures are close approximations to mildly squeezed
states.


title: Retrodictively Optimal Localisations in Phase Space

abstract:
  In a previous paper it was shown that the distribution of measured values for
a retrodictively optimal simultaneous measurement of position and momentum is
always given by the initial state Husimi function. This result is now
generalised to retrodictively optimal simultaneous measurements of an arbitrary
pair of rotated quadratures x_theta1 and x_theta2. It is shown, that given any
such measurement, it is possible to find another such measurement,
informationally equivalent to the first, for which the axes defined by the two
quadratures are perpendicular. It is further shown that the distribution of
measured values for such a meaurement belongs to the class of generalised
Husimi functions most recently discussed by Wuensche and Buzek. The class
consists of the subset of Wodkiewicz's operational probability distributions
for which the filter reference state is a squeezed vaccuum state.


title: Strong excitations of a Bose--Einstein condensate: Barrier resonances

abstract:
  We study the dynamics of a forced condensed atom cloud and relate the
behavior to a classical Mathieu oscillator in a singular potential. It is found
that there are wide resonances which can strongly affect the dynamics even when
dissipation is present. The behavior is characteristic of condensed clouds of
any shape and has experimental relevance.


title: Localization of Events in Space-Time

abstract:
  The present paper deals with the quantum coordinates of an event in
space-time, individuated by a quantum object. It is known that these
observables cannot be described by self-adjoint operators or by the
corresponding spectral projection-valued measure. We describe them by means of
a positive-operator-valued (POV) measure in the Minkowski space-time,
satisfying a suitable covariance condition with respect to the Poincare' group.
This POV measure determines the probability that a measurement of the
coordinates of the event gives results belonging to a given set in space-time.
We show that this measure must vanish on the vacuum and the one-particle
states, which cannot define any event. We give a general expression for the
Poincare' covariant POV measures. We define the baricentric events, which lie
on the world-line of the centre-of-mass, and we find a simple expression for
the average values of their coordinates. Finally, we discuss the conditions
which permit the determination of the coordinates with an arbitrary accuracy.


title: Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal

abstract:
  Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of photon production due to changes in the properties
of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric
bubble. This mechanism can be re-phrased in terms of the Casimir effect and has
recently been the subject of considerable controversy. The present paper probes
Schwinger's suggestion in detail: Using the sudden approximation we calculate
Bogolubov coefficients relating the QED vacuum in the presence of the expanded
bubble to that in the presence of the collapsed bubble. In this way we derive
an estimate for the spectrum and total energy emitted. We verify that in the
sudden approximation there is an efficient production of photons, and further
that the main contribution to this dynamic Casimir effect comes from a volume
term, as per Schwinger's original calculation. However, we also demonstrate
that the timescales required to implement Schwinger's original suggestion are
not physically relevant to sonoluminescence. Although Schwinger was correct in
his assertion that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence. In
other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018,
quant-ph/9905034) we have developed a variant of Schwinger's model that is
compatible with the physically required timescales.


title: Measuring quantum optical Hamiltonians

abstract:
  We show how recent state-reconstruction techniques can be used to determine
the Hamiltonian of an optical device that evolves the quantum state of
radiation. A simple experimental setup is proposed for measuring the
Liouvillian of phase-insensitive devices. The feasibility of the method with
current technology is demonstrated on the basis of Monte Carlo simulated
experiments.


title: Controlling Quantum State Reduction

abstract:
  Every measurement leaves the object in a family of states indexed by the
possible outcomes. This family, called the posterior states, is usually a
family of the eigenstates of the measured observable, but it can be an
arbitrary family of states by controlling the object-apparatus interaction. A
potentially realizable object-apparatus interaction measures position in such a
way that the posterior states are the translations of an arbitrary wave
function. In particular, position can be measured without perturbing the object
in a momentum eigenstate.


title: Maximal violation of Bell's inequality and atomic cascade photons

abstract:
  A correlation inequality is derived from local realism and a supplementary
assumption. This inequality is violated by a factor of 1.5 in the case of real
experiments, whereas previous inequalities such as Clauser-Horne-Shimony-Holt
inequality of 1969 and Clauser-Horne inequality of 1974 are violated by a
factor of $\sqrt 2$. Thus the magnitude of violation of this inequality is
approximately 20.7% larger than the magnitude of violation of previous
inequalities. Moreover, the present inequality can be used to test locality
very simply because it requires the measurements of only two detection
probabilities. In contrast, Clauser-Horne inequality requires the measurements
of five detection probabilities.


title: Composite absorbing potentials

abstract:
  The multiple scattering interferences due to the addition of several
contiguous potential units are used to construct composite absorbing potentials
that absorb at an arbitrary set of incident momenta or for a broad momentum
interval.


title:
The addition of the lower level to spectrums of matrix and scalar
  components of d=2 SUSY Hamiltonian

abstract:
  Supersymmetrical quantum--mechanical system is consider in the case of d=2.
The problem of addition of the lower level to spectrums of matrix and scalar
components of d=2 SUSY Hamiltonian is investigated. It is shown that in the
case, the level E=0 may be degenerate. The multi--dimensional scalar
Hamiltonians with energy spectra coinciding up to finite number of discrete
levels are constructed.


title: Quantum Whispers

abstract:
  It is shown that with the use of entanglement a specific two party
communication task can be done with a systematically smaller expected error
than any possible classical protocol could do. The example utilises the very
tight correlation between separate spin measurements on a singlet state for
small differences in the angles of these two measurements. An extension of this
example to many parties arranged in a row with only local, one-to-one
communication (whispering) is then considered. It is argued that in this
scenario there exists no reliable classical protocol, whereas in the quantum
case there does.


title:
Collectivity, Phase Transitions and Exceptional Points in Open Quantum
  Systems

abstract:
  Phase transitions in open quantum systems, which are associated with the
formation of collective states of a large width and of trapped states with
rather small widths, are related to exceptional points of the Hamiltonian.
Exceptional points are the singularities of the spectrum and eigenfunctions,
when they are considered as functions of a coupling parameter. In the present
paper this parameter is the coupling strength to the continuum. It is shown
that the positions of the exceptional points (their accumulation point in the
thermodynamical limit) depend on the particular type and energy dependence of
the coupling to the continuum in the same way as the transition point of the
corresponding phase transition.


title: Scale decoherence in inhomogeneous potentials

abstract:
  Finite precision measurement factors the Hilbert space of a quantum system
into a tensor product $H_{coarse} \otimes H_{fine}$. This is mathematically
equivalent to the partition into system and environment which forms the arena
for decoherence, so we describe the consequences of the inaccessibility of
$H_{fine}$ as scale decoherence. Considering the experimentally important case
of a harmonic oscillator potential as well as a periodic piecewise constant
potential, we show that scale decoherence occurs for inhomogeneous potentials
and may explain part of the decoherence observed in recent and proposed
experiments on mesoscopic superpositions of quantum states.


title:
Optical Tachyons in Parametric Amplifiers: How Fast Can Quantum
  Information Travel?

abstract:
  We show that optical tachyonic dispersion corresponding to superluminal
(faster than-light) group velocities characterizes parametrically amplifying
media. The turn-on of parametric amplification in finite media, followed by
illumination by spectrally narrow probe wavepackets, can give rise to transient
tachyonic wavepackets. In the stable (sub-threshold) operating regime of an
optical phase conjugator it is possible to transmit probe pulses with a
superluminally advanced peak, whereas conjugate reflection is always
subluminal. In the unstable (above-threshold) regime, superluminal response
occurs both in reflection and in transmission, at times preceding the onset of
exponential growth due to the instability. Remarkably, the quantum information
transmitted by probe or conjugate pulses, albeit causal, is confined to times
corresponding to superluminal velocities. These phenomena are explicitly
analyzed for four-wave mixing, stimulated Raman scattering and parametric
downconversion.


title:
Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2
  Particles

abstract:
  We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A
semiclassical propagator and a trace formula are derived and are shown to be
determined by the classical orbits of a relativistic point particle. In
addition, two phase factors enter, one of which can be calculated from the
Thomas precession of a classical spin transported along the particle orbits.
For the second factor we provide an interpretation in terms of dynamical and
geometric phases.

categories: quant-ph chao-dyn math-ph math.MP nlin.CD


title: Shape Invariance and Its Connection to Potential Algebra

abstract:
  Exactly solvable potentials of nonrelativistic quantum mechanics are known to
be shape invariant. For these potentials, eigenvalues and eigenvectors can be
derived using well known methods of supersymmetric quantum mechanics. The
majority of these potentials have also been shown to possess a potential
algebra, and hence are also solvable by group theoretical techniques. In this
paper, for a subset of solvable problems, we establish a connection between the
two methods and show that they are indeed equivalent.


title: Quantum Harmonic Sieve: Learning DNF with a Classical Example Oracle

abstract:
  This paper has been withdrawn by the authors due to a problem with
*efficiently* predicting the large fourier coefficients. It is being reworked
and will be resubmitted in the near future.


title: Frequency up-converted radiation from a cavity moving in vacuum

abstract:
  We calculate the photon emission of a high finesse cavity moving in vacuum.
The cavity is treated as an open system. The field initially in the vacuum
state accumulates a dephasing depending on the mirrors motion when bouncing
back and forth inside the cavity. The dephasing is not linearized in our
calculation, so that qualitatively new effects like pulse shaping in the time
domain and frequency up-conversion in the spectrum are found. Furthermore we
predict the existence of a threshold above which the system should show
self-sustained oscillations.


title: Quantum teleportation of a single-photon wave packet

abstract:
  A quantum teleportation scheme based on the EPR-pair entangled with respect
to the ``energy+time'' variables is proposed. Teleportation of the multimode
state of a single-photon wave packet is considered.


title: Hydrodynamical quantum state reconstruction

abstract:
  The density matrix of a nonrelativistic wave-packet in an arbitrary,
one-dimensional and time-dependent potential can be reconstructed by measuring
hydrodynamical moments of the Wigner distribution. An n-th order Taylor
polynomial in the off-diagonal variable is obtained by measuring the
probability distribution at n+1 discrete time values.


title: Is quantum mechanics non-local?

abstract:
  A recent proof, couched in the symbolic language of modal logic, shows that a
well-defined formulation of the question posed in the title is answered
affirmatively. In a paper with the same title Unruh has tried in various ways
to translate the symbolic proof into normal prose, and has claimed that the
proof must fail in some way or another. A correct translation is given here,
and it is explained why the difficulties encountered by Unruh do not actually
arise.


title:
Generating and monitoring Schr\"odinger cats in conditional measurement
  on a beam splitter

abstract:
  Preparation of Schr\"odinger-cat-like states via conditional output
measurement on a beam splitter is studied. In the scheme, a mode prepared in a
squeezed vacuum is mixed with a mode prepared in a Fock state and photocounting
is performed in one of the output channels of the beam splitter. In this way
the mode in the other output channel is prepared in a Schr\"odinger-cat-like
state that is either a photon-subtracted or a photon-added Jacobi polynomial
squeezed vacuum state, depending upon the difference between the number of
photons in the input Fock state and the number of photons in the output Fock
state onto which it is projected. Two possible photocounting schemes are
considered, and the problem of monitoring cats that are ``hidden'' in a
statistical mixture of states is studied.


title: True Collapse and False Collapse

abstract:
  We emphasize that standard quantum theory (SQT) is incomplete because it
doesn't describe what is experimentally observed, namely events, nor does it
satisfactorily define the circumstances under which events may occur. Simple
models are given (all of which have the same density matrix evolution) to
illustrate schemes which claim to complete SQT. It is shown how the model based
upon the Continuous Spontaneous Localization (CSL) theory, in which an
individual statevector undergoes "True Collapse," gives a satisfactory
description of events. It is argued that various "decoherence" based
approaches, illustrated by models in which a density matrix undergoes "False
Collapse," do not satisfactorily resolve these problems of SQT.


title: Tales and Tails and Stuff and Nonsense

abstract:
  In an informal way I review collapse models and my part in constructing them,
and I recall some encounters with Abner Shimony. In particular, I address the
question of the nature of spacetime reality in collapse models, stimulated by
Abner's criticism of the "tail" possessed by statevectors in such models.


title: On a Resolution of the Identity in Terms of Coherent States

abstract:
  Transformations of coherent states of the free particle by bounded and
semibounded symmetry operators are considered. Resolution of the identity
operator in terms of the transformed states is analyzed. A generalized identity
resolution is formulated. Darboux transformation operators are analyzed as
operators defined in a Hilbert space. Coherent states of multisoliton
potentials are studied.


title: On the problem of interactions in quantum theory

abstract:
  The structure of representations describing systems of free particles in the
theory with the invariance group SO(1,4) is investigated. The property of the
particles to be free means as usual that the representation describing a
many-particle system is the tensor product of the corresponding single-particle
representations (i.e. no interaction is introduced). It is shown that the mass
operator contains only continuous spectrum in the interval $(-\infty,\infty)$
and such representations are unitarily equivalent to ones describing
interactions (gravitational, electromagnetic etc.). This means that there are
no bound states in the theory and the Hilbert space of the many-particle system
contains a subspace of states with the following property: the action of free
representation operators on these states is manifested in the form of different
interactions. Possible consequences of the results are discussed.


title:
Reconstruction of diagonal elements of density matrix using maximum
  likelihood estimation

abstract:
  The data of the experiment of Schiller et al., Phys. Rev. Lett. 77 (1996)
2933, are alternatively evaluated using the maximum likelihood estimation. The
given data are fitted better than by the standard deterministic approach.
Nevertheless, the data are fitted equally well by a whole family of states.
Standard deterministic predictions correspond approximately to the envelope of
these maximum likelihood solutions.


title: Generalized Husimi Functions: Analyticity and Information Content

abstract:
  The analytic properties of a class of generalized Husimi functions are
discussed, with particular reference to the problem of state reconstruction.
The class consists of the subset of Wodkiewicz's operational probability
distributions for which the filter reference state is a squeezed vacuum state.
The fact that the function is analytic means that perfectly precise knowledge
of its values over any small region of phase space provides enough information
to reconstruct the density matrix. If, however, one only has imprecise
knowledge of its values, then the amplification of statistical errors which
occurs when one attempts to carry out the continuation seriously limits the
amount of information which can be extracted. To take account of this fact a
distinction is made between explicate, or experimentally accessible
information, and information which is only present in implicate, experimentally
inaccessible form. It is shown that an explicate description of various aspects
of the system can be found localised on various 2 real dimensional surfaces in
complexified phase space. In particular, the continuation of the function to
the purely imaginary part of complexified phase space provides an explicate
description of the Wigner function.


title: Information measures and classicality in quantum mechanics

abstract:
  We study information measures in quantu mechanics, with particular emphasis
on providing a quantification of the notions of classicality and
predictability. Our primary tool is the Shannon - Wehrl entropy I. We give a
precise criterion for phase space classicality and argue that in view of this
a) I provides a measure of the degree of deviation from classicality for closed
system b) I - S (S the von Neumann entropy) plays the same role in open systems
We examine particular examples in non-relativistic quantum mechanics. Finally,
(this being one of our main motivations) we comment on field classicalisation
on early universe cosmology.


title: Consistent Quantum Counterfactuals

abstract:
  An analysis using classical stochastic processes is used to construct a
consistent system of quantum counterfactual reasoning. When applied to a
counterfactual version of Hardy's paradox, it shows that the probabilistic
character of quantum reasoning together with the ``one framework'' rule
prevents a logical contradiction, and there is no evidence for any mysterious
nonlocal influences. Counterfactual reasoning can support a realistic
interpretation of standard quantum theory (measurements reveal what is actually
there) under appropriate circumstances.


title: Arrival Times in Quantum Theory from an Irreversible Detector Model

abstract:
  We investigate a detector scheme designed to measure the arrival of a
particle at $x=0$ during a finite time interval. The detector consists of a two
state system which undergoes a transition from one state to the other when the
particle crosses $x=0$, and possesses the realistic feature that it is
effectively irreversible as a result of being coupled to a large environment.
The probabilities for crossing or not crossing $x=0$ thereby derived coincide
with earlier phenomenologically proposed expressions involving a complex
potential. The probabilities are compared with similar previously proposed
expressions involving sums over paths, and a connection with time operator
approaches is also indicated.


title:
Quantum probability distribution of arrival times and probability
  current density

abstract:
  This paper compares the proposal made in previous papers for a quantum
probability distribution of the time of arrival at a certain point with the
corresponding proposal based on the probability current density. Quantitative
differences between the two formulations are examined analytically and
numerically with the aim of establishing conditions under which the proposals
might be tested by experiment. It is found that quantum regime conditions
produce the biggest differences between the formulations which are otherwise
near indistinguishable. These results indicate that in order to discriminate
conclusively among the different alternatives, the corresponding experimental
test should be performed in the quantum regime and with sufficiently high
resolution so as to resolve small quantum efects.


title: NMR Quantum Automata in Doped Crystals

abstract:
  In a lattice ${\cal L}$ of nuclear spins with ABCABCABC... type periodic
structure embedded in a single-crystal solid, each ABC-unit can be used to
store quantum information and the information can be moved around via some
cellular shifting mechanism. Impurity doping marks a special site
D$\not\in{\cal L}$ which together with the local spin lattice constitute a
quantum automaton where the D site serves as the input/output port and
universal quantum logic is done through two-body interactions between two spins
at D and a nearby site. The novel NMR quantum computer can be easily scaled up
and may work at low temperature to overcome the problem of exponential decay in
signal-to-noise ratio in room temperature NMR.


title:
Dynamics of decoherence in continuous atom-optical quantum nondemolition
  measurements

abstract:
  The Lindblad approach to continuous quantum measurements is applied to a
system composed of a two-level atom interacting with a stationary quantized
electromagnetic field through a dispersive coupling fulfilling quantum
nondemolition criteria. Two schemes of measurements are examined. The first one
consists in measuring the atomic electric dipole, which indirectly allows one
to infer the photon distribution inside the cavity. The second one schematizes
a measurement of photon momentum, which permits to describe the atomic level
distribution. Decoherence of the corresponding reduced density matrices is
studied in detail for both cases, and its relationship to recent experiments is
finally discussed.


title:
Electron acceleration due to photon absorption: A possible origin of the
  infinity problems in relativistic quantum fields

abstract:
  Based on the concept of extended particles recently introduced we perform a
Gedankenexperiment accelerating single electrons with photons of suitably low
frequency. Accounting for relativistic time dilation due to the acquired
velocity and in infinite repetition of single absorption processes it can be
shown that the kinetic energy in the infinite limit is equal to m_{e} c^{2}/2.
However, the inertial mass of the electron seems enhanced, and it can be
established that this enhancement is described by the relativistic mass effect.
It appears, therefore, that although there exists a singularity in interactions
- the frequency required to accelerate the particle near the limit of c becomes
infinite - the energy of the particle itself approaches a finite limit.
Comparing with calculations of the Lamb-shift by Bethe this result seems to
provide the ultimate justification for the renormalization procedures employed.


title: Decoherent Histories and Hydrodynamic Equations

abstract:
  For a system consisting of a large collection of particles, a set of
variables that will generally become effectively classical are the local
densities (number, momentum, energy). That is, in the context of the decoherent
histories approach to quantum theory, it is expected that histories of these
variables will be approximately decoherent, and that their probabilites will be
strongly peaked about hydrodynamic equations. This possibility is explored for
the case of the diffusion of the number density of a dilute concentration of
foreign particles in a fluid. This system has the appealing feature that the
microscopic dynamics of each individual foreign particle is readily obtained
and the approach to local equilibrium may be seen explicitly. It is shown that,
for certain physically reasonable initial states, the probabilities for
histories of number density are strongly peaked about evolution according to
the diffusion equation. Decoherence of these histories is also shown for a
class of initial states which includes non-trivial superpositions of number
density. Histories of phase space densities are also discussed. The case of
histories of number, momentum and energy density for more general systems, such
as a dilute gas, is also discussed in outline. When the initial state is a
local equilibrium state, it is shown that the histories are trivally
decoherent, and that the probabilities for histories are peaked about
hydrodynamic equations. An argument for decoherence of more general initial
states is given.


title:
Quantum Theory in the Rigged Hilbert Space-Irreversibility from
  Causality

abstract:
  After a review of the arrows of time, we describe the possibilities of a
time-asymmetry in quantum theory. Whereas Hilbert space quantum mechanics is
time-symmetric, the rigged Hilbert space formulation, which arose from Dirac's
bra-ket formalism, allows the choice of asymmetric boundary conditions
analogous to the retarded solutions of the Maxwell equations for the radiation
arrow of time. This led to irreversibility on the microphysical level as
exemplified by decaying states or resonances. Resonances are mathematically
represented by Gamow kets, functionals over a space of very well-behaved (Hardy
class) vectors, which have been chosen by a boundary condition (outgoing for
decaying states). Gamow states have all the properties that one heuristically
needs for quasistable states. For them a Golden Rule can be derived from the
fundamental probabilities that fulfills the time-asymmetry condition which
could not be realized in the Hilbert space.


title: When does a Measurement or Event Occur

abstract:
  Within quantum mechanics it is possible to assign a probability to the chance
that a measurement has been made at a specific time t. However, the
interpretation of such a probability is far from clear. We argue that a recent
measuring scheme of Rovelli's (quant-ph/9802020) yields probabilities which do
not correspond to the conventional probabilities usually assigned in quantum
mechanics. The same arguments also apply to attempts to use the probability
current to measure the time at which a particle arrives at a given location.


title:
Decoherence, Einselection, and the Existential Interpretation (the Rough
  Guide)

abstract:
  The roles of decoherence and environment-induced superselection in the
emergence of the classical from the quantum substrate are described. The
stability of correlations between the einselected quantum pointer states and
the environment allows them to exist almost as objectively as classical states
were once thought to exist: There are ways of finding out what is the pointer
state of the system which utilize redundancy of their correlations with the
environment, and which leave einselected states essentially unperturbed. This
relatively objective existence of certain quantum states facilitates
operational definition of probabilities in the quantum setting. Moreover, once
there are states that `exist' and can be `found out', a `collapse' in the
traditional sense is no longer necessary --- in effect, it has already
happened. The records of the observer will contain evidence of an effective
collapse. The role of the preferred states in the processing and storage of
information is emphasized. The existential interpretation based on the
relatively objective existence of stable correlations between the einselected
states of observers memory and in the outside Universe is formulated and
discussed.


title:
On Reichenbach's common cause principle and Reichenbach's notion of
  common cause

abstract:
  It is shown that, given any finite set of pairs of random events in a Boolean
algebra which are correlated with respect to a fixed probability measure on the
algebra, the algebra can be extended in such a way that the extension contains
events that can be regarded as common causes of the correlations in the sense
of Reichenbach's definition of common cause. It is shown, further, that, given
any quantum probability space and any set of commuting events in it which are
correlated with respect to a fixed quantum state, the quantum probability space
can be extended in such a way that the extension contains common causes of all
the selected correlations, where common cause is again taken in the sense of
Reichenbach's definition. It is argued that these results very strongly
restrict the possible ways of disproving Reichenbach's Common Cause Principle.


title: The broadcast quantum channel for classical information transmission

abstract:
  It is well known that quantum theory forbids the exact copying of an unknown
quantum state. Therefore in broadcasting of classical information by a quantum
channel an additional contribution to the error in the decoding is expected. We
consider the optimal copying transformation which is adapted to classical
information transmission by two linearly independent quantum states, and show
that there is no additional contribution to the error. Instead the clones are
correlated, and this breaks their usefulness: The entanglement increases with
non-orthogonality of the states. The capacity of the corresponding quantum
channel is considered also.


title: Does quantum chaos exist? (A quantum Lyapunov exponents approach.)

abstract:
  We shortly review the progress in the domain of deterministic chaos for
quantum dynamical systems. With the appropriately extended definition of
quantum Lyapunov exponent we analyze various quantum dynamical maps. It is
argued that, within Quantum Mechanics, irregular evolution for properly chosen
observables can coexist with regular and predictable evolution of states.


title:
Implementation of a Quantum Search Algorithm on a Nuclear Magnetic
  Resonance Quantum Computer

abstract:
  We demonstrate an implementation of a quantum search algorithm on a two qubit
NMR quantum computer based on cytosine.


title: Quantum Logic Gates and Nuclear Magnetic Resonance Pulse Sequences

abstract:
  We demonstrate how NMR can in principle be used to implement all the elements
required to build quantum computers, and briefly discuss the potential
applications of insights from quantum logic to the development of novel pulse
sequences with applications in more conventional NMR experiments.


title: Practical free-space quantum key distribution over 1 km

abstract:
  A working free-space quantum key distribution (QKD) system has been developed
and tested over an outdoor optical path of ~1 km at Los Alamos National
Laboratory under nighttime conditions. Results show that QKD can provide secure
real-time key distribution between parties who have a need to communicate
secretly. Finally, we examine the feasibility of surface to satellite QKD.


title: Entanglement and thermodynamical analogies

abstract:
  We provide some new properties of entanglement of formation. In particular,
we obtain an additive lower bound for entanglement of formation. Subsequently
we develop the concept of local orthogonality of ensembles which leads to the
mixed states with distillable entanglement equal to entanglement of formation.
Then we consider thermodynamical analogies within the entanglement processing
domain. Especially, we exploit analogy entanglement -- energy. In this scheme
the total entanglement i.e. the amount of singlet pairs needed for local
preparation of a state corresponds to internal energy while the free
entanglement defined as the number of pairs which can be recovered from the
state (distillable entanglement) is the counterpart of free energy. In
particular, it leads us to the question about ``temperature'' of entanglement.
We also propose a scheme of the search of representative state for given
entanglement which can be viewed as an analogue of the Jaynes maximum entropy
principle.


title: Optimal Copying of One Quantum Bit

abstract:
  A quantum copying machine producing two (in general non-identical) copies of
an arbitrary input state of a two-dimensional Hilbert space (qubit) is studied
using a quality measure based on distinguishability of states, rather than
fidelity. The problem of producing optimal copies is investigated with the help
of a Bloch sphere representation, and shown to have a well-defined solution,
including cases in which the two copies have unequal quality, or the quality
depends upon the input state (is ``anisotropic'' in Bloch sphere language), or
both. A simple quantum circuit yields the optimal copying machine. With a
suitable choice of parameters it becomes an optimal eavesdropping machine for
some versions of quantum cryptography, or reproduces the Buzek and Hillery
result for isotropic copies.


title: Is the EPR paradox really a paradox?

abstract:
  The EPR paradox and the meaning of the Bell inequality are discussed. It is
shown that considering the quantum objects as carrying with them ''instruction
kits'' telling them what to do when meeting a measurement apparatus any paradox
disappears. In this view the quantum state is characterized by the prescribed
behaviour rather than by the specific value a parameter assumes as a result of
an interaction.


title: Time Machines and the Breakdown of Unitarity

abstract:
  We present a generic way of thinking about time machines from the view of a
far away observer. In this model the universe consists of three (or more)
regions: One containing the entrance of the time machine, another the exit and
the remaining one(s) the rest of the universe. In the latter we know ordinary
quantum mechanics to be valid and thus are able to write down a Hamiltonian
describing this generic time machine. We prove the time-evolution operator to
be non-symmetric. Various interpretations of this irreversibility are given.


title: Full observation of single-atom dynamics in cavity QED

abstract:
  We report the use of broadband heterodyne spectroscopy to perform continuous
measurement of the interaction energy between one atom and a high-finesse
optical cavity, during individual transit events of $\sim 250$ $\mu$s duration.
Measurements over a wide range of atom-cavity detunings reveal the transition
from resonant to dispersive coupling, via the transfer of atom-induced signals
from the amplitude to the phase of light transmitted through the cavity. By
suppressing all sources of excess technical noise, we approach a measurement
regime in which the broadband photocurrent may be interpreted as a classical
record of conditional quantum evolution in the sense of recently developed
quantum trajectory theories.


title: In-loop squeezing is real squeezing to an in-loop atom

abstract:
  Electro-optical feedback can produce an in-loop photocurrent with arbitrarily
low noise. This is not regarded as evidence of `real' squeezing because
squeezed light cannot be extracted from the loop using a linear beam splitter.
Here I show that illuminating an atom (which is a nonlinear optical element)
with `in-loop' squeezed light causes line-narrowing of one quadrature of the
atom's fluorescence. This has long been regarded as an effect which can only be
produced by squeezing. Experiments on atoms using in-loop squeezing should be
much easier than those with conventional sources of squeezed light.


title: New Concept of Dynamic Complexity in Quantum Mechanics and Beyond

abstract:
  The qualitatively new concept of dynamic complexity in quantum mechanics is
based on a new paradigm appearing within a nonperturbational analysis of the
Schroedinger equation for a generic Hamiltonian system. The unreduced analysis
explicitly provides the complete, consistent solution as a set of many
incompatible components ('realisations') which should permanently and
probabilistically replace one another, since each of them is 'complete' in the
ordinary sense. This discovery leads to the universally applicable concept of
dynamic complexity and self-consistent, realistic resolution of the stagnating
problems of quantum chaos, quantum measurement, indeterminacy and wave
reduction. The peculiar, 'mysterious' character of quantum behaviour itself is
seen now as a result of a dynamically complex, intrinsically multivalued
behaviour of interacting fields at the corresponding lowest levels of the (now
completely causal) structure of reality. Incorporating the results of the
canonical theories as an over-simplified limiting case, this new approach
urgently needs support, since its causality and completeness are directly
extendible to arbitrary cases of complex behaviour of real systems, in sharp
contrast to the dominating inefficient empiricism of 'computer experimentation'
with primitive mechanistic (i. e. dynamically single-valued) 'models' of the
irreducibly multivalued reality.


title: On Quantum Mechanics

abstract:
  We discuss the axiomatic basis of quantum mechanics and show that it is
neither general nor consistent, since its axioms are incompatible with each
other and moreover it does not incorporate the magnetic quantization as in the
cyclotron motion. A general and consistent system of axioms is conjectured
which incorporates also the magnetic quantization.