title:
Quantum and classical stochastic dynamics: Exactly solvable models by
  supersymmetric methods

abstract:
  A supersymmetric method for the construction of so-called conditionally
exactly solvable quantum systems is reviewed and extended to classical
stochastic dynamical systems characterized by a Fokker-Planck equation with
drift. A class of drift-potentials on the real line as well as on the half line
is constructed for which the associated Fokker-Planck equation can be solved
exactly. Explicit drift potentials, which describe mono-, bi-, meta-or unstable
systems, are constructed and their decay rates and modes are given in closed
form.

categories: quant-ph cond-mat.stat-mech math-ph math.MP nlin.SI solv-int


title:
On how to Produce Entangled States Violating Bell's Inequalities in
  Quantum Theory

abstract:
  Feynman's path integrals provide a hidden variable description of quantum
mechanics (and quantum field theories). The time evolution kernel is unitary in
Minkowski time, but generically it becomes real and non-negative in Euclidean
time. It follows that the entangled state correlations, that violate Bell's
inequalities in Minkowski time, obey the inequalities in Euclidean time. This
observation emphasises the link between violation of Bell's inequalities in
quantum mechanics and unitarity of the theory. Search for an evolution kernel
that cannot be conveniently made non-negative leads to effective interactions
that violate time reversal invariance. Interactions giving rise to geometric
phases in the effective description of the theory, such as the anomalous
Wess-Zumino interactions, have this feature. I infer that they must be present
in any set-up that produces entangled states violating Bell's inequalities.
Such interactions would be a crucial ingredient in a quantum computer.


title: Fluorescence control through multiple interference mechanisms

abstract:
  We discuss the spontaneous emission from a coherently prepared and microwave
driven doublet of potentially closely spaced excited states to a common ground
level. Multiple interference mechanisms are identified which may lead to
fluorescence inhibition in well-separated regions of the spectrum or act
jointly in cancelling the spontaneous emission. In addition to phase
independent quantum interferences due to combined absorptions and emissions of
driving field photons, we distinguish two competing phase dependent
interference mechanisms as means of controlling the fluorescence. The
indistinguishable quantum paths may involve the spontaneous emission from the
same state of the doublet, originating from the two different components of the
initial coherent superposition. Alternatively the paths involve a different
spontaneous photon from each of two decaying states, necessarily with the same
polarization. This makes these photons indistinguishable in principle within
the uncertainty of the two decay rates. The phase dependence arises for both
mechanisms because the interfering paths differ by an unequal number of
stimulated absorptions and emissions of the microwave field photons.


title:
Differential cross section for Aharonov--Bohm effect with non standard
  boundary conditions

abstract:
  A basic analysis is provided for the differential cross section
characterizing Aharonov--Bohm effect with non standard (non regular) boundary
conditions imposed on a wave function at the potential barrier. If compared
with the standard case two new features can occur: a violation of rotational
symmetry and a more significant backward scattering.


title: Insufficient reason and entropy in quantum theory

abstract:
  The objective of the consistent-amplitude approach to quantum theory has been
to justify the mathematical formalism on the basis of three main assumptions:
the first defines the subject matter, the second introduces amplitudes as the
tools for quantitative reasoning, and the third is an interpretative rule that
provides the link to the prediction of experimental outcomes. In this work we
introduce a natural and compelling fourth assumption: if there is no reason to
prefer one region of the configuration space over another then they should be
`weighted' equally. This is the last ingredient necessary to introduce a unique
inner product in the linear space of wave functions. Thus, a form of the
principle of insufficient reason is implicit in the Hilbert inner product.
Armed with the inner product we obtain two results. First, we elaborate on an
earlier proof of the Born probability rule. The implicit appeal to insufficient
reason shows that quantum probabilities are not more objective than classical
probabilities. Previously we had argued that the consistent manipulation of
amplitudes leads to a linear time evolution; our second result is that time
evolution must also be unitary. The argument is straightforward and hinges on
the conservation of entropy. The only subtlety consists of defining the correct
entropy; it is the array entropy, not von Neumann's. After unitary evolution
has been established we proceed to introduce the useful notion of observables
and we explore how von Neumann's entropy can be linked to Shannon's information
theory. Finally, we discuss how various connections among the postulates of
quantum theory are made explicit within this approach.

categories: quant-ph cond-mat.stat-mech gr-qc math-ph math.MP


title:
Characterizing GHZ Correlations in Nondegenerate Parametric Oscillation
  via Phase Measurements

abstract:
  We present a potential realization of the Greenberger, Horne and Zeilinger
ALL or NOTHING contradiction of quantum mechanics with local realism using
phase measurement techniques in a simple photon number triplet. Such a triplet
could be generated using nondegenerate parametric oscillation.


title: Photon Frequency Entanglement Swapping

abstract:
  We propose a simple non-linear crystal based optical scheme for experimental
realization of the frequency entanglement swapping between the photons
belonging to two independent biphotons.


title: Resonance Photon Generation in a Vibrating Cavity

abstract:
  The problem of photon creation from vacuum due to the nonstationary Casimir
effect in an ideal one-dimensional Fabry--Perot cavity with vibrating walls is
solved in the resonance case, when the frequency of vibrations is close to the
frequency of some unperturbed electromagnetic mode: $\omega_w=p(\pi
c/L_0)(1+\delta)$, $|\delta|\ll 1$, (p=1,2,...). An explicit analytical
expression for the total energy in all the modes shows an exponential growth if
$|\delta|$ is less than the dimensionless amplitude of vibrations $\epsilon\ll
1$, the increment being proportional to $p\sqrt{\epsilon^2-\delta^2}$. The rate
of photon generation from vacuum in the (j+ps)th mode goes asymptotically to a
constant value $cp^2\sin^2(\pi j/p)\sqrt{\epsilon^2-\delta^2}/[\pi L_0
(j+ps)]$, the numbers of photons in the modes with indices p,2p,3p,... being
the integrals of motion. The total number of photons in all the modes is
proportional to $p^3(\epsilon^2-\delta^2) t^2$ in the short-time and in the
long-time limits. In the case of strong detuning $|\delta|>\epsilon$ the total
energy and the total number of photons generated from vacuum oscillate with the
amplitudes decreasing as $(\epsilon/\delta)^2$ for $\epsilon\ll|\delta|$. The
special cases of p=1 and p=2 are studied in detail.


title: The manipulation problem in quantum mechanics

abstract:
  We explain the meaning of dynamical manipulation, and we illustrate its
mechanism by using a system composed of a charged particle in a Penning trap.
It is shown that by means of appropriate electric shocks (delta-like pulses)
applied to the trap walls one can induce the squeezing transformation. The
geometric phases associated to some cyclic evolutions, induced either by the
standard fields of the Penning trap or by the superposition of these plus a
rotating magnetic field, are analysed


title:
Quantum chaos in the framework of complex probability processes.
  Thermodynamics of nonrelativistic vaccum

abstract:
  The problem of random motion of 1D quantum reactive harmonic oscillator
(QRHO) is formulated in terms of a wave functional regarded as a complex
probability process in an extended space. In the complex stochastic
differential equation (SDE) for this process the variables are separated with
the help of the Langevin-type model SDE introduced in the functional space. The
complete positive Fokker-Plank measure of the functional space is obtained. The
average wave function of roaming QRHO is obtained by means of functional
integration over the process with the complete Fokker-Plank measure in the
functional space. The local and averaged transition matrices of roaming QRHO
were constructed. The thermodynamics of nonrelativistic vacuum is investigated
in detail and expressions for the internal energy, Helmholtzian energy and
entropy are obtained. The oscillator's ground state energy, its shift and
broadening are calculated.


title: Violation of Bell's inequality under strict Einstein locality conditions

abstract:
  We observe strong violation of Bell's inequality in an Einstein, Podolsky and
Rosen type experiment with independent observers. Our experiment definitely
implements the ideas behind the well known work by Aspect et al. We for the
first time fully enforce the condition of locality, a central assumption in the
derivation of Bell's theorem. The necessary space-like separation of the
observations is achieved by sufficient physical distance between the
measurement stations, by ultra-fast and random setting of the analyzers, and by
completely independent data registration.


title: The Error in Bell's Theorem

abstract:
  An error in the proof of Bell's Theorem is identified and a semiclassical
model of the EPRB experiment is presented


title: Quantum computation over continuous variables

abstract:
  This paper provides necessary and sufficient conditions for constructing a
universal quantum computer over continuous variables. As an example, it is
shown how a universal quantum computer for the amplitudes of the
electromagnetic field might be constructed using simple linear devices such as
beam-splitters and phase shifters, together with squeezers and nonlinear
devices such as Kerr-effect fibers and atoms in optical cavities. Such a device
could in principle perform `quantum floating point' computations. Problems of
noise, finite precision, and error correction are discussed.


title:
The transition from a classical to a quantum world as a passage from
  extensive to non-extensive thermodynamics

abstract:
  We study the thermodynamical properties of the quantum kicked rotator,
coarsened by an external fluctuation with a weak intensity D, by means of the
Tsallis entropy with a changing entropic index q. The genuine entropic index,
corresponding to given values of D and $\hbar$ is that making the Tsallis
entropy increase linearly in time, and it is proved to become q <1 for suitably
large values of $\hbar $: This indicates a subdiffusional regime which, in
turn, signals the occurrence of quantum localization. Thus the process of
Anderson localization is shown to be compatible with a thermodynamical
representation provided that a non-extensive form of entropy is used.


title: Density Matrices and Geometric Phases for n-state Systems

abstract:
  An explicit parameterization is given for the density matrices for $n$-state
systems. The geometry of the space of pure and mixed states and the entropy of
the $n$-state system is discussed. Geometric phases can arise in only specific
subspaces of the space of all density matrices. The possibility of obtaining
nontrivial abelian and nonabelian geometric phases in these subspaces is
discussed.


title: Energy-Sensitive and "Classical-like" Distances Between Quantum States

abstract:
  We introduce the concept of the ``polarized'' distance, which distinguishes
the orthogonal states with different energies. We also give new inequalities
for the known Hilbert-Schmidt distance between neighbouring states and express
this distance in terms of the quasiprobability distributions and the normally
ordered moments. Besides, we discuss the distance problem in the framework of
the recently proposed ``classical-like'' formulation of quantum mechanics,
based on the symplectic tomography scheme. The examples of the Fock, coherent,
``Schroedinger cats,'' squeezed, phase, and thermal states are considered.


title: Observable Dirac Electron in Accelerated Frames

abstract:
  We present a new quantum algebraic description of an electron localized in
space-time. Positions in space and time, mass and Clifford generators are
defined as quantum operators. Commutation relations and relativistic shifts
under frame transformations are determined within a unique algebraic framework.
Redshifts, i.e. shifts under transformations to uniformly accelerated frames,
are evaluated and found to differ from the expressions of classical relativity.


title: Entanglement of atoms via cold controlled collisions

abstract:
  We show that by using cold controlled collisions between two atoms one can
achieve conditional dynamics in moving trap potentials. We discuss implementing
two qubit quantum--gates and efficient creation of highly entangled states of
many atoms in optical lattices.


title: Minimal coupling and Feynman's proof

abstract:
  The non quantum relativistic version of the proof of Feynman for the Maxwell
equations is discussed in a framework with a minimum number of hypotheses
required. From the present point of view it is clear that the classical
equations of motion corresponding to the gauge field interactions can be
deduced from the minimal coupling rule, and we claim here resides the essence
of the proof of Feynman.


title: Teleportation: Dream or Reality?

abstract:
  Since its discovery in 1993, we witness an intensive theoretical and
experimental effort centered on teleportation. Very recently it was claimed in
the press that ``quantum teleportation has been achieved in the laboratory''
(T. Sudbery, Nature, 390, p. 551). Here, I briefly review this research
focusing on the connection to nonlocal measurements, and question Sudbery's
statement. A philosophical inquiry about the paradoxical meaning of
teleportation in the framework of the many-worlds interpretation is added.


title: Opaque predicates, veiled sets and their logic

abstract:
  Motivated by considerations in the foundations of quantum mechanics and
inspired by the literature on vague predicates, we introduce the concept of an
opaque predicate. While in the case of vague predicates there is a kind of
indeterminacy with respect to the predicate, in the sense that the vagueness
concerns whether a well-determined object satisfies it or not, in the case of
opaque predicates the indeterminacy is with regard to the objects which should
satisfy them. In other words, their extensions are not well-defined, despite
the fact that the conditions for an object to satisfy the predicates are
well-known. We suggest that such opaque predicates (and more generally, what we
call opaque relations) can be characterized by a logic which encompasses a
semantics founded in quasi-set theory, and call their extensions veiled sets.


title:
A Family of Indecomposable Positive Linear Maps based on Entangled
  Quantum States

abstract:
  We introduce a new family of indecomposable positive linear maps based on
entangled quantum states. Central to our construction is the notion of an
unextendible product basis. The construction lets us create indecomposable
positive linear maps in matrix algebras of arbitrary high dimension.


title: Creation of photons in an oscillating cavity with two moving mirrors

abstract:
  We study the creation of photons in a one dimensional oscillating cavity with
two perfectly conducting moving walls. By means of a conformal transformation
we derive a set of generalized Moore's equations whose solution contains the
whole information of the radiation field within the cavity. For the case of
resonant oscillations we solve these equations using a renormalization group
procedure that appropriately deals with the secular behaviour present in a
naive perturbative approach. We study the time evolution of the energy density
profile and of the number of created photons inside the cavity.


title:
Building partially entangled states with Grover's amplitude
  amplification process

abstract:
  We discuss how to build some partially entangled states of $n$ two-state
quantum systems (qubits). The optimal partially entangled state with a high
degree of symmetry is considered to be useful for overcoming a shot noise limit
of Ramsey spectroscopy under some decoherence. This state is invariant under
permutation of any two qubits and inversion between the ground state $|0\ket$
and an excited state $|1\ket$ for each qubit. We show that using selective
phase shifts in certain basis vectors and Grover's inversion about average
operations, we can construct this high symmetric entangled state by
$({polynomial in $n$})\times 2^{n/2}$ successive unitary transformations that
are applied on two or three qubits. We can apply our method to build more
general entangled states.


title:
Spatial fragmentation of a Bose-Einstein condensate in a double-well
  potential

abstract:
  We present a theoretical study of the ground state of a Bose-Einstein
condensate with repulsive inter-particle interactions in a double-well
potential, using a restricted variational principle. Within such an approach,
there is a transition from a single condensate to a fragmented condensate as
the strength of the central barrier of the potential is increased. We determine
the nature of this transition through approximate analytic as well as numerical
solutions of our model in the regime where the inter-particle interactions can
be treated perturbatively. The degree of fragmentation of the condensate is
characterized by the degrees of first-order and second-order spatial coherence
across the barrier.


title: Quantum Measurements, Information and Entropy Production

abstract:
  In order to understand the Landau-Lifshitz conjecture on the relationship
between quantum measurements and the thermodynamic second law, we discuss the
notion of ``diabatic'' and ``adiabatic'' forces exerted by the quantum object
on the classical measurement apparatus. The notion of heat and work in
measurements is made manifest in this approach, and the relationship between
information entropy and thermodynamic entropy is explored.


title: Sympathetic cooling of an atomic Bose-Fermi gas mixture

abstract:
  Sympathetic cooling of an atomic Fermi gas by a Bose gas is studied by
solution of the coupled quantum Boltzmann equations for the confined gas
mixture. Results for equilibrium temperatures and relaxation dynamics are
presented, and some simple models developed. Our study illustrate that a
combination of sympathetic and forced evaporative cooling enables the Fermi gas
to be cooled to the degenerate regime where quantum statistics, and mean field
effects are important. The influence of mean field effects on the equilibrium
spatial distributions is discussed qualitatively.


title: The halting problem for universal quantum computers

abstract:
  The halting of universal quantum computers is shown to be incompatible with
the constraint of unitarity of the dynamics.


title:
Quantum dynamics in canonical and micro-canonical ensembles. Part II.
  Tunneling in double well potential

abstract:
  In the second part of this paper in micro canonical ensemble the new
numerical approach for consideration of quantum dynamics and calculations of
the average values of quantum operators and time correlation functions in the
Wigner representation of quantum statistical mechanics has been developed. The
numerical results have been obtained for series of the average values of
quantum operators as well as for the time correlation function characterizing
the energy level structure, the momentum flow of tunneling particles at barrier
crossing and the absorption spectra of electron in potential well. The
developed quantum dynamics method was tested by comparison of numerical results
with analytical estimations. Tunneling transitions and the effect of the quasi
stationary state has been considered as the reason of the peculiarities in
behaviour of the time correlation functions and position and momentum
dispersions. Possibility of applying the developed approach to the theory of
classical wave propagation in random media have been also considered. For
classical waves some results have been obtained for Gaussian beam propagation
in 2D and 3D waveguides.


title: Cavity Loss Induced Generation of Entangled Atoms

abstract:
  We discuss the generation of entangled states of two two-level atoms inside
an optical resonator. When the cavity decay is continuously monitored, the
absence of photon-counts is associated with the presence of an atomic entangled
state. In addition to being conceptually simple, this scheme could be
demonstrated with presently available technology. We describe how such a state
is generated through conditional dynamics, using quantum jump methods,
including both cavity damping and spontaneous emission decay, and evaluate the
fidelity and relative entropy of entanglement of the generated state compared
with the target entangled state.


abstract:
  We claim that the nonlocality without entanglement revealed quite recently by
Bennett {\it et al.} [quant-ph/9804053] should be rather interpreted as {\it
Einstein-Podolsky-Rosen paradox without entanglement}. It would be true
nonlocality without entanglement if one knew that quantum mechnics provides the
best possible means for extracting information from physical system i.e. that
it is ``operationally complete''.


title: A Note on Quantum Errors and Their Correction

abstract:
  This note presents a few observations on the nonlocal nature of quantum
errors and the expected performance of the recently proposed quantum
error-correction codes that are based on the assumption that the errors are
either bit-flip or phase-flip or both.


title: An Introduction to Quantum Computers

abstract:
  This is a short introduction to quantum computers, quantum algorithms and
quantum error correcting codes. Familiarity with the principles of quantum
theory is assumed. Emphasis is put on a concise presentation of the principles
avoiding lengthy discussions.


title:
Coherent population transfer beyond the adiabatic limit: generalized
  matched pulses and higher-order trapping states

abstract:
  We show that the physical mechanism of population transfer in a 3-level
system with a closed loop of coherent couplings (loop-STIRAP) is not equivalent
to an adiabatic rotation of the dark-state of the Hamiltonian but coresponds to
a rotation of a higher-order trapping state in a generalized adiabatic basis.
The concept of generalized adiabatic basis sets is used as a constructive tool
to design pulse sequences for stimulated Raman adiabatic passage (STIRAP) which
give maximum population transfer also under conditions when the usual condition
of adiabaticty is only poorly fulfilled. Under certain conditions for the
pulses (generalized matched pulses) there exists a higher-order trapping state,
which is an exact constant of motion and analytic solutions for the atomic
dynamics can be derived.


title: Eigenvalue bounds for a class of singular potentials in N dimensions

abstract:
  The eigenvalue bounds obtained earlier [J. Phys. A: Math. Gen. 31 (1998) 963]
for smooth transformations of the form V(x) = g(x^2) + f(1/x^2) are extended to
N-dimensions. In particular a simple formula is derived which bounds the
eigenvalues for the spiked harmonic oscillator potential V(x) = x^2 +
lambda/x^alpha, alpha > 0, lambda > 0, and is valid for all discrete
eigenvalues, arbitrary angular momentum ell, and spatial dimension N.


title: Quantum evolution according to real clocks

abstract:
  We characterize good clocks, which are naturally subject to fluctuations, in
statistical terms. We also obtain the master equation that governs the
evolution of quantum systems according to these clocks and find its general
solution. This master equation is diffusive and produces loss of coherence.
Moreover, real clocks can be described in terms of effective interactions that
are nonlocal in time. Alternatively, they can be modeled by an effective
thermal bath coupled to the system.


title: Exactly soluble models of decoherence

abstract:
  Superselection rules induced by the interaction with the environment are a
basis to understand the emergence of classical observables within quantum
theory. The aim of this article is to investigate the decoherence effects,
which lead to superselection sectors, with the help of exactly soluble
Hamiltonian models. Starting from the examples of Araki and of Zurek more
general models with scattering are presented for which the projection operators
onto the induced superselection sectors do no longer commute with the
Hamiltonian. The example of an environment given by a free quantum field
indicates that infrared divergence plays an essential role for the emergence of
induced superselection sectors. For all models the induced superselection
sectors are uniquely determined by the Hamiltonian, whereas the time scale of
the decoherence depends crucially on the initial state of the total system.


title: Motional Quantum Error Correction

abstract:
  We examine the dynamics of a qubit stored in the motional degrees of freedom
of an ultra-cold ion in an ion trap which is subject to the decoherence effects
of a finite-temperature bath. We discover an encoding of the qubit, in two of
the motional modes of the ion, which is stable against the occurrence of either
none or one quantum jump. For the case of a zero-temperature bath we describe
how to transfer only the information concerning the occurrence of quantum jumps
and their types to a measuring apparatus, without affecting the ion's motional
state significantly. We then describe how to generate a unitary restoration of
the qubit given the jump information, through Raman processes generated by a
series of laser pulses.


title:
Superrevivals in the quantum dynamics of a particle confined in a finite
  square well potential

abstract:
  We examine the revival features in wave packet dynamics of a particle
confined in a finite square well potential. The possibility of tunneling
modifies the revival pattern as compared to an infinite square well potential.
We study the dependence of the revival times on the depth of the square well
and predict the existence of superrevivals. The nature of these superrevivals
is compared with similar features seen in the dynamics of wavepackets in an
anharmonic oscillator potential.


title: Violations of Local Realism in the Innsbruck GHZ Experiment

abstract:
  It is shown that a careful analysis of the `wrong' events (those not present
in the usual formulations of the GHZ argument), which are a necessary feature
of the tests of local realism involving independent sources, permits one to
show that there is no local realistic model, which is capable to describe
recent GHZ experiments performed in Innsbruck


title:
Suppression of Classical and Quantum Radiation Pressure Noise via
  Electro-Optic Feedback

abstract:
  We present theoretical results that demonstrate a new technique to be used to
improve the sensitivity of thermal noise measurements: intra-cavity intensity
stabilisation. It is demonstrated that electro-optic feedback can be used to
reduce intra-cavity intensity fluctuations, and the consequent radiation
pressure fluctuations, by a factor of two below the quantum noise limit. We
show that this is achievable in the presence of large classical intensity
fluctuations on the incident laser beam. The benefits of this scheme are a
consequence of the sub-Poissonian intensity statistics of the field inside a
feedback loop, and the quantum non-demolition nature of radiation pressure
noise as a readout system for the intra-cavity intensity fluctuations.


title: Noiseless phase quadrature amplification via electro-optic feed-forward

abstract:
  Theoretical results are presented which show that noiseless phase quadrature
amplification is possible, and limited experimentally only by the efficiency of
the phase detection system. Experimental results obtained using a Nd:YAG laser
show a signal gain of 10dB and a signal transfer ratio of T_s=0.9. This result
easily exceeds the standard quantum limit for signal transfer. The results also
explicitly demonstrate the phase sensitive nature of the amplification process.


title:
Finite-Length Soliton Solutions of the Local Homogeneous Nonlinear
  Schroedinger Equation

abstract:
  We found a new kind of soliton solutions for the 5-parameter family of the
potential-free Stenflo-Sabatier-Doebner-Goldin nonlinear modifications of the
Schr\"odinger equation. In contradistinction to the "usual'' solitons like
{\cosh[b(x-kt)]}^{-a}\exp[i(kx-ft)], the new {\em Finite-Length Solitons} (FLS)
are nonanalytical functions with continuous first derivatives, which are
different from zero only inside some finite regions of space. The simplest
one-dimensional example is the function which is equal to
{\cos[g(x-kt)]}^{1+d}\exp[i(kx-ft)] (with d>0) for |x-kt|<\pi/(2g), being
identically equal to zero for |x-kt|>\pi/(2g). The FLS exist even in the case
of a weak nonlinearity, whereas the ``usual'' solitons exist provided the
nonlinearity parameters surpass some critical values.


title:
Optical pumping in dense atomic media: Limitations due to reabsorption
  of spontaneously emitted photons

abstract:
  Resonant optical pumping in dense atomic media is discussed, where the
absorption length is less than the smallest characteristic dimension of the
sample. It is shown that reabsorption and multiple scattering of spontaneous
photons (radiation trapping) can substantially slow down the rate of optical
pumping. A very slow relaxation out of the target state of the pump process is
then sufficient to make optical pumping impossible. As model systems an
inhomogeneously and a radiatively broadened 3-level system resonantly driven
with a strong broad-band pump field are considered.


title:
Separability of very noisy mixed states and implications for NMR quantum
  computing

abstract:
  We give a constructive proof that all mixed states of N qubits in a
sufficiently small neighborhood of the maximally mixed state are separable. The
construction provides an explicit representation of any such state as a mixture
of product states. We give upper and lower bounds on the size of the
neighborhood, which show that its extent decreases exponentially with the
number of qubits. We also discuss the implications of the bounds for NMR
quantum computing.


title: Tunneling Times and Superluminality: a Tutorial

abstract:
  Experiments have shown that individual photons penetrate an optical tunnel
barrier with an effective group velocity considerably greater than the vacuum
speed of light. The experiments were conducted with a two-photon parametric
down-conversion light source, which produced correlated, but random, emissions
of photon pairs. The two photons of a given pair were emitted in slightly
different directions so that one photon passed through the tunnel barrier,
while the other photon passed through the vacuum. The time delay for the
tunneling photon relative to its twin was measured by adjusting the path length
difference between the two photons in a Hong-Ou-Mandel interferometer, in order
to achieve coincidence detection. We found that the photon transit time through
the barrier was smaller than the twin photon's transit time through an equal
distance in vacuum, indicating that the process of tunneling in quantum
mechanics is superluminal. Various conflicting theories of tunneling times are
compared with experiment.


title: Complete quantum teleportation using nuclear magnetic resonance

abstract:
  Quantum mechanics provides spectacular new information processing abilities
(Bennett 1995, Preskill 1998). One of the most unexpected is a procedure called
quantum teleportation (Bennett et al 1993) that allows the quantum state of a
system to be transported from one location to another, without moving through
the intervening space. Partial implementations of teleportation (Bouwmeester et
al 1997, Boschi et al 1998) over macroscopic distances have been achieved using
optical systems, but omit the final stage of the teleportation procedure. Here
we report an experimental implementation of the full quantum teleportation
operation over inter-atomic distances using liquid state nuclear magnetic
resonance (NMR). The inclusion of the final stage enables for the first time a
teleportation implementation which may be used as a subroutine in larger
quantum computations, or for quantum communication. Our experiment also
demonstrates the use of quantum process tomography, a procedure to completely
characterize the dynamics of a quantum system. Finally, we demonstrate a
controlled exploitation of decoherence as a tool to assist in the performance
of an experiment.


title: de-Broglie Wave-Front Engineering

abstract:
  We propose a simple method for the deterministic generation of an arbitrary
continuous quantum state of the center-of-mass of an atom. The method's spatial
resolution gradually increases with the interaction time with no apparent
fundamental limitations. Such de-Broglie Wave-Front Engineering of the atomic
density can find applications in Atom Lithography, and we discuss possible
implementations of our scheme in atomic beam experiments.


title: Quantum statistics of atoms in microstructures

abstract:
  This paper proposes groove-like potential structures for the observation of
quantum information processing by trapped particles. As an illustration the
effect of quantum statistics at a 50-50 beam splitter is investigated. For
non-interacting particles we regain the results known from photon experiments,
but we have found that particle interactions destroy the perfect bosonic
correlations. Fermions avoid each other due to the exclusion principle and
hence they are far less sensitive to particle interactions. For bosons, the
behavior can be explained with simple analytic considerations which predict a
certain amount of universality. This is verified by detailed numerical
calculations.


title: A History of Feynman's Sum over Histories in Quantum Mechanics

abstract:
  A history of Feynman's sum over histories is presented in brief. A focus is
placed on the progress of path-integration techniques for exactly
path-integrable problems in quantum mechanics.

categories: quant-ph hep-th math-ph math.MP physics.hist-ph


title: Supersymmetric quantum mechanics with nonlocal potentials

abstract:
  We consider supersymmetric quantum mechanical models with both local and
nonlocal potentials. We present a nonlocal deformation of exactly solvable
local models. Its energy eigenfunctions and eigenvalues are determined exactly.
We observe that both our model Hamiltonian and its supersymmetric partner may
have normalizable zero-energy ground states, in contrast to local models with
nonperiodic or periodic potentials.


title: A semiclassical approach to the Dirac equation

abstract:
  We derive a semiclassical time evolution kernel and a trace formula for the
Dirac equation. The classical trajectories that enter the expressions are
determined by the dynamics of relativistic point particles. We carefully
investigate the transport of the spin degrees of freedom along the trajectories
which can be understood geometrically as parallel transport in a vector bundle
with SU(2) holonomy. Furthermore, we give an interpretation in terms of a
classical spin vector that is transported along the trajectories and whose
dynamics, dictated by the equation of Thomas precession, gives rise to
dynamical and geometric phases every orbit is weighted by. We also present an
analogous approach to the Pauli equation which we analyse in two different
limits.

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


title:
Quantum limit of decoherence: Environment induced superselection of
  energy eigenstates

abstract:
  We investigate decoherence in the limit where the interaction with the
environment is weak and the evolution is dominated by the self Hamiltonian of
the system. We show that in this case quantized eigenstates of energy emerge as
pointer states selected through the predictability sieve.


title: A new entanglement measure induced by the Hilbert-Schmidt norm

abstract:
  In this letter we discuss a new entanglement measure. It is based on the
Hilbert-Schmidt norm of operators. We give an explicit formula for calculating
the entanglement of a large set of states on C^2 \times C^2. Furthermore we
find some relations between the entanglement of relative entropy and the
Hilbert-Schmidt entanglement. A rigorous definition of partial transposition is
given in the appendix.


title:
Quantum noise and correlations in resonantly enhanced wave mixing based
  on atomic coherence

abstract:
  We investigate the quantum properties of fields generated by resonantly
enhanced wave mixing based on atomic coherence in Raman systems. We show that
such a process can be used for generation of pairs of Stokes and anti-Stokes
fields with nearly perfect quantum correlations, yielding almost complete (i.e.
100%) squeezing without the use of a cavity.
  We discuss the extension of the wave mixing interactions into the domain of a
few interacting light quanta.


title:
Time evolution of condensed state of interacting bosons with reduced
  number fluctuation in a leaky box

abstract:
  We study the time evolution of the Bose-Einstein condensate of interacting
bosons confined in a leaky box, when its number fluctuation is initially (t=0)
suppressed. We take account of quantum fluctuations of all modes, including k =
0. We identify a ``natural coordinate'' b_0 of the interacting bosons, by which
many physical properties can be simply described. Using b_0, we successfully
define the cosine and sine operators for interacting many bosons. The
wavefunction, which we call the ``number state of interacting bosons'' (NSIB),
of the ground state that has a definite number N of interacting bosons can be
represented simply as a number state of b_0. We evaluate the time evolution of
the reduced density operator \rho(t) of the bosons in the box with a finite
leakage flux J, in the early time stage for which Jt << N. It is shown that
\rho(t) evolves from a single NSIB at t = 0, into a classical mixture of NSIBs
of various values of N at t > 0. We define a new state called the
``number-phase squeezed state of interacting bosons'' (NPIB). It is shown that
\rho(t) for t>0 can be rewritten as the phase-randomized mixture (PRM) of
NPIBs. It is also shown that the off-diagonal long-range order (ODLRO) and the
order parameter defined by it do not distinguish the NSIB and NPIB. On the
other hand, the other order parameter \Psi, defined as the expectation value of
the boson operator, has different values among these states. For each element
of the PRM of NPIBs, we show that \Psi evolves from zero to a finite value very
quickly. Namely, after the leakage of only two or three bosons, each element
acquires a full, stable and definite (non-fluctuating) value of \Psi.


title:
Realistic theory of microscopic phenomena; a new solution of
  hidden-variable problem

abstract:
  It has been shown that quantum paradoxes have followed from one special
assumption, i.e., from attributing basic physical meaning to Hamiltonian
eigenfunctions and representing all physical states by vectors of the Hilbert
space spanned on these eigenfunctions. However, any paradoxical properties
disappear if the physical states are represented by vectors from the extended
Hilbert space on which the scattering theory of Lax and Phillips has been
based. On the other side, all stationary characteristics and experimentally
verified quantum-mechanical predictions remain the same. The extended
mathematical model is also in full agreement with results of EPR experiments,
if one takes into account that a further assumption (in addition to locality
condition) is involved in derivation of Bell's inequalities as shown recently
(see: quant-ph/9808005).


title:
Stationary States in Saturated Two-Photon Processes and Generation of
  Phase-Averaged Mixtures of Even and Odd Quantum States

abstract:
  We consider a relaxation of a single mode of the quantized field in a
presence of one- and two-photon absorption and emission processes. Exact
stationary solutions of the master equation for the diagonal elements of the
density matrix in the Fock basis are found in the case of completely saturated
two-photon emission. If two-photon processes dominate over single-photon ones,
the stationary state is a mixture of phase averaged even and odd coherent
states.


title: The Symmetry Underlying Spin and the Dirac Equation

abstract:
  It is shown, in the context of a recent formulation of elementary particles
in terms of, what may be called, a Quantum Mechanical Kerr-Newman metric, that
spin is a consequence of a space-time cut off at the Compton wavelength and
Compton time scale. On this basis, we deduce the Dirac equation from a simple
coordinate transformation.


title: Bloch-Like Quantum Multiple Reflections of Atoms

abstract:
  We show that under certain circumstances an atom can follow an oscillatory
motion in a periodic laser profile with a Gaussian envelope. These oscillations
can be well explained by using a model of energetically forbidden spatial
regions. The similarities and differences with Bloch oscillations are
discussed. We demonstrate that the effect exists not only for repulsive but
also for attractive potentials, i.e. quantum multiple reflections are also
possible.


title: Thermodynamics of the Casimir Effect - Asymptotic Considerations -

abstract:
  We study the Casimir effect with different temperatures between the plates
($T$) resp. outside of them ($T'$). If we consider the inner system as the
black body radiation for a special geometry, then contrary to common belief the
temperature approaches a constant value for vanishing volume during isentropic
processes. This means: the reduction of the degrees of freedom can not be
compensated by a concentration of the energy during an adiabatic contraction of
the two-plate system. Looking at the Casimir pressure, we find one unstable
equilibrium point for isothermal processes with $T > T'$. For isentropic
processes there is additionally one stable equilibrium point for larger values
of the distances between the two plates.}


title: Two-atom dark states in electromagnetic cavities

abstract:
  The center-of-mass motion of two two-level atoms coupled to a single damped
mode of an electromagnetic resonator is investigated. For the case of one atom
being initially excited and the cavity mode in the vacuum state it is shown
that the atomic time evolution is dominated by the appearance of dark states.
These states, in which the initial excitation is stored in the internal atomic
degrees of freedom and the atoms become quantum mechanically entangled, are
almost immune against photon loss from the cavity. Various properties of the
dark states within and beyond the Raman-Nath approximation of atom optics are
worked out.


title: Non-linear operations in quantum information theory

abstract:
  Quantum information theory is used to analize various non-linear operations
on quantum states. The universal disentanglement machine is shown to be
impossible, and partial (negative) results are obtained in the state-dependent
case. The efficiency of the transformation of non-orthogonal states into
orthogonal ones is discussed.


title: Theory of dressed states in quantum optics

abstract:
  The dual Dyson series [M.Frasca, Phys. Rev. A {\bf 58}, 3439 (1998)], is used
to develop a general perturbative method for the study of atom-field
interaction in quantum optics. In fact, both Dyson series and its dual, through
renormalization group methods to remove secular terms from the perturbation
series, give the opportunity of a full study of the solution of the
Schr\"{o}dinger equation in different ranges of the parameters of the given
hamiltonian. In view of recent experiments with strong laser fields, this
approach seems well-suited to give a clarification and an improvement of the
applications of the dressed states as currently done through the eigenstates of
the atom-field interaction, showing that these are just the leading order of
the dual Dyson series when the Hamiltonian is expressed in the interaction
picture. In order to exploit the method at the best, a study is accomplished of
the well-known Jaynes-Cummings model in the rotating wave approximation, whose
exact solution is known, comparing the perturbative solutions obtained by the
Dyson series and its dual with the same approximations obtained by Taylor
expanding the exact solution. Finally, a full perturbative study of high-order
harmonic generation is given obtaining, through analytical expressions, a clear
account of the power spectrum using a two-level model, even if the method can
be successfully applied to a more general model that can account for ionization
too. The analysis shows that to account for the power spectrum it is needed to
go to first order in the perturbative analysis. The spectrum obtained gives a
way to measure experimentally the shift of the energy levels of the atom
interacting with the laser field by looking at the shifting of hyper-Raman
lines.


title:
Quantum cryptography based on photon ``frequency'' states: example of a
  possible realization

abstract:
  A quantum cryptosystem is proposed using single-photon states with different
frequency spectra as information carriers. A possible experimental
implementation of the cryptosystem is discussed.


title: The Non-mechanistic Character of Quantum Computation

abstract:
  The higher than classical efficiency exhibited by some quantum algorithms is
here ascribed to their non-mechanistic character, which becomes evident by
joining the notions of entanglement and quantum measurement. Measurement
analogically sets a (partial) constraint on the output of the computation of a
hard-to-reverse function. This constraint goes back in time along the
reversible computation process, computing the reverse function, which yields
quantum efficiency. The evolution, comprising wave function collapse (here a
revamped notion), is non-mechanistic as it is driven by both an initial
condition and a final constraint. It seems that the more the output is
constrained by measurement, the higher can be the efficiency. Setting a
complete constraint, by means of a special Zeno effect, yields (speculatively)
NP-complete=P.


title: Nelsonian Mechanics Revisited

abstract:
  In de Broglie and Bohm's pilot-wave theory, as is well known, it is possible
to consider alternative particle dynamics while still preserving the quantum
distribution. I present the analogous result for Nelson's stochastic theory,
thus characterising the most general diffusion processes that preserve the
quantum equilibrium distribution, and discuss the analogy with the construction
of the dynamics for Bell's beable theories. I briefly comment on the problem of
convergence to the quantum distribution and on possible experimental
constraints on the alternative dynamics.


title: Maximally Realistic Causal Quantum Mechanics

abstract:
  We recently constructed a causal quantum mechanics in 2 dim. phase space
which is more realistic than the de Broglie-Bohm mechanics as it reproduces not
just the position but also the momentum probability density of ordinary quantum
theory. Here we present an even more ambitious construction in 2n dim. phase
space. We conjecture that the causal Hamiltonian quantum mechanics presented
here is `maximally realistic'. The positive definite phase space density
reproduces as marginals the correct quantum probability densities of $n+1$
different complete commuting sets of observables (e.g. $\vec q$, $\vec p$ and
$n-1$ other sets). In general the particle velocities do not coincide with the
de Broglie-Bohm velocities.


title:
Comment on testing Bell's inequality with Rydberg atoms entangled
  through cavity photons

abstract:
  Rydberg atoms traversing a micromaser cavity one after the other can emerge
in correlated states, and according to Copenhagen quantum mechanics this may
lead to a violation of Bell's inequality, that is, to a Bell sum S>2. S is here
calculated in various ideal physical situations including those with (1)
different initial states of the atoms, (2) different free adjustable
parameters, being either the phase or the turning angle of a classical
radiation field put behind the cavity, and (3) either equal or different Rabi
angles for successive atoms. The experiments are crucial for a realist
interpretation which predicts S<2 or S=2 because particles of different kinds
(photons and atoms) are involved.


title:
Pulse Sequences for NMR Quantum Computers: How to Manipulate Nuclear
  Spins While Freezing the Motion of Coupled Neighbours

abstract:
  We show how to divide a coupled multi-spin system into a small subset of
``active'' spins that evolve under chemical shift or scalar coupling operators,
and a larger subset of ``spectator'' spins which are returned to their initial
states, as if their motion had been temporarily frozen. This allows us to
implement basic one-qubit and two-qubit operations from which general
operations on $N$-qubits can be constructed, suitable for quantum computation.
The principles are illustrated by experiments on the three coupled protons of
2,3-dibromopropanoic acid, but the method is applicable to any spin-1/2 nuclei
and to systems containing arbitrary numbers of coupled spins.


title: NMR Quantum Computation with a hyperpolarized nuclear spin bulk

abstract:
  We consider two new quantum gate mechanisms based on nuclear spins in
hyperpolarized solid $^{129}Xe$ and HCl mixtures and inorganic semiconductors.
We propose two schemes for implementing a controlled NOT (CNOT) gate based on
nuclear magnetic resonance (NMR) spectroscopy and magnetic resonance imaging
(MRI) from hyperpolarized solid $^{129}Xe$ and HCl mixtures and optically
pumped NMR in semiconductors. Such gates might be built up with particular
spins addressable based on MRI techniques and optical pumping and optical
detection techniques. The schemes could be useful for implementing actual
quantum computers in terms of a cellular automata architecture.


title: Quantum, Chaos and the Universe

abstract:
  In this paper we suggest a formulation that would bear out the spirit of
Prigogine's "Order Out of Chaos" and Wheeler's "Law Without Law". In it a
typical elementary particle length, namely the pion Compton wavelength arises
from the random motion of the N particles in the universe of dimension R. It is
then argued in the light of recent work that this is the origin of the laws of
physics and leads to a cosmology consistent with observation.


title: Lower Bounds for Quantum Search and Derandomization

abstract:
  We prove lower bounds on the error probability of a quantum algorithm for
searching through an unordered list of N items, as a function of the number T
of queries it makes. In particular, if T=O(sqrt{N}) then the error is lower
bounded by a constant. If we want error <1/2^N then we need T=Omega(N) queries.
We apply this to show that a quantum computer cannot do much better than a
classical computer when amplifying the success probability of an RP-machine. A
classical computer can achieve error <=1/2^k using k applications of the
RP-machine, a quantum computer still needs at least ck applications for this
(when treating the machine as a black-box), where c>0 is a constant independent
of k. Furthermore, we prove a lower bound of Omega(sqrt{log N}/loglog N)
queries for quantum bounded-error search of an ordered list of N items.


title: Maximally Causal Quantum Mechanics

abstract:
  We present a new causal quantum mechanics in one and two dimensions developed
recently at TIFR by this author and V. Singh. In this theory both position and
momentum for a system point have Hamiltonian evolution in such a way that the
ensemble of system points leads to position and momentum probability densities
agreeing exactly with ordinary quantum mechanics.


title:
Schroedinger equation as the universal continuum limit of
  nonrelativistic coherent hopping on a cubic spatial lattice

abstract:
  The Schroedinger equation with scalar and vector potentials is the continuum
limit of any coherent hopping process (where position eigenstates superpose
with neighbouring eigenstates after a time step) whose hopping amplitudes are
homogeneous in quadratic order of the inverse lattice spacing, inhomogeneous in
first order, and satisfying a summability condition with respect to
higher-than-next neighbours.


title:
Local-field approach to the interaction of an ultracold dense Bose gas
  with a light field

abstract:
  The propagation of the electromagnetic field of a laser through a dense Bose
gas is examined and nonlinear operator equations for the motion of the center
of mass of the atoms are derived. The goal is to present a self-consistent set
of coupled Maxwell-Bloch equations for atomic and electromagnetic fields
generalized to include the atomic center-of-mass motion. Two effects are
considered: The ultracold gas forms a medium for the Maxwell field which
modifies its propagation properties. Combined herewith is the influence of the
dipole-dipole interaction between atoms which leads to a density dependent
shift of the atomic transition frequency. It is expressed in a position
dependent detuning and is the reason for the nonlinearity. This results in a
direct and physically transparent way from the quantum field theoretical
version of the local-field approach to electrodynamics in quantum media. The
equations for the matter fields are general. Previously published nonlinear
equations are obtained as limiting cases. As an atom optical application the
scattering of a dense beam of a Bose gas is studied in the Raman-Nath regime.
The main conclusion is that for increasing density of the gas the dipole-dipole
interaction suppresses or enhances the scattering depending on the sign of the
detuning.


title: Early Gedanken Experiments of Quantum Mechanics Revisited

abstract:
  The famous gedanken experiments of quantum mechanics have played crucial
roles in developing the Copenhagen interpretation. They are studied here from
the perspective of standard quantum mechanics, with no ontological
interpretation involved. Bohr's investigation of these gedanken experiments,
based on the uncertainty relation with his interpretation, was the origin of
the Copenhagen interpretation and is still widely adopted, but is shown to be
not consistent with the quantum mechanical view. We point out that in most of
these gedanken experiments, entanglement plays a crucial role, while its
buildup does not change the uncertainty of the concerned quantity in the way
thought by Bohr. Especially, in the gamma ray microscope and recoiling
double-slit gedanken experiments, we expose the entanglement based on momentum
exchange. It is shown that even in such cases, the loss of interference is only
due to the entanglement with other degrees of freedom, while the uncertainty
relation argument, which has not been questioned up to now, is not right.


title: Product Representations and the Quantization of Constrained Systems

abstract:
  We study special systems with infinitely many degrees of freedom with regard
to dynamical evolution and fulfillment of constraint conditions. Attention is
focused on establishing a meaningful functional framework, and for that
purpose, coherent states and reproducing kernel techniques are heavily
exploited. Several examples are given.


title: Quantum codes on a lattice with boundary

abstract:
  A new type of local-check additive quantum code is presented. Qubits are
associated with edges of a 2-dimensional lattice whereas the stabilizer
operators correspond to the faces and the vertices. The boundary of the lattice
consists of alternating pieces with two different types of boundary conditions.
Logical operators are described in terms of relative homology groups.


title: Conditions for a class of entanglement transformations

abstract:
  Suppose Alice and Bob jointly possess a pure state, $|\psi\ra$. Using local
operations on their respective systems and classical communication it may be
possible for Alice and Bob to transform $|\psi\ra$ into another joint state
$|\phi\ra$. This Letter gives necessary and sufficient conditions for this
process of entanglement transformation to be possible. These conditions reveal
a partial ordering on the entangled states, and connect quantum entanglement to
the algebraic theory of majorization. As a consequence, we find that there
exist essentially different types of entanglement for bipartite quantum
systems.


title: Remarks on identical particles in de Broglie-Bohm theory

abstract:
  It is argued that the topological approach to the (anti-)symmetrisation
condition for the quantum state of a collection of identical particles, defined
in the `reduced' configuration space, is particularly natural from the
perspective of de Broglie-Bohm pilot-wave theory.


title:
A simple Example of Definitions of Truth, Validity, Consistency, and
  Completeness in Quantum Mechanics

abstract:
  Besides their use for efficient computation, quantum computers are a base for
studying quantum systems that create valid physical theories using mathematics
and physics. An essential part of the validation process for quantum mechanics
is the development of a coherent theory of mathematics and quantum mechanics
together. Such a theory should combine mathematical logical concepts with
quantum mechanics. That this might be possible is shown here by defining truth,
validity, consistency, and completeness for a quantum mechanical version of a
simple classical expression enumeration machine described by Smullyan. It is
seen that for an interpretation based on a Feynman path sum over expression
path states, truth, consistency, and completeness have different properties
than for the classical system. For instance the truth of a sentence S is
defined only on the paths containing S. It is undefined elsewhere. Also S and
its negation can both be true provided they appear on separate paths. This
satisfies the definition of consistency. It is seen that validity and
completeness connect the system dynamics to the truth of the sentences. It is
proved that validity implies consistency. The requirements of validity and
maximal completeness strongly restrict the possible dynamics of the system.
Aspects of the existence of a valid, maximally complete dynamics are discussed.
An exponentially efficient quantum computer is described that is also valid and
complete.


title: A Quick Glance at Quantum Cryptography

abstract:
  The recent application of the principles of quantum mechanics to cryptography
has led to a remarkable new dimension in secret communication. As a result of
these new developments, it is now possible to construct cryptographic
communication systems which detect unauthorized eavesdropping should it occur,
and which give a guarantee of no eavesdropping should it not occur.
  CONTENTS P3. Cryptographic systems before quantum cryptography P7. Preamble
to quantum cryptography P10. The BB84 quantum cryptographic protocol without
noise P16. The BB84 quantum cryptographic protocol with noise P19..The B92
quantum cryptographic protocol P21. EPR quantum cryptographic protocols P25.
Other protocols P25. Eavesdropping stategies and counter measures P26.
Conclusion P29. Appendix A. The no cloning theorem P30. Appendix B. Proof that
an undetectable eavesdropper can obtain no information from the B92 protocol
P31. Appendix C. Part of a Rosetta stone for quantum mechanics P44. References


title: Space-time counterfactuals

abstract:
  A definition is proposed to give precise meaning to the counterfactual
statements that often appear in discussions of the implications of quantum
mechanics. Of particular interest are counterfactual statements which involve
events occurring at space-like separated points, which do not have an absolute
time ordering. Some consequences of this definition are discussed.


title:
Reducing spatially correlated noise and decoherence with quantum error
  correcting codes

abstract:
  It is shown that the noise process in quantum computation can be described by
spatially correlated decoherence and dissipation. We demonstrate that the
conventional quantum error correcting codes correcting for single-qubit errors
are applicable for reducing spatially correlated noise.


title:
Decoherence of quantum wavepackets due to interaction with conformal
  spacetime fluctuations

abstract:
  One of the biggest problems faced by those attempting to combine quantum
theory and general relativity is the experimental inaccessibility of the
unification scale. In this paper we show how incoherent conformal waves in the
gravitational field, which may be produced by quantum mechanical zero-point
fluctuations, interact with the wavepackets of massive particles. The result of
this interaction is to produce decoherence within the wavepackets which could
be accessible in experiments at the atomic scale.
  Using a simple model for the coherence properties of the gravitational field
we derive an equation for the evolution of the density matrix of such a
wavepacket. Following the primary state diffusion programme, the most promising
source of spacetime fluctuations for detection are the above zero-point energy
fluctuations. According to our model, the absence of intrinsic irremoveable
decoherence in matter interferometry experiments puts bounds on some of the
parameters of quantum gravity theories. Current experiments give \lambda > 18.
, where \lambda t_{Planck} is an effective cut-off for the validity of
low-energy quantum gravity theories.


title:
Experimental study of a photon as a subsystem of an entangled two-photon
  state

abstract:
  The state of the signal-idler photon pair of spontaneous parametric down
conversion(SPDC) is a typical nonlocal entangled pure state with zero entropy.
The precise correlation of the subsystems is completely described by the state.
However, it is an experimental choice to study only one subsystem and to ignore
the other. What can we learn about the measured subsystem and the remaining
parts? Results of this kind of measurements look peculiar. The experiment
confirms that the two subsystems are both in mixed states with entropy greater
than zero. One can only obtain statistical knowledge of the subsystems in this
kind of measurement.


title: Algebraic Nature of Shape-Invariant and Self-Similar Potentials

abstract:
  Self-similar potentials generalize the concept of shape-invariance which was
originally introduced to explore exactly-solvable potentials in quantum
mechanics. In this article it is shown that previously introduced algebraic
approach to the latter can be generalized to the former. The infinite Lie
algebras introduced in this context are shown to be closely related to the
q-algebras. The associated coherent states are investigated.


title: Quantum noise in ideal operational amplifiers

abstract:
  We consider a model of quantum measurement built on an ideal operational
amplifier operating in the limit of infinite gain, infinite input impedance and
null output impedance and with a feddback loop. We evaluate the intensity and
voltage noises which have to be added to the classical amplification equations
in order to fulfill the requirements of quantum mechanics. We give a
description of this measurement device as a quantum network scattering quantum
fluctuations from input to output ports.


title: Conditional quantum-state transformation at a beam splitter

abstract:
  Using conditional measurement on a beam splitter, we study the transformation
of the quantum state of the signal mode within the concept of two-port
non-unitary transformation. Allowing for arbitrary quantum states of both the
input reference mode and the output reference mode on which the measurement is
performed, we show that the non-unitary transformation operator can be given as
an $s$-ordered operator product, where the value of $s$ is entirely determined
by the absolute value of the beam splitter reflectance (or transmittance). The
formalism generalizes previously obtained results that can be recovered by
simple specification of the non-unitary transformation operator. As an
application, we consider the generation of Schr\"odinger-cat-like states. An
extension to mixed states and imperfect detection is outlined.


title: Multi-time correlations in relaxing quantum dynamical systems

abstract:
  In this paper, we consider the long time asymptotics of multi-time
correlation functions for quantum dynamical systems that are sufficiently
random to relax to a ``reference state''. In particular, the evolution of such
systems must have a continuous spectrum. Special attention is paid to general
dynamical clustering conditions and their consequences for the structure of
fluctuations of temporal averages.


title: Nonlinear level crossing models

abstract:
  We examine the effect of nonlinearity at a level crossing on the probability
for nonadiabatic transitions $P$. By using the Dykhne-Davis-Pechukas formula,
we derive simple analytic estimates for $P$ for two types of nonlinear
crossings. In the first type, the nonlinearity in the detuning appears as a
{\it perturbative} correction to the dominant linear time dependence. Then
appreciable deviations from the Landau-Zener probability $P_{LZ}$ are found to
appear for large couplings only, when $P$ is very small; this explains why the
Landau-Zener model is often seen to provide more accurate results than
expected. In the second type of nonlinearity, called {\it essential}
nonlinearity, the detuning is proportional to an odd power of time. Then the
nonadiabatic probability $P$ is qualitatively and quantitatively different from
$P_{LZ}$ because on the one hand, it vanishes in an oscillatory manner as the
coupling increases, and on the other, it is much larger than $P_{LZ}$. We
suggest an experimental situation when this deviation can be observed.


title: Transition times in the Landau-Zener model

abstract:
  This paper presents analytic formulas for various transition times in the
Landau-Zener model. Considerable differences are found between the transition
times in the diabatic and adiabatic bases, and between the jump time (the time
for which the transition probability rises to the region of its asymptotic
value) and the relaxation time (the characteristic damping time of the
oscillations which appear in the transition probability after the crossing).
These transition times have been calculated by using the exact values of the
transition probabilities and their derivatives at the crossing point and
approximations to the time evolutions of the transition probabilities in the
diabatic basis, derived earlier \protect{[}N. V. Vitanov and B. M. Garraway,
Phys. Rev. A {\bf 53}, 4288 (1996)\protect{]}, and similar results in the
adiabatic basis, derived in the present paper.


title: Quantum local-field corrections and spontaneous decay

abstract:
  A recently developed scheme [S. Scheel, L. Knoll, and D.-G. Welsch, Phys.
Rev. A 58, 700 (1998)] for quantizing the macroscopic electromagnetic field in
linear dispersive and absorbing dielectrics satisfying the Kramers-Kronig
relations is used to derive the quantum local-field correction for the standard
virtual-sphere-cavity model. The electric and magnetic local-field operators
are shown to be consistent with QED only if the polarization noise is fully
taken into account. It is shown that the polarization fluctuations in the local
field can dramatically change the spontaneous decay rate, compared with the
familiar result obtained from the classical local-field correction. In
particular, the spontaneous emission rate strongly depends on the radius of the
local-field virtual cavity.


title: Experimental Realization of A Two Bit Phase Damping Quantum Code

abstract:
  Using nuclear magnetic resonance techniques, we experimentally investigated
the effects of applying a two bit phase error detection code to preserve
quantum information in nuclear spin systems. Input states were stored with and
without coding, and the resulting output states were compared with the
originals and with each other. The theoretically expected result, net reduction
of distortion and conditional error probabilities to second order, was indeed
observed, despite imperfect coding operations which increased the error
probabilities by approximately 5%. Systematic study of the deviations from the
ideal behavior provided quantitative measures of different sources of error,
and good agreement was found with a numerical model. Theoretical questions in
quantum error correction in bulk nuclear spin systems including fidelity
measures, signal strength and syndrome measurements are discussed.


title: Local Transition Functions of Quantum Turing Machines

abstract:
  Foundations of the notion of quantum Turing machines are investigated.
According to Deutsch's formulation, the time evolution of a quantum Turing
machine is to be determined by the local transition function. In this paper,
the local transition functions are characterized for fully general quantum
Turing machines, including multi-tape quantum Turing machines, extending the
results due to Bernstein and Vazirani.


title:
Gauge transformations for a driven quantum particle in an infinite
  square well

abstract:
  Quantum mechanics of a particle in an infinite square well under the
influence of a time-dependent electric field is reconsidered. In some gauge,
the Hamiltonian depends linearly on the momentum operator which is symmetric
but not self-adjoint when defined on a finite interval. In spite of this
symmetric part, the Hamiltonian operator is shown to be self-adjoint. This
follows from a theorem by Kato and Rellich which guarantees the stability of a
self-adjoint operator under certain symmetric perturbations. The result, which
has been assumed tacitly by other authors, is important in order to establish
the equivalence of different Hamiltonian operators related to each other by
quantum gauge transformations. Implications for the quantization procedure of a
particle in a box are pointed out.


title:
An Alternative Commutation Relation Between Position and Momentum
  Operators of Massless Particles

abstract:
  It seems that the problem of finding a suitable position operator for photon
has been solved in a recently published work which is based on a new
commutation relation between position and momentum operators of massless
particles[1]. Although the authors of [1] have presented a classical reasoning
in favour of the new commutator,here we are going to find this new commutator
based on a quantum mechanical argument.


title:
Mathematical and Physical Examination of the Locality Condition in
  Bell's Theorem

abstract:
  Using the Clauser-Horne model of Bell's theorem, the locality condition is
examined and it is shown the corresponding formulation is equivalent to a
factorization process consisting of three stages. The first stage is introduced
based on the conditional probability definition in classical theory of
probability and the other two stages are based on previously-known relations
named as outcome and parameter independence conditions.


title: Tools for Quantum Algorithms

abstract:
  We present efficient implementations of a number of operations for quantum
computers. These include controlled phase adjustments of the amplitudes in a
superposition, permutations, approximations of transformations and
generalizations of the phase adjustments to block matrix transformations. These
operations generalize those used in proposed quantum search algorithms.


title: Measurement in Quantum Mechanics: From Probabilities to Objective Events

abstract:
  The problem of measurement in quantum mechanics is reanalyzed within a
general, strictly probabilistic framework (without reduction postulate). Based
on a novel comprehensive definition of measurement the natural emergence of
objective events is demonstrated and their formal representation within quantum
mechanics is obtained. In order to be objective an event is required to be
observable or readable in at least two independent, mutually non-interfering
ways with necessarily agreeing results. Consistency in spite of unrestricted
validity of reversibility of the evolution or the superposition principle is
demonstrated and the role played by state reduction, in a properly defined
restricted sense, is discussed. Some general consequences are pointed out.


title:
Time-dependent Schr\"odinger equations having isomorphic symmetry
  algebras. I. Classes of interrelated equations

abstract:
  In this paper, we focus on a general class of Schr\"odinger equations that
are time-dependent and quadratic in X and P. We transform Schr\"odinger
equations in this class, via a class of time-dependent mass equations, to a
class of solvable time-dependent oscillator equations. This transformation
consists of a unitary transformation and a change in the ``time'' variable. We
derive mathematical constraints forthe transformation and introduce two
examples.


title:
Time-dependent Schr\"odinger equations having isomorphic symmetry
  algebras. II. Symmetry algebras, coherent and squeezed states

abstract:
  Using the transformations from paper I, we show that the Schr\"odinger
equations for: (1)systems described by quadratic Hamiltonians, (2) systems with
time-varying mass, and (3) time-dependent oscillators, all have isomorphic Lie
space-time symmetry algebras. The generators of the symmetry algebras are
obtained explicitly for each case and sets of number-operator states are
constructed. The algebras and the states are used to compute
displacement-operator coherent and squeezed states. Some properties of the
coherent and squeezed states are calculated. The classical motion of these
states is deomonstrated.


title: Quantized Space-Time and Time's Arrow

abstract:
  Motivated by the latest direct detection of time assymetry in Kaon decay at
CERN and Fermilab, we suggest a theoretical rationale for this puzzle, in terms
of quantized time.


title:
Entanglement and visibility at the output of a Mach-Zehnder
  interferometer

abstract:
  We study the entanglement between the two beams exiting a Mach-Zehnder
interferometer fed by a couple of squeezed-coherent states with arbitrary
squeezing parameter. The quantum correlations at the output are function of the
internal phase-shift of the interferometer, with the output state ranging from
a totally disentangled state to a state whose degree of entanglement is an
increasing function of the input squeezing parameter. A couple of squeezed
vacuum at the input leads to maximum entangled state at the output. The fringes
visibilities resulting from measuring the coincidence counting rate or the
squared difference photocurrent are evaluated and compared each other.
Homodyne-like detection turns out to be preferable in almost all situations,
with the exception of the very low signals regime.


title: Creation of coherent atomic superpositions by fractional STIRAP

abstract:
  We discuss a simple scheme for preparing atoms and molecules in an arbitrary
preselected coherent superposition of quantum states. The technique, which we
call fractional stimulated Raman adiabatic passage ({\it f-STIRAP}), is based
upon (incomplete) adiabatic population transfer between an initial state
$\psi_1$ and state $\psi_3$ through an intermediate state $\psi_2$. As in
STIRAP, the Stokes pulse arrives before the pump pulse, but unlike STIRAP, the
two pulses terminate simultaneously while maintaining a constant ratio of
amplitudes. The independence of f-STIRAP from details of pulse shape and pulse
area makes it the analog of conventional STIRAP in the creation of coherent
superpositions of states. We suggest a smooth realization of f-STIRAP which
requires only two laser pulses (which can be derived from a single laser) and
at the same time ensures the automatic fulfillment of the asymptotic conditions
at early and late times. Furthermore, we provide simple analytic estimates of
the robustness of f-STIRAP against variations in the pulse intensity, the pulse
delay, and the intermediate-state detuning, and discuss its possible extension
to multistate systems.


title: A note on quantum black-box complexity of almost all Boolean functions

abstract:
  We show that, for almost all N-variable Boolean functions f, at least
N/4-O(\sqrt{N} log N) queries are required to compute f in quantum black-box
model with bounded error.


title:
Exact Solutions for the General Nonstationary Oscillator with a Singular
  Perturbation

abstract:
  Three linearly independent Hermitian invariants for the nonstationary
generalized singular oscillator (SO) are constructed and their complex linear
combination is diagonalized. The constructed family of eigenstates contains as
subsets all previously obtained solutions for the SO and includes all Robertson
and Schr\"odinger intelligent states for the three invariants. It is shown that
the constructed analogues of the SU(1,1) group-related coherent states for the
SO minimize the Robertson and Schr\"odinger relations for the three invariants
and for every pair of them simultaneously. The squeezing properties of the new
states are briefly discussed.


title: Quantum Error Correction and Reversible Operations

abstract:
  I give a pedagogical account of Shor's nine-bit code for correcting arbitrary
errors on single qubits, and I review work that determines when it is possible
to maintain quantum coherence by reversing the deleterious effects of
open-system quantum dynamics. The review provides an opportunity to introduce
an efficient formalism for handling superoperators. I present and prove some
bounds on entanglement fidelity, which might prove useful in analyses of
approximate error correction.


title:
Equivalence of Local and Separable Realizations of the
  Discontinuity-Inducing Contact Interaction and Its Perturbative
  Renormalizability

abstract:
  We prove that the separable and local approximations of the
discontinuity-inducing zero-range interaction in one-dimensional quantum
mechanics are equivalent. We further show that the interaction allows the
perturbative treatment through the coupling renormalization.
  Keywords: one-dimensional system, generalized contact interaction,
renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.Md

categories: quant-ph cond-mat nlin.SI nucl-th solv-int


title:
The Symmetry Underlying Spin and the Dirac Equation:FOOTPRINTS of
  Quantized Space-Time

abstract:
  It is shown, in the context of a recent formulation of elementary particles
in terms of, what may be called, a Quantum Mechanical Kerr-Newman metric, that
spin is a consequence of a space-time cut off at the Compton wavelength and
Compton time scale. On this basis, we deduce the Dirac equation from a simple
coordinate transformation. Time irreversibility is seen to follow providing a
rationale for the Kaon puzzle. So also, the handedness of the neutrino can be
explained.


title:
Derivation of classical capacity of quantum channel for discrete
  information source

abstract:
  In this letter, we prove that the classical capacity of quantum channel for
$M$ symmetric states is achieved by an uniform distribution on a priori
probabilities. We also investigate non-symmetric cases such as a ternary
amplitude shift keyed signal set and a 16-ary quadrature amplitude modulated
signal set in coherent states.


title: Effect of dissipative forces on the theory of a single-atom microlaser

abstract:
  We describe a one-atom microlaser involving Poissonian input of atoms with a
fixed flight time through an optical resonator. The influence of the cavity
reservoir during the interactions of successive individual atoms with the
cavity field is included in the analysis. The atomic decay is also considered
as it is nonnegligible in the optical regime. During the random intervals of
absence of any atom in the cavity, the field evolves under its own dynamics. We
discuss the steady-state characteristics of the cavity field. Away from laser
threshold, the field can be nonclassical in nature.


title:
Comments on ``Differential cross section for Aharonov-Bohm effect with
  nonstandard boundary conditions''

abstract:
  We show that the violation of rotational symmetry for differential cross
section for Aharonov-Bohm effect with nonstandard boundary conditions has been
known for some time. Moreover, the results were applied to discuss the Hall
effect and persistent currents of fermions in a plane pierced by a flux tube.


title:
The conditionally exactly solvable potentials: A misunderstanding
  (comment on "Conditionally exactly soluble class of quantum potentials")

abstract:
  In the paper "Conditionally exactly soluble class of quantum potentials" by
A. de Souza Dutra [Phys. Rev. A 47 (1993) R2435] the whole $s-$wave spectrum of
bound states in potentials $V_1(r)=A/r+B/r^{1/2}+G_0/r^2$ with
$G_0=-3\hbar/32\mu$ and $V_2(r)=A r^{2/3}+B/r^{2/3}+g_0/r^2$ with
$g_0=-5\hbar^2/72\mu$ has been constructed in closed form. We show that both
the result and the method of its derivation are not correct.


title: Cosmic quantum measurement

abstract:
  Hardy's theorem states that the hidden variables of any realistic theory of
quantum measurement, whose predictions agree with ordinary quantum theory, must
have a preferred Lorentz frame. This presents the conflict between special
relativity and any realistic dynamics of quantum measurement in a severe form.
The conflict is resolved using a `measurement field', which provides a timelike
function of spacetime points and a definition of simultaneity in the context of
a curved spacetime. Locally this theory is consistent with special relativity,
but globally, special relativity is not enough; the time dilation of general
relativity and the standard cosmic time of the Robertson-Walker cosmologies are
both essential. A simple but crude example is a relativistic quantum
measurement dynamics based on the nonrelativistic measurement dynamics of
L\"uders.


title: Optimization approach to entanglement distillation

abstract:
  We put forward a method for optimized distillation of partly entangled pairs
of qubits into a smaller number of more entangled pairs by recurrent local
unitary operations and projections. Optimized distillation is achieved by
minimization of a cost function with up to 30 real parameters, which is chosen
to be sensitive to the fidelity and the projection probability at each step. We
show that in many cases this approach can significantly improve the
distillation efficiency in comparison to the present methods.


title: On Multipartite Pure-State Entanglement

abstract:
  We show that pure states of multipartite quantum systems are multiseparable
(i.e. give separable density matrices on tracing any party) if and only if they
have a generalized Schmidt decomposition. Implications of this result for the
quantification of multipartite pure-state entanglement are discussed. Further,
as an application of the techniques used here, we show that any purification of
a bipartite PPT bound entangled state is tri-inseparable, i.e. has none of its
three bipartite partial traces separable.


title: Defending Time-Symmetrized Quantum Counterfactuals

abstract:
  Recently, several authors have criticized the time-symmetrized quantum theory
originated by the work of Aharonov et al. (1964). The core of this criticism
was a proof, appearing in various forms, which showed that the counterfactual
interpretation of time-symmetrized quantum theory cannot be reconciled with
standard quantum theory. I, (Vaidman, 1996a, 1997) have argued that the
apparent contradiction is due to a logical error and introduced consistent
time-symmetrized quantum counterfactuals. Here I repeat my arguments defending
the time-symmetrized quantum theory and reply to the criticism of these
arguments by Kastner (1999).


title:
Numerical simulations of fundamental processes in cavity QED: Atomic
  decay

abstract:
  We present results of numerical investigation of a microscopic dynamics of a
two-level atom embedded into a ``linear crystal'' of other two-level atoms.
These additional atoms play a role of a material media. All atoms interact with
a multimode cavity field. We study how the decay of the initially excited atom
is affected by the presence of material media and spectral properties of the
cavity field.


title:
Generally relativistical Tetrode-Weyl-Fock-Ivanenko formalism and
  behaviour of quantum-mechanical particles of spin 1/2 in the Abelian monopole
  field

abstract:
  Some attention in the literature has been given to the case of a particle of
spin 1/2 on the background of the external monopole potential. Some aspects of
this problem are reexamined here. The primary technical novelty is that the
tetrad generally relativistic method of Tetrode-Weyl-Fock-Ivanenko for
describing a spinor particle is exploited. The choice of the formalism has
turned out to be of great fruitfulness for examining the system. It is matter
that, as known, the use of a special spherical tetrad in the theory of a spin
1/2 particle had led Schrodinger to a basis of remarkable features. The basis
has been used with great efficiency by Pauli in his investigation on the pro-
blem of allowed spherically symmetric wave functions in quantum mechanics. For
our purposes, just several simple rules extracted from the much more com-
prehensive Pauli's analysis will be quite sufficient; those are almost mnemo-
nic working regulations. So, one may remember some very primary facts of D-
functions theory and then produce automatically proper wave functions. It seems
rather likely, that there may exist a generalized analog of such a re-
presentation for J(i)-operators, that might be successfully used whenever in a
linear problem there exists a spherical symmetry, irrespective of the con-
crete embodiment of such a symmetry. In particular, the case of electron in the
external Abelian monopole field completely come under the Sch-Pau method.


title: On the factorization method in quantum mechanics

abstract:
  New exactly solvable problems have already been studied by using a
modification of the factorization method introduced by Mielnik. We review this
method and its connection with the traditional factorization method. The survey
includes the discussion on a generalization of the factorization energies used
in the traditional Infeld and Hull method.


title: Feedback-control of quantum systems using continuous state-estimation

abstract:
  We present a formulation of feedback in quantum systems in which the best
estimates of the dynamical variables are obtained continuously from the
measurement record, and fed back to control the system. We apply this method to
the problem of cooling and confining a single quantum degree of freedom, and
compare it to current schemes in which the measurement signal is fed back
directly in the manner usually considered in existing treatments of quantum
feedback. Direct feedback may be combined with feedback by estimation, and the
resulting combination, performed on a linear system, is closely analogous to
classical LQG control theory with residual feedback.


title: Quantum caustics in the Gaussian slit experiment

abstract:
  We study classical and quantum caustics for system with quadratic Lagrangian.
Gaussian slit experiment is examined and it is pointed out that the focusing
around caustics is stabilized against initial momentum fluctuations by quantum
effect.


title:
Realization of a Four Parameter Family of Generalized One-Dimensional
  Contact Interactions by Three Nearby Delta Potentials with Renormalized
  Strengths

abstract:
  We propose a new method to construct a four parameter family of
quantum-mechanical point interactions in one dimension, which is known as all
possible self-adjoint extensions of the symmetric operator $T=-\Delta \lceil
C^{\infty}_{0}({\bf R} \backslash\{0\})$. It is achieved in the small distance
limit of equally spaced three neighboring Dirac's $\delta$ potentials. The
strength for each $\delta$ is appropriately renormalized according to the
distance and it diverges, in general, in the small distance limit. The validity
of our method is ensured by numerical calculations. In general cases except for
usual $\delta$, the wave function discontinuity appears around the interaction
and one can observe such a tendency even at a finite distance level.


title:
Generally relativistical Daffin-Kemmer formalis and behaviour of
  quantm-mechanical particle of spin 1 in the Abelian monopole field

abstract:
  It is shown that the manner of introducing theinteraction between a spin 1
particle and external classical gravitational field can be successfully uni-
fied with the approach that occurred with regard to a spin 1/2 particle and was
first developed by Tetrode, Weyl, Fock, Ivanenko. On that way a general- ly
relativistical Duffin-Kemmer equation is costructed. So, the manner of
extending the flat space Dirac equation to general relativity case indicates
clearly that the Lorentz group underlies equally both these theories. In other
words, the Lorentz group retains its importance and significance at changing
the Minkowski space model to an arbitrary curved space-time. In contrast to
this, at generalizing the Proca formulation, we automatically destroy any
relations to the Lorentz group, although the definition itself for a spin 1
particle as an elementary object was based on just this group. Such a gravity's
sensitiveness to the fermion-boson division might appear rather strange and
unattractive asymmetry, being subjected to the criticism. Moreover, just this
feature has brought about a plenty of speculation on this matter. In any case,
this peculiarity of particle-gravity field inter- action is recorded almost in
every handbook. In the paper, on the base of the Duffin-Kemmer formalism
developed, the problem of a vector particle in the Abelian monopole potential
is considered.


title:
Measure of irregularity for Dirac, Schwinger, Wu-Yang's bases in the
  Abelian monopole theory and affecting of the gauge symmetry principle by
  allowance of singularity in physics

abstract:
  In the literature concerning the monopole matter, three gauges: Dirac,
Schwinger, and Wu-Yang's, have been contrasted to each other, and the Wu-Yang's
often appears as the most preferable one. The article aims to analyse this view
by interpreting the monopole situation in terms of the conventioal Fourier
series theory; in particular, having relied on the Dirichlet theorem. It is
shown that the monopole case can be labelled as a very spesific and even rather
simple class of problems in the frame of that theory: all the three monopole
gauges amount to practicaly the same one-dimentional problem for functions
given on the interval [0,pi] having a single point of discontinuity; these
three vary only in its location.In addition, some general aspects of the
Aharonov-Bohm effect are discussed; the way of how any singular potentials such
as monopole's, being allowed in physics, touche the essence of the physical
gauge principle itself is considered.


title:
Does the quantum collapse make sense? Quantum Mechanics vs
  Multisimultaneity in interferometer-series experiments

abstract:
  It is argued that the three assumptions of quantum collapse, one photon-one
count, and relativity of simultaneity cannot hold together: Nonlocal
correlations can depend on the referential frames of the beam-splitters but not
of the detectors. New experiments using interferometers in series are proposed
which make it possible to test Quantum Mechanics vs Multisimultaneity.


title: Nonclassical Fields and the Nonlinear Interferometer

abstract:
  We demonstrate several new results for the nonlinear interferometer, which
emerge from a formalism which describes in an elegant way the output field of
the nonlinear interferometer as two-mode entangled coherent states. We clarify
the relationship between squeezing and entangled coherent states, since a weak
nonlinear evolution produces a squeezed output, while a strong nonlinear
evolution produces a two-mode, two-state entangled coherent state. In between
these two extremes exist superpositions of two-mode coherent states manifesting
varying degrees of entanglement for arbitrary values of the nonlinearity. The
cardinality of the basis set of the entangled coherent states is finite when
the ratio $\chi / \pi$ is rational, where $\chi$ is the nonlinear strength. We
also show that entangled coherent states can be produced from product coherent
states via a nonlinear medium without the need for the interferometric
configuration. This provides an important experimental simplification in the
process of creating entangled coherent states.


title: A realistic interpretation of the density matrix I: Basic concepts

abstract:
  A realistic interpretation of Schroedinger and Dirac equations for density
matrices is proposed, in which the difference between the position arguments of
the density matrix is considered as an objective extra space dimension.
"Particle" solutions are found, which are perfectly localized both in position
space and in momentum space (the position and momentum operators commute in the
density matrix representation); definitions for all observable quantities are
given and the values associated to the "particle" solutions are the correct
ones, both for the non-relativistic and the relativistic case. Finally, a
non-linear interaction (the electromagnetic one) is introduced in an attempt to
single out the "particle" solutions of the Dirac equation from all other
solutions; the dynamical evolution of the electromagnetic field is described by
the classical (unquantized) Maxwell equations.


title: Maximally entangled states and the Bell inequality

abstract:
  Kar's recent proof showing that a maximally entangled state of two spin-1/2
particles gives the largest violation of a Bell inequality is extended to N
spin-1/2 particles (with N greater than or equal to 3). In particular, it is
shown that all the states yielding a direct contradiction with the assumption
of local realism do generally consist of a superposition of maximally entangled
states.


title: Purification via entanglement swapping and conserved entanglement

abstract:
  We investigate the purification of entangled states by local actions using a
variant of entanglement swapping. We show that there exists a measure of
entanglement which is conserved in this type of purification procedure.


title:
Laser Cooling of two trapped ions: Sideband cooling beyond the
  Lamb-Dicke limit

abstract:
  We study laser cooling of two ions that are trapped in a harmonic potential
and interact by Coulomb repulsion. Sideband cooling in the Lamb-Dicke regime is
shown to work analogously to sideband cooling of a single ion. Outside the
Lamb-Dicke regime, the incommensurable frequencies of the two vibrational modes
result in a quasi-continuous energy spectrum that significantly alters the
cooling dynamics. The cooling time decreases nonlinearly with the linewidth of
the cooling transition, and the effect of trapping states which may slow down
the cooling is considerably reduced. We show that cooling to the ground state
is possible also outside the Lamb-Dicke regime. We develop the model and use
Quantum Monte Carlo calculations for specific examples. We show that a rate
equation treatment is a good approximation in all cases.


title: Non-equal-time Poisson brackets

abstract:
  The standard definition of the Poisson brackets is generalized to the
non-equal-time Poisson brackets. Their relationship to the equal-time Poisson
brackets, as well as to the equal- and non-equal-time commutators, is
discussed.

categories: quant-ph hep-th math-ph math.MP physics.class-ph


title: Optimal state estimation for d-dimensional quantum systems

abstract:
  We establish a connection between optimal quantum cloning and optimal state
estimation for d-dimensional quantum systems. In this way we derive an upper
limit on the fidelity of state estimation for d-dimensional pure quantum states
and, furthermore, for generalized inputs supported on the symmetric subspace.


title: Decoherence and the theory of continuous quantum measurements

abstract:
  Decoherence of a quantum system (which then starts to display classical
features) results from the interaction of the system with the environment, and
is well described in the framework of the theory of continuous quantum
measurements (CQM). Reviewed are the various approaches to the CQM theory, and
the approach based on the effective complex Hamiltonians is discussed in
greater detail. The effective complex Hamiltonian is derived from the
restricted path integral, which emphasizes the role of information in the
dynamics of the system being measured. The complex Hamiltonian is used for
analyzing the CQM of energy in a two-level system. Such measurement is
demonstrated to be capable of monitoring the quantum transition, and the back
effect of monitoring on the probability of transition is analyzed. The
realization of this type of measurement by a long series of soft observations
of the system is presented.


title: Quantum teleportation with squeezed vacuum states

abstract:
  We show how the partial entanglement inherent in a two mode squeezed vacuum
state admits two different teleportation protocols. These two protocols refer
to the different kinds of joint measurements that may be made by the sender.
One protocol is the recently implemented quadrature phase approach of
Braunstein and Kimble[Phys. Rev. Lett.{\bf 80}, 869 (1998)]. The other is based
on recognising that a two mode squeezed vacuum state is also entangled with
respect to photon number difference and phase sum. We show that this protocol
can also realise teleportation, however limitations can arise due to the fact
that the photon number spectrum is bounded from below by zero. Our examples
show that a given entanglement resource may admit more than a single
teleportation protocol and the question then arises as to what is the optimum
protocol in the general case.