title: Macroscopic and mesoscopic matter waves

abstract:
  It has been shown earlier that matter waves which are known to lie typically
in the range of a few Angstrom, can also manifest in the macrodomain with a
wave length of a few centimeters, for electrons propagating along a magnetic
field. This followed from the predictions of a probability amplitude theory by
the author in the classical macrodomain of the dynamics of charged particles in
a magnetic field. It is shown in this paper that this case constitutes only a
special case of a generic situation whereby composite systems such as atoms and
molecules in their highly excited internal states,can exhibit matter wave
manifestation in macro and mesodomains. The wave length of these waves is
determined, not by the mass of the particle as in the case of the de Broglie
wave, but by the frequency, associated with the internal state of excitation,
and is given by a nonquantal expression, $\lambda =2\pi v/\omega$, $v$ being
the velocity of the particle. For the electrons in a magnetic field the
frequency corresponds to the gyrofrequency, $\Omega$ and the nonquantal wave
length is given by $\lambda = 2\pi v_{\parallel}/\Omega$; $v_{\parallel}$ being
the velocity of electrons along the magnetic field.


title:
Universal property of the information entropy in fermionic and bosonic
  systems

abstract:
  It is shown that a similar functional form $S=a+b\ln N$ holds approximately
for the information entropy S as function of the number of particles N for
atoms, nuclei and atomic clusters (fermionic systems) and correlated
boson-atoms in a trap (bosonic systems). It is also seen that rigorous
inequalities previously found to hold between S and the kinetic energy T for
fermionic systems, hold for bosonic systems as well. It is found that
Landsberg's order parameter $\Omega$ is an increasing function of N for the
above systems. It is conjectured that the above properties are universal i.e.
they do not depend on the kind of constituent particles (fermions or correlated
bosons) and the size of the system.


title:
Activating NPPT distillation with an infinitesimal amount of bound
  entanglement

abstract:
  We show that bipartite quantum states of any dimension, which do not have a
positive partial transpose, become 1-distillable when one adds an infinitesimal
amount of bound entanglement. To this end we investigate the activation
properties of a new class of symmetric bound entangled states of full rank. It
is shown that in this set there exist universal activator states capable of
activating the distillation of any NPPT state.


title: The Casimir energy of a massive fermion field revisited

abstract:
  We introduce a general, simple and effective method of evaluating the zero
point energy of a quantum field under the influence of arbitrary boundary
conditions imposed on the field on flat surfaces perpendicular to a chosen
spatial direction. As an example we apply the method to the Casimir effect
associated with a massive fermion field on which MIT bag model type of boundary
conditions are imposed.


title: Darboux transformations for quasi-exactly solvable Hamiltonians

abstract:
  We construct new quasi-exactly solvable one-dimensional potentials through
Darboux transformations. Three directions are investigated:
  Reducible and two types of irreducible second-order transformations. The
irreducible transformations of the first type give singular intermediate
potentials and the ones of the second type give complex-valued intermediate
potentials while final potentials are meaningful in all cases.
  These developments are illustrated on the so-called radial sextic oscillator.


title: Fidelity of Single Qubit Maps

abstract:
  We describe a simple way of characterizing the average fidelity between a
unitary (or anti-unitary) operator and a general operation on a single qubit,
which only involves calculating the fidelities for a few pure input states, and
discuss possible applications to experimental techniques including Nuclear
Magnetic Resonance (NMR).


title: Exact Description of Decoherence in Optical Cavities

abstract:
  The exact reduced dynamics for the independent oscillator model in the RWA
approximation at zero and finite temperatures is derived. It is shown that the
information about the interaction and the environment is encapsulated into
three time dependent coefficients of the master equation, one of which vanishes
in the zero temperature case. In currently used optical cavities all the
information about the field dynamics is contained into {\it two} (or three)
experimentally accesible and physically meaningful real functions of time. From
the phenomenological point of view it suffices then to carefully measure two
({\it three}) adequate observables in order to map the evolution of any initial
condition, as shown with several examples: (generalized) coherent states, Fock
states, Schr\"odinger cat states, and squeezed states.


title: Decoherence demystified : The hydrodynamic viewpoint

abstract:
  The hydrodynamic formulation of quantum mechanics is used to elucidate the
mechanism for decoherence, the suppression of interference effects in a system
evolving from an initial coherent superposition. Analysis of time-dependent
trajectory ensembles, flux maps, and elements of the stress tensor for two
composite systems, in one of which the system is uncoupled to the environment,
leads to the decoherence mechanism. For the uncoupled case, the quantum force
acting on the fluid elements directs flux toward an attractor where the
interference feature arises. For the coupled case, the classical force acting
on each fluid element counters the quantum force and leads to gradual
separation of the components of the initial superposition. Concomitantly, fluid
stress is relieved when flux vectors diverge from a repellor in the mid-region
between the separating wavepackets, thus suppressing formation of the
interference feature.


title:
Finding optimal strategies for minimum-error quantum-state
  discrimination

abstract:
  We propose a numerical algorithm for finding optimal measurements for
quantum-state discrimination. The theory of the semidefinite programming
provides a simple check of the optimality of the numerically obtained results.


title: Controlled light storage in a double lambda system

abstract:
  It is shown theoretically that after light storing in a medium of four-level
atoms it is possible to release a new pulse of a different frequency, the
process being steered by another driving beam. It is also possible to store one
pulse and to release two different ones, with their time separation and heights
being controlled.


title: Topological decomposition of composite quantum state spaces

abstract:
  We present a two-part program for state space decomposition. States are
classified into entanglement classes based on local unitary transformations,
and then characterized as elements of topological spaces using the language of
fibre bundles.


title: Equivalence classes of non-local unitary operations

abstract:
  We study when a multipartite non--local unitary operation can
deterministically or probabilistically simulate another one when local
operations of a certain kind -in some cases including also classical
communication- are allowed. In the case of probabilistic simulation and
allowing for arbitrary local operations, we provide necessary and sufficient
conditions for the simulation to be possible. Deterministic and probabilistic
interconversion under certain kinds of local operations are used to define
equivalence relations between gates. In the probabilistic, bipartite case this
induces a finite number of classes. In multiqubit systems, however, two unitary
operations typically cannot simulate each other with non-zero probability of
success. We also show which kind of entanglement can be created by a given
non--local unitary operation and generalize our results to arbitrary operators.


title:
Lorentz-Invariant Time-Energy Uncertainty Relation for Relativistic
  Photon

abstract:
  The time-energy uncertainty relation is discussed for a relativistic massless
particle. The Lorentz-invariant uncertainty relation is obtained between the
root-mean-square energy deviation and the scatter of registration time. The
interconnection between this uncertainty relation and its classical analogue is
established.


title:
Nonlocality degradation of two-mode squeezed vacuum in absorbing optical
  fibers

abstract:
  Transfer of nonlocal two-mode squeezed vacuum state through symmetrical and
asymmetrical lossy channel is analysed and we demonstrate that the nonlocality
is more robust against losses, than it has been previously suggested. It can be
important for security of continuous-variable quantum cryptography employing
entangled states.


title: Quantum Zeno subspaces

abstract:
  The quantum Zeno effect is recast in terms of an adiabatic theorem when the
measurement is described as the dynamical coupling to another quantum system
that plays the role of apparatus. A few significant examples are proposed and
their practical relevance discussed. We also focus on decoherence-free
subspaces.


title:
Frequency Hopping in Quantum Interferometry: Efficient Up-Down
  Conversion for Qubits and Ebits

abstract:
  A novel single-photon Mach-Zehnder interferometer terminated at two different
frequencies realizes the nonlinear frequency conversion of optical quantum
superposition states. The information-preserving character of the relevant
unitary transformation has been experimentally demonstrated for input qubits
and ebits. Besides its own intrinsic fundamental interest, the new scheme will
find important applications in modern quantum information technology.


title: Quantum Property Testing

abstract:
  A language L has a property tester if there exists a probabilistic algorithm
that given an input x only asks a small number of bits of x and distinguishes
the cases as to whether x is in L and x has large Hamming distance from all y
in L. We define a similar notion of quantum property testing and show that
there exist languages with quantum property testers but no good classical
testers. We also show there exist languages which require a large number of
queries even for quantumly testing.


title: Sub-Planck spots of Schroedinger cats and quantum decoherence

abstract:
  Heisenberg's principle$^1$ states that the product of uncertainties of
position and momentum should be no less than Planck's constant $\hbar$. This is
usually taken to imply that phase space structures associated with sub-Planck
($\ll \hbar$) scales do not exist, or, at the very least, that they do not
matter. I show that this deeply ingrained prejudice is false: Non-local
"Schr\"odinger cat" states of quantum systems confined to phase space volume
characterized by `the classical action' $A \gg \hbar$ develop spotty structure
on scales corresponding to sub-Planck $a = \hbar^2 / A \ll \hbar$. Such
structures arise especially quickly in quantum versions of classically chaotic
systems (such as gases, modelled by chaotic scattering of molecules), that are
driven into nonlocal Schr\"odinger cat -- like superpositions by the quantum
manifestations of the exponential sensitivity to perturbations$^2$. Most
importantly, these sub-Planck scales are physically significant: $a$ determines
sensitivity of a quantum system (or of a quantum environment) to perturbations.
Therefore sub-Planck $a$ controls the effectiveness of decoherence and
einselection caused by the environment$^{3-8}$. It may also be relevant in
setting limits on sensitivity of Schr\"odinger cats used as detectors.


title: Choi's Proof and Quantum Process Tomography

abstract:
  Quantum process tomography is a procedure by which an unknown quantum
operation can be fully experimentally characterized. We reinterpret Choi's
proof of the fact that any completely positive linear map has a Kraus
representation [Lin. Alg. and App., 10, 1975] as a method for quantum process
tomography. Furthermore, the analysis for obtaining the Kraus operators are
particularly simple in this method.


title: Quantum Computing and a Unified Approach to Fast Unitary Transforms

abstract:
  A quantum computer directly manipulates information stored in the state of
quantum mechanical systems. The available operations have many attractive
features but also underly severe restrictions, which complicate the design of
quantum algorithms. We present a divide-and-conquer approach to the design of
various quantum algorithms. The class of algorithm includes many transforms
which are well-known in classical signal processing applications. We show how
fast quantum algorithms can be derived for the discrete Fourier transform, the
Walsh-Hadamard transform, the Slant transform, and the Hartley transform. All
these algorithms use at most O(log^2 N) operations to transform a state vector
of a quantum computer of length N.


title:
Measurement of Wigner function via atomic beam deflection in Raman- Nath
  regime

abstract: This paper has been withdrawn by the author(s)


title: Dynamical Reduction Models with General Gaussian Noises

abstract:
  We consider the effect of replacing in stochastic differential equations
leading to the dynamical collapse of the statevector, white noise stochastic
processes with non white ones. We prove that such a modification can be
consistently performed without altering the most interesting features of the
previous models. One of the reasons to discuss this matter derives from the
desire of being allowed to deal with physical stochastic fields, such as the
gravitational one, which cannot give rise to white noises. From our point of
view the most relevant motivation for the approach we propose here derives from
the fact that in relativistic models the occurrence of white noises is the main
responsible for the appearance of untractable divergences. Therefore, one can
hope that resorting to non white noises one can overcome such a difficulty. We
investigate stochastic equations with non white noises, we discuss their
reduction properties and their physical implications. Our analysis has a
precise interest not only for the above mentioned subject but also for the
general study of dissipative systems and decoherence.


title: Space-adiabatic Decoupling to All Orders

abstract:
  A systematic perturbation scheme is developed for approximate solutions to
the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian.
For a particular isolated energy band, the basic approach is to separate
kinematics from dynamics. The kinematics is defined through a subspace of the
full Hilbert space for which transitions to other band subspaces are suppressed
to all orders and the dynamics operates in that subspace in terms of an
effective intraband Hamiltonian. As novel applications we discuss the
Born-Oppenheimer theory to second order and derive the nonperturbative
definition of the g-factor of the electron within nonrelativistic quantum
electrodynamics.


title:
Hamiltonian models of multiphoton processes and four--photon squeezed
  states via nonlinear canonical transformations

abstract:
  We introduce nonlinear canonical transformations that yield effective
Hamiltonians of multiphoton down conversion processes, and we define the
associated non-Gaussian multiphoton squeezed states as the coherent states of
the multiphoton Hamiltonians. We study in detail the four-photon processes and
the associated non-Gaussian four-photon squeezed states. The realization of
squeezing, the behavior of the field statistics, and the structure of the phase
space distributions show that these states realize a natural four-photon
generalization of the two-photon squeezed states.


title:
Comment on "Fun and frustration with quarkonium in a 1+1 dimension," by
  R. S. Bhalerao and B. Ram [Am. J. Phys. 69 (7), 817-818 (2001)]

abstract:
  We present the correct solution of the Dirac equation in 1+1 dimensions with
the Lorentz scalar potential V(x)=g|x|.


title: An algebraic approach to the Tavis-Cummings problem

abstract:
  An algebraic method is introduced for an analytical solution of the
eigenvalue problem of the Tavis-Cummings (TC) Hamiltonian, based on
polynomially deformed su(2), i.e. su_n(2), algebras. In this method the
eigenvalue problem is solved in terms of a specific perturbation theory,
developed here up to third order. Generalization to the N-atom case of the Rabi
frequency and dressed states is also provided. A remarkable enhancement of
spontaneous emission of N atoms in a resonator is found to result from
collective effects.


title:
Procedures for Converting among Lindblad, Kraus and Matrix
  Representations of Quantum Dynamical Semigroups

abstract:
  Given an quantum dynamical semigroup expressed as an exponential
superoperator acting on a space of N-dimensional density operators, eigenvalue
methods are presented by which canonical Kraus and Lindblad operator sum
representations can be computed. These methods provide a mathematical basis on
which to develop novel algorithms for quantum process tomography, the
statistical estimation of superoperators and their generators, from a wide
variety of experimental data. Theoretical arguments and numerical simulations
are presented which imply that these algorithms will be quite robust in the
presence of random errors in the data.


title: Entangling many atomic ensembles through laser manipulation

abstract:
  We propose an experimentally feasible scheme to generate
Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement between many
atomic ensembles based on laser manipulation and single-photon detection. The
scheme, with inherent fault tolerance to the dominant noise and efficient
scaling of the efficiency with the number of ensembles, allows to maximally
entangle many atomic ensemble within the reach of current technology. Such a
maximum entanglement of many ensembles has wide applications in demonstration
of quantum nonlocality, high-precision spectroscopy, and quantum information
processing.


title:
Vector coherent state representations, induced representations, and
  geometric quantization: I. Scalar coherent state representations

abstract:
  Coherent state theory is shown to reproduce three categories of
representations of the spectrum generating algebra for an algebraic model: (i)
classical realizations which are the starting point for geometric quantization;
(ii) induced unitary representations corresponding to prequantization; and
(iii) irreducible unitary representations obtained in geometric quantization by
choice of a polarization. These representations establish an intimate relation
between coherent state theory and geometric quantization in the context of
induced representations.


title:
Vector coherent state representations, induced representations, and
  geometric quantization: II. Vector coherent state representations

abstract:
  It is shown here and in the preceeding paper (quant-ph/0201129) that vector
coherent state theory, the theory of induced representations, and geometric
quantization provide alternative but equivalent quantizations of an algebraic
model. The relationships are useful because some constructions are simpler and
more natural from one perspective than another. More importantly, each approach
suggests ways of generalizing its counterparts. In this paper, we focus on the
construction of quantum models for algebraic systems with intrinsic degrees of
freedom. Semi-classical partial quantizations, for which only the intrinsic
degrees of freedom are quantized, arise naturally out of this construction. The
quantization of the SU(3) and rigid rotor models are considered as examples.


title: On the mass of elementary carriers of gravitational interaction

abstract:
  Based on the theory of submicroscopic quantum mechanics recently constructed
by the author the mass of elementary spatial excitations called inertons, which
accompany a moving particle, is estimated herein. These excitations are treated
as carriers of both inertial and gravitational properties of the particle.


title:
Implementation of Quantum Fourier Transform and Simulation of Wave
  Functions by Fixed Interaction

abstract:
  We study a quantum computer with fixed and permanent interaction of diagonal
type between qubits. It is controlled only by one-qubit quick transformations.
It is shown how to implement Quantum Fourier Transform and to solve Shroedinger
equations with linear and quadratic potentials by a quantum computer of such
type. The method is adaptable to the wide range of interactions of diagonal
form between qubits and to the case when different pairs of qubits interact
variously.


title:
New type of fields in Maxwells equations: their properties and method of
  detection

abstract:
  A theoretical analysis of the excitation of an infinitely long solenoid by
oscillating current has revealed the existence of specific potentials in the
space outside the solenoid, which can affect electron diffraction in an
experiment similar to the Aharonov-Bohm effect. Thus, these time-dependent
potentials are physical fields possessing a number of specific features, which
set them off from the fields known heretofore.


title:
Experimental Nonlocality Proof of Quantum Teleportation and Entanglement
  Swapping

abstract:
  Quantum teleportation strikingly underlines the peculiar features of the
quantum world. We present an experimental proof of its quantum nature,
teleporting an entangled photon with such high quality that the nonlocal
quantum correlations with its original partner photon are preserved. This
procedure is also known as entanglement swapping. The nonlocality is confirmed
by observing a violation of Bell's inequality by 4.5 standard deviations. Thus,
by demonstrating quantum nonlocality for photons that never interacted our
results directly confirm the quantum nature of teleportation.


title:
Failure of Effective Potential Approach: Nucleus-Electron Entanglement
  in the He-Ion

abstract:
  Entanglement may be considered a resource for quantum-information processing,
as the origin of robust and universal equilibrium behaviour, but also as a
limit to the validity of an effective potential approach, in which the
influence of certain interacting subsystems is treated as a potential. Here we
show that a closed three particle (two protons, one electron) model of a He-ion
featuring realistic size, interactions and energy scales of electron and
nucleus, respectively, exhibits different types of dynamics depending on the
initial state: For some cases the traditional approach, in which the nucleus
only appears as the center of a Coulomb potential, is valid, in others this
approach fails due to entanglement arising on a short time-scale. Eventually
the system can even show signatures of thermodynamical behaviour, i.e. the
electron may relax to a maximum local entropy state which is, to some extent,
independent of the details of the initial state.


title:
Distribution of local entropy in the Hilbert space of bi-partite quantum
  systems: Origin of Jaynes' principle

abstract:
  For a closed bi-partite quantum system partitioned into system proper and
environment we interprete the microcanonical and the canonical condition as
constraints for the interaction between those two subsystems. In both cases the
possible pure-state trajectories are confined to certain regions in Hilbert
space. We show that in a properly defined thermodynamical limit almost all
states within those accessible regions represent states of some maximum local
entropy. For the microcanonical condition this dominant state still depends on
the initial state; for the canonical condition it coincides with that defined
by Jaynes' principle. It is these states which thermodynamical systems should
generically evolve into.


title:
The Casimir Problem of Spherical Dielectrics: Numerical Evaluation for
  General Permittivities

abstract:
  The Casimir mutual free energy F for a system of two dielectric concentric
nonmagnetic spherical bodies is calculated, at arbitrary temperatures. The
present paper is a continuation of an earlier investigation [Phys. Rev. E {\bf
63}, 051101 (2001)], in which F was evaluated in full only for the case of
ideal metals (refractive index n=infinity). Here, analogous results are
presented for dielectrics, for some chosen values of n. Our basic calculational
method stems from quantum statistical mechanics. The Debye expansions for the
Riccati-Bessel functions when carried out to a high order are found to be very
useful in practice (thereby overflow/underflow problems are easily avoided),
and also to give accurate results even for the lowest values of l down to l=1.
Another virtue of the Debye expansions is that the limiting case of metals
becomes quite amenable to an analytical treatment in spherical geometry. We
first discuss the zero-frequency TE mode problem from a mathematical viewpoint
and then, as a physical input, invoke the actual dispersion relations. The
result of our analysis, based upon the adoption of the Drude dispersion
relation at low frequencies, is that the zero-frequency TE mode does not
contribute for a real metal. Accordingly, F turns out in this case to be only
one half of the conventional value at high temperatures. The applicability of
the Drude model in this context has however been questioned recently, and we do
not aim at a complete discussion of this issue here. Existing experiments are
low-temperature experiments, and are so far not accurate enough to distinguish
between the different predictions. We also calculate explicitly the
contribution from the zero-frequency mode for a dielectric. For a dielectric,
this zero-frequency problem is absent.


title: Properties of multi-partite dark states

abstract:
  We investigate and define dark and semi-dark states for multiple qudit
systems. For two-level systems, semi-dark and dark states are equivalent. We
show that the semi-dark states are equivalent to the singlet states of the
rotation group. They exist for many multiple qudit systems, whereas dark states
are quite rare. We then show that when a dark state is collapsed onto another
dark state of fewer parties, the resulting state is again dark. Furthermore,
one can use two orthogonal multi-qudit dark states to construct a
decoherence-free qudit.


title: Quantum and Stochastic Branching Programs of Bounded Width

abstract:
  In this paper we show that one qubit polynomial time computations are at
least as powerful as $\NC^1$ circuits. More precisely, we define syntactic
models for quantum and stochastic branching programs of bounded width and prove
upper and lower bounds on their power. We show any $\NC^1$ language can be
accepted exactly by a width-2 quantum branching program of polynomial length,
in contrast to the classical case where width 5 is necessary unless
$\NC^1=\ACC$. This separates width-2 quantum programs from width-2 doubly
stochastic programs as we show the latter cannot compute the middle bit of
multiplication. Finally, we show that bounded-width quantum and stochastic
programs can be simulated by classical programs of larger but bounded width,
and thus are in $\NC^1$. The change in the revised version is the addition of
the syntactic condition.


title: Quantum Chinos Game: winning strategies through quantum fluctuations

abstract:
  We apply several quantization schemes to simple versions of the Chinos game.
Classically, for two players with one coin each, there is a symmetric stable
strategy that allows each player to win half of the times on average. A partial
quantization of the game (semiclassical) allows us to find a winning strategy
for the second player, but it is unstable w.r.t. the classical strategy.
However, in a fully quantum version of the game we find a winning strategy for
the first player that is optimal: the symmetric classical situation is broken
at the quantum level.


title:
Initial experiments concerning quantum information processing in
  rare-earth-ion doped crystals

abstract:
  In this paper initial experiments towards constructing simple quantum gates
in a solid state material are presented. Instead of using specially tailored
materials, the aim is to select a subset of randomly distributed ions in the
material, which have the interaction necessary to control each other and
therefore can be used to do quantum logic operations. The experimental results
demonstrate that part of an inhomogeneously broadened absorption line can be
selected as a qubit and that a subset of ions in the material can control the
resonance frequency of other ions. This opens the way for the construction of
quantum gates in rare-earth-ion doped crystals.


title:
Dissipation in a 2-dimensional Hilbert space: Various forms of complete
  positivity

abstract:
  We consider the time evolution of the density matrix $\rho$ in a
2-dimensional complex Hilbert space. We allow for dissipation by adding to the
von Neumann equation a term $D[\rho]$, which is of Lindblad type in order to
assure complete positivity of the time evolution. We present five equivalent
forms of $D[\rho]$. In particular, we connect the familiar dissipation matrix
$L$ with a geometric version of $D[\rho]$, where $L$ consists of a positive sum
of projectors onto planes in $\mathbf{R}^3$. We also study the minimal number
of Lindblad terms needed to describe the most general case of $D[\rho]$. All
proofs are worked out comprehensively, as they present at the same time a
practical procedure how to determine explicitly the different forms of
$D[\rho]$. Finally, we perform a general discussion of the asymptotic behaviour
$t \to \infty$ of the density matrix and we relate the two types of asymptotic
behaviour with our geometric version of $D[\rho]$.


title: On the role of entanglement in quantum computational speed-up

abstract:
  For any quantum algorithm operating on pure states we prove that the presence
of multi-partite entanglement, with a number of parties that increases
unboundedly with input size, is necessary if the quantum algorithm is to offer
an exponential speed-up over classical computation. Furthermore we prove that
the algorithm can be classically efficiently simulated to within a prescribed
tolerance \eta even if a suitably small amount of global entanglement
(depending on \eta) is present. We explicitly identify the occurrence of
increasing multi-partite entanglement in Shor's algorithm. Our results do not
apply to quantum algorithms operating on mixed states in general and we discuss
the suggestion that an exponential computational speed-up might be possible
with mixed states in the total absence of entanglement. Finally, despite the
essential role of entanglement for pure state algorithms, we argue that it is
nevertheless misleading to view entanglement as a key resource for quantum
computational power.


title: Quantum Neural Networks

abstract:
  This paper initiates the study of quantum computing within the constraints of
using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a
polylogarithmic number of computation steps. The current research in the
literature has focussed on using a polynomial number of qubits. A new
mathematical model of computation called \emph{Quantum Neural Networks (QNNs)}
is defined, building on Deutsch's model of quantum computational network. The
model introduces a nonlinear and irreversible gate, similar to the speculative
operator defined by Abrams and Lloyd. The precise dynamics of this operator are
defined and while giving examples in which nonlinear Schr\"{o}dinger's
equations are applied, we speculate on its possible implementation. The many
practical problems associated with the current model of quantum computing are
alleviated in the new model. It is shown that QNNs of logarithmic size and
constant depth have the same computational power as threshold circuits, which
are used for modeling neural networks. QNNs of polylogarithmic size and
polylogarithmic depth can solve the problems in \NC, the class of problems with
theoretically fast parallel solutions. Thus, the new model may indeed provide
an approach for building scalable parallel computers.


title: Bayesian feedback versus Markovian feedback in a two-level atom

abstract:
  We compare two different approaches to the control of the dynamics of a
continuously monitored open quantum system. The first is Markovian feedback as
introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. {\bf 70},
548 (1993)]. The second is feedback based on an estimate of the system state,
developed recently by Doherty {\em et al.} [Phys. Rev. A {\bf 62}, 012105
(2000)]. Here we choose to call it, for brevity, {\em Bayesian feedback}. For
systems with nonlinear dynamics, we expect these two methods of feedback
control to give markedly different results. The simplest possible nonlinear
system is a driven and damped two-level atom, so we choose this as our model
system. The monitoring is taken to be homodyne detection of the atomic
fluorescence, and the control is by modulating the driving. The aim of the
feedback in both cases is to stabilize the internal state of the atom as close
as possible to an arbitrarily chosen pure state, in the presence of inefficient
detection and other forms of decoherence. Our results (obtain without recourse
to stochastic simulations) prove that Bayesian feedback is never inferior, and
is usually superior, to Markovian feedback. However it would be far more
difficult to implement than Markovian feedback and it loses its superiority
when obvious simplifying approximations are made. It is thus not clear which
form of feedback would be better in the face of inevitable experimental
imperfections.


title:
An interferometric complementarity experiment in a bulk Nuclear Magnetic
  Resonance ensemble

abstract:
  We have experimentally demonstrated the interferometric complementarity,
which relates the distinguishability $D$ quantifying the amount of which-way
(WW) information to the fringe visibility $V$ characterizing the wave feature
of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR)
techniques. We primarily concern on the intermediate cases: partial fringe
visibility and incomplete WW information. We propose a quantitative measure of
$D$ by an alternative geometric strategy and investigate the relation between
$D$ and entanglement. By measuring $D$ and $V$ independently, it turns out that
the duality relation $D^{2}+V^{2}=1$ holds for pure quantum states of the
markers.


title: Quantum breaking time near classical equilibrium points

abstract:
  By using numerical and semiclassical methods, we evaluate the quantum
breaking, or Ehrenfest time for a wave packet localized around classical
equilibrium points of autonomous one-dimensional systems with polynomial
potentials. We find that the Ehrenfest time diverges logarithmically with the
inverse of the Planck constant whenever the equilibrium point is exponentially
unstable. For stable equilibrium points, we have a power law divergence with
exponent determined by the degree of the potential near the equilibrium point.


title:
Analytical solution to the Schrodinger equation of a laser-driven
  correlated two-particle system

abstract:
  The time-dependent quantum system of two laser-driven electrons in a harmonic
oscillator potential is analysed, taking into account the repulsive Coulomb
interaction between both particles. The Schrodinger equation of the
two-particle system is shown to be analytically soluble in case of arbitrary
laser frequencies and individual oscillator frequencies, defining the system.
Quantum information processing could be a possible field of application


title:
Additivity of the Classical Capacity of Entanglement-Breaking Quantum
  Channels

abstract:
  We show that for the tensor product of an entanglement-breaking quantum
channel with an arbitrary quantum channel, both the minimum entropy of an
output of the channel and the Holevo-Schumacher-Westmoreland capacity are
additive. In addition, for the tensor product of two arbitrary quantum
channels, we give a bound involving entanglement of formation for the amount of
subadditivity (for minimum entropy output) or superadditivity (for channel
capacity) that can occur.


title:
Counter-propagating entangled photons from a waveguide with periodic
  nonlinearity

abstract:
  The conditions required for spontaneous parametric down-conversion in a
waveguide with periodic nonlinearity in the presence of an unguided pump field
are established. Control of the periodic nonlinearity and the physical
properties of the waveguide permits the quasi-phase matching equations that
describe counter-propagating guided signal and idler beams to be satisfied. We
compare the tuning curves and spectral properties of such counter-propagating
beams to those for co-propagating beams under typical experimental conditions.
We find that the counter-propagating beams exhibit narrow bandwidth permitting
the generation of quantum states that possess discrete-frequency entanglement.
Such states may be useful for experiments in quantum optics and technologies
that benefit from frequency entanglement.


title: Rate equation theory of sub-Poissonian laser light

abstract:
  Lasers essentially consist of single-mode optical cavities containing
two-level atoms with a supply of energy called the pump and a sink of energy,
perhaps an optical detector. The latter converts the light energy into a
sequence of electrical pulses corresponding to photo-detection events. It was
predicted in 1984 on the basis of Quantum Optics and verified experimentally
shortly thereafter that when the pump is non-fluctuating the emitted light does
not fluctuate much. Precisely, this means that the variance of the number of
photo-detection events observed over a sufficiently long period of time is much
smaller than the average number of events. Light having that property is said
to be ``sub-Poissonian''. The theory presented rests on the concept introduced
by Einstein around 1905, asserting that matter may exchange energy with a wave
at angular frequency $\omega$ only by multiples of $\hbar\omega$. The optical
field energy may only vary by integral multiples of $\hbar\omega$ as a result
of matter quantization and conservation of energy. A number of important
results relating to isolated optical cavities containing two-level atoms are
first established on the basis of the laws of Statistical Mechanics. Next, the
laser system with a pump and an absorber of radiation is treated. The
expression of the photo-current spectral density found in that manner coincides
with the Quantum Optics result. The concepts employed in this paper are
intuitive and the algebra is elementary. The paper supplements a previous OQE
tutorial paper in establishing a connection between the theory of laser noise
and Statistical Mechanics.


title: Tradeoffs in the Quantum Search Algorithm

abstract:
  Quantum search is a quantum mechanical technique for searching N
possibilities in only sqrt(N) steps. This has been proved to be the best
possible algorithm for the exhuastive search problem in the sense the number of
queries it requires cannot be reduced. However, as this paper shows, the number
of non-query operations, and thus the total number of operations, can be
reduced. The number of non-query unitary operations can be reduced by a factor
of log N/alpha*log(log N) while increasing the number of queries by a factor of
only (1+(log N)^{-alpha}). Various choices of alpha yield different variants of
the algorithm. For example, by choosing alpha to be O(log N/log(log N)), the
number of non-query unitary operations can be reduced by 40% while increasing
the number of queries by just two.


title: Quantum universal variable-length source coding

abstract:
  We construct an optimal quantum universal variable-length code that achieves
the admissible minimum rate, i.e., our code is used for any probability
distribution of quantum states. Its probability of exceeding the admissible
minimum rate exponentially goes to 0. Our code is optimal in the sense of its
exponent. In addition, its average error asymptotically tends to 0.


title: Exponents of quantum fixed-length pure state source coding

abstract:
  We derive the optimal exponent of the error probability of the quantum
fixed-length pure state source coding in both cases of blind coding and visible
coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81,
1714 (1998))'s universal code. In the direct part, a group representation
theoretical type method is essential. In the converse part, Nielsen and Kempe
(PRL, 86, 5184 (2001))'s lemma is essential.


title:
Two quantum analogues of Fisher information from a large deviation
  viewpoint of quantum estimation

abstract:
  We discuss two quantum analogues of Fisher information, symmetric logarithmic
derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher
information from a large deviation viewpoint of quantum estimation and prove
that the former gives the true bound and the latter gives the bound of
consistent superefficient estimators. In another comparison, it is shown that
the difference between them is characterized by the change of the order of
limits.


title:
Experimental Implementation of Remote State Preparation by Nuclear
  Magnetic Resonance

abstract:
  We have experimentally implemented remote state preparation (RSP) of a qubit
from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled
chloroform $^{13}$CHCl$_{3}$ over interatomic distances using liquid-state
nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of
qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch
sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP
scheme can be generalized to prepare a large number of qubit states and may be
used in other quantum information processing and quantum computing.


title:
Quantum description of light pulse scattering on a single atom in
  waveguides

abstract:
  We present a time dependent quantum calculation of the scattering of a
few-photon pulse on a single atom. The photon wave packet is assumed to
propagate in a transversely strongly confined geometry, which ensures strong
atom-light coupling and allows a quasi 1D treatment. The amplitude and phase of
the transmitted, reflected and transversely scattered part of the wave packet
strongly depend on the pulse length (bandwidth) and energy. For a transverse
mode size of the order of $\lambda^2$, we find nonlinear behavior for a few
photons already, or even for a single photon. In a second step we study the
collision of two such wave packets at the atomic site and find striking
differences between Fock state and coherent state wave packets of the same
photon number.


title: Long-range magnetic interaction due to the Casimir effect

abstract:
  The zero-point quantum fluctuations of the electromagnetic field in vacuum
are known to give rise to a long-range attractive force between metal plates
(Casimir effect). For ferromagnetic layers separated by vacuum, it is shown
that the interplay of the Casimir effect and of the magneto-optical Kerr effect
gives rise to a long-range magnetic interaction. The Casimir magnetic force is
found to decay as $D^{-1}$ in the limit of short distances, and as $D^{-5}$ in
the limit of long distances. Explicit expressions for realistic systems are
given in the large and small distance limits. An experimental test of the
Casimir magnetic interaction is proposed.


title: Logical network implementation for cluster states and graph codes

abstract:
  In a previous paper a straight forward construction method for quantum error
correcting codes, based on graphs, has been presented. These graph codes are
directly related to cluster states which have been introduced by Briegel and
Raussendorf. We show that the preparation of a cluster state as well as the
coding operation for a graph code, can be implemented by a logical network.
Concerning the qubit case each vertex corresponds to an Hadamard gate and each
edge corresponds to a controlled not gate.


title:
"Spectral Implementation" for creating a labeled pseudo-pure state and
  the Bernstein-Vazirani's algorithm in a four-qubit nuclear magnetic resonance
  quantum processor

abstract:
  A quantum circuit is introducted to describe the preparation of a labeled
pseudo-pure state by mutiplet-component excitation scheme which has been
experimentally implemented on a 4-qubit nuclear magnetic resonance quantum
processor. Meanwhile, we theoretically analyze and numerically inverstigate the
low-power selective single-pulse implementation of a controlled-rotation gate,
which manifests its validity in our experiment. Based on the labeled
pseudo-pure state prepared, a 3-qubit Bernstein-Vazirani algorithm has been
experimentally demonstrated by spectral implementation. The "answers" of the
computations are indentified from the split speak positions in the spectra of
the observer spin, which are equivalent to projective measurements required by
the algorithms.


title: Conditions for the confirmation of three-particle non-locality

abstract:
  The notion of genuine three-particle non-locality introduced by Svetlichny
\cite{Svetlichny} is discussed. Svetlichny's inequality which can distinguish
between genuine three-particle non-locality and two-particle non-locality is
analyzed by reinterpreting it as a frustrated network of correlations. Its
quantum mechanical maximum violation is derived and a situation is presented
that produces the maximum violation. It is shown that the measurements
performed in recent experiments to demonstrate GHZ entanglement
\cite{Bouwmeester}, \cite{Pan} do not allow this inequality to be violated, and
hence can not be taken as confirmation of genuine three-particle non-locality.
Modifications to the experiments that would make such a confirmation possible
are discussed.


title:
Exhibition of the periodicity of Quantum Fourier Transformation in
  Nuclear Magnetic Resonance

abstract:
  The remarkable capability of quantum Fourier transformation (QFT) to extract
the periodicity of a given periodic function has been exhibited by using
nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments
were performed. In a full QFT, the periodicity were validated with state
tomography and fidelity measurements. For a simplified QFT, the three-qubit
pseudo-pure state was created by introducting an additional observer spin, and
the spectra recorded on the observer spin showed intuitively the power of QFT\
to find the periodicity. Experimentally realizing the QFT provides a critical
step to implement the renowned Shor's quantum factoring algorithm and many
other algorithms. Moveover, it can be applied to the study of quantum chaos and
other quantum information processing.


title: Master Equation for Light emitted by correlated Atoms

abstract:
  A master equation for light generated by atoms, which states are prepared by
a pumping mechanism that produces atomic correlations, is derived in the
Fokker-Planck approximation. It has been found that two-particle correlations
only play the role under this approach. Then the equation is applied for
describing micromaser operations and light noise is discussed. We consider the
correlated atomic states prepared by telecloning protocols.


title:
Limitations of squeezing due to collisional decoherence in Bose-Einstein
  condensates

abstract:
  We study the limitations for entanglement due to collisional decoherence in a
Bose-Einstein condensate. Specifically we consider relative number squeezing
between photons and atoms coupled out from a homogeneous condensate. We study
the decay of excited quasiparticle modes due to collisions, in condensates of
atoms with one or two internal degrees of freedom. The time evolution of these
modes is determined in the linear response approximation to the deviation from
equilibrium. We use Heisenberg-Langevin equations to derive equations of motion
for the densities and higher correlation functions which determine the
squeezing. In this way we can show that decoherence due to quasiparticle
interactions imposes an important limit on the degree of number squeezing which
may be achieved. Our results are also relevant for the determination of
decoherence times in other experiments based on entanglement, e.g. the slowing
and stopping of light in condensed atomic gases using dark states.


title: Spin Solitons and Quantum Control of Spin Chain Dynamics

abstract:
  Experiments in coherent spectroscopy correspond to control of quantum
mechanical ensembles guiding them from initial to final target states by
unitary transformations. The control inputs (pulse sequences) that accomplish
these unitary transformations should take as little time as possible so as to
minimize the effects of relaxation and to optimize the sensitivity of the
experiments. Here, we present a radically different and generally applicable
approach to efficient control of dynamics in spin chains of arbitrary length.
The approach relies on the creation of localized spin waves, ``spin solitons'',
and efficient propagation of these soliton states through the spin chain. The
methods presented are expected to find immediate applications in control of
spin dynamics in coherent spectroscopy and quantum information processing.


title:
Realization of Fredkin Gate by Three Transition Pulses in NMR Quantum
  Information Processor

abstract:
  The three-qubit conditional swap gate(Fredkin gate) is a universal gate that
can be used to create any logic circuit and has many direct usages. In this
paper, we experimentally realized Fredkin gate with only three transition
pulses in solution of alanine. It appears that no experimental realization of
Fredkin gate with fewer pulses has yet been reported up to now. In addition,
the simple structure of our scheme makes it easy to be implemented in
experiments.


title: Semiclassical Neural Network

abstract:
  We have constructed a simple semiclassical model of neural network where
neurons have quantum links with one another in a chosen way and affect one
another in a fashion analogous to action potentials. We have examined the role
of stochasticity introduced by the quantum potential and compare the system
with the classical system of an integrate-and-fire model by Hopfield. Average
periodicity and short term retentivity of input memory are noted.


title: Neural Networks with c-NOT Gated Nodes

abstract:
  We try to design a quantum neural network with qubits instead of classical
neurons with deterministic states, and also with quantum operators replacing
teh classical action potentials. With our choice of gates interconnecting teh
neural lattice, it appears that the state of the system behaves in ways
reflecting both the strengths of coupling between neurons as well as initial
conditions. We find that depending whether there is a threshold for emission
from excited to ground state, the system shows either aperiodic oscillations or
coherent ones with periodicity depending on the strength of coupling.


title:
Casimir energy of a dilute dispersive dielectric ball: realistic
  microscopic model

abstract:
  The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at
zero temperature is derived analytically within a microscopic realistic model
of dielectrics for an arbitrary physically possible frequency dispersion of
dielectric permittivity. Divergences are absent in calculations, a minimum
interatomic distance is a physical cut-off. Casimir surface force is proved to
be attractive. A physical definition of the Casimir energy is discussed.


title:
Thermodynamical aspects of the Casimir force between real metals at
  nonzero temperature

abstract:
  We investigate the thermodynamical aspects of the Casimir effect in the case
of plane parallel plates made of real metals. The thermal corrections to the
Casimir force between real metals were recently computed by several authors
using different approaches based on the Lifshitz formula with diverse results.
Both the Drude and plasma models were used to describe a real metal. We
calculate the entropy density of photons between metallic plates as a function
of the surface separation and temperature. Some of these approaches are
demonstrated to lead to negative values of entropy and to nonzero entropy at
zero temperature depending on the parameters of the system. The conclusion is
that these approaches are in contradiction with the third law of thermodynamics
and must be rejected. It is shown that the plasma dielectric function in
combination with the unmodified Lifshitz formula is in perfect agreement with
the general principles of thermodynamics. As to the Drude dielectric function,
the modification of the zero-frequency term of the Lifshitz formula is outlined
that not to violate the laws of thermodynamics.


title: Going beyond GHZ paradox

abstract:
  We present numerical data showing, that three qutrit correlations for a pure
state, which is not maximally entangled, violate local realism more strongly
than three-qubit correlations. The strength of violation is measured by the
minimal amount of noise that must be admixed to the system so that the noisy
correlations have a local and realistic model.


title:
Information cloning of harmonic oscillator coherent states and its
  fidelity

abstract:
  We show that in the case of unknown {\em harmonic oscillator coherent states}
it is possible to achieve what we call {\it perfect information cloning}. By
this we mean that it is still possible to make arbitrary number of copies of a
state which has {\it exactly} the same information content as the original
unknown coherent state. By making use of this {\it perfect information cloning}
it would be possible to estimate the original state through measurements and
make arbitrary number of copies of the estimator. We define the notion of a
{\em Measurement Fidelity}. We show that this information cloning gives rise,
in the case of $1\to N$, to a {\em distribution} of {\em measurement
fidelities} whose average value is ${1\over 2}$ irrespective of the number of
copies originally made. Generalisations of this to the $M\to MN$ case as well
as the measurement fidelities for Gaussian cloners are also given.


title: Asymmetrical Quantum Cryptographic Algorithm

abstract:
  A cryptographic algorithm is proposed based on fully quantum mechanical keys
and ciphers. Encryption and decryption are carried out via an appropriate
measurement process on entangled states as governed by a quantum mechanical,
asymmetrical and dynamical public key distribution. The use of public keys
leads to a high availability of our scheme, while their quantum nature is shown
to ensure unconditional security of the proposed algorithm.


title: Mathematical Physics and Life

abstract:
  It is a fascinating subject to explore how well we can understand the
processes of life on the basis of fundamental laws of physics. It is emphasised
that viewing biological processes as manipulation of information extracts their
essential features. This information processing can be analysed using
well-known methods of computer science. The lowest level of biological
information processing, involving DNA and proteins, is the easiest one to link
to physical properties. Physical underpinnings of the genetic information that
could have led to the universal language of 4 nucleotide bases and 20 amino
acids are pointed out. Generalisations of Boolean logic, especially features of
quantum dynamics, play a crucial role.

categories: quant-ph cond-mat physics.bio-ph q-bio.BM


title: Recurrence in Quantum Mechanics

abstract:
  We first compare the mathematical structure of quantum and classical
mechanics when both are formulated in a C*-algebraic framework. By using finite
von Neumann algebras, a quantum mechanical analogue of Liouville's theorem is
then proposed. We proceed to study Poincare recurrence in C*-algebras by
mimicking the measure theoretic setting. The results are interpreted as
recurrence in quantum mechanics, similar to Poincare recurrence in classical
mechanics.


title: Born--Infeld action for gravitational and electroweak fields

abstract:
  This paper has been withdrawn due to upload of another version of it as a new
preprint: gr-qc/0404097


title:
Comment on ``Experimental Nonlocality Proof of Quantum Teleportation and
  Entanglement Swapping''

abstract:
  In quant-ph/0201134 Jennewein et al. report experiments demonstrating
entanglement swapping under various conditions. In one instance, they claim to
have exhibited Bell inequality violations by a pair of photons prior to
performing any entangling operations on the pair. However, the Bell inequality
violation results in this case from post-selection of the data, not from
quantum non-locality.


title:
Nonlinear QM as a fractal Brownian motion with complex diffusion
  constant

abstract:
  A new nonlinear Schroedinger equation is obtained explicitly from the fractal
Brownian motion of a massive particle with a complex-valued diffusion constant.
Real-valued energy (momentum) plane wave and soliton solutions are found in the
free particle case. The hydro-dynamical model analog yields another (new)
nonlinear QM wave equation with physically meaningful soliton solutions. One
remarkable feature of this nonlinear Schroedinger equation based on a fractal
Brownian motion model, over all the other nonlinear QM models, is that the
quantum-mechanical energy functional coincides with the field theory one.


title: Atom laser coherence and its control via feedback

abstract:
  We present a quantum-mechanical treatment of the coherence properties of a
single-mode atom laser. Specifically, we focus on the quantum phase noise of
the atomic field as expressed by the first-order coherence function, for which
we derive analytical expressions in various regimes. The decay of this function
is characterized by the coherence time, or its reciprocal, the linewidth. A
crucial contributor to the linewidth is the collisional interaction of the
atoms. We find four distinct regimes for the linewidth with increasing
interaction strength. These range from the standard laser linewidth, through
quadratic and linear regimes, to another constant regime due to quantum
revivals of the coherence function. The laser output is only coherent (Bose
degenerate) up to the linear regime. However, we show that application of a
quantum nondemolition measurement and feedback scheme will increase, by many
orders of magnitude, the range of interaction strengths for which it remains
coherent.


title: Spin squeezing via quantum feedback

abstract:
  We propose a quantum feedback scheme for producing deterministically
reproducible spin squeezing. The results of a continuous nondemolition atom
number measurement are fed back to control the quantum state of the sample. For
large samples and strong cavity coupling, the squeezing parameter minimum
scales inversely with atom number, approaching the Heisenberg limit.
Furthermore, ceasing the measurement and feedback when this minimum has been
reached will leave the sample in the maximally squeezed spin state.


title: Scaling of Entanglement close to a Quantum Phase Transitions

abstract:
  In this Letter we discuss the entanglement near a quantum phase transition by
analyzing the properties of the concurrence for a class of exactly solvable
models in one dimension. We find that entanglement can be classified in the
framework of scaling theory. Further, we reveal a profound difference between
classical correlations and the non-local quantum correlation, entanglement: the
correlation length diverges at the phase transition, whereas entanglement in
general remains short ranged.


title: Quantum Computer with Fixed Interaction is Universal

abstract:
  It is proved that a quantum computer with fixed and permanent interaction of
diagonal type between qubits proposed in the work quant-ph/0201132 is
universal. Such computer is controlled only by one-qubit quick transformations,
and this makes it feasible.


title: Decoherence Sturdy Memories in the Presence of Quantum Dissipation

abstract:
  We consider N identical oscillators coupled to a single environment and show
that the conditions for the existence of decoherence free subspaces are
degeneracy of the oscillator frequencies and separability of the coupling with
the environment. A formal exact equation for the evolution in the case of two
oscillators is found and the decoherence free subspace is explicitly
determined. A full analytical solution for any initial condition and general
parameters (frequencies and dissipation constants) is given in the markovian
approximation and zero temperature. We find that slight relaxation of
degeneracy and separability conditions leads to the appearence of two
components in the dynamical evolution with very different decoherence times.
The ratio between the characteristic time of the weak and strong decoherent
components is given by $\tau_{WD}/\tau_{SD}\approx k/\delta k$, where $\delta
k$ is a measure of the nonseparability of the coupling to the environment and
$k$ is the mean decay constant of the oscillators.


title:
Cole-Hopf Like Transformation for Schr\"odinger Equations Containing
  Complex Nonlinearities

abstract:
  We consider systems, which conserve the particle number and are described by
Schr\"odinger equations containing complex nonlinearities. In the case of
canonical systems, we study their main symmetries and conservation laws. We
introduce a Cole-Hopf like transformation both for canonical and noncanonical
systems, which changes the evolution equation into another one containing
purely real nonlinearities, and reduces the continuity equation to the standard
form of the linear theory. This approach allows us to treat, in a unifying
scheme, a wide variety of canonical and noncanonical nonlinear systems, some of
them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z,
03.65.-w, 05.45.-a, 11.30.Na, 11.40.Dw


title: An Improved Quantum Scheduling Algorithm

abstract:
  The scheduling problem consists of finding a common 1 in two remotely located
N bit strings. Denote the number of 1s in the string with the fewer 1s by
epsilon*N. Classically, it needs at least O(epsilon*N) bits of communication to
find the common 1 (ignoring logarithmic factors). The best known quantum
algorithm would require O(sqrt(N)) qubits of communication. This paper gives a
modified quantum algorithm to find the common 1 with only O(sqrt(epsilon*N))
qubits of communication.


title: Nonlocality, Asymmetry, and Distinguishing Bipartite States

abstract:
  Entanglement is an useful resource because some global operations cannot be
locally implemented using classical communication. We prove a number of results
about what is and is not locally possible. We focus on orthogonal states, which
can always be globally distinguished. We establish the necessary and sufficient
conditions for a general set of 2x2 quantum states to be locally
distinguishable, and for a general set of 2xn quantum states to be
distinguished given an initial measurement of the qubit. These results reveal a
fundamental asymmetry to nonlocality, which is the origin of ``nonlocality
without entanglement'', and we present a very simple proof of this phenomenon.


title: Cluster of Dipolar Coupled Spins as a Quantum Memory Storage

abstract:
  Spin dynamics of a cluster of coupled spins 1/2 can be manipulated to store
and process a large amount of information. A new type of dynamic response makes
it possible to excite coherent long-living signals, which can be used for
exchanging information with a mesoscopic quantum system. An experimental
demonstration is given for a system of 19 proton spins of a liquid crystal
molecule.


title: Fast fault-tolerant filtering of quantum codewords

abstract:
  The stabilization of a quantum computer by repeated error correction can be
reduced almost entirely to repeated preparation of blocks of qubits in quantum
codeword states. These are multi-particle entangled states with a high degree
of symmetry. The required accuracy can be achieved by measuring parity checks,
using imperfect apparatus, and rejecting states which fail them. This filtering
process is considered for t-error-correcting codes with t>1. It is shown how to
exploit the structure of the codeword and the check matrix, so that the filter
is reduced to a minimal form where each parity check need only be measured
once, not > t times by the (noisy) verification apparatus. This both raises the
noise threshold and also reduces the physical size of the computer. A method
based on latin rectangles is proposed, which enables the most parallel version
of a logic gate network to be found, for a class of networks including those
used in verification. These insights allowed the noise threshold to be
increased by an order of magnitude.


title: Quantum Tunneling and Caustics under Inverse Square Potential

abstract:
  Quantization of a harmonic oscillator with inverse square potential
$V(x)=(m{\omega^2}/2){x^2}+g/{x^2}$ on the line $-\infty<x<\infty$ is
re-examined. It is shown that, for $0<g<3{\hbar^2}/(8m)$, the system admits a
U(2) family of inequivalent quantizations allowing for quantum tunneling
through the potenatial barrier at $x=0$. In the family is a distinguished
quantization which reduces smoothly to the harmonic oscillator as $g\to 0$, in
contrast to the conventional quantization applied to the Calogero model which
prohibits the tunneling and has no such limit. The tunneling renders the
classical caustics anomalous at the quantum level, leading to the possibility
of copying an arbitrary state from one side $x>0$, say, to the other $x<0$.


title: 3 omega method for specific heat and thermal conductivity measurements

abstract:
  We present a 3 omega method for simultaneously measuring the specific heat
and thermal conductivity of a rod- or filament-like specimen using a way
similar to a four-probe resistance measurement. The specimen in this method
needs to be electrically conductive and with a temperature-dependent
resistance, for acting both as a heater to create a temperature fluctuation and
as a sensor to measure its thermal response. With this method we have
successfully measured the specific heat and thermal conductivity of platinum
wire specimens at cryogenic temperatures, and measured those thermal quantities
of tiny carbon nanotube bundles some of which are only 10^-9 g in mass.


title: Quantum Computation--The Ultimate Frontier

abstract:
  The discovery of an algorithm for factoring which runs in polynomial time on
a quantum computer has given rise to a concerted effort to understand the
principles, advantages, and limitations of quantum computing. At the same time,
many different quantum systems are being explored for their suitability to
serve as a physical substrate for the quantum computer of the future. I discuss
some of the theoretical foundations of quantum computer science, including
algorithms and error correction, and present a few physical systems that have
shown promise as a quantum computing platform. Finally, we discuss a spin-off
of the quantum computing revolution: quantum technologies.


title: Linear Optics Quantum Communication over Long Distances

abstract:
  We propose a feasible scheme for teleporting an arbitrary polarization state
or entanglement of photons by requiring only single-photon (SP) sources, simple
linear optical elements and SP quantum non-demolition measurements. An unknown
SP polarization state can be faithfully teleported either to a duplicate
polarization state or to an entangled state. Our proposal can be used to
implement long-distance quantum communication in a simple way. The scheme is
within the reach of current technology and significantly simplifies the
realistc implementation of long-distance high-fidelity quantum communication
with photon qubits.


title: Entanglement and the SU(2) phase states in atomic systems

abstract:
  We show that a system of 2n identical two-level atoms interacting with n
cavity photons manifests entanglement and that the set of entangled states
coincides with the so-called SU(2) phase states. In particular, violation of
classical realism in terms of the GHZ and GHSH conditions is proved. We discuss
a new property of entanglement expressed in terms of local measurements. We
also show that generation of entangled states in the atom-photon systems under
consideration strongly depends on the choice of initial conditions and that the
parasitic influence of cavity detuning can be compensated through the use of
Kerr medium.


title:
Time-optimal Hamiltonian simulation and gate synthesis using homogeneous
  local unitaries

abstract:
  Motivated by experimental limitations commonly met in the design of solid
state quantum computers, we study the problems of non-local Hamiltonian
simulation and non-local gate synthesis when only homogeneous local unitaries
are performed in order to tailor the available interaction. Homogeneous (i.e.
identical for all subsystems) local manipulation implies a more refined
classification of interaction Hamiltonians than the inhomogeneous case, as well
as the loss of universality in Hamiltonian simulation. For the case of
symmetric two-qubit interactions, we provide time-optimal protocols for both
Hamiltonian simulation and gate synthesis.


title:
Schwinger, Pegg and Barnett approaches and a relationship between
  angular and Cartesian quantum descriptions II: Phase Spaces

abstract:
  Following the discussion -- in state space language -- presented in a
preceding paper, we work on the passage from the phase space description of a
degree of freedom described by a finite number of states (without classical
counterpart) to one described by an infinite (and continuously labeled) number
of states. With that it is possible to relate an original Schwinger idea to the
Pegg and Barnett approach to the phase problem. In phase space language, this
discussion shows that one can obtain the Weyl-Wigner formalism, for both
Cartesian {\em and} angular coordinates, as limiting elements of the discrete
phase space formalism.


title: The entanglement of purification

abstract:
  We introduce a measure of both quantum as well as classical correlations in a
quantum state, the entanglement of purification. We show that the (regularized)
entanglement of purification is equal to the entanglement cost of creating a
state $\rho$ asymptotically from maximally entangled states, with negligible
communication. We prove that the classical mutual information and the quantum
mutual information divided by two are lower bounds for the regularized
entanglement of purification. We present numerical results of the entanglement
of purification for Werner states in ${\cal H}_2 \otimes {\cal H}_2$.


title:
Two-Time Correlation Functions: Stochastic and Conventional Quantum
  Mechanics

abstract:
  An investigation of two-time correlation functions is reported within the
framework of (i) Stochastic Quantum Mechanics and (ii) conventional
Heisenberg-Schr\"odinger Quantum Mechanics. The spectral functions associated
with the two-time electric dipole correlation functions are worked out in
detail for the case of the hydrogen atom. While the single time averages are
identical for stochastic and conventional quantum mechanics, differences arise
in the two approaches for multiple time correlation functions.


title:
Single-photon quantum nondemolition detectors constructed with linear
  optics and projective measurements

abstract:
  Optical quantum nondemolition devices can provide essential tools for quantum
information processing. Here, we describe several optical interferometers that
signal the presence of a single photon in a particular input state without
destroying it. We discuss both entanglement-assisted and
non-entanglement-assisted interferometers, with ideal and realistic detectors.
We found that existing detectors with 88% quantum efficiency and single-photon
resolution can yield output fidelities of up to 89%, depending on the input
state. Furthermore, we construct expanded protocols to perform QND detections
of single photons that leave the polarization invariant. For detectors with 88%
efficiency we found polarization-preserving output fidelities of up to 98.5%.


title: Arbitrarily Accurate Eigenvalues for General Anharmonic Potentials

abstract:
  We show that the Riccati form of the Schrodinger equation can be reformulated
in terms of two linear equations depending on an arbitrary function G. When $G$
and the potential are polynomials, the solutions of these two equations are
entire functions (L and K) and the zeroes of K are identical to those of the
wave function. Requiring such a zero at a large but finite value of the
argument yields the low energy eigenstates with exponentially small errors.
Judicious choice of G can improve dramatically the numerical treatment. The
method yields many significant digits with modest computer means.

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


title: Parallel transport in an entangled ring

abstract:
  This paper defines a notion of parallel transport in a lattice of quantum
particles, such that the transformation associated with each link of the
lattice is determined by the quantum state of the two particles joined by that
link. We focus particularly on a one-dimensional lattice--a ring--of entangled
rebits, which are binary quantum objects confined to a real state space. We
consider states of the ring that maximize the correlation between nearest
neighbors, and show that some correlation must be sacrificed in order to have
non-trivial parallel transport around the ring. An analogy is made with lattice
gauge theory, in which non-trivial parallel transport around closed loops is
associated with a reduction in the probability of the field configuration. We
discuss the possibility of extending our result to qubits and to higher
dimensional lattices.


title:
Spontaneous localization for a charged particle in non-relativistic
  quantum mechanics

abstract:
  The interaction of a moving charged particle with its coherent
electromagnetic field is analysed in the framework of non-relativistic quantum
mechanics. It is shown that, when this interaction is taken into account, a
spatially localized state may have a mean energy lower than the one
corresponding to a delocalized state.


title: Classical limit of the Kepler problem and the contraction of phase space

abstract: Paper withdrawn, see math-ph/0505072


title:
Describing mixed spin-space entanglement of pure states of
  indistinguishable particles using an occupation number basis

abstract:
  Quantum mechanical entanglement is a resource for quantum computation,
quantum teleportation, and quantum cryptography. The ability to quantify this
resource correctly has thus become of great interest to those working in the
field of quantum information theory. In this paper, we show that all existing
entanglement measures but one fail important tests of fitness when applied to n
particle, m site states of indistinguishable particles, where n,m>=2. The
accepted method of measuring the entanglement of a bipartite system of
distinguishable particles is to use the von Neumann entropy of the reduced
density matrix of one half of the system. We show that expressing the full
density matrix using a site-spin occupation number basis, and reducing with
respect to that basis, gives an entanglement which meets all currently known
fitness criteria for systems composed of either distinguishable or
indistinguishable particles.
  We consider an output state from a previously published thought experiment, a
state which is entangled in both spin and spatial degrees of freedom, and show
that the site entropy measure gives the correct total entanglement. We also
show how the spin-space entanglement transfer occurring within the apparatus
can be understood in terms of the transfer of probability from single-occupancy
to double-occupancy sectors of the density matrix.


title: Advancement of estimation fidelity in continuous quantum measurement

abstract:
  We estimate an unknown qubit from the long sequence of n random polarization
measurements of precision Delta. Using the standard Ito-stochastic equations of
the aposteriori state in the continuous measurement limit we calculate the
advancement of fidelity. We show that the standard optimum value 2/3 is
achieved asymptotically for n >> Delta^2 / 96 >> 1. We append a brief
derivation of novel Ito-equations for the estimate state.


title: Most Bell Operators do not Significantly Violate Locality

abstract:
  The worst violation of Bell's inequality for $n$ qbits is of size
$2^{\frac{n-1}{2}}$ and it is obtained by a specific operator acting on a
specific state. We show, to the contrary, that for a vast majority of Bell
operators the worst violation is bounded by $O((n\log n)^{{1/2}})$, below
experimental detection. With respect to the extremal operators, introduced by
Werner and Wolf [Phys. Rev. A 64, 032112 (2001)], we show that a large majority
of them have a norm bounded by $O(n^{{1/2}})$.


title: Thermodynamic interpretation of quantum error correcting criterion

abstract:
  Shanon's fundamental coding theorems relate classical information theory to
thermodynamics. More recent theoretical work has been successful in relating
quantum information theory to thermodynamics. For example, Schumacher proved a
quantum version of Shannon's 1948 classical noiseless coding theorem. In this
note, we extend the connection between quantum information theory and
thermodynamics to include quantum error correction. There is a standard
mechanism for describing errors that may occur during the transmission,
storage, and manipulation of quantum information. One can formulate a criterion
of necessary and sufficient conditions for the errors to be detectable and
correctable. We show that this criterion has a thermodynamical interpretation.


title: Control aspects of holonomic quantum computation

abstract:
  A unifying framework for the control of quantum systems with non-Abelian
holonomy is presented. It is shown that, from a control theoretic point of
view, holonomic quantum computation can be treated as a control system evolving
on a principal fiber bundle. An extension of methods developed for these
classical systems may be applied to quantum holonomic systems to obtain insight
into the control properties of such systems and to construct control algorithms
for two established examples of the computing paradigm.


title:
On the structure of a reversible entanglement generating set for
  three--partite states

abstract:
  We show that Einstein--Podolsky--Rosen--Bohm (EPR) and
Greenberger--Horne--Zeilinger--Mermin (GHZ) states can not generate, through
local manipulation and in the asymptotic limit, all forms of three--partite
pure--state entanglement in a reversible way. The techniques that we use
suggest that there may be a connection between this result and the
irreversibility that occurs in the asymptotic preparation and distillation of
bipartite mixed states.


title:
Topos Theoretical Reference Frames on the Category of Quantum
  Observables

abstract:
  An observable effects a schematization of the Quantum event structure by
correlating Boolean algebras picked by measurements with the Borel algebra of
the real line. In a well-defined sense Boolean observables play the role of
coordinatizing objects in the Quantum world, by picking Boolean figures and
subsequently opening Boolean windows for the perception of the latter,
interpreted as local measurement charts. A mathematical scheme for the
implementation of this thesis is being proposed based on Category theoretical
methods. The scheme leads to a manifold representation of Quantum structure in
terms of topos-theoretical Boolean reference frames. The coordinatizing objects
give rise to structure preserving maps with the modeling objects as their
domains, effecting finally an isomorphism between quantum event algebra objects
and Boolean localization systems for the masurement of observables.


title: Conditional entropies and their relation to entanglement criteria

abstract:
  We discuss conditional Renyi and Tsallis entropies for bipartite quantum
systems of finite dimension. We investigate the relation between the positivity
of conditional entropies and entanglement properties. It is in particular shown
that any state having a negative conditional entropy with respect to any value
of the entropic parameter is distillable since it violates the reduction
criterion. Moreover we show that the entanglement of Werner states in odd
dimensions can neither be detected by entropic criteria nor by any other
spectral criterion.


title:
Are there quantum bounds on the recyclability of clock signals in low
  power computers?

abstract:
  Even if a logical network consists of thermodynamically reversible gate
operations, the computation process may have high dissipation rate if the gate
implementation is controlled by external clock signals. It is an open question
whether the global clocking mechanism necessarily envolves irreversible
processes. However, one can show that it is not possible to extract any timing
information from a micro-physical clock without disturbing it. Applying recent
results of quantum information theory we can show a hardware-independent lower
bound on the timing information that is necessarily destroyed if one tries to
copy the signal. The bound becomes tighter for low energy signals, i.e., the
timing information gets more and more quantum.


title: Comments on "Dirac theory in spacetime algebra"

abstract:
  In contrast to formulations of the Dirac theory by Hestenes and by the
current author, the formulation recently presented by W. P. Joyce [J. Phys. A:
Math. Gen. 34 (2001) 1991--2005] is equivalent to the usual Dirac equation only
in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation
can be solutions either of the Dirac equation in the Hestenes form or of the
same equation with the sign of the mass reversed, and in general they are
mixtures of the two possibilities. Because of this relationship, Joyce obtains
twice as many linearly independent plane-wave solutions for a given momentum
eigenvalue as exist in the conventional theory. A misconception about the
symmetry of the Hestenes equation and the geometric significance of the
algebraic spinors is also briefly discussed.


title:
Book review of Z. Haba, Feynman Integral and Random Dynamics in Quantum
  Physics

abstract:
  The book deals with a stochastic formulation of path integration in real
time, by rotating the_space_ variables over exp(i pi/4). Preliminary chapters
deal with quantum and classical mechanics, probability theory and stochastic
calculus, and the conventional approach to path integration through the Trotter
product formula. Subsequently, the stochastic formulation in complex space is
established, and applied to semi-classical expansions, nonlinear oscillations,
quantum dynamics on analytic manifolds, dissipative systems (i.e., those which
are open in that they interact with an environment), tunneling, field theory,
and computer simulations.


title:
Permutation symmetry for the tomographic probability distribution of a
  system of identical particles

abstract:
  The symmetry properties under permutation of tomograms representing the
states of a system of identical particles are studied. Starting from the action
of the permutation group on the density matrix we define its action on the
tomographic probability distribution. Explicit calculations are performed in
the case of the two-dimensional harmonic oscillator.


title:
Capture and release of a conditional state of a cavity QED system by
  quantum feedback

abstract:
  Detection of a single photon escaping an optical cavity QED system prepares a
non-classical state of the electromagnetic field. The evolution of the state
can be modified by changing the drive of the cavity. For the appropriate
feedback, the conditional state can be captured (stabilized) and then released.
This is observed by a conditional intensity measurement that shows suppression
of vacuum Rabi oscillations for the length of the feedback pulse and their
subsequent return.


title: Locality and reality revisited

abstract:
  Bell gave the now standard definition of a local hidden variable theory and
showed that such theories cannot reproduce the predictions of quantum mechanics
without violating his ``free will'' criterion: experimenters' measurement
choices can be assumed to be uncorrelated with properties of the measured
system prior to measurement.
  An alternative is considered here: a probabilistic theory of hidden variables
underlying quantum mechanics could be statistically local, in the sense that it
supplies global configuration probabilities which are defined by expressions
involving only local terms. This allows Bell correlations without relying on
{\it either} a conspiracy theory in which prior common causes correlate the
system state with experimenters' choices {\it or} a reverse causation principle
in which experimenters' choices affect the earlier system states. In
particular, there is no violation of the free will criterion. It gives a
different perspective on Bell correlations, in which the puzzle is not that
apparently non-local correlations should emerge from rules involving local
quantities, but rather that we do not see more general non-local correlations
that allow paradox-immune forms of superluminal signalling.


title:
Design of Strongly Modulating Pulses to Implement Precise Effective
  Hamiltonians for Quantum Information Processing

abstract:
  We describe a method for improving coherent control through the use of
detailed knowledge of the system's Hamiltonian. Precise unitary transformations
were obtained by strongly modulating the system's dynamics to average out
unwanted evolution. With the aid of numerical search methods, pulsed
irradiation schemes are obtained that perform accurate, arbitrary, selective
gates on multi-qubit systems. Compared to low power selective pulses, which
cannot average out all unwanted evolution, these pulses are substantially
shorter in time, thereby reducing the effects of relaxation. Liquid-state NMR
techniques on homonuclear spin systems are used to demonstrate the accuracy of
these gates both in simulation and experiment. Simulations of the coherent
evolution of a 3-qubit system show that the control sequences faithfully
implement the unitary operations, typically yielding gate fidelities on the
order of 0.999 and, for some sequences, up to 0.9997. The experimentally
determined density matrices resulting from the application of different control
sequences on a 3-spin system have overlaps of up to 0.99 with the expected
states, confirming the quality of the experimental implementation.


title: Quantum DNF Learnability Revisited

abstract:
  We describe a quantum PAC learning algorithm for DNF formulae under the
uniform distribution with a query complexity of $\tilde{O}(s^{3}/\epsilon +
s^{2}/\epsilon^{2})$, where $s$ is the size of DNF formula and $\epsilon$ is
the PAC error accuracy. If $s$ and $1/\epsilon$ are comparable, this gives a
modest improvement over a previously known classical query complexity of
$\tilde{O}(ns^{2}/\epsilon^{2})$. We also show a lower bound of $\Omega(s\log
n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF
of size $s$ with $n$ inputs under the uniform distribution.


title: Ultraviolet analysis of one dimensional quantum systems

abstract:
  Starting from the study of one-dimensional potentials in quantum mechanics
having a small distance behavior described by a harmonic oscillator, we extend
this way of analysis to models where such a behavior is not generally expected.
In order to obtain significant results we approach the problem by a
renormalization group method that can give a fixed point Hamiltonian that has
the shape of a harmonic oscillator. In this way, good approximations are
obtained for the ground state both for the eigenfunction and the eigenvalue for
problems like the quartic oscillator, the one-dimensional Coulomb potential
having a not normalizable ground state solution and for the one-dimensional
Kramers-Henneberger potential. We keep a coupling constant in the potential and
take it running with a generic cut-off that goes to infinity. The solution of
the Callan-Symanzik equation for the coupling constant generates the harmonic
oscillator Hamiltonian describing the behavior of the model at very small
distances (ultraviolet behavior). This approach, although algorithmic in its
very nature, does not appear to have a simple extension to obtain excited state
behavior. Rather, it appears as a straightforward non-perturbative method.

categories: quant-ph hep-th math-ph math.AP math.MP physics.atom-ph


title: Photon Statistics of a Single Atom Intracavity EIT-Kerr System

abstract:
  We explore the photon statistics of light emitted from a system comprising a
single four--level atom strongly coupled to a high-finesse optical cavity mode
which is driven by a coherent laser field. In the weak driving regime this
system is found to exhibit a photon blockade effect. For intermediate driving
strengths we find a sudden change in the photon statistics of the light emitted
from the cavity. Photon antibunching switches to photon bunching over a very
narrow range of intracavity photon number. It is proven that this sudden change
in photon statistics occurs due to the existence of robust quantum interference
of transitions between the dressed states of the atom-cavity system.
Furthermore, it is shown that the strong photon bunching is a nonclassical
effect for certain values of driving field strength, violating classical
inequalities for field correlations.


title:
Time evolution in the Morse potential using supersymmetry: dissociation
  of the NO molecule

abstract:
  We present an algebraic method for treating molecular vibrations in the Morse
potential perturbed by an external laser field. By the help of a complete and
normalizable basis we transform the Schr\"{o}dinger equation into a system of
coupled ordinary differential equations. We apply our method to calculate the
dissociation probability of the NO molecule excited by chirped laser pulses.
The dependence of the molecular dipole-moment on the interatomic separation is
determined by a quantum-chemical method, and the corresponding transition
dipole moments are given by approximate analytic expressions. These turn out to
be very small between neighboring stationary states around the vibrational
quantum number $m=42$, therefore we propose to use additional pulses in order
to skip this trapping state, and to obtain a reasonable dissociation
probability.


title:
On the uncertainty relations and squeezed states for the quantum
  mechanics on a circle

abstract:
  The uncertainty relations for the position and momentum of a quantum particle
on a circle are identified minimized by the corresponding coherent states. The
sqeezed states in the case of the circular motion are introduced and discussed
in the context of the uncertainty relations.


title: Strong-driving-assisted multipartite entanglement in cavity QED

abstract:
  We propose a method of generating multipartite entanglement by considering
the interaction of a system of N two-level atoms in a cavity of high quality
factor with a strong classical driving field. It is shown that, with a
judicious choice of the cavity detuning and the applied coherent field
detuning, vacuum Rabi coupling produces a large number of important
multipartite entangled states. It is even possible to produce entangled states
involving different cavity modes. Tuning of parameters also permits us to
switch from Jaynes-Cummings to anti-Jaynes-Cummings like interaction.


title: Entangled coherent states and squeezing in N trapped ions

abstract:
  We consider a resonant bichromatic excitation of N trapped ions that
generates displacement and squeezing in their collective motion conditioned to
their ionic internal state, producing eventually Scrhodinger cat states and
entangled squeezing. Furthermore, we study the case of tetrachromatic
illumination or producing the so called entangled coherent states in two
motional normal modes.


title: Entangling atoms in bad cavities

abstract:
  We propose a method to produce entangled spin squeezed states of a large
number of atoms inside an optical cavity. By illuminating the atoms with
bichromatic light, the coupling to the cavity induces pairwise exchange of
excitations which entangles the atoms. Unlike most proposals for entangling
atoms by cavity QED, our proposal does not require the strong coupling regime
g^2/\kappa\Gamma>> 1, where g is the atom cavity coupling strength, \kappa is
the cavity decay rate, and \Gamma is the decay rate of the atoms. In this work
the important parameter is Ng^2/\kappa\Gamma, where N is the number of atoms,
and our proposal permits the production of entanglement in bad cavities as long
as they contain a large number of atoms.


title: Quantum solution to the Newcomb's paradox

abstract:
  We show that quantum game theory offers solution to the famous Newcomb's
paradox (free will problem). Divine foreknowledge is not necessary for
successful completion of the game because quantum theory offers a way to
discern human intentions in such way that the human retain her/his free will
but cannot profit from changing decision. Possible interpretation in terms of
quantum market games is proposed.


title: Molecular vibration in cold collision theory

abstract:
  Cold collisions of ground state oxygen molecules with Helium have been
investigated in a wide range of cold collision energies (from 1 $\mu$K up to 10
K) treating the oxygen molecule first as a rigid rotor and then introducing the
vibrational degree of freedom. The comparison between the two models shows that
at low energies the rigid rotor approximation is very accurate and able to
describe all the dynamical features of the system. The comparison between the
two models has also been extended to cases where the interaction potential He -
O$_2$ is made artificially stronger. In this case vibration can perturb rate
constants, but fine-tuning the rigid rotor potential can alleviate the
discrepancies between the two models.


title: The Pure State Space of Quantum Mechanics as Hermitian Symmetric Space

abstract:
  The pure state space of Quantum Mechanics is investigated as Hermitian
Symmetric Kaehler manifold. The classical principles of Quantum Mechanics
(Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum
Probability Principle) and Spectral Theory of observables are discussed in this
non linear geometrical context.


title: Separable-entangled frontier in a bipartite harmonic system

abstract:
  We consider a statistical mixture of two identical harmonic oscillators which
is characterized by four parameters, namely, the concentrations (x and y) of
diagonal and nondiagonal bipartite states, and their associated thermal-like
noises (T/a and T, respectively). The fully random mixture of two spins 1/2 as
well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular
instances. By using the conditional nonextensive entropy as introduced by Abe
and Rajagopal, we calculate the separable-entangled frontier. Although this
procedure is known to provide a necessary but in general not sufficient
condition for separability, it does recover, in the particular case x=T=0 (for
all a), the 1/3 exact result known as Peres' criterion. This is an indication
of reliability of the calculation of the frontier in the entire parameter
space. The x=0 frontier remarkably resembles to the critical line associated
with standard diluted ferromagnetism where the entangled region corresponds to
the ordered one and the separable region to the paramagnetic one. The entangled
region generically shrinks for increasing T or increasing a.


title: Pancharatnam revisited

abstract:
  Some recent ideas concerning Pancharatnam's prescription of relative phase
between quantal states are delineated. Generalisations to mixed states and
entangled two-photon states are discussed. An experimental procedure to test
the geometric phase as a Pancharatnam relative phase is described. We further
put forward a spatial split-beam dual to Pancharatnam's relative phase.


title: A Physical Quantum Model in a Smooth Topos

abstract:
  We strengthen the case that the new logical perspective afforded by topos
theory is suitable to the task of describing the physical world around us. In
exploring some of the aspects of construction of a simple quantum-mechanical
system in a mathematical universe different from that represented by set
theory, we show that more thought and a better appreciation of the assumptions
going into any mathematical model of the physical world are needed. We reflect
on some of the mathematical consequences of this wider perspective of physics,
explaining one interpretation of probabilistic values and numerical
calculations in two mathematical universes governed by the less restrictive
intuitionistic logic, and known to support the theory of synthetic differential
geometry.


title: Reconstruction of motional states of neutral atoms via MaxEnt principle

abstract:
  We present a scheme for a reconstruction of states of quantum systems from
incomplete tomographic-like data. The proposed scheme is based on the Jaynes
principle of Maximum Entropy. We apply our algorithm for a reconstruction of
motional quantum states of neutral atoms. As an example we analyze the
experimental data obtained by the group of C. Salomon at the ENS in Paris and
we reconstruct Wigner functions of motional quantum states of Cs atoms trapped
in an optical lattice.


title: Matrix Elements of Generalized Coherent Operators

abstract:
  Explicit forms are given of matrix elements of generalized coherent operators
based on Lie algebras su(1,1) and su(2). We also give a kind of factorization
formula of the associated Laguerre polynomials.