title:
Linear optics and projective measurements alone suffice to create
  large-photon-number path entanglement

abstract:
  We propose a method for preparing maximal path entanglement with a definite
photon number N, larger than two, using projective measurements. In contrast
with the previously known schemes, our method uses only linear optics.
Specifically, we exhibit a way of generating four-photon, path-entangled states
of the form |4,0> + |0,4>, using only four beam splitters and two detectors.
These states are of major interest as a resource for quantum interferometric
sensors as well as for optical quantum lithography and quantum holography.


title: Degree of entanglement for two qubits

abstract:
  We demonstrate that any pure bipartite state of two qubits may be decomposed
into a superposition of a maximally entangled state and an orthogonal
factorizable one. Although there are many such decompositions, the weights of
the two superposed states are, remarkably, unique. We propose a measure of
entanglement based on this decomposition. We also demonstrate that this measure
is connected to three measures of entanglement previously set forth: maximal
violation of Bell's inequality, concurrence, and two-particle visibility.


title:
Decoherence of anomalously-fluctuating states of finite macroscopic
  systems

abstract:
  In quantum systems of a macroscopic size V, such as interacting many
particles and quantum computers with many qubits, there exist pure states such
that fluctuations of some intensive operator A is anomalously large, <\delta
A^2> = O(V^0), which is much larger than that assumed in thermodynamics,
<\delta A^2> = O(1/V). By making full use of the locality, we show, starting
from Hamiltonians of macroscopic degrees of freedom, that such states decohere
at anomalously fast rates when they are weakly perturbed from environments.


title: Quantum computation with trapped polar molecules

abstract:
  We propose a novel physical realization of a quantum computer. The qubits are
electric dipole moments of ultracold diatomic molecules, oriented along or
against an external electric field. Individual molecules are held in a 1-D trap
array, with an electric field gradient allowing spectroscopic addressing of
each site. Bits are coupled via the electric dipole-dipole interaction. Using
technologies similar to those already demonstrated, this design can plausibly
lead to a quantum computer with $\gtrsim 10^4$ qubits, which can perform $\sim
10^5$ CNOT gates in the anticipated decoherence time of $\sim 5$ s.


title: Continuous variable quantum cryptography using coherent states

abstract:
  We propose several methods for quantum key distribution (QKD) based upon the
generation and transmission of random distributions of coherent or squeezed
states, and we show that they are are secure against individual eavesdropping
attacks. These protocols require that the transmission of the optical line
between Alice and Bob is larger than 50 %, but they do not rely on
"non-classical" features such as squeezing. Their security is a direct
consequence of the no-cloning theorem, that limits the signal to noise ratio of
possible quantum measurements on the transmission line. Our approach can also
be used for evaluating various QKD protocols using light with gaussian
statistics.


title: Satellite potentials for hypergeometric Natanzon potentials

abstract:
  As a result of the so(2,1) of the hypergeometric Natanzon potential a set of
potentials related to the given one is determined. The set arises as a result
of the action of the so(2,1) generators.


title: Coherent states on spheres

abstract:
  We describe a family of coherent states and an associated resolution of the
identity for a quantum particle whose classical configuration space is the
d-dimensional sphere S^d. The coherent states are labeled by points in the
associated phase space T*(S^d). These coherent states are NOT of Perelomov type
but rather are constructed as the eigenvectors of suitably defined annihilation
operators. We describe as well the Segal-Bargmann representation for the
system, the associated unitary Segal-Bargmann transform, and a natural
inversion formula. Although many of these results are in principle special
cases of the results of B. Hall and M. Stenzel, we give here a substantially
different description based on ideas of T. Thiemann and of K. Kowalski and J.
Rembielinski. All of these results can be generalized to a system whose
configuration space is an arbitrary compact symmetric space. We focus on the
sphere case in order to be able to carry out the calculations in a
self-contained and explicit way.


title:
Structured quantum search in NP-complete problems using the cumulative
  density of states

abstract:
  In the multitarget Grover algorithm, we are given an unstructured N-element
list of objects S_i containing a T-element subset tau and function f, called an
oracle, such that f(S_i)=1 if S_i is in tau, otherwise f(S_i) = 0. By using
quantum parallelism, an element of tau can be retrieved in O(sqrt(N/T)) steps,
compared to O(N/T) for any classical algorithm. It is shown here that in
combinatorial optimization problems with N=4^M, the density of states can be
used in conjunction with the multitarget Grover algorithm to construct a
sequence of oracles that structure the search so that the optimum state is
obtained with certainty in O(log(N)) steps.


title:
Simulating Hamiltonians in Quantum Networks: Efficient Schemes and
  Complexity Bounds

abstract:
  We address the problem of simulating pair-interaction Hamiltonians in n node
quantum networks where the subsystems have arbitrary, possibly different,
dimensions. We show that any pair-interaction can be used to simulate any other
by applying sequences of appropriate local control sequences. Efficient schemes
for decoupling and time reversal can be constructed from orthogonal arrays.
Conditions on time optimal simulation are formulated in terms of spectral
majorization of matrices characterizing the coupling parameters. Moreover, we
consider a specific system of n harmonic oscillators with bilinear interaction.
In this case, decoupling can efficiently be achieved using the combinatorial
concept of difference schemes. For this type of interactions we present optimal
schemes for inversion.


title: Separability of Rank Two Quantum States

abstract:
  Explicit sufficient and necessary conditions for separability of higher
dimensional quantum systems with rank two density matrices are given. A
nonseparability inequality is also presented, for the case where one of the
eigenvectors corresponding to nonzero eigenvalues is a maximally entangled
state.


title:
Resonant and off-resonant transients in electromagnetically induced
  transparency: turn-on and turn-off dynamics

abstract:
  This paper presents a wide-ranging theoretical and experimental study of
non-adiabatic transient phenomena in a $\Lambda $ EIT system when a strong
coupling field is rapidly switched on or off. The theoretical treatment uses a
Laplace transform approach to solve the time-dependent density matrix equation.
The experiments are carried out in a Rb$^{87}$ MOT. The results show transient
probe gain in parameter regions not previously studied, and provide insight
into the transition dynamics between bare and dressed states.


title:
Vacuum fluctuation force on a rigid Casimir cavity in a gravitational
  field

abstract:
  We discuss the possibility of verifying the equivalence principle for the
zero-point energy of quantum electrodynamics, by evaluating the force, produced
by vacuum fluctuations, acting on a rigid Casimir cavity in a weak
gravitational field. The resulting force has opposite direction with respect to
the gravitational acceleration; the order of magnitude for a multi-layer cavity
configuration is derived and experimental feasibility is discussed, taking into
account current technological resources.


title: The Feynman Propagator from a Single Path

abstract:
  We show that it is possible to construct the Feynman Propagator in one
dimension, without quantization, from a single continuous space-time path.


title: Modified de Broglie-Bohm approach to quantum mechanics

abstract:
  A modified de Broglie-Bohm (dBB) approach to quantum mechanics is presented.
In this new deterministic theory, which uses complex methods in an intermediate
step, the problem of zero velocity for bound states encountered in the dBB
formulation does not appear. Also this approach is equivalent to standard
quantum mechanics when averages of dynamical variables like position, momentum
and energy are taken.


title: Quantum stochastic approach to the description of quantum measurements

abstract:
  In the present paper we consider the problem of description of an arbitrary
generalized quantum measurement with outcomes in a measurable space. Analyzing
the unitary invariants of a measuring process, we present the most general form
of a possible integral representation of an instrument, which differs from the
representations of an instrument available in the mathematical and physical
literature. We introduce the notion of a quantum stochastic representation of
an instrument, whose elements are wholly determined by the unitary invariants
of a measuring process. We show that the description of a generalized direct
quantum measurement can be considered in the frame of a new general approach,
which we call the quantum stochastic approach (QSA), based on the notion of a
family of quantum stochastic evolution operators, satisfying the orthonormality
relation and describing the conditional evolution of a quantum system under a
measurement. The QSA allows to give: a) the complete statistical description of
any generalized direct quantum measurement (a POV measure and a family of
posterior states); b) the complete description in a Hilbert space of the
stochastic behaviour of a quantum system under a measurement in the sense of
specification of the probabilistic transition law governing the change from the
initial state of a quantum system to a final one under a single measurement; c)
to formalize the consideration of all possible types of quantum measurements.
For measurements continuous in time the QSA allows, in particular, to define in
the most general case (without assuming any Markov property) the notion of
posterior pure state trajectories (quantum trajectories) and to give their
probabilistic treatment.


title:
Applications of the Quon Algebra: 3-D Harmonic Oscillator and the Rotor
  Model

abstract:
  In this work we present a method to build in a systematic way a many-body
quon basis state. In particular, we show a closed expression for a given number
N of quons, restricted to the permutational symmetric subspace, which belongs
to the whole quonic space. The method is applied to two simple problems: the
three-dimensional harmonic oscillator and the rotor model and compared to
previous quantum algebra results. The differences obtained and possible future
applications are also discussed.


title: Quantum Key Distribution with Continuous Variables in Optics

abstract:
  We discuss a quantum key distribution scheme in which small phase and
amplitude modulations of quantum limited, CW light beams carry the key
information. We identify universal constraints on the level of shared
information between the intended receiver (Bob) and any eavesdropper (Eve) and
use this to make a general evaluation of the security and efficiency of the
scheme. We show that a scheme based on coherent light offers competitive secret
key bit transmission rates.


title: Storing unitary operators in quantum states

abstract:
  We present a scheme to store unitary operators with self-inverse generators
in quantum states and a general circuit to retrieve them with definite success
probability. The continuous variable of the operator is stored in a
single-qubit state and the information about the kind of the operator is stored
in classical states with finite dimension. The probability of successful
retrieval is always 1/2 irrespective of the kind of the operator, which is
proved to be maximum. In case of failure, the result can be corrected with
additional quantum states. The retrieving circuit is almost as simple as that
which handles only the single-qubit rotations and CNOT as the basic operations.
An interactive way to transfer quantum dynamics, that is, to distribute
naturally copy-protected programs for quantum computers is also presented using
this scheme.


title:
Quantum machine language and quantum computation with Josephson
  junctions

abstract:
  An implementation method of a gate in a quantum computer is studied in terms
of a finite number of steps evolving in time according to a finite number of
basic Hamiltonians, which are controlled by on-off switches. As a working
example, the case of a particular implementation of the two qubit computer
employing a simple system of two coupled Josephson junctions is considered. The
binary values of the switches together with the time durations of the steps
constitute the quantum machine language of the system.


title: Separability and the stella octangula

abstract:
  A geometrical picture of separability of 2 x 2 composite quantum systems,
showing the region of separable density matrices in the space of hermitian
matrices, is given. It rests on the criterion of separability given by Peres,
and it is an extension of the ``Horodecki diagram'' and the ``stella
octangula'' described by Aravind.


title: Quantum interference in optical fields and atomic radiation

abstract:
  We discuss the connection between quantum interference effects in optical
beams and radiation fields emitted from atomic systems. We illustrate this
connection by a study of the first- and second-order correlation functions of
optical fields and atomic dipole moments. We explore the role of correlations
between the emitting systems and present examples of practical methods to
implement two systems with non-orthogonal dipole moments. We also derive
general conditions for quantum interference in a two-atom system and for a
control of spontaneous emission. The relation between population trapping and
dark states is also discussed. Moreover, we present quantum dressed-atom models
of cancellation of spontaneous emission, amplification on dark transitions,
fluorescence quenching and coherent population trapping.


title: On the Quantum Black-Box Complexity of Majority

abstract:
  We describe a quantum black-box network computing the majority of N bits with
zero-sided error eps using only 2N/3 + O(sqrt{N (log log N + log 1/eps)})
queries: the algorithm returns the correct answer with probability at least 1 -
eps, and "I don't know" otherwise. Our algorithm is given as a randomized "XOR
decision tree" for which the number of queries on any input is strongly
concentrated around a value of at most 2N/3. We provide a nearly matching lower
bound of 2N/3 - O(sqrt(N)) on the expected number of queries on a worst-case
input in the randomized XOR decision tree model with zero-sided error o(1). Any
classical randomized decision tree computing the majority on N bits with
zero-sided error 1/2 has cost N.


title: Robustness of Multi-Party Entanglement

abstract:
  How common is large-scale entanglement in nature? As a first step towards
addressing this question, we study the robustness of multi-party entanglement
under local decoherence, modeled by partially depolarizing channels acting
independently on each subsystem. Surprisingly, we find that n-qubit GHZ
entanglement can stand more than 55 % local depolarization in the limit of n
going to infinity, and that GHZ states are more robust than other generic
states of 3 and 4 qubits. We also study spin-squeezed states in the limit n
going to infinity and find that they too can stand considerable local
depolarization.


title: An integral version of Shor's factoring algorithm

abstract:
  We consider a version of Shor's quantum factoring algorithm such that the
quantum Fourier transform is replaced by an extremely simple one where
decomposition coefficients take only the values of $1,i,-1,-i$. In numerous
calculations which have been carried out so far, our algorithm has been
surprisingly stable and never failed. There are numerical indications that the
probability of period finding given by the algorithm is a slowly decreasing
function of the number to be factorized and is typically less than in Shor's
algorithm. On the other hand, quantum computer (QC), capable of implementing
our algorithm, will require a much less amount of resources and will be much
less error-sensitive than standard QC. We also propose a modification of
Coppersmith' Approximate Fast Fourier Transform. The numerical results show
that the probability is signifacantly amplified even in the first post integral
approximation. Our algorithm can be very useful at early stages of development
of quantum computer.


title: A Comparison of Quantum Oracles

abstract:
  A standard quantum oracle $S_f$ for a general function $f: Z_N \to Z_N $ is
defined to act on two input states and return two outputs, with inputs
$\ket{i}$ and $\ket{j}$ ($i,j \in Z_N $) returning outputs $\ket{i}$ and
$\ket{j \oplus f(i)}$. However, if $f$ is known to be a one-to-one function, a
simpler oracle, $M_f$, which returns $\ket{f(i)}$ given $\ket{i}$, can also be
defined. We consider the relative strengths of these oracles. We define a
simple promise problem which minimal quantum oracles can solve exponentially
faster than classical oracles, via an algorithm which cannot be naively adapted
to standard quantum oracles. We show that $S_f$ can be constructed by invoking
$M_f$ and $(M_f)^{-1}$ once each, while $\Theta(\sqrt{N})$ invocations of $S_f$
and/or $(S_f)^{-1}$ are required to construct $M_f$.


title:
Interaction-Free Measurement applied to Quantum Computation: a New CNOT
  Gate

abstract:
  In this paper, we propose a new direction of research for the realization of
the quantum controlled-not gate based on a technique called ``interaction-free
measurement'', where qubits are two-level atoms (or ions) and information is
mediated from one qubit to another by lasers in superpositions of $\pi$ and
$2\pi$ pulses. We investigate the advantages and limitations of such a gate and
discuss possible applicability.


title: Coherent Superposition States as Quantum Rulers

abstract:
  We explore the sensitivity of an interferometer based on a quantum circuit
for coherent states. We show that its sensitivity is at the Heisenberg limit.
Moreover we show that this arrangement can measure very small length intervals.


title: Quantum coherence generated by interference-induced state selectiveness

abstract:
  The relations between quantum coherence and quantum interference are
discussed. A general method for generation of quantum coherence through
interference-induced state selection is introduced and then applied to `simple'
atomic systems under two-photon transitions, with applications in quantum
optics and laser cooling.


title: Coherent States and Geometric Phases in Calogero-Sutherland Model

abstract:
  Exact coherent states in the Calogero-Sutherland models (of time-dependent
parameters) which describe identical harmonic oscillators interacting through
inverse-square potentials are constructed, in terms of the classical solutions
of a harmonic oscillator. For quasi-periodic coherent states of the
time-periodic systems, geometric phases are evaluated. For the $A_{N-1}$
Calogero-Sutherland model, the phase is calculated for a general coherent
state. The phases for other models are also considered.


title: Geometric Strategy for the Optimal Quantum Search

abstract:
  We explore quantum search from the geometric viewpoint of a complex
projective space $CP$, a space of rays. First, we show that the optimal quantum
search can be geometrically identified with the shortest path along the
geodesic joining a target state, an element of the computational basis, and
such an initial state as overlaps equally, up to phases, with all the elements
of the computational basis. Second, we calculate the entanglement through the
algorithm for any number of qubits $n$ as the minimum Fubini-Study distance to
the submanifold formed by separable states in Segre embedding, and find that
entanglement is used almost maximally for large $n$. The computational time
seems to be optimized by the dynamics as the geodesic, running across entangled
states away from the submanifold of separable states, rather than the amount of
entanglement itself.


title:
Analytic stochastic treatment of a nonlinear quantum model with negative
  diffusion

abstract:
  We apply a proposal of Yuen and Tombesi, for treating stochastic problems
with negative diffusion, to the analytically soluble problem of the single-mode
anharmonic oscillator. We find that the associated stochastic realizations
include divergent trajectories. It is possible, however, to solve the
stochastic problem exactly, but the averaging must be performed with great
care.


title: Single and double slit scattering of wave packets

abstract:
  The scattering of wave packets from a single slit and a double slit with the
Schr\"odinger equation, is studied numerically and theoretically.
  The phenomenon of diffraction of wave packets in space and time in the
backward region, previously found for barriers and wells, is encountered here
also.
  A new phenomenon of forward diffraction that occurs only for packets thiner
than the slit, or slits, is calculated numerically as well as, in a theoretical
approximation to the problem. This diffraction occurs at the opposite end of
the usual diffraction phenomena with monochromatic waves.


title: Characterisation of an entanglement-free evolution

abstract:
  Two or more quantum systems are said to be in an entangled or
non-factorisable state if their joint (supposedly pure) wave-function is not
expressible as a product of individual wave functions but is instead a
superposition of product states. It is only when the systems are in a
factorisable state that they can be considered to be separated (in the sense of
Bell). We show that whenever two quantum systems interact with each other, it
is impossible that all factorisable states remain factorisable during the
interaction unless the full Hamiltonian does not couple these systems so to say
unless they do not really interact. We also present certain conditions under
which particular factorisable states remain factorisable although they
represent a bipartite system whose components mutually interact and pay a
particular attention to the case where the two particles interact mutually
through an action at a distance in the three dimensional space.


title: Path Integration on a Quantum Computer

abstract:
  We study path integration on a quantum computer that performs quantum
summation. We assume that the measure of path integration is Gaussian, with the
eigenvalues of its covariance operator of order j^{-k} with k>1. For the Wiener
measure occurring in many applications we have k=2. We want to compute an
$\e$-approximation to path integrals whose integrands are at least Lipschitz.
We prove:
  1. Path integration on a quantum computer is tractable.
  2. Path integration on a quantum computer can be solved roughly $\e^{-1}$
times faster than on a classical computer using randomization, and
exponentially faster than on a classical computer with a worst case assurance.
  3.The number of quantum queries is the square root of the number of function
values needed on a classical computer using randomization. More precisely, the
number of quantum queries is at most $4.22 \e^{-1}$. Furthermore, a lower bound
is obtained for the minimal number of quantum queries which shows that this
bound cannot be significantly improved.
  4.The number of qubits is polynomial in $\e^{-1}$. Furthermore, for the
Wiener measure the degree is 2 for Lipschitz functions, and the degree is 1 for
smoother integrands.


title:
Exponential lower bound on the highest fidelity achievable by quantum
  error-correcting codes

abstract:
  On a class of memoryless quantum channels which includes the depolarizing
channel, the highest fidelity of quantum error-correcting codes of length n and
rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function
E(R). The E(R) is positive below some threshold R', which implies R' is a lower
bound on the quantum capacity.


title:
Necessary conditions for the efficient simulation of Hamiltonians using
  local unitary operations

abstract:
  We study necessary conditions for the efficient simulation of both bipartite
and multipartite Hamiltonians, which are independent of the eigenvalues and
based on the algebraic-geometric invariants introduced in [1-2]. Our results
indicate that the problem of efficient simulation of Hamiltonians for arbitrary
and multipartite quantum systems cannot be described by using only eigenvalues,
unlike that in the two-qubit case.


title: From Schr\"odinger's Equation to the Quantum Search Algorithm

abstract:
  The quantum search algorithm is a technique for searching N possibilities in
only sqrt(N) steps. Although the algorithm itself is widely known, not so well
known is the series of steps that first led to it, these are quite different
from any of the generally known forms of the algorithm. This paper describes
these steps, which start by discretizing Schr\"odinger's equation. This paper
also provides a self-contained introduction to the quantum search algorithm
from a new perspective.


title:
Narrow Spectral Feature In Resonance Fluorescence With A Single
  Monochromatic Laser Field

abstract:
  We describe the resonance fluorescence spectrum of an atomic three-level
system where two of the states are coupled by a single monochromatic laser
field. The influence of the third energy level, which interacts with the two
laser-coupled states only via radiative decays, is studied in detail. For a
suitable choice of parameters, this system gives rise to a very narrow
structure at the laser frequency in the fluorescence spectrum which is not
present in the spectrum of a two-level atom. We find those parameter ranges by
a numerical analysis and use the results to derive analytical expressions for
the additional narrow peak. We also derive an exact expression for the peak
intensity under the assumption that a random telegraph model is applicable to
the system. This model and a simple spring model are then used to describe the
physical origins of the additional peak. Using these results, we explain the
connection between our system, a three-level system in V-configuration where
both transitions are laser driven, and a related experiment which was recently
reported.


title: Casimir force under the influence of real conditions

abstract:
  The Casimir force is calculated analytically for configurations of two
parallel plates and a spherical lens (sphere) above a plate with account of
nonzero temperature, finite conductivity of the boundary metal and surface
roughness. The permittivity of the metal is described by the plasma model. It
is proved that in case of the plasma model the scattering formalism of quantum
field theory in Matsubara formulation underlying Lifshitz formula is well
defined and no modifications are needed concerning the zero-frequency
contribution. The temperature correction to the Casimir force is found
completely with respect to temperature and perturbatively (up to the second
order in the relative penetration depth of electromagnetic zero-point
oscillations into the metal) with respect to finite conductivity. The
asymptotics of low and high temperatures are presented and contributions of
longitudinal and perpendicular modes are determined separately. Serving as an
example, aluminium test bodies are considered showing good agreement between
the obtained analytical results and previously performed numerical
computations. The roughness correction is formally included and formulas are
given permitting to calculate the Casimir force under the influence of all
relevant factors.


title:
Semiclassical stability analysis of a two-photon laser including spatial
  variation of the cavity field

abstract:
  We investigate the dynamics of a two-photon laser under conditions where the
spatial variation of the cavity field along the cavity axis is important. Main
attention is paid to linear stability analysis and numerical investigation of a
two-photon laser for the Maxwell-Bloch equations. The model assumes pumping to
the upper state of the two-photon transition. We consider the Maxwell-Bloch
equations on the basis of which we study the stability analysis of the steady
state of the system. The system is taken to be contained in a ring-laser
cavity. Asymptotic expansion of the eigenvalue and analytic information are
obtained in some realistic limits, such as very large reflectivity, very small
cavity losses, or very small population relaxation rate. The results are
illustrated with an application to a specific atomic system (Potassium) as an
amplifying medium.


title:
Comment on "Classical interventions in quantum systems II. Relativistic
  invariance"

abstract:
  In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A.
Peres argued that quantum mechanics is consistent with special relativity by
proposing that the operators that describe time evolution do not need to
transform covariantly, although the measurable quantities need to transform
covariantly. We discuss the weaknesses of this proposal.


title: Quantum Nonlocality for a Mixed Entangled Coherent State

abstract:
  Quantum nonlocality is tested for an entangled coherent state, interacting
with a dissipative environment. A pure entangled coherent state violates Bell's
inequality regardless of its coherent amplitude. The higher the initial
nonlocality, the more rapidly quantum nonlocality is lost. The entangled
coherent state can also be investigated in the framework of $2\times2$ Hilbert
space. The quantum nonlocality persists longer in $2\times2$ Hilbert space.
When it decoheres it is found that the entangled coherent state fails the
nonlocality test, which contrasts with the fact that the decohered entangled
state is always entangled.


title: Toward Quantum Behavioral Finances: Bohmian Approach

abstract:
  We apply methods of quantum mechanics for mathematical modeling of price
dynamics at the financial market. We propose to describe behavioral financial
factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model
of quantum mechanics. Trajectories of prices are determined by two financial
potentials: classical-like $V(q)$ ("hard" market conditions, e.g., natural
resources) and quantum-like $U(q)$ (behavioral market conditions). On one hand,
our Bohmian model is a quantum-like model for the financial market, cf. with
works of W. Segal, I. E. Segal, E. Haven, E. W.Piotrowski, J. Sladkowski. On
the other hand, (since Bohmian mechanics provides the possibility to describe
individual price trajectories) it belongs to the domain of extended research on
deterministic dynamics for financial assets (C.W. J. Granger, W.A. Barnett, A.
J. Benhabib, W.A. Brock, C. Sayers, J. Y. Campbell, A. W. Lo, A. C. MacKinlay,
A. Serletis, S. Kuchta, M. Frank, R. Gencay, T. Stengos, M. J. Hinich, D.
Patterson, D. A. Hsieh, D. T. Caplan, J.A. Scheinkman, B. LeBaron and many
others).


title: From Coupled Pendulums to Quantum Search

abstract:
  Quantum search is a quantum mechanical technique for searching N
possibilities in only sqrt(N) steps. This paper gives a fresh perspective on
the algorithm in terms of a resonance phenomenon which is implemented through
classical coupled oscillators. Consider N oscillators, one of which is of a
different resonant frequency. We could identify which one this is by measuring
the oscillation frequency of each oscillator, a procedure that would take about
N cycles. We show how, by coupling the oscillators together in a very simple
way, it is possible to identify the different one in only sqrt(N) cycles. An
extension of this technique to the quantum case leads to the quantum search
algorithm.


title: Mixed-state entanglement and quantum communication

abstract:
  We present basics of mixed-state entanglement theory. The first part of the
article is devoted to mathematical characterizations of entangled states. In
second part we discuss the question of using mixed-state entanglement for
quantum communication. In particular, a type of entanglement that is not
directly useful for quantum communcation (called bound entanglement) is
analysed in detail.


title: Coherence and squeezing in superpositions of spin coherent states

abstract:
  We consider the superpositions of spin coherent states and study the
coherence properties and spin squeezing in these states. The spin squeezing is
examined using a new version of spectroscopic squeezing criteria. The results
show that the antibuching effect can be enhanced and spin squeezing can be
generated in the superpositions of two spin coherent states.


title: Conditions for the local manipulation of Gaussian states

abstract:
  We present a general necessary and sufficient criterion for the possibility
of a state transformation from one mixed Gaussian state to another of a
bi-partite continuous-variable system with two modes. The class of operations
that will be considered is the set of local Gaussian completely positive
trace-preserving maps.


title: Semi-classical States in the Context of Constrained Systems

abstract:
  Algebraic quantization scheme has been proposed as an extension of the Dirac
quantization scheme for constrained systems. Semi-classical states for
constrained systems is also an independent and important issue, particularly in
the context of quantum geometry. In this work we explore this issue within the
framework of algebraic quantization scheme by means of simple explicit
examples. We obtain semi-classical states as suitable coherent states a la
Perelomov. Remarks on possible generalizations are also included.


title:
Demonstration of Non-Deterministic Quantum Logic Operations using Linear
  Optical Elements

abstract:
  Knill, Laflamme, and Milburn recently showed that non-deterministic quantum
logic operations could be performed using linear optical elements, additional
photons (ancilla), and post-selection based on the output of single-photon
detectors [Nature 409, 46 (2001)]. Here we report the experimental
demonstration of two logic devices of this kind, a destructive controlled-NOT
(CNOT) gate and a quantum parity check. These two devices can be combined with
a pair of entangled photons to implement a conventional (non-destructive) CNOT
that succeeds with a probability of 1/4.


title: Relativity of representations in quantum mechanics

abstract:
  Only the position representation is used in introductory quantum mechanics
and the momentum representation is not usually presented until advanced
undergraduate courses. To emphasize the relativity of the representations of
the abstract formulation of quantum mechanics, two examples of representations
related to the operators aX+(1-a)P and (XP+PX)/2 are presented.


title: Coherent Decays of Atoms

abstract: Re-considering this work.


title:
Linear Order Matrix Inversion Method with Help from Quantum Searching
  Algorithm

abstract:
  Presented here is a matrix inversion method utilizing quantum searching
algorithm. In this method, huge Hilbert space as a whole spanned by myriad of
eigen states is searched and evaluated efficiently by sequential reduction in
dimension one by one. Total iteration steps required for search are
proportional to the number of unknown variables. Our method could solve very
large linear equations with sufficiently high probability faster than any
existing classical algorithms, which roughly depends on the cube of unknown
variables.


title: Multi-Photon Entanglement Concentration and Quantum Cryptography

abstract:
  Multi-photon states from parametric down-conversion can be entangled both in
polarization and photon number. Maximal high-dimensional entanglement can be
concentrated from these states via photon counting. This makes them natural
candidates for quantum key distribution, where the presence of more than one
photon per detection interval has up to now been considered as undesirable. We
propose a simple multi-photon protocol for the case of low losses and point out
the robustness of the entanglement under photon loss.


title: Quantum times of arrival for multiparticle states

abstract:
  Using the concept of crossing state and the formalism of second quantization,
we propose a prescription for computing the density of arrivals of particles
for multiparticle states, both in the free and the interacting case. The
densities thus computed are positive, covariant in time for time independent
hamiltonians, normalized to the total number of arrivals, and related to the
flux. We investigate the behaviour of this prescriptions for bosons and
fermions, finding boson enhancement and fermion depletion of arrivals.


title: Repulsive Casimir Force between Dielectric Planes

abstract:
  In 1948 H.B.G.Casimir predicted that an attractive force between two
perfectly conducting neutral plates exists due to changes in the
electromagnetic vacuum energy caused by the influence of the plates. In 1956
E.M. Lifshitz derived an extension of Casimir's expression applicable to finite
temperatures and arbitrary dielectric constants for the two half-spaces and the
gap in between them. It is shown in this brief report that, while the Lifshitz
formula predicts an attractive force for the case of identical dielectric
constants for the two half-spaces, a repulsive force results in some
circumstances when the dielectric constants are not identical. The reason for
the repulsive force and possible applications will be considered.


title: Generating Entangled Two-Photon States with Coincident Frequencies

abstract:
  It is shown that parametric downconversion, with a short-duration pump pulse
and a long nonlinear crystal that is appropriately phase matched, can produce a
frequency-entangled biphoton state whose individual photons are coincident in
frequency. Quantum interference experiments which distinguish this state from
the familiar time-coincident biphoton state are described.


title: Exact results for accepting probabilities of quantum automata

abstract:
  One of the properties of Kondacs-Watrous model of quantum finite automata
(QFA) is that the probability of the correct answer for a QFA cannot be
amplified arbitrarily. In this paper, we determine the maximum probabilities
achieved by QFAs for several languages. In particular, we show that any
language that is not recognized by an RFA (reversible finite automaton) can be
recognized by a QFA with probability at most 0.7726...


title: The spin statistics theorem -- did Pauli get it right?

abstract:
  In this article, we begin with a review of Pauli's version of the
spin-statistics theorem and then show, by re-defining the parameter associated
with the Lie-Algebra structure of angular momentum, that another interpretation
of the theorem may be given. It will be found that the vanishing commutator and
anticommutator relationships can be associated with independent and dependent
probability events respectively, and not spin value. Consequently, it gives a
more intuitive understanding of quantum field theory and it also suggests that
the distinction between timelike and spacelike events might be better described
in terms of local and non-local events. Pacs: 3.65, 5.30, 3.70.+k


title: High-sensitivity force measurement using entangled probes

abstract:
  We show the possibility to improve the measurement sensitivity of a weak
force by using two meters in an entangled state. This latter can be achieved by
exploiting radiation pressure effects.


title: Reply to `Singularities of the mixed state phase'

abstract:
  The only difference between Bhandari's viewpoint [quant-ph/0108058] and ours
[Phys. Rev. Lett. 85, 2845 (2000)] is that our phase is defined modulo $2\pi$,
whereas Bhandari argues that two phases that differ by $2\pi n$, $n$ integer,
may be distinguished experimentally in a history-dependent manner.


title: Entanglement and the factorization-approximation

abstract:
  For a bi-partite quantum system defined in a finite dimensional Hilbert space
we investigate in what sense entanglement change and interactions imply each
other. For this purpose we introduce an entanglement operator, which is then
shown to represent a non-conserved property for any bi-partite system and any
type of interaction. This general relation does not exclude the existence of
special initial product states, for which the entanglement remains small over
some period of time, despite interactions. For this case we derive an
approximation to the full Schroedinger equation, which allows the treatment of
the composite systems in terms of product states. The induced error is
estimated. In this factorization-approximation one subsystem appears as an
effective potential for the other. A pertinent example is the Jaynes-Cummings
model, which then reduces to the semi-classical rotating wave approximation.


title: Distinguishability Measures and Ensemble Orderings

abstract:
  It is shown that different distinguishability measures impose different
orderings on ensembles of $N$ pure quantum states. This is demonstrated using
ensembles of equally-probable, linearly independent, symmetrical pure states,
with the maximum probabilities of correct hypothesis testing and unambiguous
state discrimination being the distinguishability measures. This finding
implies that there is no absolute scale for comparing the distinguishability of
any two ensembles of $N$ quantum states, and that distinguishability comparison
is necessarily relative to a particular discrimination strategy.


title: Gravitational effects on a rigid Casimir cavity

abstract:
  Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a
weak gravitational field. Such a force is here evaluated and is found to have
opposite direction with respect to the gravitational acceleration; the order of
magnitude for a multi-layer cavity configuration is analyzed and experimental
detection is discussed, bearing in mind the current technological resources.


title:
Wannier threshold law for two electron escape in the presence of an
  external electric field

abstract:
  We consider double ionization of atoms or ions by electron impact in the
presence of a static electric field. As in Wanniers analysis of the analogous
situation without external field the dynamics near threshold is dominated by a
saddle. With a field the saddle lies in a subspace of symmetrically escaping
electrons. Near threshold the classical cross section scales with excess energy
E like sigma=E^alpha, where the exponent alpha can be determined from the
stability of the saddle and does not depend on the field strength. For example,
if the remaining ion has charge Z=2, the exponent is 1.292, significantly
different from the 1.056 without the field.


title:
Maximum entanglement of quantum-dot systems with single excitation in
  the spin van der Waals model

abstract:
  Time evolution of entanglement of N quantum dots is analyzed within the
spin-1/2 van der Waals (or Lipkin-Meshkov-Glick) XY model. It is shown that,
for a single dot initially excited and disentangled from the remaining
unexcited dots, the maximum bipartite entanglement can be obtained in the
systems of N=2,...,6 dots only.


title: Two-mode heterodyne phase detection

abstract:
  We present an experimental scheme that achieves ideal phase detection on a
two-mode field. The two modes $a$ and $b$ are the signal and image band modes
of an heterodyne detector, with the field approaching an eigenstate of the
photocurrent $\hat{Z}=a+b^{\dag}$. The field is obtained by means of a
high-gain phase-insensitive amplifier followed by a high-transmissivity
beam-splitter with a strong local oscillator at the frequency of one of the two
modes.


title: Indistinguishability and improper mixtures

abstract:
  All quantum mixtures are what d'Espagnat has termed "improper." His "proper"
mixture cannot be created -- if welcher weg, or distinguishing, information
exists, an improper mixture results, while in the absence of such information,
the resulting "mixture" is a pure state. D'Espagnat has claimed that an
interpretation of the improper mixture in terms of subensembles leads to
logical inconsistency; this claim is shown to be incorrect, as d'Espagnat's
argument fails to account for the indistinguishability of the pure-state
subensembles.


title: Manifestation of the Arnol'd Diffusion in Quantum Systems

abstract:
  We study an analog of the classical Arnol'd diffusion in a quantum system of
two coupled non-linear oscillators one of which is governed by an external
periodic force with two frequencies. In the classical model this very weak
diffusion happens in a narrow stochastic layer along the coupling resonance,
and leads to an increase of total energy of the system. We show that the
quantum dynamics of wave packets mimics, up to some extent, global properties
of the classical Arnol'd diffusion. This specific diffusion represents a new
type of quantum dynamics, and may be observed, for example, in 2D semiconductor
structures (quantum billiards) perturbed by time-periodic external fields.

categories: quant-ph cond-mat.stat-mech nlin.CD physics.atom-ph


title:
Classical Communication via the Einstein-Podolsky-Rosen Channel Alone: A
  Proposed Experimental Test

abstract:
  We uncover an apparent instance of classical information transfer via only
the Einstein-Podolsky-Rosen channel in a quantum optical protocol between Alice
and Bob, involving two-photon maximal path entanglement and based on a recent
Innsbruck experiment. The signal is traced to the appearance of coherent
reduction due to the onset of spatial degeneracy in the eigenvalue spectrum for
Alice's measurement. We present our result primarily as an issue for
experimental testing rather than as a definitive prediction at this stage.


title: Limits of fractality: Zeno boxes and relativistic particles

abstract:
  Physical fractals invariably have upper and lower limits for their fractal
structure. Berry has shown that a particle sharply confined to a box has a wave
function that is fractal both in time and space, with no lower limit. In this
article, two idealizations of this picture are softened and a corresponding
lower bound for fractality obtained. For a box created by repeated measurements
(\`a la the quantum Zeno effect), the lower bound is $\Delta x\sim \Delta t
(\hbar/{mL})$ with $\Dt$ the interval between measurements and $L$ is the size
of the box. For a relativistic particle, the lower bound is the Compton
wavelength, $\hbar/mc$. The key step in deriving both results is to write the
propagator as a sum over classical paths.


title: Against "knowledge"

abstract:
  Quantum "states" are objective probability measures. Because their dependence
on a time is not the time dependence of an evolving state, they are neither
states of Nature nor "states of knowledge." There is no such thing as an
evolving state. This disposes of the problem posed by the apparent existence of
two modes of evolution. What essentially stands in the way of a consistent
ontological interpretation of the quantum theory is our habit of projecting
into the quantum world the detached, intrinsically differentiated
spatiotemporal background of classical physics, for this is what entails the
existence of an evolving state. An objective probability measure is the formal
expression of an objective indefiniteness, such as the positional
indefiniteness that contributes to "fluff out" matter. An objective
indefiniteness entails that the values of certain observables are extrinsic
(possessed because they are indicated) rather than intrinsic (indicated because
they are possessed). This dependence on value-indicating facts is not a
dependence on anything external to the quantum world. The latter constitutes a
free-standing reality that owes nothing to observers, "information," or our
interventions into "the course of Nature."


title: Asymptotic behaviour of the probability density in one dimension

abstract:
  We demonstrate that the probability density of a quantum state moving freely
in one dimension may decay faster than 1/t. Inverse quadratic and cubic
dependences are illustrated with analytically solvable examples. Decays faster
than 1/t allow the existence of dwell times and delay times.


title: Quantum computer and its quasiclassical model

abstract:
  Could the theories with hidden variables be employed for creation of a
quantum computer? A particular scheme of quasiclassical model quantum computer
structure is describe.


title: Bell's Inequalities In 4-dimension Rieman's Space

abstract:
  It is shown that the nature of quantum statistics can study in assumption of
existence of a background of random gravitational fields and waves, distributed
isotropically in the space. This background is capable of correlating phases of
oscillations of identical microobjects. If such a background of random
gravitational fields and waves is considered as hidden variables. It is shown
that the classic physical of Bells observable in the 4-dimensions Rieman's
space gives the value matching the experimental data. The nature of the
entanglement states we are study here.


title: Rigged Hilbert Space Treatment of Continuous Spectrum

abstract:
  The ability of the Rigged Hilbert Space formalism to deal with continuous
spectrum is demonstrated within the example of the square barrier potential.
The non-square integrable solutions of the time-independent Schrodinger
equation are used to define Dirac kets, which are (generalized) eigenvectors of
the Hamiltonian. These Dirac kets are antilinear functionals over the space of
physical wave functions. They are also basis vectors that expand any physical
wave function in a Dirac basis vector expansion. It is shown that an acceptable
physical wave function must fulfill stronger conditions than just square
integrability--the space of physical wave functions is not the whole Hilbert
space but rather a dense subspace of the Hilbert space. We construct the
position and energy representations of the Rigged Hilbert Space generated by
the square barrier potential Hamiltonian. We shall also construct the unitary
operator that transforms from the position into the energy representation. We
shall see that in the energy representation the Dirac kets act as the
antilinear Schwartz delta functional. In constructing the Rigged Hilbert Space
of the square barrier potential, we will find a systematic procedure to
construct the Rigged Hilbert Space of a large class of spherically symmetric
potentials. The example of the square barrier potential will also make apparent
that the natural framework for the solutions of a Schrodinger operator with
continuous spectrum is the Rigged Hilbert Space rather than just the Hilbert
space.


title: Optimizing Completely Positive Maps using Semidefinite Programming

abstract:
  Recently, a lot of attention has been devoted to finding physically
realisable operations that realise as closely as possible certain desired
transformations between quantum states, e.g. quantum cloning, teleportation,
quantum gates, etc. Mathematically, this problem boils down to finding a
completely positive trace-preserving (CPTP) linear map that maximizes the
(mean) fidelity between the map itself and the desired transformation. In this
note we want to draw attention to the fact that this problem belongs to the
class of so-called semidefinite programming (SDP) problems. As SDP problems are
convex, it immediately follows that they do not suffer from local optima.
Furthermore, this implies that the numerical optimization of the CPTP map can,
and should, be done using methods from the well-established SDP field, as these
methods exploit convexity and are guaranteed to converge to the real solution.
Finally, we show how the duality inherent to convex and SDP problems can be
exploited to prove analytically the optimality of a proposed solution. We give
an example of how to apply this proof method by proving the optimality of Hardy
and Song's proposed solution for the universal qubit $\theta$-shifter
(quant-ph/0102100).


title:
Decoherence in trapped ions due to polarization of the residual
  background gas

abstract:
  We investigate the mechanism of damping and heating of trapped ions
associated with the polarization of the residual background gas induced by the
oscillating ions themselves. Reasoning by analogy with the physics of surface
electrons in liquid helium, we demonstrate that the decay of Rabi oscillations
observed in experiments on 9Be+ can be attributed to the polarization phenomena
investigated here. The measured sensitivity of the damping of Rabi oscillations
with respect to the vibrational quantum number of a trapped ion is also
predicted in our polarization model.


title: A note on quantum one-way permutations

abstract:
  We discuss the question of the existence of quantum one-way permutations.
First, we prove the equivalence between inverting a permutation and that of
constructing a polynomial size network for reflecting about a given quantum
state. Next, we consider the question: if a state is difficult to prepare, is
the operator reflecting about that state difficult to construct? By revisiting
Grover's algorithm, we present the relationship between this question and the
existence of one-way permutations. Moreover, we compare our method to Grover's
algorithm and discuss possible applications of our results.


title: Structure and Parametrization of Stochastic Maps of Density Matrices

abstract:
  The generic linear evolution of the density matrix of a system with a
finite-dimensional state space is by stochastic maps which take a density
matrix linearly into the set of density matrices. These dynamical stochastic
maps form a linear convex set that may be viewed as supermatrices. The property
of hermiticity of density matrices renders an associated supermatrix hermitian
and hence diagonalizable; but the positivity of the density matrix does not
make this associated supermatrix positive. If it is positive, the map is called
completely positive and they have a simple parametrization. This is extended to
all positive (not completely positive) maps. A contraction of a norm-preserving
map of the combined system can be contracted to obtain all dynamical maps. The
reconstruction of the extended dynamics is given.


title: Quantum Theory and Probabilities

abstract:
  It is often stated that quantum mechanics only makes statistical predictions
and that a quantum state is described by the various probability distributions
associated with it. Can we describe a quantum state completely in terms of
probabilities and then use it to describe quantum dynamics? What is the origin
of the probability distribution for a maximally specified quantum state?
  Is quantum mechanics `local' or is there an essential nonlocality
(nonseparability) inherent in quantum mechanics? These questions are discussed
in this paper. The decay of an unstable quantum state and the time dependence
of a minimum uncertainty states for future times as well as past times are also
discussed.


title: Teleportation of Entangled States of a Vacuum-One Photon Qubit

abstract:
  We report the experimental realization of teleporting an entangled qubit. The
qubit is physically implemented by a two-dimensional subspace of states of a
mode of the electromagnetic field, specifically, the space spanned by the
vacuum and the one photon state. Our experiment follows along lines suggested
by H. W. Lee and J. Kim, Phys. Rev. A, 63, 012305 (2000) and E.Knill,
R.Laflamme and G.Milburn Nature 409: 46 (2001).


title: Control of Switched Networks via Quantum Methods

abstract:
  We illustrate a technique for specifying piecewise constant controls for
classes of switched electrical networks, typically used in converting power in
a dc-dc converter. This procedure makes use of decompositions of SU(2) to
obtain controls that are piecewise constant and can be constrained to be
bang-bang with values 0 or 1. Complete results are presented for a third order
network first. An example, which shows that the basic strategy is viable for
fourth order circuits, is also given. The former evolves on SO(3), while the
latter evolves on SO(4). Since the former group is intimately related to SU(2)
while the latter is related to SU(2)xSU(2), the methodology of this paper uses
factorizations of SU(2). The systems in this paper are single input systems
with drift. In this paper, no approximations or other artifices are used to
remove the drift. Instead, the drift is important in the determination of the
controls. Periodicity arguments are rarely used.


title: Quantum Computing Using an Open System and Projected Subspace

abstract:
  Using the subdynamical kinetic equation for an open quantum system, a
formulation is presented for performing decoherence-free (DF) quantum computing
in Rigged Liouville Space (RLS). Three types of interactions were considered,
and in each case, stationary and evolutionary states were evaluated for DF
behavior in both the total space and the projected subspace. Projected
subspaces were found using the subdynamics kinetic equation. It was shown that
although the total space may be decoherent, the subspace can be DF. In the
projected subspace, the evolution of the density operator may be time
asymmetric. Hence, a formulation for performing quantum computing in RLS or
rigged Hilbert space (RHS) was proposed, and a quantum Controlled-Not Logical
gate with corresponding operations in RLS (RHS) was constructed. A generalized
quantum Turing machine in RHS was also discussed. Key Words: Quantum Computing,
Subdynamics, Rigged Liouvile Space, Decoherence, Open System PACS:
05.30.-d+85.30+82.20.Db+84.35.+i


title:
Intense field stabilization in circular polarization: 3D time-dependent
  dynamics

abstract:
  We investigate the stabilization of a hydrogen atom in circularly polarized
laser fields. We use a time-dependent, fully three dimensional approach to
study the quantum dynamics of the hydrogen atom subject to high intensity,
short wavelength laser pulses. We find enhanced survival probability as the
field is increased under fixed envelope conditions. We also confirm wavepacket
dynamics seen in prior time-dependent computations restricted to two
dimensions.


title:
Measuring Energy, Estimating Hamiltonians, and the Time-Energy
  Uncertainty Relation

abstract:
  Suppose that the Hamiltonian acting on a quantum system is unknown and one
wants to determine what is the Hamiltonian. We show that in general this
requires a time $\Delta t$ which obeys the uncertainty relation $\Delta t
\Delta H \gtrsim 1$ where $\Delta H$ is a measure of how accurately the unknown
Hamiltonian must be estimated. We then apply this result to the problem of
measuring the energy of an unknown quantum state. It has been previously shown
that if the Hamiltonian is known, then the energy can in principle be measured
in an arbitrarily short time. On the other hand we show that if the Hamiltonian
is not known then an energy measurement necessarily takes a minimum time
$\Delta t$ which obeys the uncertainty relation $\Delta t \Delta E \gtrsim 1$
where $\Delta E$ is the precision of the energy measurement. Several examples
are studied to address the question of whether it is possible to saturate these
uncertainty relations. Their interpretation is discussed in detail.


title: Limitations on quantum information from black hole physics

abstract:
  After reviewing the relation of entropy to information, I derive the entropy
bound as applied to bounded weakly gravitating systems, and review the bound's
applications to cosmology as well as its extensions to higher dimensions. I
then discuss why black holes behave as 1-D objects when emitting entropy, which
suggests that a black hole swallows information at a rate restricted by the
one-channel information capacity. I discuss fundamental limitations on the
information borne by signal pulses in curved spacetime, from which I verify the
mentioned bound on the rate of information disposal by a black hole.


title:
Quantum Certificate Verification: Single versus Multiple Quantum
  Certificates

abstract:
  The class MA consists of languages that can be efficiently verified by
classical probabilistic verifiers using a single classical certificate, and the
class QMA consists of languages that can be efficiently verified by quantum
verifiers using a single quantum certificate. Suppose that a verifier receives
not only one but multiple certificates. In the classical setting, it is obvious
that a classical verifier with multiple classical certificates is essentially
the same with the one with a single classical certificate. However, in the
quantum setting where a quantum verifier is given a set of quantum certificates
in tensor product form (i.e. each quantum certificate is not entangled with
others), the situation is different, because the quantum verifier might utilize
the structure of the tensor product form. This suggests a possibility of
another hierarchy of complexity classes, namely the QMA hierarchy. From this
point of view, we extend the definition of QMA to QMA(k) for the case quantum
verifiers use k quantum certificates, and analyze the properties of QMA(k).
  To compare the power of QMA(2) with that of QMA(1) = QMA, we show one
interesting property of ``quantum indistinguishability''. This gives a strong
evidence that QMA(2) is more powerful than QMA(1). Furthermore, we show that,
for any fixed positive integer $k \geq 2$, if a language L has a one-sided
bounded error QMA(k) protocol with a quantum verifier using k quantum
certificates, L necessarily has a one-sided bounded error QMA(2) protocol with
a quantum verifier using only two quantum certificates.


title:
A non-local, Lorentz-invariant, hidden-variable interpretation of
  relativistic quantum mechanics based on particle trajectories

abstract:
  We demonstrate how to construct a lorentz-invariant, hidden-variable
interpretation of relativistic quantum mechanics based on particle
trajectories. The covariant theory that we propose employs a multi-time
formalism and a lorentz-invariant rule for the coordination of the space-time
points on the individual particle trajectories. In this way we show that there
is no contradiction between nonlocality and lorentz invariance in quantum
mechanics. The approach is illustrated for relativistic bosons, using a simple
model to discuss the individual non-locally correlated particle motion which
ensues when the wavefunction is entangled. A simple example of measurement is
described.


title: Correlation experiments in nonlinear quantum mechanics

abstract:
  We show how one can compute multiple-time multi-particle correlation
functions in nonlinear quantum mechanics in a way which guarantees locality of
the formalism.


title: Entangled light from white noise

abstract:
  An atom that couples to two distinct leaky optical cavities is driven by an
external optical white noise field. We describe how entanglement between the
light fields sustained by two optical cavities arises in such a situation. The
entanglement is maximized for intermediate values of the cavity damping rates
and the intensity of the white noise field, vanishing both for small and for
large values of these parameters and thus exhibiting a
stochastic-resonance-like behaviour. This example illustrates the possibility
of generating entanglement by exclusively incoherent means and sheds new light
on the constructive role noise may play in certain tasks of interest for
quantum information processing.


title: Noisy Grover's search algorithm

abstract:
  External environment influences on Grover's search algorithm modeled by
quantum noise are investigated. The algorithm is shown to be robust under that
external dissipation. Explicitly we prove that the resulting search positive
maps acting on unsorted N-dimensional database made of projective density
matrices depend on x the strength of the environment, and that there are
infinitely many x values for which search is successful after O(\sqrt{N})
queries. These algorithms are quantum entropy increasing.


title:
Extracting Quantum Entanglement (General Entanglement Purification
  Protocols)

abstract:
  We study the problem of general entanglement purification protocols. Suppose
Alice and Bob share a bipartite state $\rho$ which is ``reasonably close'' to
perfect EPR pairs. The only information Alice and Bob possess is a lower bound
on the fidelity of $\rho$ and a maximally entangled state. They wish to
``purify'' $\rho$ using local operations and classical communication and create
a state that is arbitrarily close to EPR pairs. We prove that on average, Alice
and Bob cannot increase the fidelity of the input state significantly. We also
construct protocols that may fail with a small probability, and otherwise will
output states arbitrarily close to EPR pairs with very high probability. Our
constructions are efficient, i.e., they can be implemented by polynomial-size
quantum circuits.


title: Diffraction of complex molecules by structures made of light

abstract:
  We demonstrate that structures made of light can be used to coherently
control the motion of complex molecules. In particular, we show diffraction of
the fullerenes C60 and C70 at a thin grating based on a standing light wave. We
prove experimentally that the principles of this effect, well known from atom
optics, can be successfully extended to massive and large molecules which are
internally in a thermodynamic mixed state and which do not exhibit narrow
optical resonances. Our results will be important for the observation of
quantum interference with even larger and more complex objects.


title: Atomic entanglement near a realistic microsphere

abstract:
  We study a scheme for entangling two-level atoms located close to the surface
of a dielectric microsphere. The effect is based on medium-assisted spontaneous
decay, rigorously taking into account dispersive and absorptive properties of
the microsphere. We show that even in the weak-coupling regime, where the
Markov approximation applies, entanglement up to 0.35 ebits between two atoms
can be created. However, larger entanglement and violation of Bell's inequality
can only be achieved in the strong-coupling regime.


title:
Quantum Computation Based on Magic-Angle-Spinning Solid State Nuclear
  Magnetic Resonance Spectroscopy

abstract:
  Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR)
spectroscopy is shown to be a promising technique for implementing quantum
computing. The theory underlying the principles of quantum computing with
nuclear spin systems undergoing MAS is formulated in the framework of
formalized quantum Floquet theory. The procedures for realizing state labeling,
state transformation and coherence selection in Floquet space are given. It
suggests that by this method, the largest number of qubits can easily surpass
that achievable with other techniques. Unlike other modalities proposed for
quantum computing, this method enables one to adjust the dimension of the
working state space, meaning the number of qubits can be readily varied. The
universality of quantum computing in Floquet space with solid state NMR is
discussed and a demonstrative experimental implementation of Grover's search is
given.


title: On non-Adiabatic Holonomoic Quantum Computer

abstract:
  Non-adiabatic non-Abelian geometric phase of spin-3/2 system in the rotating
magnetic field is considered. Explicit expression for the corresponding
effective non-Abelian gauge potential is obtained. This formula can be used for
construction of quantum gates in quantum computations.


title: Quantum cloning of orthogonal qubits

abstract:
  An optimal universal cloning transformation is derived that produces M copies
of an unknown qubit from a pair of orthogonal qubits. For M>6, the
corresponding cloning fidelity is higher than that of the optimal copying of a
pair of identical qubits. It is shown that this cloning transformation can be
implemented probabilistically via parametric down-conversion by feeding the
signal and idler modes of a nonlinear crystal with orthogonally polarized
photons.


title: Decoherence of geometric phase gates

abstract:
  We consider the effects of certain forms of decoherence applied to both
adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit
we illustrate path-dependent sensitivity to anisotropic noise and for two
qubits we quantify the loss of entanglement as a function of decoherence.


title: Algorithmic Information Theoretic Issues in Quantum Mechanics

abstract:
  taking aside the review part, a finite-cardinality's set of new ideas
concerning algorithmic information issues in Quantum Mechanics is introduced
and analyzed


title: Comment on "Stable Quantum Computation of Unstable Classical Chaos"

abstract:
  This is a 1-page comment on a wrong paper that recently appeared in PRL
(Phys. Rev. Lett. 86 (23), 5393 (2001), also quant-ph/0101004). The authors
claim to have shown that using a quantum computer gives an "exponential
advantage" for simulating and studying classical chaotic systems.


title: Generalized Quantum Search Hamiltonian

abstract:
  There are hamiltonians that solve a search problem of finding one of $N$
items in $O(\sqrt{N})$ steps. They are hamiltonians to describe an oscillation
between two states. In this paper we propose a generalized search hamiltonian,
$H_{g}$. Then the known search hamiltonians become special cases of $H_{g}$.
  From the generalized search hamiltonian, we present remarkable results that
searching with 100% is subject only to the phase factor in $H_{g}$ and
independent to the number of states or initialization.


title: Thermal and quantum noise in active systems

abstract:
  We present a quantum network approach to the treatment of thermal and quantum
fluctuations in measurement devices. The measurement is described as a
scattering process of input fluctuations towards output ones. We present the
results obtained with this method for the treatment of a cold damped capacitive
accelerometer.


title: Quantum non ideal measurements

abstract:
  We analyse non ideal quantum measurements described as scattering processes
providing an estimator of the measured quantity. The sensitivity is expressed
as an equivalent input noise. We address the Von Neumann problem of chained
measurements and show the crucial role of preamplification.


title:
EPR-Bell Tests with Unsharp Observables and Relativistic Quantum
  Measurement

abstract:
  In this contribution I will review the analysis of the
Einstein-Podolsky-Rosen argument, Bell's inequalities and of associated
experiments for spins in terms of positive operator valued measures.
Specifically, I will explore the relation between the
Clauser-Horne-Shimony-Holt inequality and a fundamental \emph{classicality}
property of observables -- their \emph{coexistence}. A derivation of Bell's
inequalities for unsharp spins will be given which follows a reconstruction by
Mittelstaedt and Stachow of the original EPR argument. In this context we
discuss the need for a consistent relativistic description of localised
measurements, carried out in spacelike separated regions of spacetime on
spatially extended, entangled systems.


title: Real continuum

abstract:
  Some physical consequences of the negation of the continuum hypothesis are
considered. It is shown that quantum and classical mechanics are component
parts of the multicomponent description of the set of variable infinite
cardinality. Existence and properties of the set follow directly from the
independence of the continuum hypothesis. Particular emphasis is laid on
set-theoretic aspect.


title: An Entropic Uncertainty Principle for Quantum Measurements

abstract:
  The entropic uncertainty principle as outlined by Maassen and Uffink for a
pair of non-degenerate observables in a finite level qusystem is generalized
here to the case of a pair of arbitrary quantum measurements. In particular,
our result includes not only the case of projectivmeasurements (or
equivalently, observables) exhibiting degeneracy but also an uncertainty
principle for a single measurement.


abstract:
  I think the title and content of the recent Letter by Georgeot and
Shepelyanski [PRL 86, 5393 (2001), also quant-ph/0101004)] are not correct. As
long as the classical Arnold map is considered, the classical computational
algorithm can be made exactly equivalent with the quantum one. The claimed
advantage of the Letter's quantum algorithm disappears if we correctly restrict
the statistical analysis for the classical Arnold system.


title: Two Qubit Quantum Computing in a Projected Subspace

abstract:
  A formulation for performing quantum computing in a projected subspace is
presented, based on the subdynamical kinetic equation (SKE) for an open quantum
system. The eigenvectors of the kinetic equation are shown to remain invariant
before and after interaction with the environment. However, the eigenvalues in
the projected subspace exhibit a type of phase shift to the evolutionary
states. This phase shift does not destroy the decoherence-free (DF) property of
the subspace because the associated fidelity is 1. This permits a universal
formalism to be presented - the eigenprojectors of the free part of the
Hamiltonian for the system and bath may be used to construct a DF projected
subspace based on the SKE. To eliminate possible phase or unitary errors
induced by the change in the eigenvalues, a cancellation technique is proposed,
using the adjustment of the coupling time, and applied to a two qubit computing
system. A general criteria for constructing a DF projected subspace from the
SKE is discussed. Finally, a proposal for using triangulation to realize a
decoherence-free subsystem based on SKE is presented. The concrete formulation
for a two-qubit model is given exactly. Our approach is novel and general, and
appears applicable to any type of decoherence. Key Words: Quantum Computing,
Decoherence, Subspace, Open System PACS number: 03.67.Lx,33.25.+k,.76.60.-k


title: Parrondo games as lattice gas automata

abstract:
  Parrondo games are coin flipping games with the surprising property that
alternating plays of two losing games can produce a winning game. We show that
this phenomenon can be modelled by probabilistic lattice gas automata.
Furthermore, motivated by the recent introduction of quantum coin flipping
games, we show that quantum lattice gas automata provide an interesting
definition for quantum Parrondo games.


title: NMR Quantum Information Processing and Entanglement

abstract:
  In this essay we discuss the issue of quantum information and recent nuclear
magnetic resonance (NMR) experiments. We explain why these experiments should
be regarded as quantum information processing (QIP) despite the fact that, in
present liquid state NMR experiments, no entanglement is found. We comment on
how these experiments contribute to the future of QIP and include a brief
discussion on the origin of the power of quantum computers.


title: Limitations on quantum control

abstract:
  In this note we give an introduction to the topic of quantum control,
explaining what its objectives are, and describing some of its limitations.


title:
Quantum channel of continuous variable teleportation and nonclassicality
  of quantum states

abstract:
  Noisy teleportation of nonclassical quantum states via a two-mode
squeezed-vacuum state is studied with the completely positive map and the
Glauber-Sudarshan $P$-function. Using the nonclassical depth as a measure of
transmission performance, we compare the teleportation scheme with the direct
transmission through a noisy channel. The noise model is based on the coupling
to the vacuum field. It is shown that the teleportation channel has better
transmission performance than the direct transmission channel in a certain
region. The bounds for such region and for obtaining the nonvanished
nonclassicality of the teleported quantum states are also discussed. Our model
shows a reasonable agreement with the observed teleportation fidelity in the
experiment by Furusawa et al. [Science {\bf 282}, 706 (1998)]. We finally
mention the required conditions for transmitting nonclassical features in real
experiments.


title: Comment on relationship between atomic squeezed and entangled states

abstract:
  The ability of parameter recently proposed by Sorensen et al. (Nature, 409,
63 (2001)) to characterize entanglement or inseparability is investigated for a
system of two two-level atoms interacting with a single mode of radiation
field. For comparison we employ the necessary and sufficient criterion of Peres
and Horodecki for inseparability of bipartite states. We show that for diagonal
atomic density matrix the parameter of Sorensen et al. fails to show entangled
nature of collective atomic state whereas same state is inseparable in
accordance with Peres-Horodecki criterion.


title: Decoherence for classically chaotic quantum maps

abstract:
  We study the behavior of an open quantum system, with an $N$--dimensional
space of states, whose density matrix evolves according to a non--unitary map
defined in two steps: A unitary step, where the system evolves with an
evolution operator obtained by quantizing a classically chaotic map (baker's
and Harper's map are the two examples we consider). A non--unitary step where
the evolution operator for the density matrix mimics the effect of diffusion in
the semiclassical (large $N$) limit. The process of decoherence and the
transition from quantum to classical behavior are analyzed in detail by means
of numerical and analitic tools. The existence of a regime where the entropy
grows with a rate which is independent of the strength of the diffusion
coefficient is demonstrated. The nature of the processes that determine the
production of entropy is analyzed.


title:
Implementation of quantum search algorithm using classical Fourier
  optics

abstract:
  We report on an experiment on Grover's quantum search algorithm showing that
{\em classical waves} can search a $N$-item database as efficiently as quantum
mechanics can. The transverse beam profile of a short laser pulse is processed
iteratively as the pulse bounces back and forth between two mirrors. We
directly observe the sought item being found in $\sim\sqrt{N}$ iterations, in
the form of a growing intensity peak on this profile. Although the lack of
quantum entanglement limits the {\em size} of our database, our results show
that entanglement is neither necessary for the algorithm itself, nor for its
efficiency.


title: Formal solutions of stargenvalue equations

abstract:
  The formal solution of a general stargenvalue equation is presented, its
properties studied and a geometrical interpretation given in terms of
star-hypersurfaces in quantum phase space. Our approach deals with discrete and
continuous spectra in a unified fashion and includes a systematic treatment of
non-diagonal stargenfunctions. The formalism is used to obtain a complete
formal solution of Wigner quantum mechanics in the Heisenberg picture and to
write a general formula for the stargenfunctions of Hamiltonians quadratic in
the phase space variables in arbitrary dimension. A variety of systems is then
used to illustrate the former results.


title:
Generalized Coherent States Associated with the $C_{\lambda}$-Extended
  Oscillator

abstract:
  Two new types of coherent states associated with the $C_{\lambda}$-extended
oscillator, where $C_{\lambda}$ is the cyclic group of order $\lambda$, are
introduced. They satisfy a unity resolution relation in the
$C_{\lambda}$-extended oscillator Fock space (or in some subspace thereof) and
give rise to Bargmann representations of the latter, wherein the generators of
the $C_{\lambda}$-extended oscillator algebra are realized as
differential-operator-valued matrices.


title: Quantum Chaos and Quantum Algorithms

abstract:
  It was recently shown (quant-ph/9909074) that parasitic random interactions
between the qubits in a quantum computer can induce quantum chaos and put into
question the operability of a quantum computer. In this work I investigate
whether already the interactions between the qubits introduced with the
intention to operate the quantum computer may lead to quantum chaos. The
analysis focuses on two well--known quantum algorithms, namely Grover's search
algorithm and the quantum Fourier transform. I show that in both cases the same
very unusual combination of signatures from chaotic and from integrable
dynamics arises.


title: On quantum and approximate privacy

abstract:
  This paper studies privacy and secure function evaluation in communication
complexity. The focus is on quantum versions of the model and on protocols with
only approximate privacy against honest players. We show that the privacy loss
(the minimum divulged information) in computing a function can be decreased
exponentially by using quantum protocols, while the class of privately
computable functions (i.e., those with privacy loss 0) is not enlarged by
quantum protocols. Quantum communication combined with small information
leakage on the other hand makes certain functions computable (almost) privately
which are not computable using either quantum communication without leakage or
classical communication with leakage. We also give an example of an exponential
reduction of the communication complexity of a function by allowing a privacy
loss of $o(1)$ instead of privacy loss 0.


title:
Universal continuous-variable quantum computation: Requirement of
  optical nonlinearity for photon counting

abstract:
  Although universal continuous-variable quantum computation cannot be achieved
via linear optics (including squeezing), homodyne detection and feed-forward,
inclusion of ideal photon counting measurements overcomes this obstacle. These
measurements are sometimes described by arrays of beam splitters to distribute
the photons across several modes. We show that such a scheme cannot be used to
implement ideal photon counting and that such measurements necessarily involve
nonlinear evolution. However, this requirement of nonlinearity can be moved
"off-line," thereby permitting universal continuous-variable quantum
computation with linear optics.


title: Are Quantum Computing Models Realistic?

abstract:
  The commonly used circuit model of quantum computing leaves out the problems
of imprecision in the initial state preparation, particle statistics
(indistinguishability of particles belonging to the same quantum state), and
error correction (current techniques cannot correct all small errors). The
initial state in the circuit model computation is obtained by applying
potentially imprecise Hadamard gate operations whereas useful quantum
computation requires a state with no uncertainty. We review some limitations of
the circuit model and speculate on the question if a hierarchy of quantum-type
computing models exists.


title:
An Implementation of the Deutsch-Jozsa Algorithm on Molecular Vibronic
  Coherences Through Four-Wave Mixing: a Theoretical Study

abstract:
  Time-Frequency Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) was
recently proposed as a means to implement quantum logic using the molecular
ro-vibrational manifold as a quantum register [R. Zadoyan et al., Chem. Phys.
266, 323 (2001)]. We give a concrete example of how this can be accomplished
through an illustrative algorithm that solves the Deutsch-Jozsa problem. We use
realistic molecular parameters to recognize that, as the problem size expands,
shaped pulses must be tailored to maintain fidelity of the algorithm.


title: Internal Symmetry Group and Density Matrix of Fields with Spins 0, 1

abstract:
  The internal symmetry group U(3,1) of the neutral vector fields with two
spins 0 and 1 is investigated. Massless fields correspond to the generalized
Maxwell equations with the gradient term. The symmetry transformations in the
coordinate space are integro-differential transformations. Using the method of
the Hamiltonian formalism the conservation tensors are found, and the quantized
theory is studied. The necessity to introduce an indefinite metric is shown.
The internal symmetry group U(3,1) being considered, after the transition to
electrodynamics, reduces to the U(2) group. It is shown that the group of dual
transformations is the subgroup of the group under consideration.
  All the linearly independent solutions of the equation for a free particle
obtained in terms of the projection matrix-dyads.


title:
On some algebraic problems arising in quantum mechanical description of
  biological systems

abstract:
  The biological hierarchy and the differences between living and non-living
systems are considered from the standpoint of quantum mechanics. The
hierarchical organization of biological systems requires hierarchical
organization of quantum states. The construction of the hierarchical space of
state vectors is presented. The application of similar structures to quantum
information processing is considered.


title:
Impossibility Criterion for Obtaining Pure Entangled States From Mixed
  States By Purifying Protocols

abstract:
  Purifying noisy entanglement is a protocol which can increase the
entanglement of a mixed state (as a source)at expense of the entanglement of
others(as an ancilla)by collective measurement. A protocol with which one can
get a pure entangled state from a mixed state is defined as purifying mixed
states. We address a basic question: can one get a pure entangled state from a
mixed state? We give a necessary and sufficient condition of purifying a mixed
state by fit local operations and classical communication and show that for a
class of source states and ancilla states in arbitrary bipartite systems
purifying mixed states is impossible by finite rounds of purifying protocols.
For $2\otimes 2$ systems, it is proved that arbitrary states cannot be purified
by individual measurement. The possible application and meaning of the
conclusion are discussed.


title:
A Necessary And Sufficient Condition of Distillability with unite
  fidelity from Finite Copies of a Mixed State: The Most Efficient Purification
  Protocol

abstract:
  It is well known that any entangled mixed state in $2\otimes 2$ systems can
be purified via infinite copies of the mixed state. But can one distill a pure
maximally entangled state from finite copies of a mixed state in any bipartite
system by local operation and classical communication? This is more meaningful
in practical application. We give a necessary and sufficient condition of this
distillability. This condition can be expressed as: there exists
distillable-subspaces. According to this condition, one can judge whether a
mixed state is distillable or not easily. We also analyze some properties of
distillable-subspaces, and discuss the most efficient purification protocols.
Finally, we discuss the distillable enanglement of two-quibt system for the
case of finite copies.


title: Quantum-like approach to financial risk: quantum anthropic principle

abstract:
  We continue the analysis of quantum-like description of market phenomena and
economics. We show that it is possible to define a risk inclination operator
acting in some Hilbert space that has a lot of common with quantum description
of the harmonic oscillator. The approach has roots in the recently developed
quantum game theory and quantum computing. A quantum anthropic principle is
formulated


title: Oscillating decay of an unstable system

abstract:
  We study the short-time and medium-time behavior of the survival probability
in the frame of the $N$-level Friedrichs model. The time evolution of an
arbitrary unstable initial state is determined. We show that the survival
probability may oscillate significantly during the so-called exponential era.
This result explains qualitatively the experimental observations of the NaI
decay.


title: Stimulated emission of polarization-entangled photons

abstract:
  Entangled photon pairs -- discrete light quanta that exhibit non-classical
correlations -- play a crucial role in quantum information science (for example
in demonstrations of quantum non-locality and quantum cryptography). At the
macroscopic optical field level non-classical correlations can also be
important, as in the case of squeezed light, entangled light beams and
teleportation of continuous quantum variables. Here we use stimulated
parametric down-conversion to study entangled states of light that bridge the
gap between discrete and macroscopic optical quantum correlations. We
demonstrate experimentally the onset of laser-like action for entangled
photons. This entanglement structure holds great promise in quantum information
science where there is a strong demand for entangled states of increasing
complexity.


title:
Lie Symmetry, discrete symmetry and supersymmetry of the Pauli
  Hamiltonian

abstract:
  Starting from the full group of symmetries of a system we select a discrete
subset of transformations which allows to introduce the Clifford algebra of
operators generating new supercharges of extended supersymmetry. The system
defined by the Pauli Hamiltonian is discussed.


title: A Dynamical Theory of Markovian Diffusion

abstract:
  A dynamical treatment of Markovian diffusion is presented and several
applications discussed. The stochastic interpretation of quantum mechanics is
considered within this framework. A model for Brownian movement which includes
second order quantum effects is derived.


title: CNOT operator and its similar matrices in quantum computation

abstract:
  We present a theoretical result, which is based on the linear algebra theory
(similar operators). The obtained theoretical results optimize the experimental
technique to construct quantum computer e.g., reduces the number of steps to
perform the logical CNOT (XOR) operation. The present theoretical technique can
also be generalized to the other operators in in quantum computation and
information theory.


title: Formalization of the distinguishability heuristics

abstract: Withdrawn. Replaced by quant-ph/0308160 (cf accompanying txt file)


title: A fully efficient secure quantum cryptography protocol

abstract:
  The paper has been withdrawn by the author since the protocol is not new. It
is just the oldest version of BB84.


title: Conventions in relativity theory and quantum mechanics

abstract:
  The conventionalistic aspects of physical world perception are reviewed with
an emphasis on the constancy of the speed of light in relativity theory and the
irreversibility of measurements in quantum mechanics. An appendix contains a
complete proof of Alexandrov's theorem using mainly methods of affine geometry.


title: De Broglie Wavelength Reduction for a Multi-photon Wave Packet

abstract:
  An experiment is proposed that permits the observation of the reduced de
Broglie wavelengths of two and four-photon wave packets using present
technology. It is suggested to use a Mach-Zehnder setup and feed both input
ports with light generated by a single non-degenerate down-conversion source.
The strong quantum correlations of the light in conjunction with
boson-enhancement at the input beam splitter allow to detect a two- and
fourfold decrease in the observed de Broglie wavelength with perfect
visibility. This allows a reduction of the observed de Broglie wavelength below
the wavelength of the source.


title: "Stopping" of light and quantum memories for photons

abstract:
  A coherent technique for the control of photon propagation in optically thick
media and its application for quantum memories is discussed. Raman adiabatic
passage with an externally controlled Stokes field can be used to transfer the
quantum state of a light pulse (``flying'' qubit) to a collective
spin-excitation (stationary qubit) and thereby slow down its propagation
velocity to zero. The process is reversible and has a potential fidelity of
unity without the necessity for strongly coupling resonators. A simple
quasi-particle picture (dark-state polariton) of the transfer is presented. The
analytic theory is supplemented with exact numerical solutions. Finally the
influence of decoherence mechanisms on collective storage states, which are
N-particle entangled states, is analyzed.


title: A stationary source of non-classical or entangled atoms

abstract:
  A scheme for generating continuous beams of atoms in non-classical or
entangled quantum states is proposed and analyzed. For this the recently
suggested transfer technique of quantum states from light fields to collective
atomic excitation by Stimulated Raman adiabatic passage [M.Fleischhauer and
M.D. Lukin, Phys.Rev.Lett. 84, 5094 (2000)] is employed and extended to matter
waves.


title: Biphoton focusing for two-photon excitation

abstract:
  We study two-photon excitation using biphotons generated via the process of
spontaneous parametric down-conversion in a nonlinear crystal. We show that the
focusing of these biphotons yields an excitation distribution that is
essentially the same as the distribution of one-photon excitation at the pump
wavelength. We also demonstrate that biphoton excitation in the image region
yields a distribution whose axial width is approximately that of the crystal
thickness and whose transverse width is that of the pump at the input to the
crystal.


title: Quantum Electrodynamics is free from the Einstein-Podolsky-Rosen paradox

abstract:
  I show that Quantum Electrodynamics (QED) predicts a sort of uncertainty
principle on the number of the "soft photons" that can be produced in
coincidence with the particles that are observed in any EPR experiment. This
result is argued to be sufficient to remove the original EPR paradox. A
signature of this soft-photons solution of the EPR paradox would be the
observation of apparent symmetry violation in single events. On the other hand,
in the case of the EPR experiments that have actually been realized, the QED
correlations are argued to be very close to those calculated by the previous,
incomplete treatment, which showed a good agreement with the data. Finally, the
usual interpretation of the correlations themselves as a real sign of
nonlocality is also criticized.


title: A magnetic model with a possible Chern-Simons phase

abstract:
  An elementary family of local Hamiltonians $H_{\c ,\ell}, \ell = 1,2,3,
ldots$, is described for a $2-$dimensional quantum mechanical system of spin
$={1/2}$ particles. On the torus, the ground state space $G_{\circ,\ell}$ is
$(\log)$ extensively degenerate but should collapse under $\l$perturbation" to
an anyonic system with a complete mathematical description: the quantum double
of the $SO(3)-$Chern-Simons modular functor at $q= e^{2 \pi i/\ell +2}$ which
we call $DE \ell$. The Hamiltonian $H_{\circ,\ell}$ defines a
\underline{quantum} \underline{loop}\underline{gas}. We argue that for $\ell =
1$ and 2, $G_{\circ,\ell}$ is unstable and the collapse to $G_{\epsilon, \ell}
\cong DE\ell$ can occur truly by perturbation. For $\ell \geq 3$,
$G_{\circ,\ell}$ is stable and in this case finding $G_{\epsilon,\ell} \cong DE
\ell$ must require either $\epsilon > \epsilon_\ell > 0$, help from finite
system size, surface roughening (see section 3), or some other trick, hence the
initial use of quotes ${\l}\quad$". A hypothetical phase diagram is included in
the introduction.


title: Aspects of a Two-Level Atom in Squeezed Displaced Fock States

abstract:
  This paper presents some results on some aspects of the two-level atom
interacting with a single-mode with the privileged field mode being in the
squeezed displaced Fock state (SDFS). The exact results are employed to perform
a careful investigation of the temporal evolution of the atomic inversion,
entropy and phase distribution. It is shown that the interference between
component states leads to non-classical oscillations in the photon number
distribution. At mid revival time the field is almost in the pure state.
  We have briefly discussed the evolution of the Q function of the cavity
field. The connection between the field entropy and the collapses and revivals
of the atomic inversion has been established. We find that the phase
probability distribution of the field reflect the collapses and revivals of the
level occupation probabilities in most situations. The interaction brings about
the symmetrical splitting of the phase probability distribution. The general
conclusions reached are illustrated by numerical results.


title: Causal Interpretation and Quantum Phase Space

abstract:
  We show that the de Broglie-Bohm interpretation can be easily implemented in
quantum phase space through the method of quasi-distributions. This method
establishes a connection with the formalism of the Wigner function. As a
by-product, we obtain the rules for evaluating the expectation values and
probabilities associated with a general observable in the de Broglie-Bohm
formulation. Finally, we discuss some aspects of the dynamics.


title:
Decoherence and robustness of parity-dependent entanglement in the
  dynamics of a trapped ion

abstract:
  We study the entanglement between the 2D vibrational motion and two ground
state hyperfine levels of a trapped ion, Under particular conditions this
entanglement depends on the parity of the total initial vibrational quanta. We
study the robustness of this quantum coherence effect with respect to the
presence of non-dissipative sources of decoherence, and of an imperfect initial
state preparation.


title: Conditions for complex spectra in a class of PT symmetric potentials

abstract:
  We study a wide class of solvable PT symmetric potentials in order to
identify conditions under which these potentials have regular solutions with
complex energy. Besides confirming previous findings for two potentials, most
of our results are new. We demonstrate that the occurrence of conjugate energy
pairs is a natural phenomenon for these potentials. We demonstrate that the
present method can readily be extended to further potential classes.


title: A quantum measurement of the spin direction

abstract:
  We give a first physical model for the quantum measurement of the spin
direction. It is an Arthurs-Kelly model that involves a kind of magnetic-dipole
interaction of the spin with three modes of radiation. We show that in a limit
of infinite squeezing of radiation the optimal POVM for the measurement of the
spin direction is achieved for spin 1/2.


title: Quantum Statistics Can Suppress Classical Interference

abstract:
  Classical optical interference experiments correspond to a measurement of the
first-order correlation function of the electromagnetic field. The converse of
this statement: experiments that measure the first order correlation functions
do not distinguish between the quantum and classical theories of light, does
not always hold. A counterexample is given.