title:
The system with discrete interactions I: Some comments about the
  principles of quantum theory

abstract:
  The model of the physical system with discrete interactions is based on the
postulates that
  (i) parameters of the physical system are defined in process of its
interaction;
  (ii) the process of interaction is discrete.
  Consequently ordering of the events in the system is not automatically
implied based on the values of time, but must be specified explicitly. This
suggests the specific logic of events as well as complex character of the
function, which describes stochastic behavior of the system, hence the
parameters of the system are defined by Hermitian operators in the Hilbert
space of functions.
  The model gives an essential way to introduce the basic notions and obtain
the results of the quantum theory, to derive the meaning of the main physical
parameters, such as momentum or electric charge. Based on the proposed
postulates, Schrodinger equation for the particle is deduced in a way similar
to inferring of Smoluchowski equation in the classical statistical mechanics.
  Similarly, the equations of motion of linear fields are established by
considering Smoluchowski-type equations for amplitudes of harmonics.
  The concept of discrete interaction gives a way to de-couple the object of
experiment and a testing device (the traditional source of controversy in
quantum theory), though at expense of limitation of the principle of locality.


title:
The system with discrete interactions II: Behavior of the relativistic
  particle in space and in time

abstract:
  The principles of behavior of the system with discrete interactions are
applied to description of motion of the relativistic particle. Applying the
concept of non-local behavior both to position in space and to time, the
apparently covariant equation of motion of the particle (Klein-Gordon) is
defined. Based on the assumption that the form of the equation has to be
invariant in inertial reference frames, the principle of constancy of the speed
of light can be deduced. Consequently the basic statements of special
relativity can be established in relation to the principles of discrete
interaction.
  The condition that Klein-Gordon equation was established without explicit use
of the principle of correspondence gives a way to specify the area of
applicability of the statement about the speed of light as the maximal speed of
propagation of information. This would permit interpretation of superluminal
phenomena with no contradictions to special relativity.
  The conventional interpretation of time as a category which specifies
succession and coexistence of events leads to interpreting of the Klein-Gordon
and related equations (such as Maxwell or Dirac) as equations of the fields.
This would justify the procedure of second quantization, so that the states of
the field are identified with the sets of particles.


title: Time of Arrival from Bohmian Flow

abstract:
  We develop a new conception for the quantum mechanical arrival time
distribution from the perspective of Bohmian mechanics. A detection probability
for detectors sensitive to quite arbitrary spacetime domains is formulated.
Basic positivity and monotonicity properties are established. We show that our
detection probability improves and generalises earlier proposals by Leavens and
McKinnon. The difference between the two notions is illustrated through
application to a free wave packet.


title: Discrimination between non perfectly known states

abstract:
  Discrimination task is treated in the case of only partial prior information
from measurements of unknown states. The construction of the optimal
discrimination device and estimation of unknown states is performed
simultaneously. A communication through a noisy quantum channel is formulated
in terms of the proposed discrimination protocol.


title: Gravitational decoherence of atomic interferometers

abstract:
  We study the decoherence of atomic interferometers due to the scattering of
stochastic gravitational waves. We evaluate the `direct' gravitational effect
registered by the phase of the matter waves as well as the `indirect' effect
registered by the light waves used as beam-splitters and mirrors for the matter
waves. Considering as an example the space project HYPER, we show that both
effects are negligible for the presently studied interferometers.


title: Comparison of two unknown pure quantum states

abstract:
  We investigate the extent to which we can establish whether or not two
quantum systems have been prepared in the same state. We investigate the
possibility of universal unambiguous state comparison. We show that it is
impossible to conclusively identify two pure unknown states as being identical,
and construct the optimal measurement for conclusively identifying them as
being different. We then derive optimal strategies for state comparison when
the state of each system is one of two known states.


title: Entangled-photon ellipsometry

abstract:
  Performing reliable measurements in optical metrology, such as those needed
in ellipsometry, requires a calibrated source and detector, or a
well-characterized reference sample. We present a novel interferometric
technique to perform reliable ellipsometric measurements. This technique relies
on the use of a non-classical optical source, namely polarization-entangled
twin photons generated by spontaneous parametric downconversion from a
nonlinear crystal, in conjunction with a coincidence-detection scheme.
Ellipsometric measurements acquired with this scheme are absolute, i.e., they
require neither source nor detector calibration, nor do they require a
reference.


title: Decoherence of Quantum Damped Oscillators

abstract:
  Quantum dissipation is studied within two model oscillators, the
Caldirola-Kanai (CK) oscillator as an open system with one degree of freedom
and the Bateman-Feshbach-Tikochinsky (BFT) oscillator as a closed system with
two degrees of freedom. Though these oscillators describe the same classical
damped motion, the CK oscillator retains the quantum coherence, whereas the
damped subsystem of the BFT oscillator exhibits both quantum decoherence and
classical correlation. Furthermore the amplified subsystem of the BFT
oscillator shows the same degree of quantum decohernce and classical
correlation.


title: Scheme for the generation of an entangled four-photon W-state

abstract:
  We present a scheme to produce an entangled four-photon W-state by using
linear optical elements. The symmetrical setup of linear optical elements
consists of four beam splitters, four polarization beam splitters and four
mirrors. A photon EPR-pair and two single photons are required as the input
modes. The projection on the W-state can be made by a four-photon coincidence
measurement. Further, we show that by means of a horizontally oriented
polarizer in front of one detector the W-state of three photons can be
generated.


title: Anomalies in Quantum Mechanics: the 1/r^2 Potential

abstract:
  An anomaly is said to occur when a symmetry that is valid classically becomes
broken as a result of quantization. Although most manifestations of this
phenomenon are in the context of quantum field theory, there are at least two
cases in quantum mechanics--the two dimensional delta function interaction and
the 1/r^2 potential. The former has been treated in this journal; in this
article we discuss the physics of the latter together with experimental
consequences.


title: Entropy on the von Neumann lattice and its evaluation

abstract:
  Based on the recently introduced averaging procedure in phase space, a new
type of entropy is defined on the von Neumann lattice. This quantity can be
interpreted as a measure of uncertainty associated with simultaneous
measurement of the position and momentum observables in the discrete subset of
the phase space. Evaluating for a class of the coherent states, it is shown
that this entropy takes a stationary value for the ground state, modulo a unit
cell of the lattice in such a class. This value for the ground state depends on
the ratio of the position lattice spacing and the momentum lattice spacing. It
is found that its minimum is realized for the perfect square lattice, i.e.,
absence of squeezing. Numerical evaluation of this minimum gives 1.386....


title:
Geometric quantization of time-dependent completely integrable
  Hamiltonian systems

abstract:
  A time-dependent completely integrable Hamiltonian system is quantized with
respect to time-dependent action-angle variables near an instantly compact
regular invariant manifold. Its Hamiltonian depends only on action variables,
and has a time-independent countable energy spectrum.


title:
General Framework for the Behaviour of Continuously Observed Open
  Quantum Systems

abstract:
  We develop the general quantum stochastic approach to the description of
quantum measurements continuous in time. The framework, that we introduce,
encompasses the various particular models for continuous-time measurements
condsidered previously in the physical and the mathematical literature.


title: Continuous Unitary Transformations

abstract:
  In the present time we observe a growing number of publications where the,
so-called, flow equations are successfully used to diagonalize Hamiltonians by
means of an appropriate unitary transformation. Here we discuss and compare the
flow equations (FE) method (proposed in 1994) with the method of one step
continuous unitary transformations (OS CUT) (proposed in 1982). It is shown
that the FE method can be considered as a generalization of the OS CUT approach
to the case of parameter dependent generator. The OS CUT method gives linear
differential equations for the diagonalization procedure. In the FE method the
system of differential equations is nonlinear. Finally we discuss the
generalization of idea of continuous unitary transformations for the case of
quantum equations of motion (Heisenberg picture and density matrix).


title: Stability of quantum states of finite macroscopic systems

abstract:
  We study the stabilities of quantum states of macroscopic systems, against
noises, against perturbations from environments, and against local
measurements. We show that the stabilities are closely related to the cluster
property, which describes the strength of spatial correlations of fluctuations
of local observables, and to fluctuations of additive operators. The present
theory has many applications, among which we discuss the mechanism of phase
transitions in finite systems and quantum computers with a huge number of
qubits.


title:
A Local Hidden Variables Model for Experiments involving Photon Pairs
  Produced in Parametric Down Conversion

abstract:
  In previous articles we have developed a theory of down conversion in
nonlinear crystals, based on the Wigner representation of the radiation field.
Taking advantage of the fact that the Wigner function is always positive in
parametric down conversion experiments, we construct a local hidden variables
model where the amplitudes of the field modes are taken as random variables
whose probability distribution is the Wigner function. In order to achieve our
goal we give a model of detection which is fully local but departs from quantum
theory. In our model the zeropoint (vacuum) level of radiation lies below a
threshold of the detectors and only signals above the threshold are detectable.
The predictions of the model agree with those of quantum mechanics if the
signal intensities surpase some level and the efficiency is low. This is
consistent with the known fact that quantum mechanics is compatible with local
realism in that case (a fact called the ``efficiency loophole''). Our model
gives a number of constraints which do not follow from the quantum theory of
detection and are experimentally testable.


title: Bohmian trajectories and Klein's paradox

abstract:
  We compute the Bohmian trajectories of the incoming scattering plane waves
for Klein's potential step in explicit form. For finite norm incoming
scattering solutions we derive their asymptotic space-time localization and we
compute some Bohmian trajectories numerically. The paradox, which appears in
the traditional treatments of the problem based on the outgoing scattering
asymptotics, is absent.


title: Bell's inequalities and indeterminism

abstract:
  The inequality of Clauser and Horne [ Phys. Rev. D 10, 526 (1974)], intended
to overcome the limited scope of other inequalities to deterministic theories,
is shown to have a resticted validity even in case of perfect detectors and
perfect angular correlations.


title: A description of entanglement in terms of quantum phase

abstract:
  We explore the role played by the phase in an accurate description of the
entanglement of bipartite systems. We first present an appropriate polar
decomposition that leads to a truly Hermitian operator for the phase of a
single qubit. We also examine the positive operator-valued measures that can
describe the qubit phase properties. When dealing with two qubits, the relative
phase seems to be a natural variable to understand entanglement. In this
spirit, we propose a measure of entanglement based on this variable.


title: The quantum measurement problem enhanced

abstract:
  The quantum measurement problem as formalised by Bassi and Ghirardi [Phys.
Lett. A 275 (2000)373] without taking recourse to sharp apparatus observables
is extended to cover impure initial states.


title:
Improving fidelity of continuous-variable teleportation via local
  operations

abstract:
  We study the Braunstein-Kimble setup for teleportation of quantum state of a
single mode of optical field. We assume that the sender and receiver share a
two-mode Gaussian state and we identify optimum local Gaussian operations that
maximize the teleportation fidelity. We consider fidelity of teleportation of
pure Gaussian states and we also introduce fidelity of the teleportation
transformation. We show on an explicit example that in some cases the optimum
local operation is not a simple unitary symplectic transformation but some more
general completely positive map.


title: Multipartite Classical and Quantum Secrecy Monotones

abstract:
  In order to study multipartite quantum cryptography, we introduce quantities
which vanish on product probability distributions, and which can only decrease
if the parties carry out local operations or carry out public classical
communication. These ``secrecy monotones'' therefore measure how much secret
correlations are shared by the parties. In the bipartite case we show that the
mutual information is a secrecy monotone. In the multipartite case we describe
two different generalisations of the mutual information, both of which are
secrecy monotones. The existence of two distinct secrecy monotones allows us to
show that in multipartite quantum cryptography the parties must make
irreversible choices about which multipartite correlations they want to obtain.
Secrecy monotones can be extended to the quantum domain and are then defined on
density matrices. We illustrate this generalisation by considering tri-partite
quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We
show that before carrying out measurements on the state, the parties must make
an irreversible decision about what probability distribution they want to
obtain.


title:
Relativistically invariant extension of the de Broglie-Bohm theory of
  quantum mechanics

abstract:
  We show that quantum mechanics can be given a Lorentz-invariant realistic
interpretation by applying our recently proposed relativistic extension of the
de Broglie-Bohm theory to deduce non-locally correlated, Lorentz-invariant
individual particle motions for the Einstein-Podolsky-Rosen experiment and the
double-interferometer experiment proposed by Horne, Shimony and Zeilinger.


title: Fermi's "Golden Rule" and Non-Exponential Decay

abstract:
  A study is made of the behavior of unstable states in simple models which
nevertheless are realistic representations of situations occurring in nature.
It is demonstrated that a non-exponential decay pattern will ultimately
dominate decay due to a lower limit to the energy. The survival rate approaches
zero faster than the inverse square of the time when the time goes to infinity.


title: Holonomic quantum logic gates

abstract:
  This is a brief overview of quantum holonomies in the context of quantum
computation. We choose an adequate set of quantum logic gates, namely, a phase
gate, the Hadamard gate, and a conditional-phase gate and show how they can be
implemented by purely geometric means. Such gates may be more resilient to
certain types of errors.


title: V\"axj\"o Interpretation of Quantum Mechanics

abstract:
  We present critical arguments against individual interpretation of Bohr's
complementarity and Heisenberg's uncertainty principles. Statistical
interpretation of these principles is discussed in the contextual framework. We
support the possibility to use Statistical Contextual Realist Interpretation of
quantum formalism. In spite of all {\bf no-go} theorems (e.g., von Neumann,
Kochen and Specker,..., Bell,...), recently (quant-ph/0306003 and 0306069) we
constructed a realist basis of quantum mechanics. In our model both classical
and quantum spaces are rough images of the fundamental {\bf prespace.} Quantum
mechanics cannot be reduced to classical one. Both classical and quantum
representations induce reductions of prespace information.


title: Quantum entanglement and Bell inequalities in Heisenberg spin chains

abstract:
  We show that in one-dimensional isotropic Heisenberg model two-qubit thermal
entanglement and maximal violation of Bell inequalities are directly related
with a thermodynamical state function, i.e., the internal energy. Therefore
they are completely determined by the partition function, the central object of
thermodynamics. For ferromagnetic ring we prove that there is no thermal
entanglement at any temperature. Explicit relations between the concurrence and
the measure of maximal Bell inequality violation are given.


title: The No Cloning Theorem versus the Second Law of Thermodynamics

abstract:
  Asher Peres' proof that a violation of No Cloning Theorem would imply a
violation of the Second Law of Thermodynamics is shown not to take into account
the algorithmic-information's contribution to the Thermodynamical Entropy of
the semi-permeable membranes of Peres' engine.


title: Time Evolution of Two-Level Systems Driven by Periodic Fields

abstract:
  In this paper we study the time evolution of a class of two-level systems
driven by periodic fields in terms of new convergent perturbative expansions
for the associated propagator U(t). The main virtue of these expansions is that
they do not contain secular terms, leading to a very convenient method for
quantitatively studying the long-time behaviour of that systems. We present a
complete description of an algorithm to numerically compute the perturbative
expansions. In particular, we applied the algorithm to study the case of an
ac-dc field (monochromatic interaction), exploring various situations and
showing results on (time-dependent) observable quantities, like transition
probabilities. For a simple ac field, we analised particular situations where
an approximate effect of dynamical localisation is exhibited by the driven
system. The accuracy of our calculations was tested measuring the unitarity of
the propagator U(t), resulting in very small deviations, even for very long
times compared to the cycle of the driving field.


title: Quantum statistical zero-knowledge

abstract:
  In this paper we propose a definition for (honest verifier) quantum
statistical zero-knowledge interactive proof systems and study the resulting
complexity class, which we denote QSZK. We prove several facts regarding this
class that establish close connections between classical statistical
zero-knowledge and our definition for quantum statistical zero-knowledge, and
give some insight regarding the effect of this zero-knowledge restriction on
quantum interactive proof systems.


title: Coupling a single atomic quantum bit to a high finesse optical cavity

abstract:
  The quadrupole S$_{1/2}$ -- D$_{5/2}$ optical transition of a single trapped
Ca$^+$ ion, well suited for encoding a quantum bit of information, is
coherently coupled to the standing wave field of a high finesse cavity. The
coupling is verified by observing the ion's response to both spatial and
temporal variations of the intracavity field. We also achieve deterministic
coupling of the cavity mode to the ion's vibrational state by selectively
exciting vibrational state-changing transitions and by controlling the position
of the ion in the standing wave field with nanometer-precision.


title: Schrodinger cat animated on a quantum computer

abstract:
  We present a quantum algorithm which allows to simulate chaos-assisted
tunneling in deep semiclassical regime on existing quantum computers. This
opens new possibilities for investigation of macroscopic quantum tunneling and
realization of semiclassical Schr\"odinger cat oscillations. Our numerical
studies determine the decoherence rate induced by noisy gates for these
oscillations and propose a suitable parameter regime for their experimental
implementation.


title: Repulsive Casimir forces

abstract:
  We discuss repulsive Casimir forces between dielectric materials with non
trivial magnetic susceptibility. It is shown that considerations based on naive
pair-wise summation of Van der Waals and Casimir Polder forces may not only
give an incorrect estimate of the magnitude of the total Casimir force, but
even the wrong sign of the force when materials with high dielectric and
magnetic response are involved. Indeed repulsive Casimir forces may be found in
a large range of parameters, and we suggest that the effect may be realized in
known materials. The phenomenon of repulsive Casimir forces may be of
importance both for experimental study and for nanomachinery applications.


title: Clauser-Horne-Bell inequality for three three-dimensional systems

abstract:
  In this paper we show a Bell inequality of Clauser-Horne type for three
three-dimensional systems (qutrits). Violation of the inequality by quantum
mechanics is shown for the case in which each of the three observers measures
two non-commuting observables, defined by the so called unbiased symmetric six
port beamsplitters, on a maximally entangled state of three qutrits. The
strength of the violation of the inequality agrees with the numerical results
presented in Kaszlikowski et. al., quant-ph//0202019.


title: Comparison of Star and Ring Topologies for Entanglement Distribution

abstract:
  We investigate the differences between distributing entanglement using star
and ring type network topologies. Assuming symmetrically distributed users, we
asses the relative merits of the two network topologies as a function of the
number of users when the amount of resources and the type of the quantum
channel are kept fixed. For limited resources, we find that the topology better
suited for entanglement distribution could differ from that which is more
suitable for classical communications.


title:
Non-Markovian stochastic Schr\"odinger equations: Generalization to
  real-valued noise using quantum measurement theory

abstract:
  Do stochastic Schr\"odinger equations, also known as unravelings, have a
physical interpretation? In the Markovian limit, where the system {\em on
average} obeys a master equation, the answer is yes. Markovian stochastic
Schr\"odinger equations generate quantum trajectories for the system state
conditioned on continuously monitoring the bath. For a given master equation,
there are many different unravelings, corresponding to different sorts of
measurement on the bath. In this paper we address the non-Markovian case, and
in particular the sort of stochastic \sch equation introduced by Strunz, Di\'
osi, and Gisin [Phys. Rev. Lett. 82, 1801 (1999)]. Using a quantum measurement
theory approach, we rederive their unraveling which involves complex-valued
Gaussian noise. We also derive an unraveling involving real-valued Gaussian
noise. We show that in the Markovian limit, these two unravelings correspond to
heterodyne and homodyne detection respectively. Although we use quantum
measurement theory to define these unravelings, we conclude that the stochastic
evolution of the system state is not a true quantum trajectory, as the identity
of the state through time is a fiction.


title: A quantum protocol for cheat-sensitive weak coin flipping

abstract:
  We present a quantum protocol for the task of weak coin flipping. We find
that, for one choice of parameters in the protocol, the maximum probability of
a dishonest party winning the coin flip if the other party is honest is
1/sqrt(2). We also show that if parties restrict themselves to strategies
wherein they cannot be caught cheating, their maximum probability of winning
can be even smaller. As such, the protocol offers additional security in the
form of cheat sensitivity.


title: Quantum Theory and Classical Information

abstract:
  Transmission of classical information using quantum objects such as polarized
photons is studied. The classical (Shannon) channel capacity and its relation
to quantum (von Neumann) channel capacity is investigated for various receiver
arrangements.
  A quantum channel with transmission impairment caused by attenuation and
random polarization noise is considered. It is shown that the maximal (von
Neumann) capacity of such a channel can be realized by a simple symbol by
symbol detector followed by a classical error correcting decoder.
  For an intensity limited optical channel capacity is achieved by on-off
keying (OOK). The capacity per unit cost is shown to be 1 nat/photon = 1.44
bit/photon, slightly larger than the 1 bit/photon obtained by orthogonal
quantum signals.


title: The Quantum Monty Hall Problem

abstract:
  We consider a quantum version of a well-known statistical decision problem,
whose solution is, at first sight, counter-intuitive to many. In the quantum
version a continuum of possible choices (rather than a finite set) has to be
considered. It can be phrased as a two person game between a player P and a
quiz master Q. Then P always has a strategy at least as good as in the
classical case, while Q's best strategy results in a game having the same value
as the classical game. We investigate the consequences of Q storing his
information in classical or quantum ways. It turns out that Q's optimal
strategy is to use a completely entangled quantum notepad, on which to encode
his prior information.


title: Further results on the cross norm criterion for separability

abstract:
  In the present paper the cross norm criterion for separability of density
matrices is studied. In the first part of the paper we determine the value of
the greatest cross norm for Werner states, for isotropic states and for Bell
diagonal states. In the second part we show that the greatest cross norm
criterion induces a novel computable separability criterion for bipartite
systems. This new criterion is a necessary but in general not a sufficient
criterion for separability. It is shown, however, that for all pure states, for
Bell diagonal states, for Werner states in dimension d=2 and for isotropic
states in arbitrary dimensions the new criterion is necessary and sufficient.
Moreover, it is shown that for Werner states in higher dimensions (d greater
than 2), the new criterion is only necessary.


title: Fundamentals of Quantum Information Theory

abstract:
  In this paper we give a self contained introduction to the conceptional and
mathematical foundations of quantum information theory. In the first part we
introduce the basic notions like entanglement, channels, teleportation etc. and
their mathematical description. The second part is focused on a presentation of
the quantitative aspects of the theory. Topics discussed in this context
include: entanglement measures, channel capacities, relations between both,
additivity and continuity properties and asymptotic rates of quantum
operations. Finally we give an overview on some recent developments and open
questions.


title: Quantum Discord and Maxwell's Demons

abstract:
  Quantum discord was proposed as an information theoretic measure of the
``quantumness'' of correlations. I show that discord determines the difference
between the efficiency of quantum and classical Maxwell's demons in extracting
work from collections of correlated quantum systems.


title: On quantum channels

abstract:
  One of the most challenging open problems in quantum information theory is to
clarify and quantify how entanglement behaves when part of an entangled state
is sent through a quantum channel. Of central importance in the description of
a quantum channel or completely positive map (CP-map) is the dual state
associated to it. The present paper is a collection of well-known, less known
and new results on quantum channels, presented in a unified way. We will show
how this dual state induces nice characterizations of the extremal maps of the
convex set of CP-maps, and how normal forms for states defined on a Hilbert
space with a tensor product structure lead to interesting parameterizations of
quantum channels.


title:
Decoherence by a nonlinear environment: canonical vs. microcanonical
  case

abstract:
  We compare decoherence induced in a simple quantum system (qubit) for two
different initial states of the environment: canonical (fixed temperature) and
microcanonical (fixed energy), for the general case of a fully interacting
oscillator environment. We find that even a relatively compact oscillator bath
(with the effective number of degrees of freedom of order 10), initially in a
microcanonical state, will typically cause decoherence almost indistinguishable
from that by a macroscopic, thermal environment, except possibly at
singularities of the environment's specific heat (critical points). In the
latter case, the precise magnitude of the difference between the canonical and
microcanonical results depends on the critical behavior of the dissipative
coefficient, characterizing the interaction of the qubit with the environment.


title: Bell's inequality for n spin-s particles

abstract:
  The Mermin-Klyshko inequality for n spin-1/2 particles and two dichotomic
observables is generalized to n spin-s particles and two maximal observables.
It is shown that some multiparty multilevel Greenberger-Horne-Zeilinger states
[A. Cabello, Phys. Rev. A 63, 022104 (2001)] maximally violate this inequality
for any s. For a fixed n, the magnitude of the violation is constant for any s,
which provides a simple demonstration and generalizes the conclusion reached by
Gisin and Peres for two spin-s particles in the singlet state [Phys. Lett. A
162, 15 (1992)]. For a fixed s, the violation grows exponentially with n, which
provides a generalization to any s of Mermin's conclusion for n spin-1/2
particles [Phys. Rev. Lett. 65, 1838 (1990)].


title: Unstable systems and quantum Zeno phenomena in quantum field theory

abstract:
  We analyze the Zeno phenomenon in quantum field theory. The decay of an
unstable system can be modified by changing the time interval between
successive measurements (or by varying the coupling to an external system that
plays the role of measuring apparatus). We speak of quantum Zeno effect if the
decay is slowed and of inverse quantum Zeno (or Heraclitus) effect if it is
accelerated. The analysis of the transition between these two regimes requires
close scrutiny of the features of the interaction Hamiltonian. We look in
detail at quantum field theoretical models of the Lee type.


title: Vacuum induced Spin-1/2 Berry phase

abstract:
  We calculate the Berry phase of a spin-1/2 particle in a magnetic field
considering the quantum nature of the field. The phase reduces to the standard
Berry phase in the semiclassical limit and eigenstate of the particle acquires
a phase in the vacuum. We also show how to generate a vacuum induced Berry
phase considering two quantized modes of the field which has a interesting
physical interpretation.


title:
Computation of the phase induced by non-newtonian gravitational
  potentials in atom interferometry

abstract:
  In this letter we present a computation of the phase induced by test masses
of different geometry, in the framework of non-newtonian gravitation, on an
ideal separated arms atom interferometer. We deduce the related limits on the
non-newtonian gravitational strength in the sub-millimeter region for the
potential range. These limits would be comparable with the best existing
experimental limits but with the advantage of using a microscopic probe.


title:
Direct Measurement of the Photon Statistics of a Triggered Single Photon
  Source

abstract:
  We studied intensity fluctuations of a single photon source relying on the
pulsed excitation of the fluorescence of a single molecule at room temperature.
We directly measured the Mandel parameter Q(T) over 4 orders of magnitude of
observation timescale T, by recording every photocount. On timescale of a few
excitation periods, subpoissonian statistics is clearly observed and the
probablility of two-photons events is 10 times smaller than Poissonian pulses.
On longer times, blinking in the fluorescence, due to the molecular triplet
state, produces an excess of noise.


title: A Quantum Neural Network Computes Entanglement

abstract:
  An outstanding problem in quantum computing is the calculation of
entanglement, for which no closed-form algorithm exists. Here we solve that
problem, and demonstrate the utility of a quantum neural computer, by showing,
in simulation, that such a device can be trained to calculate the entanglement
of an input state, something neither an algorithmic quantum computer nor a
classical neural net can do.


title: Procrastinated Codes

abstract: This paper has been withdrawn by the author.


title: A Quantum Rosetta Stone for Interferometry

abstract:
  Heisenberg-limited measurement protocols can be used to gain an increase in
measurement precision over classical protocols. Such measurements can be
implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey
spectroscopes. We address the formal equivalence between the Mach-Zehnder
interferometer, the Ramsey spectroscope, and the discrete Fourier transform.
Based on this equivalence we introduce the ``quantum Rosetta stone'', and we
describe a projective-measurement scheme for generating the desired
correlations between the interferometric input states in order to achieve
Heisenberg-limited sensitivity. The Rosetta stone then tells us the same method
should work in atom spectroscopy.


title:
Bell's theorem and Bohr's principle that the measurement must be
  classical

abstract:
  In a recent paper Karl Hess and Walter Philipp claim that hidden local
variables cannot be ruled out. We argue that their claim is only valid if one
gives up Bohr's principle that the measuring instruments must be classical, and
this principle belongs to the foundations of scientific knowledge: Therefore,
nonlocal influences can be considered demonstrated.


title:
Universal Quantum Logic from Zeeman and Anisotropic Exchange
  Interactions

abstract:
  Some of the most promising proposals for scalable solid-state quantum
computing, e.g., those using electron spins in quantum dots or donor electron
or nuclear spins in Si, rely on a two-qubit quantum gate that is ideally
generated by an isotropic exchange interaction. However, an anisotropic
perturbation arising from spin-orbit coupling is inevitably present. Previous
studies focused on removing the anisotropy. Here we introduce a new universal
set of quantum logic gates that takes advantage of the anisotropic
perturbation. The price is a constant but modest factor in additional pulses.
The gain is a scheme that is compatible with the naturally available
interactions in spin-based solid-state quantum computers.


title: Adaptive Phase Measurements

abstract:
  In this thesis I consider the general problem of how to make the best
possible phase measurements using feedback. Both the optimum input state and
optimum feedback are considered for both single-mode dyne measurements and
two-mode interferometric measurements. I derive the optimum input states under
general dyne measurements when the mean photon number is fixed, both for
general states and squeezed states. I propose a new feedback scheme that
introduces far less phase uncertainty than mark II feedback, and is very close
to the theoretical limit. I also derive results for the phase variance when
there is a time delay in the feedback loop, showing that there is a lower limit
to the introduced phase variance, and this is approached quite accurately under
some conditions. I derive the optimum input states for interferometry, showing
that the phase uncertainty scales as 1/N for all the common measures of
uncertainty. This is contrasted with the |j0>_z state, which does not scale as
1/N for all measures of phase uncertainty. I introduce an adaptive feedback
scheme that is very close to optimum, and can give scaling very close to 1/N
for the uncertainty. Lastly I consider the case of continuous measurements, for
both the dyne and interferometric cases.


title: Changes of the topological charge of vortices

abstract:
  We consider changes of the topological charge of vortices in quantum
mechanics by investigating analytical examples where the creation or
annihilation of vortices occurs. In classical hydrodynamics of non-viscous
fluids the Helmholtz-Kelvin theorem ensures that the velocity field circulation
is conserved. We discuss applicability of the theorem in the hydrodynamical
formulation of quantum mechanics showing that the assumptions of the theorem
may be broken in quantum evolution of the wavefunction leading to a change of
the topological charge.


title: Realistic Derivation of Heisenberg Dynamics

abstract:
  Einstein conjectured long ago that much of quantum mechanics might be derived
as a statistical formalism describing the dynamics of classical systems. Bell's
Theorem experiments have ruled out complete equivalence between quantum field
theory (QFT) and classical field theory (CFT), but an equivalence between
dynamics is not only possible but provable in simple bosonic systems. Future
extensions of these results might possibly be useful in developing provably
finite variations of the standard model of physics.


title: Three-particle entanglement versus three-particle nonlocality

abstract:
  The notions of three-particle entanglement and three-particle nonlocality are
discussed in the light of Svetlichny's inequality [Phys. Rev. D 35, 3066
(1987)]. It is shown that there exist sets of measurements which can be used to
prove three-particle entanglement, but which are nevertheless useless at
proving three-particle nonlocality. In particular, it is shown that the quantum
predictions giving a maximal violation of Mermin's three-particle Bell
inequality [Phys. Rev. Lett. 65, 1838 (1990)] can be reproduced by a hybrid
hidden variables model in which nonlocal correlations are present only between
two of the particles. It should be possible, however, to test the existence of
both three-particle entanglement and three-particle nonlocality for any given
quantum state via Svetlichny's inequality.


title:
Comment on ``Time-like flows of energy-momentum and particle
  trajectories for the Klein-Gordon equation''

abstract:
  Horton, Dewdney, and Nesteruk [quant-ph/0103114] have proposed Bohm-type
particle trajectories accompanying a Klein-Gordon wave function psi on
Minkowski space. From two vector fields on space-time, W^+ and W^-, defined in
terms of psi, they intend to construct a timelike vector field W, the integral
curves of which are the possible trajectories, by the following rule: at every
space-time point, take either W = W^+ or W = W^- depending on which is
timelike.
  This procedure, however, is ill-defined as soon as both are timelike, or both
spacelike. Indeed, they cannot both be timelike, but they can well both be
spacelike, contrary to the central claim of [quant-ph/0103114]. We point out
the gap in their proof, provide a counterexample, and argue that, even for a
rather arbitrary wave function, the points where both W^+ and W^- are spacelike
can form a set of positive measure.


title: Robust control of decoherence in realistic one-qubit quantum gates

abstract:
  We present an open loop (bang-bang) scheme to control decoherence in a
generic one-qubit quantum gate and implement it in a realistic simulation. The
system is consistently described within the spin-boson model, with interactions
accounting for both adiabatic and thermal decoherence. The external control is
included from the beginning in the Hamiltonian as an independent interaction
term. After tracing out the environment modes, reduced equations are obtained
for the two-level system in which the effects of both decoherence and external
control appear explicitly. The controls are determined exactly from the
condition to eliminate decoherence, i.e. to restore unitarity. Numerical
simulations show excellent performance and robustness of the proposed control
scheme.


title: New summing algorithm using ensemble computing

abstract:
  We propose an ensemble algorithm, which provides a new approach for
evaluating and summing up a set of function samples. The proposed algorithm is
not a quantum algorithm, insofar it does not involve quantum entanglement. The
query complexity of the algorithm depends only on the scaling of the
measurement sensitivity with the number of distinct spin sub-ensembles. From a
practical point of view, the proposed algorithm may result in an exponential
speedup, compared to known quantum and classical summing algorithms. However in
general, this advantage exists only if the total number of function samples is
below a threshold value which depends on the measurement sensitivity.


title: The Laws of Physics and Cryptographic Security

abstract:
  This paper consists of musings that originate mainly from conversations with
other physicists, as together we've tried to learn some cryptography, but also
from conversations with a couple of classical cryptographers. The main thrust
of the paper is an attempt to explore the ramifications for cryptographic
security of incorporating physics into our thinking at every level. I begin by
discussing two fundamental cryptographic principles, namely that security must
not rely on secrecy of the protocol and that our local environment must be
secure, from a physical perspective. I go on to explain why by definition a
particular cryptographic task, oblivious transfer, is inconsistent with a
belief in the validity of quantum mechanics. More precisely, oblivious transfer
defines states and operations that do not exist in any (complex) Hilbert space.
I go on to argue the fallaciousness of a "black box" approach to quantum
cryptography, in which classical cryptographers just trust physicists to
provide them with secure quantum cryptographic sub-protocols, which they then
attempt to incorporate into larger cryptographic systems. Lest quantum
cryptographers begin to feel too smug, I discuss the fact that current
implementations of quantum key distribution are only technologically secure,
and not "unconditionally" secure as is sometimes claimed. I next examine the
concept of a secure lab from a physical perspective, and end by making some
observations about the cryptographic significance of the (often overlooked)
necessity for parties who wish to communicate having established physical
reference frames.


title: Entanglement of Distillation and Conditional Mutual Information

abstract:
  In previous papers, we expressed the Entanglement of Formation in terms of
Conditional Mutual Information (CMI). In this brief paper, we express the
Entanglement of Distillation in terms of CMI.


title: The Euclidean resonance and quantum tunneling

abstract:
  The extremely small probability of tunneling through an almost classical
potential barrier may become not small under the action of the specially
adapted non-stationary signal which selects the certain particle energy E_R.
For particle energies close to this value, the tunneling rate is not small
during a finite interval of time and has a very sharp peak at the energy E_R.
After entering inside the barrier, the particle emits electromagnetic quanta
and exits the barrier with a lower energy. The signal amplitude can be much
less compared to the field of the static barrier. This phenomenon can be called
the Euclidean resonance since the under-barrier motion occurs in imaginary
time. The resonance may stimulate chemical and biochemical reactions in a
selective way by adapting the signal to a certain particular chemical bond. The
resonance may be used in search of the soft alpha-decay for which a
conventional observation is impossible due to an extremely small decay rate.


title:
Experimental study of quantum decoherence using nuclear magnetic
  resonance

abstract:
  Quantum decoherence has been studied using nuclear magnetic resonance(NMR).
By choosing one qubit to simulate environment, we examine the decoherence
behavior of two quantum systems: a one qubit system and a two qubit system. The
experimental results show agreements with the theoretical predictions. Our
experiment schemes can be generalized to the case that the environment is
composed of multiple qubits.


title: Persistent currents due to point obstacles

abstract:
  We discuss properties of the two-dimensional Landau Hamiltonian perturbed by
a family of identical $\delta$ potentials arranged equidistantly along a closed
loop. It is demonstrated that for the loop size exceeding the effective size of
the point obstacles and the cyclotronic radius such a system exhibits
persistent currents at the bottom of the spectrum. We also show that the effect
is sensitive to a small disorder.


title: Making sense of a world of clicks

abstract:
  In a recent article O. Ulfbeck and A. Bohr (Foundations of Physics 31, 757,
2001) have stressed the genuine fortuitousness of detector clicks, which has
also been pointed out, in different terms, by the present author (American
Journal of Physics 68, 728, 2000). In spite of this basic agreement, the
present article raises objections to the presuppositions and conclusions of
Ulfbeck and Bohr, in particular their rejection of the terminology of
indefinite variables, their identification of reality with "the world of
experience," their identification of experience with what takes place "on the
spacetime scene," and the claim that their interpretation of quantum mechanics
is "entirely liberated" from classical notions. An alternative way of making
sense of a world of uncaused clicks is presented. This does not invoke
experience but deals with a free-standing reality, is not fettered by classical
conceptions of space and time but introduces adequate ways of thinking about
the spatiotemporal aspects of the quantum world, and does not reject indefinite
variables but clarifies the implications of their existence.


title: Why the laws of physics are just so

abstract:
  Does a world that contains chemistry entail the validity of both the standard
model of elementary particle physics and general relativity, at least as
effective theories? This article shows that the answer may very well be
affirmative. It further suggests that the very existence of stable, spatially
extended material objects, if not the very existence of the physical world, may
require the validity of these theories.


title: Hidden symmetries in deformed microwave resonators

abstract:
  We explain the ``Hidden symmetries'' observed in wavefunctions of deformed
microwave resonators in recent experiments.We also predict that other such
symmetries can be seen in microwave resonators.


title:
A realist view of the canonical EPRB experiment based on quantum theory
  and its consequences

abstract:
  A realist view of the Einstein-Podolsky-Rosen-Bohm experiment with spins
based on quantum theory is presented. This view implies that there is no action
at a distance. It also implies that the measurement result A (B) for particle 1
(2) depends on both magnet angles, and hence the probability of obtaining the
result A (B) also depends on both magnet angles. In light of these realist
implications, it is clear that what is wrong at least with local realistic
theory is not the locality or no action-at-a-distance assumption itself but
rather the formal implementation of that assumption.


title: Universal measurement apparatus controlled by quantum software

abstract:
  We propose a quantum device that can approximate any projective measurement
on a qubit. The desired measurement basis is selected by the quantum state of a
"program register". The device is optimized with respect to maximal average
fidelity (assuming uniform distribution of measurement bases). An interesting
result is that if one uses two qubits in the same state as a program the
average fidelity is higher than if he/she takes the second program qubit in the
orthogonal state (with respect to the first one). The average information
obtainable by the proposed measurements is also calculated and it is shown that
it can get different values even if the average fidelity stays constant.
Possible experimental realization of the simplest proposed device is presented.


title: Irreversible Quantum Baker Map

abstract:
  We propose a generalization of the model of classical baker map on the torus,
in which the images of two parts of the phase space do overlap. This
transformation is irreversible and cannot be quantized by means of a unitary
Floquet operator. A corresponding quantum system is constructed as a completely
positive map acting in the space of density matrices. We investigate spectral
properties of this super-operator and their link with the increase of the
entropy of initially pure states.


title:
Maximal entanglement of squeezed vacuum states via swapping with
  number-phase measurement

abstract:
  We propose a method to refine entanglement via swapping from a pair of
squeezed vacuum states by performing the Bell measurement of number sum and
phase difference. The resultant states are maximally entangled by adjusting the
two squeezing parameters to the same value. We then describe the teleportation
of number states by using the entangled states prepared in this way.


title:
Dynamics of quantum adiabatic evolution algorithm for Number
  Partitioning

abstract:
  We have developed a general technique to study the dynamics of the quantum
adiabatic evolution algorithm applied to random combinatorial optimization
problems in the asymptotic limit of large problem size $n$. We use as an
example the NP-complete Number Partitioning problem and map the algorithm
dynamics to that of an auxilary quantum spin glass system with the slowly
varying Hamiltonian. We use a Green function method to obtain the adiabatic
eigenstates and the minimum excitation gap, $g_{\rm min}={\cal O}(n 2^{-n/2})$,
corresponding to the exponential complexity of the algorithm for Number
Partitioning. The key element of the analysis is the conditional energy
distribution computed for the set of all spin configurations generated from a
given (ancestor) configuration by simulteneous fipping of a fixed number of
spins. For the problem in question this distribution is shown to depend on the
ancestor spin configuration only via a certain parameter related to the energy
of the configuration. As the result, the algorithm dynamics can be described in
terms of one-dimenssional quantum diffusion in the energy space. This effect
provides a general limitation on the power of a quantum adiabatic computation
in random optimization problems. Analytical results are in agreement with the
numerical simulation of the algorithm.


title: Time problem in quantum mechanics and weak measurements

abstract:
  A question of the time the system spends in the specified state, when the
final state of the system is given, is raised. The model of weak measurements
is used to obtain the expression for the time. The conditions for determination
of such a time are obtained.


title:
Influence of the finite duration of the measurement on the quantum Zeno
  effect

abstract:
  We analyze the influence of the finite duration of the measurement on the
quantum Zeno effect, using a simple model of the measurement. It is shown that
the influence of the finite duration of the measurement is uninportant when
this duration is small compared to the duration of the free evolution between
the measurements.


title: Matter-wave interferometer for large molecules

abstract:
  We demonstrate a near-field Talbot-Lau interferometer for C-70 fullerene
molecules. Such interferometers are particularly suitable for larger masses.
Using three free-standing gold gratings of one micrometer period and a
transversally incoherent but velocity-selected molecular beam, we achieve an
interference fringe visibility of 40 % with high count rate. Both the high
visibility and its velocity dependence are in good agreement with a quantum
simulation that takes into account the van der Waals interaction of the
molecules with the gratings and are in striking contrast to a classical moire
model.


title: Towards symmetric scheme for superdense coding between multiparties

abstract:
  Recently Liu, Long, Tong and Li [Phys. Rev. A 65, 022304 (2002)] have
proposed a scheme for superdense coding between multiparties. This scheme seems
to be highly asymmetric in the sense that only one sender effectively exploits
entanglement. We show that this scheme can be modified in order to allow more
senders to benefit of the entanglement enhanced information transmission.


title: High-fidelity quantum logic operations using linear optical elements

abstract:
  Knill, Laflamme, and Milburn [Nature 409, 46 (2001)] have shown that quantum
logic operations can be performed using linear optical elements and additional
ancilla photons. Their approach is probabilistic in the sense that the logic
devices fail to produce an output with a failure rate that scales as 1/n, where
n is the number of ancilla. Here we present an alternative approach in which
the logic devices always produce an output with an intrinsic error rate that
scales as 1/n^2,which may have several advantages in quantum computing
applications.


title: Variational-Iterative Solution of Ground State for Central Potential

abstract:
  The newly developed iterative method based on Green function defined by
quadratures along a single trajectory is combined with the variational method
to solve the ground state quantum wave function for central potentials. As an
example, the method is applied to discuss the ground state solution of Yukawa
potential, using Hulthen solution as the trial function.


title: Entanglement in a simple quantum phase transition

abstract:
  What entanglement is present in naturally occurring physical systems at
thermal equilibrium? Most such systems are intractable and it is desirable to
study simple but realistic systems which can be solved. An example of such a
system is the 1D infinite-lattice anisotropic XY model. This model is exactly
solvable using the Jordan-Wigner transform, and it is possible to calculate the
two-site reduced density matrix for all pairs of sites. Using the two-site
density matrix, the entanglement of formation between any two sites is
calculated for all parameter values and temperatures. We also study the
entanglement in the transverse Ising model, a special case of the XY model,
which exhibits a quantum phase transition. It is found that the next-nearest
neighbour entanglement (though not the nearest-neighbour entanglement) is a
maximum at the critical point. Furthermore, we show that the critical point in
the transverse Ising model corresponds to a transition in the behaviour of the
entanglement between a single site and the remainder of the lattice.


title:
Synthesis and tomographic characterization of the displaced Fock state
  of light

abstract:
  Displaced Fock states of the electromagnetic field have been synthesized by
overlapping the pulsed optical single-photon Fock state |1> with coherent
states on a high-reflection beamsplitter and completely characterized by means
of quantum homodyne tomography. The reconstruction reveals highly non-classical
properties of displaced Fock states, such as negativity of the Wigner function
and photon number oscillations. This is the first time complete tomographic
reconstruction has been performed on a highly non-classical optical state.


title:
Quantum-optical catalysis: generating "Schroedinger kittens" by means of
  linear optics

abstract:
  We report preparation and characterization of coherent superposition states t
|0> + alpha |1> of electromagnetic field by conditional measurements on a
beamsplitter. The state is generated in one of the beam splitter output
channels if a coherent state and a single-photon Fock state |1> are present in
the two input ports and a single photon is registered in the other beam
splitter output. The single photon thus plays a role of a "catalyst": it is
explicitly present in both the input and the output channels of the interaction
yet facilitates generation of a nonclassical state of light.


title:
Distinguishing locally of quantum states and the distillation of
  entanglement

abstract:
  This paper try to probe the relation of distinguishing locally and
distillation of entanglement. The distinguishing information (DI) and the
maximal distinguishing information (MDI) of a set of pure states are defined.
The interpretation of distillation of entanglement in term of information is
given. The relation between the maximal distinguishing information and
distillable entanglement is gained. As a application of this relation the
distillable entanglement of Bell-diagonal states is present.


title: A quantum stochastic approach to the spectrum of a two-level atom

abstract:
  By means of quantum stochastic calculus we construct a model for an atom with
two degenerate levels and stimulated by a laser and we compute its fluorescence
spectrum; let us stress that, once the model for the unitary atom-field
dynamics has been given, then the spectrum is computed without further
approximations. If only the absorption/emission term is included in the
interaction, we reobtain the Mollow spectrum in the case of a monochromatic
laser and the Kimble-Mandel spectrum in the case of a "phase diffusion model"
for a non monochromatic laser. However, our model can describe also another
type of light scattering, a "direct scattering" due to the response of the atom
as a whole, which we expect to be small, but which interferes with the
scattering due to the absorption/emission channel. When both the scattering
channels are introduced we obtain a modification of the Mollow-Kimble-Mandel
spectrum, which shares the main features with the usual case, but which
presents some asymmetries even in the case of no detuning.


title:
Quantum properties of transverse pattern formation in second-harmonic
  generation

abstract:
  We investigate the spatial quantum noise properties of the one dimensional
transverse pattern formation instability in intra-cavity second-harmonic
generation. The Q representation of a quasi-probability distribution is
implemented in terms of nonlinear stochastic Langevin equations. We study these
equations through extensive numerical simulations and analytically in the
linearized limit. Our study, made below and above the threshold of pattern
formation, is guided by a microscopic scheme of photon interaction underlying
pattern formation in second-harmonic generation. Close to the threshold for
pattern formation, beams with opposite direction of the off-axis critical wave
numbers are shown to be highly correlated. This is observed for the fundamental
field, for the second harmonic field and also for the cross-correlation between
the two fields. Nonlinear correlations involving the homogeneous transverse
wave number, which are not identified in a linearized analysis, are also
described. The intensity differences between opposite points of the far fields
are shown to exhibit sub-Poissonian statistics, revealing the quantum nature of
the correlations. We observe twin beam correlations in both the fundamental and
second-harmonic fields, and also nonclassical correlations between them.


title: Efficient Universal Leakage Elimination for Physical and Encoded Qubits

abstract:
  Decoherence-induced leakage errors can couple a physical or encoded qubit to
other levels, thus potentially damaging the qubit. They can therefore be very
detrimental in quantum computation and require special attention. Here we
present a general method for removing such errors by using simple decoupling
and recoupling pulse sequences. The proposed gates are experimentally
accessible in a variety of promising quantum computing proposals.


title: Decoherence in the Heisenberg model

abstract:
  We study a simplified Heisenberg spin model in order to clarify the idea of
decoherence in closed quantum systems. For this purpose, we define a new
concept: the decoherence function \Xi(t), which describes the dynamics of
decoherence in the whole system, and which is linked with the total (von
Neumann) entropy of all particles. As expected, decoherence is understood both
as a statistical process that is caused by the dynamics of the system, and also
as a matter of entropy. Moreover, the concept of decoherence time is applicable
in closed systems and we have solved its behaviour in the Heisenberg model with
respect to particle number N, density \rho and spatial dimension D in a 1/r
-type of potential. We have also studied the Poincare recurrences occurring in
these types of systems: in an N=1000 particle system the recurrence time is
close to the order of the age of the universe. This encourages us to conclude
that decoherence is the solution for quantum-classical problems not only in
practice, but also in principle.


title: On the notion of the photon

abstract:
  It is shown that the photon, the quantum of electromagnetic field, allows the
consideration in the framework of the scheme which in some aspects is typical
for the phonon, an excitation of the crystal lattice of a solid. The conclusion
is drawn that the photon may be interpreted as an elementary excitation in a
fine-grained space. The corollary is in excellent agreement with the space
structure and submicroscopic quantum mechanics, which have recently been
constructed by the author in a series of works.


title: Optimization of security costs in nested purification protocol

abstract:
  We analyse security costs in one segment of nested purification protocol in a
large quantum cryptography network, employing the quantum switchers and
repeaters. We demonstrate that exponential or even super-exponential grow of
entanglement resources occurs in dependence on number of the network switchers.
For this reason, an optimization in the nested strategy is suggested,
preventing a stronger than the exponential grow of entanglement resources.


title:
Continuous variable teleportation as a generalized thermalizing quantum
  channel

abstract:
  A quantum channel is derived for continuous variable teleportation which is
performed by means of an arbitrary entangled state and the standard protocol.
When a Gaussian entangled state such as a two-mode squeezed-vacuum state is
used, the continuous variable teleportation is equivalent to the thermalizing
quantum channel. Continuous variable dense coding is also considered. Both the
continuous variable teleportation and the continuous variable dense coding are
characterized by the same function determined by the entangled state and the
quantum measurement.


title: Quantum learning and universal quantum matching machine

abstract:
  Suppose that three kinds of quantum systems are given in some unknown states
$\ket f^{\otimes N}$, $\ket{g_1}^{\otimes K}$, and $\ket{g_2}^{\otimes K}$, and
we want to decide which \textit{template} state $\ket{g_1}$ or $\ket{g_2}$,
each representing the feature of the pattern class ${\cal C}_1$ or ${\cal
C}_2$, respectively, is closest to the input \textit{feature} state $\ket f$.
This is an extension of the pattern matching problem into the quantum domain.
Assuming that these states are known a priori to belong to a certain parametric
family of pure qubit systems, we derive two kinds of matching strategies. The
first is a semiclassical strategy which is obtained by the natural extension of
conventional matching strategies and consists of a two-stage procedure:
identification (estimation) of the unknown template states to design the
classifier (\textit{learning} process to train the classifier) and
classification of the input system into the appropriate pattern class based on
the estimated results. The other is a fully quantum strategy without any
intermediate measurement which we might call as the {\it universal quantum
matching machine}. We present the Bayes optimal solutions for both strategies
in the case of K=1, showing that there certainly exists a fully quantum
matching procedure which is strictly superior to the straightforward
semiclassical extension of the conventional matching strategy based on the
learning process.


title: Quantum Zeno effect, adiabaticity and dynamical superselection rules

abstract:
  The evolution of a quantum system undergoing very frequent measurements takes
place in a proper subspace of the total Hilbert space (quantum Zeno effect).
When the measuring apparatus is included in the quantum description, the Zeno
effect becomes a pure consequence of the dynamics. We show that for continuous
measurement processes the quantum Zeno evolution derives from an adiabatic
theorem. The system is forced to evolve in a set of orthogonal subspaces of the
total Hilbert space and a dynamical superselection rule arises. The dynamical
properties of this evolution are investigated and several examples are
considered.


title: Photons uncertainty removes Einstein-Podolsky-Rosen paradox

abstract:
  Einstein, Podolsky and Rosen (EPR) argued that the quantum-mechanical
probabilistic description of physical reality had to be incomplete, in order to
avoid an instantaneous action between distant measurements. This suggested the
need for additional "hidden variables", allowing for the recovery of
determinism and locality, but such a solution has been disproved
experimentally. Here, I present an opposite solution, based on the greater
indeterminism of the modern quantum theory of Particle Physics, predicting that
the number of photons is always uncertain. No violation of locality is allowed
for the physical reality, and the theory can fulfill the EPR criterion of
completeness.


title: Grover's search algorithm and the quantum measurement problem

abstract:
  It is suggested that the individual outcomes of a measurement process can be
understood within standard quantum mechanics in terms of the measuring
apparatus, treated as a quantum computer, executing Grover's search algorithm.


title:
Decoherence of Two-Level Systems Can Be Very Different From Brownian
  Particles

abstract:
  In quantum computation, it is of paramount importance to locate the parameter
space where maximal coherence can be preserved in the qubit system. In recent
years environment-induced decoherence based the quantum Brownian motion (QBM)
models have been applied to two level systems (2LS) interacting with an
electromagnetic field, leading to the general belief that 2LS are easily
decohered. In a recent paper C. Anastopoulos and B. L. Hu [Phys. Rev. A62,
(2000) 033821] derived a new exact non-Markovian master equation at zero
temperature, from which they showed that this belief is actually misplaced. For
a two-level atom (2LA)- electromagnetic field (EMF) system the decoherence time
is rather long, comparable to the relaxation time. Theoretically this is
because the dominant interaction is the $\hat \sigma_{\pm}$ type of coupling
between the two levels (what constitutes the qubit) and the field, not the
$\hat \sigma_z$ type, which shows the QBM behavior. Depending on the coupling
the field can act as a resonator (in an atom cavity) or as a bath (in QBM) and
produce very different decoherent behavior in the system. This is not new to
Cavity QED experimentalists: the 2LA-EMF system maintaining its coherence in
sufficiently long duration is the reason why they can manipulate them so well
to show interesting quantum coherence effects.


title: Measurement of the Casimir force between parallel metallic surfaces

abstract:
  We report on the measurement of the Casimir force between conducting surfaces
in a parallel configuration. The force is exerted between a silicon cantilever
coated with chromium and a similar rigid surface and is detected looking at the
shifts induced in the cantilever frequency when the latter is approached. The
scaling of the force with the distance between the surfaces was tested in the
0.5 - 3.0 $\mu$m range, and the related force coefficient was determined at the
15% precision level.


title:
Counterexample to an additivity conjecture for output purity of quantum
  channels

abstract:
  A conjecture arising naturally in the investigation of additivity of
classical information capacity of quantum channels states that the maximal
purity of outputs from a quantum channel, as measured by the p-norm, should be
multiplicative with respect to the tensor product of channels. We disprove this
conjecture for p>4.79. The same example (with p=infinity) also disproves a
conjecture for the multiplicativity of the injective norm of Hilbert space
tensor products.


title: Hiding classical data in multi-partite quantum states

abstract:
  We present a general technique for hiding a classical bit in multipartite
quantum states. The hidden bit, encoded in the choice of one of two possible
density operators, cannot be recovered by local operations and classical
communication without quantum communication. The scheme remains secure if
quantum communication is allowed between certain partners, and can be designed
for any choice of quantum communication patterns to be secure, but to allow
near perfect recovery for all other patterns. The maximal probability of
unwanted recovery of the hidden bit, as well as the maximal error for allowed
recovery operations can be chosen to be arbitrarily small, given sufficiently
high dimensional systems at each site. No entanglement is needed since the
hiding states can be chosen to be separable. A single ebit of prior
entanglement is not sufficient to break the scheme.


title:
On the generation of sequential unitary gates from continuous time
  Schrodinger equations driven by external fields

abstract:
  In all the various proposals for quantum computers, a common feature is that
the quantum circuits are expected to be made of cascades of unitary
transformations acting on the quantum states. A framework is proposed to
express these elementary quantum gates directly in terms of the control inputs
entering into the continuous time forced Schrodinger equation.


title: On the function sum(-k^2/s^2)

abstract:
  Some properties of the function$ \psi (s)=\sum\limits_{k=-\infty}^\infty {%
\exp (-\frac{{k^2}}{{s^2}}})$ are studied, and an interpolation formula is
given.


title: Can there be quantum correlations in a mixture of two separable states?

abstract:
  We use a recently proposed measure of quantum correlations (work deficit), to
measure the strength of the nonlocality of an equal mixture of two bipartite,
orthogonal, but locally indistinguishable separable states. This gives
supporting evidence of nonzero value for a separable state, for this measure of
nonlocality. We also show that this measure of quantum correlations places a
different order on the set of states, than the good asymptotic measures of
entanglement. And that such a different order imposed on two states by the work
deficit and any entanglement measure, cannot be explained by mixedness alone.


title:
Stabilization of Quantum Information: A Unified Dynamical-Algebraic
  Approach

abstract:
  The notion of symmetry is shown to be at the heart of all error
correction/avoidance strategies for preserving quantum coherence of an open
quantum system S e.g., a quantum computer. The existence of a non-trivial group
of symmetries of the dynamical algebra of S provides state-space sectors immune
to decoherence. Such noiseless sectors, that can be viewed as a noncommutative
version of the pointer basis, are shown to support universal quantum
computation and to be robust against perturbations. When the required symmetry
is not present one can generate it artificially resorting to active
symmetrization procedures.


title:
Discrete Time Leads to Quantum-Like Interference of Deterministic
  Particles

abstract:
  In this note we demonstrate that a quantum-like interference picture could
appear as a statistical effect of interference of deterministic particles, i.e.
particles that have trajectories and obey deterministic equations, if one
introduces a discrete time. The nature of the resulting interference picture
does not follow from the geometry of force field, but is strongly attached to
the time discreetness parameter. As a demonstration of this concept we consider
a scattering of charged particles on the charged screen with a single slit. The
resulting interference picture has a nontrivial minimum-maximum distribution
which vanishes as the time discreetness parameter goes to zero that could be
interpreted as an analog of quantum decoherence.


title: Entangled Quantum Networks

abstract:
  We present some results from simulation of a network of nodes connected by
c-NOT gates with nearest neighbors. Though initially we begin with pure states
of varying boundary conditions, the updating with time quickly involves a
complicated entanglement involving all or most nodes. As a normal c-NOT gate,
though unitary for a single pair of nodes, seems to be not so when used in a
network in a naive way, we use a manifestly unitary form of the transition
matrix with c?-NOT gates, which invert the phase as well as flipping the qubit.
This leads to complete entanglement of the net, but with variable coefficients
for the different components of the superposition. It is interesting to note
that by a simple logical back projection the original input state can be
recovered in most cases. We also prove that it is not possible for a sequence
of unitary operators working on a net to make it move from an aperiodic regime
to a periodic one, unlike some classical cases where phase-locking happens in
course of evolution. However, we show that it is possible to introduce by hand
periodic orbits to sets of initial states, which may be useful in forming
dynamic pattern recognition systems.


title: On the Entanglement Properties of Two-Rebits Systems

abstract:
  Following the recent work of Caves, Fuchs, and Rungta [Found. of Phys. Lett.
{\bf 14} (2001) 199], we discuss some entanglement properties of two-rebits
systems. We pay particular attention to the relationship between entanglement
and purity. In particular, we determine (i) the probability densities for
finding pure and mixed states with a given amount of entanglement, and (ii) the
mean entanglement of two-rebits states as a function of the participation
ratio.


title: Inhibiting decoherence via ancilla processes

abstract:
  General conditions are derived for preventing the decoherence of a single
two-state quantum system (qubit) in a thermal bath. The employed auxiliary
systems required for this purpose are merely assumed to be weak for the general
condition while various examples such as extra qubits and extra classical
fields are studied for applications in quantum information processing. The
general condition is confirmed with well known approaches towards inhibiting
decoherence. A novel approach for decoherence-free quantum memories and quantum
operations is presented by placing the qubit into the center of a sphere with
extra qubits on its surface.


title:
Stationary cantilever vibrations in the oscillating cantilever-driven
  adiabatic reversals -- magnetic resonance force microscopy technique

abstract:
  We consider theoretically the novel technique in magnetic resonance force
microscopy which is called ``oscillating cantilever-driven adiabatic
reversals''. We present analytical and numerical analysis for the stationary
cantilever vibrations in this technique. For reasonable values of parameters we
estimate the resonant frequency shift as 6Hz per the Bohr magneton. We analyze
also the regime of small oscillations of the paramagnetic moment near the
transversal plane and the frequency shift of the damped cantilever vibrations.


title: High-Order Variational Perturbation Theory for the Free Energy

abstract:
  In this paper we introduce a generalization to the algebraic Bender-Wu
recursion relation for the eigenvalues and the eigenfunctions of the anharmonic
oscillator. We extend this well known formalism to the time-dependent quantum
statistical Schroedinger equation, thus obtaining the imaginary-time evolution
amplitude by solving a recursive set of ordinary differential equations. This
approach enables us to evaluate global and local quantum statistical quantities
of the anharmonic oscillator to much higher orders than by evaluating Feynman
diagrams. We probe our perturbative results by deriving a perturbative
expression for the free energy which is then subject to variational
perturbation theory as developed by Kleinert, yielding convergent results for
the free energy for all values of the coupling strength.


title: Spin squeezing and entanglement in spinor-1 condensates

abstract:
  We analyze quantum correlation properties of a spinor-1 (f=1) Bose Einstein
condensate using the Gell-Mann realization of SU(3) symmetry. We show that
previously discussed phenomena of condensate fragmentation and spin-mixing can
be explained in terms of the hypercharge symmetry. The ground state of a
spinor-1 condensate is found to be fragmented for ferromagnetic interactions.
The notion of two bosonic mode squeezing is generalized to the two spin (U-V)
squeezing within the SU(3) formalism. Spin squeezing in the isospin subspace
(T) is found and numerically investigated. We also provide new results for the
stationary states of spinor-1 condensates.

categories: quant-ph cond-mat hep-th math-ph math.MP nucl-th


title:
Direct estimations of linear and non-linear functionals of a quantum
  state

abstract:
  We present a simple quantum network, based on the controlled-SWAP gate, that
can extract certain properties of quantum states without recourse to quantum
tomography. It can be used used as a basic building block for direct quantum
estimations of both linear and non-linear functionals of any density operator.
The network has many potential applications ranging from purity tests and
eigenvalue estimations to direct characterization of some properties of quantum
channels. Experimental realizations of the proposed network are within the
reach of quantum technology that is currently being developed.


title: Maxwell's demon and the thermodynamics of computation

abstract:
  It is generally accepted, following Landauer and Bennett, that the process of
measurement involves no minimum entropy cost, but the erasure of information in
resetting the memory register of a computer to zero requires dissipating heat
into the environment. This thesis has been challenged recently in a two-part
article by Earman and Norton. I review some relevant observations in the
thermodynamics of computation and argue that Earman and Norton are mistaken:
there is in principle no entropy cost to the acquisition of information, but
the destruction of information does involve an irreducible entropy cost.


title: Quantum Potential and Random Phase - Space Dynamics

abstract:
  We analyze limitations upon any kinetic theory inspired derivation of a
probabilistic counterpart of the Schr\"{o}dinger picture quantum dynamics.
Neither dissipative nor non-dissipative stochastic phase-space processes based
on the white-noise (Brownian motion) kinetics are valid candidates unless
additional constraints (a suitable form of the energy conservation law) are
properly incorporated in the formalism.


title:
Unpredictability of wave function's evolution in nonintegrable quantum
  systems

abstract:
  It is shown that evolution of wave functions in nonintegrable quantum systems
is unpredictable for a long time T because of rapid growth of number of
elementary computational operations $\mathcal O(T)\sim T^\alpha$. On the other
hand, the evolution of wave functions in integrable systems can be predicted by
the fast algorithms $\mathcal O(T)\sim (log_2 T)^\beta$ for logarithmically
short time and thus there is an algorithmic "compressibility" of their
dynamics. The difference between integrable and nonintegrable systems in our
approach looks identically for classical and quantum systems. Therefore the
minimal number of bit operations $\mathcal O(T)$ needed to predict a state of
system for time interval T can be used as universal sign of chaos.


title: The Quantum Universe

abstract:
  On the basis that the universe is a closed quantum system with no external
observers, we propose a paradigm in which the universe jumps through a series
of stages. Each stage is defined by a quantum state, an information content,
and rules governing temporal evolution. Only some of these rules are currently
understood; we can calculate answers to quantum questions, but we do not know
why those questions have been asked in the first place. In this paradigm, time
is synonymous with the quantum process of information extraction, rather than a
label associated with a temporal dimension. We discuss the implications for
cosmology.


title:
Three-body dynamics in one dimension: A test model for the 3-Nucleon
  system with irreducible pionic diagrams

abstract:
  We formulate the three-body problem in one dimension in terms of the
(Faddeev-type) integral equation approach. As an application, we develop a
spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one
dimension. Using simple two-body potentials that reproduce the deuteron
binding, we obtain that the three-body system binds at about 7.5 MeV. We then
consider two types of residual pionic corrections in the dynamical equation;
one related to the 2PI-exchange three-body diagram, the other to the
1PI-exchange three-body diagram. We find that the first contribution can
produce an additional binding effect of about 0.9 MeV. The second term produces
smaller binding effects, which are, however, dependent on the uncertainty in
the off-shell extrapolation of the two-body t-matrix. This presents interesting
analogies with what occurs in three dimensions. The paper also discusses the
general three-particle quantum scattering problem, for motion restricted to the
full line.


title: Nonlinear dynamics in quantum physics- the study of quantum chaos

abstract:
  We use the quantum action to study the dynamics of quantum system at finite
temperature. We construct the quantum action non-perturbatively and find
temperature dependent action parameters. Here we apply the quantum action to
study quantum chaos. We present a numerical study of a classically chaotic 2-D
Hamiltonian system - harmonic oscillators with anharmonic coupling. We compare
Poincar\'e sections for the quantum action at finite temperature with those of
classical action.


title:
Mapping a quantum state of light onto a long-lived atomic spin state:
  towards quantum memory

abstract:
  We report an experiment on mapping a quantum state of light onto the ground
state spin of an ensemble of Cs atoms with the life time of 2 milliseconds.
Quantum memory for one of the two quadrature phase operators of light is
demonstrated with vacuum and squeezed states of light. The sensitivity of the
mapping procedure at the level of approximately one photon/sec per Hz is shown.
The results pave the road towards complete (storing both quadrature phase
observables) quantum memory for Gaussian states of light. The experiment also
sheds new light on fundamental limits of sensitivity of the magneto-optical
resonance method.


title: Wavepacket reconstruction via local dynamics in a parabolic lattice

abstract:
  We study the dynamics of a wavepacket in a potential formed by the sum of a
periodic lattice and of a parabolic potential. The dynamics of the wavepacket
is essentially a superposition of ``local Bloch oscillations'', whose frequency
is proportional to the local slope of the parabolic potential. We show that the
amplitude and the phase of the Fourier transform of a signal characterizing
this dynamics contains information about the amplitude and the phase of the
wavepacket at a given lattice site. Hence, {\em complete} reconstruction of the
the wavepacket in the real space can be performed from the study of the
dynamics of the system.


title:
Gauge P-representations for quantum-dynamical problems: Removal of
  boundary terms

abstract:
  P representation techniques, which have been very successful in quantum
optics and in other fields, are also useful for general bosonic quantum
dynamical many-body calculations such as Bose-Einstein condensation. We
introduce a representation called the gauge P representation which greatly
widens the range of tractable problems. Our treatment results in an infinite
set of possible time-evolution equations, depending on arbitrary gauge
functions that can be optimized for a given quantum system. In some cases,
previous methods can give erroneous results, due to the usual assumption of
vanishing boundary conditions being invalid for those particular systems.
Solutions are given to this boundary-term problem for all the cases where it is
known to occur: two-photon absorption and the single-mode laser. We also
provide some brief guidelines on how to apply the stochastic gauge method to
other systems in general, quantify the freedom of choice in the resulting
equations, and make a comparison to related recent developments.


title:
Adiabatic creation of entangled states by a bichromatic field designed
  from the topology of the dressed eigenenergies

abstract:
  Preparation of entangled pairs of coupled two-state systems driven by a
bichromatic external field is studied. We use a system of two coupled spin-1/2
that can be translated into a three-state ladder model whose intermediate state
represents the entangled state. We show that this entangled state can be
prepared in a robust way with appropriate fields. Their frequencies and
envelopes are derived from the topological properties of the model.


title: Application of quantum inequalities to quantum optics

abstract:
  We establish a connection between quantum inequalities (known from quantum
field theory on curved spacetimes) and the degree of squeezing in
quantum-optical experiments. We prove an inequality which binds the reduction
of the electric-field fluctuations to their duration. The bigger the level of
fluctuations-suppression the shorter its duration. As an example of the
application of this inequality in the case of squeezed light whose phase is
controlled with 1% accuracy we derive a limit of -15dB on the allowed degree of
squeezing.


title: Can the states of the W-class be suitable for teleportation

abstract:
  Entangled states of the W-class are considered as a quantum channel for
teleportation or the states to be sent. The protocols have been found by
unitary transformation of the schemes, based on the multiuser GHZ channel. The
main feature of the W-quantum channels is a set of non-local operators, that
allow receivers recovering unknown state.


title: Rate-equation approach to atomic-laser light statistics

abstract:
  We consider three- and four-level atomic lasers that are either incoherently
(unidirectionally) or coherently (bidirectionally) pumped, the single-mode
cavity being resonant with the laser transition. The intra-cavity Fano factor
and the photo-current spectral density are evaluated on the basis of rate
equations.
  According to that approach, fluctuations are caused by jumps in active and
detecting atoms. The algebra is considerably simpler than the one required by
Quantum-Optics treatments.
  Whenever a comparison can be made, the expressions obtained coincide. The
conditions under which the output light exhibits sub-Poissonian statistics are
considered in detail. Analytical results, based on linearization, are verified
by comparison with Monte Carlo simulations. An essentially exhaustive
investigation of sub-Poissonian light generation by three- and four-level atoms
lasers has been performed. Only special forms were reported earlier.


title: Towards Quantum Information Theory in Space and Time

abstract:
  Modern quantum information theory deals with an idealized situation when the
spacetime dependence of quantum phenomena is neglected. However the
transmission and processing of (quantum) information is a physical process in
spacetime. Therefore such basic notions in quantum information theory as qubit,
channel, composite systems and entangled states should be formulated in space
and time. In particlular we suggest that instead of a two level system (qubit)
the basic notion in a relativistic quantum information theory should be a
notion of an elementary quantum system, i.e. an infinite dimensional Hilbert
space $H$ invariant under an irreducible representation of the Poincare group
labeled by $[m,s]$ where $m\geq 0$ is mass and $s=0,1/2,1,...$ is spin. We
emphasize an importance of consideration of quantum information theory from the
point of view of quantum field theory. We point out and discuss a fundamental
fact that in quantum field theory there is a statistical dependence between two
regions in spacetime even if they are spacelike separated. A classical
probabilistic representation for a family of correlation functions in quantum
field theory is obtained. Entangled states in space and time are considered. It
is shown that any reasonable state in relativistic quantum field theory becomes
disentangled (factorizable) at large spacelike distances if one makes local
observations. As a result a violation of Bell`s inequalities can be observed
without inconsistency with principles of relativistic quantum theory only if
the distance between detectors is rather small. We suggest a further
experimental study of entangled states in spacetime by studying the dependence
of the correlation functions on the distance between detectors.


title:
On the coherence veryfication of the continuous variable state in Fock
  space

abstract:
  Almost all novel observable phenomena in quantum optics are related to the
quantum coherence. The coherence here is determined by the relative phase
inside a state. Unfortunately, so far all the relevant experimental results in
quantum optics are insensitive to the phase information of the coherent state.
Lack of phase information may cause serious consequences in many problems in
quantum optics. For example, an ensemble of two mode squeezed states is a
classical ensemble if the phase in each state is totally random; but it is a
non-classical ensemble if the phase in each state is fixed. As a timly
application, verification of this type of phase information in an ensemble of
two mode squeezed states from the conventional laser is crucial to the validity
of the continuous variavable quantum teleportation(CVQT) experiment. Here we
give a simple scheme to distinguish two different ensemble of states: the
Rudolph-Sanders ensemble, by which each squeezed states emitted has a uniform
distribution from $0-2\pi$ on the phase value; and the van Enk-Fuchs ensemble,
which emmits identical states with a fixed(but unknown) phase for every state.
We believe our proposal can help to give a clear picture on whether the
existing two mode squeezed states so far are indeed non-classical states which
can be used as the entanglement resource.


title: A Zeno Story

abstract:
  I describe the early (1974--75) work I did on what is now called the Zeno
problem in quantum mechanics. Then I propose a new formulation which may
obviate a vexing problem of operator limits and which also may be more
measurement-compatible.


title: Quantum entropy and special relativity

abstract:
  We consider a single free spin 1/2 particle. The reduced density matrix for
its spin is not covariant under Lorentz transformations. The spin entropy is
not a relativistic scalar and has no invariant meaning.


title: Computing the Noncomputable

abstract:
  We explore in the framework of Quantum Computation the notion of
computability, which holds a central position in Mathematics and Theoretical
Computer Science. A quantum algorithm that exploits the quantum adiabatic
processes is considered for the Hilbert's tenth problem, which is equivalent to
the Turing halting problem and known to be mathematically noncomputable.
Generalised quantum algorithms are also considered for some other mathematical
noncomputables in the same and of different noncomputability classes. The key
element of all these algorithms is the measurability of both the values of
physical observables and of the quantum-mechanical probability distributions
for these values. It is argued that computability, and thus the limits of
Mathematics, ought to be determined not solely by Mathematics itself but also
by physical principles.


title: Efficient Simulation of Quantum State Reduction

abstract:
  The energy-based stochastic extension of the Schrodinger equation is a rather
special nonlinear stochastic differential equation on Hilbert space, involving
a single free parameter, that has been shown to be very useful for modelling
the phenomenon of quantum state reduction. Here we construct a general closed
form solution to this equation, for any given initial condition, in terms of a
random variable representing the terminal value of the energy and an
independent Brownian motion. The solution is essentially algebraic in
character, involving no integration, and is thus suitable as a basis for
efficient simulation studies of state reduction in complex systems.


title: Wavepackets falling under a mirror

abstract:
  We depict and analyze a new effect for wavepackets falling freely under a
barrier or well. The effect appears for wavepackets whose initial spread is
smaller than the combination $\ds \sqrt{\frac{l_g^3}{|z_0|}}$, between the
gravitational length scale $\ds l_g = \frac{1}{(2 m^2 g)^{1/3}}$ and the
initial location of the packet $z_0$. It consists of a diffractive structure
that is generated by the falling and spreading wavepacket and the waves
reflected from the obstacle. The effect is enhanced when the Gross-Pitaevskii
interaction for positive scattering length is included. The theoretical
analysis reproduces the essential features of the effect. Experiments emanating
from the findings are proposed.


title: Bounds on entanglement in qudit subsystems

abstract:
  The entanglement in a pure state of N qudits (d-dimensional distinguishable
quantum particles) can be characterised by specifying how entangled its
subsystems are. A generally mixed subsystem of m qudits is obtained by tracing
over the other N-m qudits. We examine the entanglement in the space of mixed
states of m qudits. We show that for a typical pure state of N qudits, its
subsystems smaller than N/3 qudits will have a positive partial transpose and
hence are separable or bound entangled. Additionally, our numerical results
show that the probability of finding entangled subsystems smaller than N/3
falls exponentially in the dimension of the Hilbert space. The bulk of pure
state Hilbert space thus consists of highly entangled states with multipartite
entanglement encompassing at least a third of the qudits in the pure state.


title:
Quantum nonlocality and applications in quantum-information processing
  of hybrid entangled states

abstract:
  The hybrid entangled states generated, e.g., in a trapped-ion or atom-cavity
system, have exactly one ebit of entanglement, but are not maximally entangled.
We demonstrate this by showing that they violate, but in general do not
maximally violate, Bell's inequality due to Clauser, Horne, Shimony and Holt.
These states are interesting in that they exhibit the entanglement between two
distinct degrees of freedom (one is discrete and another is continuous). We
then demonstrate these entangled states as a valuable resource in quantum
information processing including quantum teleportation, entanglement swapping
and quantum computation with "parity qubits". Our work establishes an
interesting link between quantum information protocols of discrete and
continuous variables.


title: Lower Bound for entanglement cost of antisymmetric states

abstract:
  This report gives a lower bound of entanglement cost for antisymmetric states
of bipartite d-level systems to be log_2 (d/(d-1)) ebit (for d=3, E_c >=
0.585...). The paper quant-ph/0112131 claims that the value is equal to one
ebit for d=3, since all of the eigenvalues of reduced matrix of any pure states
living in N times tensor product of antisymmetric space is not greater than
2^(-N) thus the von Neumann entropy is not less than N, but the proof is not
true. Hence whether the value is equal to or less than one ebit is not clear at
this moment.


title:
Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations
  with true probability distribution functions

abstract:
  Traditionally, the quantum Brownian motion is described by Fokker-Planck or
diffusion equations in terms of quasi-probability distribution functions, e.g.,
Wigner functions. These often become singular or negative in the full quantum
regime. In this paper a simple approach to non-Markovian theory of quantum
Brownian motion using {\it true probability distribution functions} is
presented. Based on an initial coherent state representation of the bath
oscillators and an equilibrium canonical distribution of the quantum mechanical
mean values of their co-ordinates and momenta we derive a generalized quantum
Langevin equation in $c$-numbers and show that the latter is amenable to a
theoretical analysis in terms of the classical theory of non-Markovian
dynamics. The corresponding Fokker-Planck, diffusion and the Smoluchowski
equations are the {\it exact} quantum analogues of their classical
counterparts. The present work is {\it independent} of path integral
techniques. The theory as developed here is a natural extension of its
classical version and is valid for arbitrary temperature and friction
(Smoluchowski equation being considered in the overdamped limit).


title: Quantum contact interactions

abstract:
  The existence of several exotic phenomena, such as duality and spectral
anholonomy is pointed out in one-dimensional quantum wire with a single defect.
The topological structure in the spectral space which is behind these phenomena
is identified.

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