title:
Geometric Phase of electrons due to the Spin-rotation Coupling in
  Rotating C$_{60}$ Molecules

abstract:
  The rapidly rotational motion of C$_{60}$ molecules provides us with an
ingenious way to test Mashhoon's spin-rotation coupling. The spin-rotation
coupling of electrons in the rotating C$_{60}$ molecule is considered in the
present letter. It is shown that the intrinsic spin (gravitomagnetic moment) of
the electron that can be coupled to the time-dependent rotating frequency of
rotating frame of reference (C$_{60}$ molecule) results in a geometric phase,
which may be measured through the electronic energy spectra of C$_{60}$
molecules.


title: Gravitomagnetic Field and Time-Dependent Spin-Rotation Coupling

abstract:
  The Kerr metric of spherically symmetric gravitational field is analyzed
through the coordinate transformation from the rotating frame to fixing frame,
and consequently that the inertial force field (with the exception of the
centrifugal force field) in the rotating system is one part of its
gravitomagnetic field is verified. We investigate the spin-rotation coupling
and, by making use of Lewis-Riesenfeld invariant theory, we obtain exact
solutions of the Schr\"{o}dinger equation of a spinning particle in a
time-dependent rotating reference frame. A potential application of these exact
solutions to the investigation of Earth$^{,}$s rotating frequency fluctuation
by means of neutron-gravity interferometry experiment is briefly discussed in
the present paper.


title: Progressive Decoherence and Total Environmental Disentanglement

abstract:
  The simple stationary decoherence of a two-state quantum system is discussed
from a new viewpoint of environmental entanglement. My work emphasizes that an
unconditional local state must totally be disentangled from the rest of the
universe. It has been known for long that the loss of coherence within the
given local system is gradual. Also the quantum correlations between the local
system and the rest of the universe are being destroyed gradually. I show that,
differently from local decoherence, the process of environmental
disentanglement may terminate in finite time. The time of perfect
disentanglement turns out to be on the decoherence time scale, and in a simple
case we determine the exact value of it.


abstract:
  This is the introductive paper to the volume "Symmetries in Physics:
Philosophical Reflections", Cambridge University Press, 2003. We begin with a
brief description of the historical roots and emergence of the concept of
symmetry that is at work in modern physics. Then, in section 2, we mention the
different varieties of symmetry that fall under this general umbrella,
outlining the ways in which they were introduced into physics. We also
distinguish between two different uses of symmetry: symmetry principles versus
symmetry arguments. In section 3 we make some remarks of a general nature
concerning the status and significance of symmetries in physics. Finally, in
section 4, we outline the structure of the book and the contents of each part.


title: Where was the particle?

abstract:
  The hypothesis of empty/full waves considers that a click in a detector is
triggered by a property carried by the wave-packet that impinges on that
detector. Different authors call this property particle, but according to the
terminology of this hypothesis, the term full wave is used in this text. The
present article discusses the validity of the empty/full waves hypothesis. It
is shown that the energy conservation principle imposes for a full wave a
continuous trajectory from the source to the detector. That gives legitimacy to
the question -- in case the wave function consists in a couple of
space-separated branches -- which wave-packet was a full wave before the click
in the detector, or, in other authors' terminology, where was the particle
before the detector clicked. This question is a counterfactual question. In
some multi-particle experiments, e.g. Hardy's thought-experiment with an
electron and a positron, the combination of the empty/full waves hypothesis and
counterfactual reasoning leads to a contradiction with the predictions of the
quantum theory. However, it is shown here that this contradiction is solvable
if the locality requirement is relaxed. To the difference from the local hidden
variables, it is not possible to prove or disprove the idea of empty/ full
waves, at least at present. But it is possible to ask whether this hypothesis
offers a solution to the quantum puzzles. The answer is negative. For instance
it offers no solution to the before-before loop. The question remains open
whether the empty/full waves hypothesis is correct, or "God plays dice".


title:
Distillation Protocols for Mixed States of Multilevel Qubits and the
  Quantum Renormalization Group

abstract:
  We study several properties of distillation protocols to purify multilevel
qubit states (qudits) when applied to a certain family of initial mixed
bipartite states. We find that it is possible to use qudits states to increase
the stability region obtained with the flow equations to distill qubits. In
particular, for qutrits we get the phase diagram of the distillation process
with a rich structure of fixed points. We investigate the large-$D$ limit of
qudits protocols and find an analytical solution in the continuum limit. The
general solution of the distillation recursion relations is presented in an
appendix. We stress the notion of weight amplification for distillation
protocols as opposed to the quantum amplitude amplification that appears in the
Grover algorithm. Likewise, we investigate the relations between quantum
distillation and quantum renormalization processes.


title: Superluminality in Quantum Theory

abstract:
  In the present work we investigate the possibility of superluminal
information transmission in quantum theory. We give simple and general
arguments to prove that the general structure (Hilbert's space plus
instantaneous state reduction) of the theory allows the existence of
superluminal communication. We discuss how this relates with existing
no-signalling theorems.


title: Relative phase change during quantum operation

abstract:
  Quantum operations represented by completely positive maps encompass many of
the physical processes and have been very powerful in describing quantum
computation and information processing tasks. We introduce the notion of
relative phase change for a quantum system undergoing quantum operation. We
find that the relative phase shift of a system not only depends on the state of
the system, but also depends on the initial state of the ancilla with which it
might have interacted in the past. The relative phase change during a sequence
of quantum operations is shown to be non-additive in nature. This property can
attribute a `memory' to a quantum channel. Also the notion of relative phase
shift helps us to define what we call `in-phase quantum channels'. We will
present the relative phase shift for a qubit undergoing depolarizing channel
and complete randomization and discuss their implications.


title: Entanglement and classical correlations in the quantum frame

abstract:
  The frame of classical probability theory can be generalized by enlarging the
usual family of random variables in order to encompass nondeterministic ones:
this leads to a frame in which two kinds of correlations emerge: the classical
correlation which is coded in the mixed state of the physical system and a new
correlation, to be called probabilistic entanglement, which may occur also at
pure states. We examine to what extent this characterization of correlations
can be applied to quantum mechanics. Explicit calculations on simple examples
outline that a same quantum state can show only classical correlations or only
entanglement depending on its statistical content; situations may also arise in
which the two kinds of correlations compensate each other.


title: Decoherence and Records for the Case of a Scattering Environment

abstract:
  Using non-relativistic many body quantum field theory, a master equation is
derived for the reduced density matrix of a dilute gas of massive particles
undergoing scattering interactions with an environment of light particles. The
dynamical variable that naturally decoheres (the pointer basis) is essentially
the local number density of the dilute gas. Earlier master equations for this
sort of system (such as that derived by Joos and Zeh) are recovered on
restricting to the one-particle sector for the distinguished system. The
derivation shows explicitly that the scattering environment stores information
about the system by ``measuring'' the number density. This therefore provides
an important example of the general connection between decoherence and records
indicated by the decoherent histories approach to quantum theory. It also
brings the master equation for this system into a form emphasizing the role of
local densities, which is relevant to current work on deriving hydrodynamic
equations from quantum theory.


title: Quantum Computing in the Presence of Detected Spontaneous Emission

abstract:
  A new method for quantum computation in the presence of detected spontaneous
emission is proposed. The method combines strong and fast (dynamical
decoupling) pulses and a quantum error correcting code that encodes $n$ logical
qubits into only $n+1$ physical qubits. Universal fault-tolerant quantum
computation is shown to be possible in this scheme using Hamiltonians relevant
to a range of promising proposals for the physical implementation of quantum
computers.


title: Local indistinguishability: more nonlocality with less entanglement

abstract:
  We provide a first operational method for checking indistinguishability of
orthogonal states by local operations and classical communication (LOCC). This
method originates from the one introduced by Ghosh et al. (Phys. Rev. Lett. 87,
5807 (2001) (quant-ph/0106148)), though we deal with pure states. We apply our
method to show that an arbitrary complete multipartite orthogonal basis is
indistinguishable by LOCC, if it contains at least one entangled state. We also
show that probabilistic local distinguishing is possible for full basis if and
only if all vectors are product. We employ our method to prove local
indistinguishability in an example with sets of pure states of 3X3, which shows
that one can have ``more nonlocality with less entanglement'', where ``more
nonlocality'' is in the sense of ``increased local indistinguishability of
orthogonal states''. This example also provides, to our knowledge, the only
known example where d orthogonal states in dXd are locally indistinguishable.


title:
Analytical formula connecting entangled state and the closest
  disentangled state

abstract:
  The separable state closest to a given entangled state in the relative
entropy measure is called the closest disentangled state. We provide an
analytical formula connecting the entangled state and the closest disentangled
state in two qubits. Using this formula, when any disentangled state ($\sigma$)
located at the entangle-disentangle boundary is given, entangled states to
which $\sigma$ is closest can be obtained analytically. Further, this formula
naturally defines the direction normal to the boundary surface. The direction
is uniquely determined by $\sigma$ in almost all cases.


title: How robust is a quantum gate in the presence of noise?

abstract:
  We define several quantitative measures of the robustness of a quantum gate
against noise. Exact analytic expressions for the robustness against
depolarizing noise are obtained for all unitary quantum gates, and it is found
that the controlled-not is the most robust two-qubit quantum gate, in the sense
that it is the quantum gate which can tolerate the most depolarizing noise and
still generate entanglement. Our results enable us to place several analytic
upper bounds on the value of the threshold for quantum computation, with the
best bound in the most pessimistic error model being 0.5.


title:
Discrete supersymmetries of the Schrodinger equation and non-local
  exactly solvable potentials

abstract:
  Using an isomorphism between Hilbert spaces $L^2$ and $\ell^{2}$ we consider
Hamiltonians which have tridiagonal matrix representations (Jacobi matrices) in
a discrete basis and an eigenvalue problem is reduced to solving a three term
difference equation. Technique of intertwining operators is applied to creating
new families of exactly solvable Jacobi matrices. It is shown that any thus
obtained Jacobi matrix gives rise to a new exactly solvable non-local potential
of the Schroedinger equation. We also show that the algebraic structure
underlying our approach corresponds to supersymmetry. Supercharge operators
acting in the space $\ell^{2}\times \ell^{2} $ are introduced which together
with a matrix form of the superhamiltonian close the simplest superalgebra.


title: Classical and quantum noise in measurements and transformations

abstract:
  This paper has been withdrawn. See quant-ph/0408115: G. M. D'Ariano, P.
Perinotti and P. Lo Presti, "Classical randomness in quantum measurements"


title:
Coherent states for time dependent harmonic oscillator: the step
  function

abstract:
  We study the time evolution for the quantum harmonic oscillator subjected to
a sudden change of frequency. It is based on an approximate analytic solution
to the time dependent Ermakov equation for a step function. This approach
allows for a continuous treatment that differs from former studies that involve
the matching of two time independent solutions at the time when the step
occurs.


title: Input states for quantum gates

abstract:
  We examine three possible implementations of non-deterministic linear optical
cnot gates with a view to an in-principle demonstration in the near future. To
this end we consider demonstrating the gates using currently available sources
such as spontaneous parametric down conversion and coherent states, and current
detectors only able to distinguish between zero or many photons. The
demonstration is possible in the co-incidence basis and the errors introduced
by the non-optimal input states and detectors are analysed.


title: Asymptotes and characteristic times for transmission and reflection

abstract:
  A complete one-dimensional scattering of a spinless particle on a
time-independent potential barrier is considered. To describe separately
transmitted and reflected particles in the corresponding subsets of identical
experiments, we introduce the notions of scattering channels for transmission
and reflection. We find for both channels the (unitary) scattering matrices and
reconstruct, by known out asymptotes (i.e., by the transmitted and reflected
wave packets), the corresponding in asymptotes. Unlike the out asymptotes for
transmission and reflection, their in asymptotes represent nonorthogonal
functions. As is shown, the position distributions of to-be-transmitted and
to-be-reflected particles, except their average positions, are unpredictable.
At the same time, the momentum distributions of these particles are physically
meaningful and can be observed to the full. We show that both the subensembles
of particles must start (on the average) from the same spatial point, and the
momentum distributions of to-be-scattered and scattered particles must be the
same for each scattering channel. Taking into account these properties, we
define the (individual) delay times for transmission and reflection for wave
packets of an arbitrary width. Besides, to estimate the duration of the
scattering event, we derive the expression for a (total) scattering time.


title:
Explicit solution for a Gaussian wave packet impinging on a square
  barrier

abstract:
  The collision of a quantum Gaussian wave packet with a square barrier is
solved explicitly in terms of known functions. The obtained formula is suitable
for performing fast calculations or asymptotic analysis. It also provides
physical insight since the description of different regimes and collision
phenomena typically requires only some of the terms.


title: Dirac-Like Equation for Two-Level Atom

abstract:
  We construct Dirac-like equation for describing two-level atom interacting
with resonant laser field.


title: Quantum information transfer from one system to another one

abstract:
  The topics of the paper are: a) Some anti-linear maps governing EPR tasks if
no reference bases are distinguished. b) Imperfect teleportation and the
composition rule. The ancilla is supposed pure but otherwise arbitrary. c)
Quantum telportation with distributed measurements. d) Remarks on EPR with a
mixed state, triggered by a Lueders measurement.


title:
Some Recent Developments in the Decoherent Histories Approach to Quantum
  Theory

abstract:
  A brief introduction to the decoherent histories approach to quantum theory
is given, with emphasis on its role in the discussion of the emergence of
classicality from quantum theory. Some applications are discussed, including
quantum-classical couplings, the relationship of the histories approach to
quantum state diffusion, and the application of the histories approach to
situations involving time in a non-trivial way.


title:
Experimental Realization of Entanglement Concentration and A Quantum
  Repeater

abstract:
  We report an experimental realization of entanglement concentration using two
polarization-entangled photon pairs produced by pulsed parametric
down-conversion. In the meantime, our setup also provides a proof-in-principle
demonstration of a quantum repeater. The quality of our procedure is verified
by observing a violation of Bell's inequality by more than 5 standard
deviations. The high experimental accuracy achieved in the experiment implies
that the requirement of tolerable error rate in multi-stage realization of
quantum repeaters can be fulfilled, hence providing a practical toolbox for
quantum communication over large distances.


title: The continuum limit of the Bell model

abstract:
  In a paper entitled Beables for Quantum Field Theory, John Bell has shown
that it was possible to build a realistic interpretation of any hamiltonian
lattice quantum field theory involving Fermi fields. His model is stochastic
but Bell thought that it would become deterministic in the continuum limit. We
show that it is indeed the case, under an assumption about the state of the
universe, namely that the universe is in a state obtained from the positronic
sea (all positron states occupied) by creating a finite number of negative
charges. Moreover, the continuum model can be established directly. The
physical interpretation is the following: the negative charges are in motion in
the positronic sea and their positions are the beables of the Bell model.


title: Entanglement Entropy and The Density Matrix Renormalization Group

abstract:
  Quantum entanglement entropy has a geometric character. This is illustrated
by the interpretation of Rindler space or black hole entropy as entanglement
entropy. In general, one can define a "geometric entropy", associated with an
event horizon as a boundary that concentrates a large number of quantum states.
This allows one to connect with the "density matrix renormalization group" and
to unveil its connection with the theory of quantum information. This
renormalization group has been introduced in condensed matter physics in a
heuristic manner, but it can be conceived as a method of compression of quantum
information in the presence of a horizon. We propose generalizations to
problems of interest in cosmology.


title: Decoherence in quantum spin systems

abstract:
  Computer simulations of decoherence in quantum spin systems require the
solution of the time-dependent Schrodinger equation for interacting quantum
spin systems over extended periods of time. We use exact diagonalization,
Chebyshev polynomial technique, four Suzuki-formula algorithms, and the
short-iterative-Lanczos method to solve a simple model for decoherence of a
quantum spin system by an environment consisting of quantum spins, and compare
advantages and limitations of different algorithms.


title: Propagation, breathing and transition of matter-wave packet trains

abstract:
  We find a set of new exact solutions of a quantum harmonic oscillator, which
describes some wave-packet trains with average energy being proportional to
both the quantum level and classical energy of the oscillator. Center of the
wave-packet trains may oscillate like a classical harmonic oscillator of
frequency $\omega$. Width and highness of the trains may change simultaneously
with frequency $2 \omega $ as an array of breathers. Under some perturbations
the wave-packet trains could transit between the states of different quantum
numbers. We demonstrate analytically and numerically that the wave-packet
trains can be strictly fitted to the matter-wave soliton trains observed by
Strecher et al. and reported in Nature 417, 150(2002). When the wave-packets
breathe with greater amplitudes, they show periodic collapse and revival of the
matter-wave.


title: Popper's experiment, Copenhagen Interpretation and Nonlocality

abstract:
  A thought experiment, proposed by Karl Popper, which has been experimentally
realized recently, is critically examined. A basic flaw in Popper's argument
which has also been prevailing in subsequent debates, is pointed out. It is
shown that Popper's experiment can be understood easily within the Copenhagen
interpretation of quantum mechanics. An alternate experiment, based on discrete
variables, is proposed, which constitutes Popper's test in a clearer way. It
refutes the argument of absence of nonlocality in quantum mechanics.


title:
Nonlinear interaction of two photons at a one-dimensional atom:
  spatiotemporal quantum coherence in the emitted field

abstract:
  The nonlinear photon-photon interaction mediated by a single two-level atom
is studied theoretically based on a one-dimensional model of the field-atom
interaction. This model allows us to determine the effects of an atomic
nonlinearity on the spatiotemporal coherence of a two photon state.
Specifically, the complete two photon output wave function can be obtained for
any two photon input wave function. It is shown that the quantum interference
between the components of the output state associated with different
interaction processes causes bunching and anti-bunching in the two photon
statistics. This theory may be useful for various applications in photon
manipulation, e.g. quantum information processing using photonic qubits,
quantum nondemolition measurements, and the generation of entangled photons.


title:
Bounds on the entropy generated when timing information is extracted
  from microscopic systems

abstract:
  We consider Hamiltonian quantum systems with energy bandwidth \Delta E and
show that each measurement that determines the time up to an error \Delta t
generates at least the entropy (\hbar/(\Delta t \Delta E))^2/2. Our result
describes quantitatively to what extent all timing information is quantum
information in systems with limited energy. It provides a lower bound on the
dissipated energy when timing information of microscopic systems is converted
to classical information. This is relevant for low power computation since it
shows the amount of heat generated whenever a band limited signal controls a
classical bit switch.
  Our result provides a general bound on the information-disturbance trade-off
for von-Neumann measurements that distinguish states on the orbits of
continuous unitary one-parameter groups with bounded spectrum. In contrast,
information gain without disturbance is possible for some completely positive
semi-groups. This shows that readout of timing information can be possible
without entropy generation if the autonomous dynamical evolution of the clock
is dissipative itself.


title:
Revivals and entanglement from initially entangled mixed states of a
  damped Jaynes-Cummings model

abstract:
  An exact density matrix of a phase-damped Jaynes - Cummings model (JCM) with
entangled Bell-like initial states formed from a model two-state atom and sets
of adjacent photon number states of a single mode radiation field is presented.
The entanglement of the initial states and the subsequent time evolution is
assured by finding a positive lower bound on the concurrence of local 2x2
projections of the full 2xinfinity JCM density matrix. It is found that the
time evolution of the lower bound of the concurrence systematically captures
the corresponding collapse and revival features in atomic inversion, relative
entropies of atomic and radiation, mutual entropy, and quantum deficit. The
atom and radiation subsystems exhibit alternating sets of collapses and
revivals in a complementary fashion due to the initially mixed states of the
atom and radiation employed here. This is in contrast with the result obtained
when the initial state of the dissipationless system is a factored pure state
of atom and radiation, where the atomic and radiation entropies are necessarily
the same. The magnitudes of the entanglement lower bound and the atomic and
radiation revivals become larger as both magnitude and phase of the Bell-like
initial state contribution increases. The time evolution of the entropy
difference of the total system and that of the radiation subsystem exhibits
negative regions called "supercorrelated" states which do not appear in the
atomic subsystem. Entangled initial states are found to enhance this
supercorrelated feature. Finally, the effect of phase damping is to randomize
both the subsystems for asymptotically long times .


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 -- that is,
entities that can or cannot measure nonlocal observables or carry out
conditional quantum operations -- in extracting work from collections of
correlated quantum systems.


title: A multi-photon Stokes-parameter invariant for entangled states

abstract:
  We consider the Minkowskian norm of the n-photon Stokes tensor, a scalar
invariant under the group realized by the transformations of stochastic local
quantum operations and classical communications (SLOCC). This invariant is
offered as a candidate entanglement measure for n-qubit states and discussed in
relation to measures of quantum state entanglement for certain important
classes of two-qubit and three-qubit systems. This invariant can be directly
estimated via a quantum network, obviating the need to perform laborious
quantum state tomography. We also show that this invariant directly captures
the extent of entanglement purification due to SLOCC filters.


title: Decoherence and Quantum-state Measurement in Quantum Optics

abstract:
  This paper discusses work developed in recent years, in the domain of quantum
optics, which has led to a better understanding of the classical limit of
quantum mechanics. New techniques have been proposed, and experimentally
demonstrated, for characterizing and monitoring in real time the quantum state
of an electromagnetic field in a cavity. They allow the investigation of the
dynamics of the decoherence process by which a quantum-mechanical superposition
of coherent states of the field becomes a statistical mixture.


title:
An efficient scheme for numerical simulations of the spin-bath
  decoherence

abstract:
  We demonstrate that the Chebyshev expansion method is a very efficient
numerical tool for studying spin-bath decoherence of quantum systems. We
consider two typical problems arising in studying decoherence of quantum
systems consisting of few coupled spins: (i) determining the pointer states of
the system, and (ii) determining the temporal decay of quantum oscillations. As
our results demonstrate, for determining the pointer states, the
Chebyshev-based scheme is at least a factor of 8 faster than existing
algorithms based on the Suzuki-Trotter decomposition. For the problems of
second type, the Chebyshev-based approach has been 3--4 times faster than the
Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide
spectrum of systems, with different spin baths and different Hamiltonians.


title: Quantum Cryptography Using Single Particle Entanglement

abstract:
  A quantum cryptography scheme based on entanglement between a single particle
state and a vacuum state is proposed. The scheme utilizes linear optics devices
to detect the superposition of the vacuum and single particle states. Existence
of an eavesdropper can be detected by using a variant of Bell's inequality.


title: Global-fidelity limits of state-dependent cloning of mixed states

abstract:
  By relevant modifications, the known global-fidelity limits of
state-dependent cloning are extended to mixed quantum states. We assume that
the ancilla contains some a priori information about the input state. As it is
shown, the obtained results contribute to the stronger no-cloning theorem. An
attainability of presented limits is discussed.


title: Lagrangian in quantum mechanics is a connection one-form

abstract:
  We recast Dirac's Lagrangian in quantum mechanics in the language of vector
bundles and show that the action is an operator-valued connection one-form.
Phases associated with change of frames of reference are seen to be total
differentials in the transformation of the action. The relativistic case is
discussed and we show that it gives the correct phase in the non-relativistic
limit for uniform acceleration.


title:
Two-Pulse Atomic Coherent Control (2PACC) Spectroscopy of Eley-Rideal
  Reactions. An Application of an Atom Laser

abstract:
  A spectroscopic application of the atom laser is suggested. The spectroscopy
termed 2PACC employs the coherent properties of matter-waves from a two pulse
atom laser. These waves are employed to control a gas-surface chemical
recombination reaction. The method is demonstrated for an Eley-Rideal reaction
of a hydrogen or alkali atom-laser pulse where the surface target is an
adsorbed hydrogen atom. The reaction yields either a hydrogen or alkali hydride
molecule. The desorbed gas phase molecular yield and its internal state is
shown to be controlled by the time and phase delay between two atom-laser
pulses. The calculation is based on solving the time-dependent Schrodinger
equation in a diabatic framework. The probability of desorption which is the
predicted 2PACC signal has been calculated as a function of the pulse
parameters.


title: Quantum state tomography of dissociating molecules

abstract:
  Using tomographic reconstruction we determine the complete internuclear
quantum state, represented by the Wigner function, of a dissociating I2
molecule based on femtosecond time resolved position and momentum distributions
of the atomic fragments. The experimental data are recorded by timed ionization
of the photofragments with an intense 20 fs laser pulse. Our reconstruction
method, which relies on Jaynes' maximum entropy principle, will also be
applicable to time resolved position or momentum data obtained with other
experimental techniques.


title:
Nonadditive generalization of the quantum Kullback-Leibler divergence
  for measuring the degree of purification

abstract:
  The Kullback-Leibler divergence offers an information-theoretic basis for
measuring the difference between two given distributions. Its quantum analog,
however, fails to play a corresponding role for comparing two density matrices,
if the reference states are pure states. Here, it is shown that nonadditive
(nonextensive) generalization of quantum information theory is free from such a
difficulty and the associated quantity, termed the quantum q-divergence, can in
fact be a good information-theoretic measure of the degree of purification. The
correspondence relation between the ordinary divergence and the q-divergence is
violated for the pure reference states, in general.


title:
Monotonic decrease of the quantum nonadditive divergence by projective
  measurements

abstract:
  Nonadditive (nonextensive) generalization of the quantum Kullback-Leibler
divergence, termed the quantum q-divergence, is shown not to increase by
projective measurements in an elementary manner.


title:
Trapped ions interacting with laser fields: a perturbative analysis
  without rotating wave approximation

abstract:
  The Hamiltonian describing a single ion placed in a potential trap in
interaction with a laser beam is studied by means of a suitable perturbative
approach. It is shown, in particular, that the rotating wave approximation does
not provide the correct expression, at the first perturbative order, of the
evolution operator of the system.


title: Rayleigh Scattering and Atomic Dynamics in Dissipative Optical Lattices

abstract:
  We investigate Rayleigh scattering in dissipative optical lattices. In
particular, following recent proposals (S. Guibal {\it et al}, Phys. Rev. Lett.
{\bf 78}, 4709 (1997); C. Jurczak {\it et al}, Phys. Rev. Lett. {\bf 77}, 1727
(1996)), we study whether the Rayleigh resonance originates from the
diffraction on a density grating, and is therefore a probe of transport of
atoms in optical lattices. It turns out that this is not the case: the Rayleigh
line is instead a measure of the cooling rate, while spatial diffusion
contributes to the scattering spectrum with a much broader resonance.


title: Geometrical phases for the G(4,2) Grassmannian manifold

abstract:
  We generalize the usual abelian Berry phase generated for example in a system
with two non-degenerate states to the case of a system with two doubly
degenerate energy eigenspaces. The parametric manifold describing the space of
states of the first case is formally given by the G(2,1) Grassmannian manifold,
while for the generalized system it is given by the G(4,2) one. For the latter
manifold which exhibits a much richer structure than its abelian counterpart we
calculate the connection components, the field strength and the associated
geometrical phases that evolve non-trivially both of the degenerate
eigenspaces. A simple atomic model is proposed for their physical
implementation.


title: Shor's discrete logarithm quantum algorithm for elliptic curves

abstract:
  We show in some detail how to implement Shor's efficient quantum algorithm
for discrete logarithms for the particular case of elliptic curve groups. It
turns out that for this problem a smaller quantum computer can solve problems
further beyond current computing than for integer factorisation. A 160 bit
elliptic curve cryptographic key could be broken on a quantum computer using
around 1000 qubits while factoring the security-wise equivalent 1024 bit RSA
modulus would require about 2000 qubits. In this paper we only consider
elliptic curves over GF($p$) and not yet the equally important ones over
GF($2^n$) or other finite fields. The main technical difficulty is to implement
Euclid's gcd algorithm to compute multiplicative inverses modulo $p$. As the
runtime of Euclid's algorithm depends on the input, one difficulty encountered
is the ``quantum halting problem''.


title: Revisiting Caianiello's Maximal Acceleration

abstract:
  A quantum mechanical limit on the speed of orthogonality evolution justifies
the last remaining assumption in Caianiello's derivation of the maximal
acceleration. The limit is perfectly compatible with the behaviour of
superconductors of the first type.


title:
Nonequilibrium steady states on 1-d lattice systems and Goldstone
  theorem

abstract:
  On one-dimensional two-way infinite lattice system, a property of stationary
(space-) translationally invariant states with nonvanishing current
expectations are investigated. We consider GNS representation with respect to
such a state, on which we have a group of space-time translation unitary
operators. We show, by applying Goldstone-theorem-like argument,that spectrum
of the unitary operators, energy-momentum spectrum with respect to the state,
has a singularity at the origin.

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


title: The Lie Algebra Rank Condition for Non-Bilinear Quantum System

abstract:
  The controllability condition for finite dimensional quantum systems, the
  Lie Algebra Rank Condition, has been stated assuming that the right invariant
differential system under consideration is bilinear. We remark that this
assumption is not necessary and discuss the extension to the general case.


title:
Two-Level System and Some Approximate Solutions in the Strong Coupling
  Regime

abstract:
  In this paper we treat the 2--level system interacting with external fields
without the rotating wave approximation and construct some approximate
solutions in the strong coupling regime.


title:
Entanglement and four wave mixing effects in the dissipation free
  nonlinear interaction of two photons at a single atom

abstract:
  We investigate the nonlinear interaction between two photons in a single
input pulse at an atomic two level nonlinearity. A one dimensional model for
the propagation of light to and from the atom is used to describe the precise
spatiotemporal coherence of the two photon state. It is shown that the
interaction generates spatiotemporal entanglement in the output state similar
to the entanglement observed in parametric downconversion. A method of
generating photon pairs from coherent pump light using this quantum mechanical
four wave mixing process is proposed.


title: Quantum Processors and Controllers

abstract:
  In this paper is presented an abstract theory of quantum processors and
controllers, special kind of quantum computational network defined on a
composite quantum system with two parts: the controlling and controlled
subsystems. Such approach formally differs from consideration of quantum
control as some external influence on a system using some set of Hamiltonians
or quantum gates. The model of programmed quantum controllers discussed in
present paper is based on theory of universal deterministic quantum processors
(programmable gate arrays). Such quantum devices may simulate arbitrary
evolution of quantum system and so demonstrate an example of universal quantum
control.
  Keywords: Quantum, Computer, Control, Processor, Universal


title: On the Preparation of Pure States in Resonant Microcavities

abstract:
  We consider the time evolution of the radiation field (R) and a two-level
atom (A) in a resonant microcavity in terms of the Jaynes-Cummings model with
an initial general pure quantum state for the radiation field. It is then
shown, using the Cauchy-Schwarz inequality and also a Poisson resummation
technique, that {\it perfect} coherence of the atom can in general never be
achieved. The atom and the radiation field are, however, to a good
approximation in a pure state $|\psi >_A\otimes|\psi >_R$ in the middle of what
has been traditionally called the ``collapse region'', independent of the
initial state of the atoms, provided that the initial pure state of the
radiation field has a photon number probability distribution which is
sufficiently peaked and phase differences that do not vary significantly around
this peak. An approximative analytic expression for the quantity
$\Tr[\rho^2_{A}(t)]$, where $\rho_{A}(t)$ is the reduced density matrix for the
atom, is derived. We also show that under quite general circumstances an
initial entangled pure state will be disentangled to the pure state $|\psi
>_{A\otimes R}$.


title:
Determination of bound state energies for a one-dimensional potential
  field

abstract:
  A method for determination of bound state energies for an asymmetric quantum
well with an arbitrary shape of the bottom is suggested. It is shown that how
the equation determining the energy levels can be easily derived if one knows
the electron transmission and reflection amplitudes corresponding to the part
of potential inside the well. The results are applied to three difference test
problems.


title:
A Hybrid Authentication Protocol Using Quantum Entanglement and
  Symmetric Cryptography

abstract:
  This paper presents a hybrid cryptographic protocol, using quantum and
classical resources, for authentication and authorization in a network. One or
more trusted servers distribute streams of entangled photons to individual
resources that seek to communicate. It is assumed that each resource shares a
previously distributed secret key with the trusted server, and that resources
can communicate with the server using both classical and quantum channels.
Resources do not share secret keys with each other, so that the key
distribution problem for the network is reduced from O(n^2) to O(n). Some
advantages of the protocol are that it avoids the requirement for timestamps
used in classical protocols, guarantees that the trusted server cannot know the
authentication key, can provide resistance to multiple photon splitting attacks
and can be used with BB84 or other quantum key distribution protocols.


title: On classical electrodynamics in Dirac's equation matrix form

abstract:
  In the present paper it is shown that the Maxwell theory can be finely
represented in the matrix form of Dirac's equation, if the Dirac wave function
is identified with the electromagnetic wave by defined way. It seems to us,
that such representation allows us to see new possibilities in the connection
of the classical and quantum electrodynamics.


title: The Bloch Vector for N-Level Systems

abstract:
  We determine the set of the Bloch vectors for N-level systems, generalizing
the familiar Bloch ball in 2-level systems. An origin of the structural
difference from the Bloch ball in 2-level systems is clarified.


title: Solving a problem in the quantum way

abstract:
  A general quantum algorithm for solving a problem is discussed. The number of
steps required to solve a problem using this method is independent of the
number of cases that has to be considered classically. Hence, it is more
efficient than existing classical algorithms or quantum algorithm, which
requires O(sqrt(N)) steps.


title:
Multi-Channel Inverse Scattering Problem on the Line: Thresholds and
  Bound States

abstract:
  We consider the multi-channel inverse scattering problem in one-dimension in
the presence of thresholds and bound states for a potential of finite support.
Utilizing the Levin representation, we derive the general Marchenko integral
equation for N-coupled channels and show that, unlike to the case of the radial
inverse scattering problem, the information on the bound state energies and
asymptotic normalization constants can be inferred from the reflection
coefficient matrix alone. Thus, given this matrix, the Marchenko inverse
scattering procedure can provide us with a unique multi-channel potential. The
relationship to supersymmetric partner potentials as well as possible
applications are discussed. The integral equation has been implemented
numerically and applied to several schematic examples showing the
characteristic features of multi-channel systems. A possible application of the
formalism to technological problems is briefly discussed.


title:
Is the concept of quantum probability consistent with Lorentz
  covariance?

abstract:
  Lorentz-covariant harmonic oscillator wave functions are constructed from the
Lorentz-invariant oscillator differential equation of Feynman, Kislinger, and
Ravndal for a two-body bound state. The wave functions are not invariant but
covariant. As the differential equation contains the time-separation variable,
the wave functions contain the same time-separation variable which does not
exist in Schr\"odinger wave functions. This time-separation variable can be
shown to belong to Feynman's rest of the universe, and can thus be eliminated
from the density matrix. The covariant probability interpretation is given.
This oscillator formalism explains Feynman's decoherence mechanism which is
exhibited in Feynman's parton picture.


title: Wave-packet trains of a time-dependent harmonic oscillator

abstract:
  By using a test-function method, we construct $n$ exact solutions of a
quantum harmonic oscillator with a time-dependent "spring constant". Any $n$-th
solution describes a wave-packet train consisting of $n+1$ packets. Its center
oscillates like the classically harmonic oscillator with variable frequency,
and width and highness of each packet change simultaneously. When the
deformation is small, it behaves like a soliton train, and the large
deformation is identified with collapse and revival of the wave-packet train.


title:
Experimental investigation of delayed self-interference for single
  photons

abstract:
  A photon echo experiment has been performed using accumulated highly
attenuated laser pulses. We show experimentally that the photon echo process
can be performed with, on the average, less than one photon in each pair of
excitation pulses. The results support an interpretation where this non-linear
process can be performed with, on the average, less than one photon shared
between two of the optical fields involved in the degenerate four-wave mixing
process. Further, we argue that the experiment can be interpreted as a form of
delayed self-interference for photon wave packets that do not overlap in both
space and time.


title:
Theory of deep ultraviolet generation at maximum coherence assisted by
  Stark-chirped two-photon resonance

abstract:
  A scheme is analyzed for effcient generation of vacuum ultraviolet radiation
through four-wave mixing processes assisted by the technique of Stark-chirped
rapid adiabatic passage. These opportunities are associated with pulse
excitation of laddertype short-wavelength two-photon atomic or molecular
transitions so that relaxation processes can be neglected. In this three-laser
technique, a delayed-pulse of strong oR-resonant infrared radiation sweeps the
laser-induced Stark-shift of a two-photon transition in a such way that
facilitates robust maximum two-photon coherence induced by the first
ultraviolet laser. A judiciously delayed third pulse scatters at this coherence
and generates short-wavelength radiation. A theoretical analysis of these
problems based on the density matrix is performed. A numerical model is
developed to carry out simulations of a typical experiment. The results
illustrate a behavior of populations, coherence and generated radiation along
the medium as well as opportunities of effcient generation of deep (vacuum)
ultraviolet radiation.


title: Some methods for solution of quantum detection and measurement problems

abstract:
  Representation of the quantum measurement with the help of non-orthogonal
decomposition of unit is presented in the paper for the first time. Methods for
solution of the quantum detection and measurement problems based on the
suggested representation are proposed, as well.


title: A tentative new approach to the Schr\"odinger cat problem

abstract:
  Though scientifically unconvincing, the Broglie-Bohm model has the virtue of
reproducing the observational predictions of quantum mechanics while being
conceptually crystal-clear. Hence, even if we do not believe in it, we may find
it useful in suggesting ways of removing conceptual difficulties. This
procedure is here applied to the Schr\"odinger cat riddle (in its Wigner
version). The outcome yields tentative views on the relationship between
mentality and physical reality.


title: An Algorithm of a Virtual Quantum Computer Model on a Classical Computer

abstract:
  Construction of virtual quantum states became possible due to the hypothesis
on the nature of quantum states quant-ph/0212139. This study considers a
stochastic geometrical background (stochastic gravitational background)
generating correlation (or, coherency) of various quantum non-interacting
objects. In the quantum state virtual model, a simple method of generating of
two (or more) dichotomic signals with controlled mutual correlation factor from
a single continuous stochastic process is implemented. Basing on the system
random number generator of the computer, a model of the stationary random phase
(with the nature of random geometrical background).


title: Investigating three qubit entanglement with local measurements

abstract:
  In this paper we describe how three qubit entanglement can be analyzed with
local measurements. For this purpose we decompose entanglement witnesses into
operators which can be measured locally. Our decompositions are optimized in
the number of measurement settings needed for the measurement of one witness.
Our method allows to detect true threepartite entanglement and especially
GHZ-states with only four measurement settings.


title: Quantum Arithmetic on Galois Fields

abstract:
  In this paper we discuss the problem of performing elementary finite field
arithmetic on a quantum computer. Of particular interest, is the
controlled-multiplication operation, which is the only group-specific operation
in Shor's algorithms for factoring and solving the Discrete Log Problem. We
describe how to build quantum circuits for performing this operation on the
generic Galois fields GF($p^k$), as well as the boundary cases GF($p$) and
GF($2^k$). We give the detailed size, width and depth complexity of such
circuits, which ultimately will allow us to obtain detailed upper bounds on the
amount of quantum resources needed to solve instances of the DLP on such
fields.


title:
Efficient engineering of multi-atom entanglement through single-photon
  detections

abstract:
  We propose an efficient scheme to engineer multi-atom entanglement by
detecting cavity decay through single-photon detectors. In the special case of
two atoms, this scheme is much more efficient than previous probabilistic
schemes, and insensitive to randomness in the atom's position. More generally,
the scheme can be used to prepare arbitrary superpositions of multi-atom Dicke
states without the requirements of high-efficiency detection and separate
addressing of different atoms.


title:
Parametric beating of a quantum probe field with a prepared Raman
  coherence in a far-off-resonance medium

abstract:
  We investigate the parametric beating of a quantum probe field with a
prepared Raman coherence in a far-off-resonance medium, and describe the
resulting multiplexing processes. We show that the normalized autocorrelation
functions of the probe field are exactly reproduced in the Stokes and
anti-Stokes sideband fields. We find that an initial coherent state of the
probe field can be replicated to the Raman sidebands, and an initial squeezing
of the probe field can be partially transferred to the sidebands. We show that
a necessary condition for the output fields to be in an entangled state or,
more generally, in a nonclassical state is that the input field state is a
nonclassical state.


title: Dynamic effects of electromagnetic wave on a damped two-level atom

abstract:
  We studied the dynamic effects of an electromagnetic(EM) wave with circular
polarization on a two-level damped atom. The results demonstrate interesting ac
Stark split of energy levels of damped atom. The split levels have different
energies and lifetimes, both of which depend on the interaction and the damping
rate of atom. When the frequency of the EM wave is tuned to satisfy the
resonance condition in the strong coupling limit, the transition probability
exhibits Rabi oscillation. Momentum transfer between atom and EM wave shows
similar properties as the transition probability under resonance condition. For
a damped atom interacting with EM field, there exists no longer stable state.
More importantly, if the angular frequency of the EM wave is tuned the same as
the atomic transition frequency and its amplitude is adjusted appropriately
according to the damping coefficients, we can prepare a particular 'Dressed
State' of the coupled system between atom and EM field and can keep the system
coherently in this 'Dressed state' for a very long time. This opens another way
to prepare coherent atomic states.


title: Comment on "Quantum mechanics of smeared particles"

abstract:
  In a recent article, Sastry has proposed a quantum mechanics of smeared
particles. We show that the effects induced by the modification of the
Heisenberg algebra, proposed to take into account the delocalization of a
particle defined via its Compton wavelength, are important enough to be
excluded experimentally.


title: Real clocks and the Zeno effect

abstract:
  Real clocks are not perfect. This must have an effect in our predictions for
the behaviour of a quantum system, an effect for which we present a unified
description encompassing several previous proposals. We study the relevance of
clock errors in the Zeno effect, and find that generically no Zeno effect can
be present (in such a way that there is no contradiction with currently
available experimental data). We further observe that, within the class of
stochasticities in time addressed here, there is no modification in emission
lineshapes.


title: Violation of Bell's Inequality with Photons from Independent Sources

abstract:
  We report a violation of Bell's inequality using one photon from a parametric
down-conversion source and a second photon from an attenuated laser beam. The
two photons were entangled at a beam splitter using the post-selection
technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]. A quantum
interference pattern with a visibility of 91% was obtained using the photons
from these independent sources, as compared with a visibility of 99.4% using
two photons from a central parametric down-conversion source.


title: Experimental Phase-Sensitive Cloning

abstract: This article has been withdrawn.


title: Entropy inequalities and Bell inequalities for two-qubit systems

abstract:
  Sufficient conditions for (the non-violation of) the Bell-CHSH inequalities
in a mixed state of a two-qubit system are: 1) The linear entropy of the state
is not smaller than 0.5, 2) The sum of the conditional linear entropies is
non-negative, 3) The von Neumann entropy is not smaller than 0.833, 4) The sum
of the conditional von Neumann entropies is not smaller than 0.280.


title: Topics in Koopman-von Neumann Theory

abstract:
  In this thesis we study several features of the operatorial approach to
classical mechanics pionereed by Koopman and von Neumann (KvN) in the Thirties.
In particular in the first part we study the role of the phases of the KvN
states. We analyze, within the KvN theory, the two-slit experiment and the
Aharonov-Bohm effect and we make a comparison between the classical and the
quantum case. In the second part of the thesis we study the extension of the
KvN formalism to the space of forms and Jacobi fields. We first show that all
the standard Cartan calculus on symplectic spaces can be performed via
Grassmann variables or via suitable combinations of Pauli matrices. Second we
study the extended Hilbert space of KvN which now includes forms and prove that
it is impossible to have at the same time a positive definite scalar product
and a unitary evolution. Clear physical reasons for this phenomenon are
exhibited. We conclude the thesis with some work in progress on the issue of
quantization.


title: Spherical Manifold in Quantum Evolution

abstract:
  In this paper, the projective geometry is used to describe the features of
spherical manifold and discreteness in quantum evolution. As a system evolves
in time the state vector changes and it traces out a curve in Hilbert space.
Geometrically, the evolution is represented as a closed curve in the projective
Hilbert space. In recent times many attempts have been made to describe
'length', 'distance', and 'geometric phases' and also 'parallel transport'and
symplectic geometry in various ways in the projective Hilbert space, during
quantum evolution. It is shown in this paper that for the quantum evolution in
ray space, spherical manifold and features of discreteness can be described
geometrically.


title: Invariants of multiple-qubit systems under stochastic local operations

abstract:
  We investigate the behavior of quantum states under stochastic local quantum
operations and classical communication (SLOCC) for fixed numbers of qubits. We
explicitly exhibit the homomorphism between complex and real groups for
two-qubits, and use the latter to describe the effect of SLOCC operations on
two-qubit states. We find an expression for the polarization Lorentz group
invariant length, which is the Minkowskian analog of the quantum state purity,
the corresponding Euclidean length. The construction presented is immediately
generalizable to any finite number of qubits.


title: Optimal phase covariant cloning for qubits and qutrits

abstract:
  We consider cloning transformations of equatorial qubits and qutrits, with
the transformation covariant for rotation of the phases. The optimal cloning
maps are derived without simplifying assumptions from first principles, for any
number of input and output qubits, and for a single input qutrit and any number
of output qutrits. We also compare the cloning maps for global and single
particle fidelities, and we show that the two criteria lead to different
optimal maps.


title:
A projection operator technique for solution of relativistic wave
  equation on non-compact group: the case of a charged vector-boson

abstract:
  A projection operator technique for solution of relativistic wave equation on
non-compact group has been proposed. This technique was applied to the
construction of wave equations for charged vector boson in a potential field.
The equations were shown to approximately describe a hydrogen-like atom and
allow estimating of relativistic corrections such as a fine structure of
hydrogen atom lines with high accuracy.


title: Chained Typical Subspaces - a Quantum Version of Breiman's Theorem

abstract:
  We give an equivalent finitary reformulation of the classical
Shannon-McMillan-Breiman theorem which has an immediate translation to the case
of ergodic quantum lattice systems. This version of a quantum Breiman theorem
can be derived from the proof of the quantum Shannon-McMillan theorem presented
in our previous work (math.DS/0207121).

categories: quant-ph math-ph math.DS math.MP math.OA


title:
Long distance quantum teleportation of qubits from photons at 1300 nm to
  photons at 1550 nm wavelength

abstract:
  Elementary 2-dimensional quantum states (qubits) encoded in 1300 nm
wavelength photons are teleported onto 1550 nm photons. The use of
telecommunication wavelengths enables to take advantage of standard optical
fibre and permits to teleport from one lab to a distant one, 55 m away,
connected by 2 km of fibre. A teleportation fidelity of 81.2 % is reported.
This is large enough to demonstrate the principles of quantum teleportation, in
particular that entanglement is exploited. This experiment constitutes a first
step towards a quantum repeater.


title:
Exact solution of the time-dependent harmonic plus an inverse harmonic
  potential with a time-dependent electromagnetic field

abstract:
  In this article, the problem of the charged harmonic plus an inverse harmonic
oscillator with time-dependent mass and frequency in a time-dependent
electromagnetic field is investigated. It is reduced to the problem of the
inverse harmonic oscillator with time-independent parameters and the exact wave
function is obtained.


title:
Moving Atom-Field Interactions: Quantum Motional Decoherence and
  Relaxation

abstract:
  The reduced dynamics of an atomic qubit coupled both to its own quantized
center of mass motion through the spatial mode functions of the electromagnetic
field, as well as the vacuum modes, is calculated in the influence functional
formalism. The formalism chosen can describe the entangled non-Markovian
evolution of the system with a full account of the coherent back-action of the
environment on the qubit. We find a slight increase in the decoherence due to
the quantized center of mass motion and give a condition on the mass and qubit
resonant frequency for which the effect is important. In optically resonant
alkali-metal atom systems, we find the effect to be negligibly small. The
framework presented here can nevertheless be used for general considerations of
the coherent evolution of qubits in moving atoms in an electromagnetic field.


title:
Quantum communications with time-bin entangled photons: long distance
  quantum teleportation and quantum repeaters

abstract:
  Using 2 km of standard telecom optical fibres, we teleport qubits carried by
photons of 1310 nm wavelength to qubits in another lab carried by a photons of
1550 nm wavelength. The photons to be teleported and the necessary entangled
photon pairs are created in two different non-linear crystals. The measured
mean fidelity is of 81.2 %. We discuss how this could be used as quantum
repeaters without quantum memories.


title: Decoherence in Discrete Quantum Walks

abstract:
  We present an introduction to coined quantum walks on regular graphs, which
have been developed in the past few years as an alternative to quantum Fourier
transforms for underpinning algorithms for quantum computation. We then
describe our results on the effects of decoherence on these quantum walks on a
line, cycle and hypercube. We find high sensitivity to decoherence, increasing
with the number of steps in the walk, as the particle is becoming more
delocalised with each step. However, the effect of a small amount of
decoherence can be to enhance the properties of the quantum walk that are
desirable for the development of quantum algorithms, such as fast mixing times
to uniform distributions.


title: Noncommuting Coordinates in the Landau Problem

abstract:
  Basic ideas about noncommuting coordinates are summarized, and then
coordinate noncommutativity, as it arises in the Landau problem, is
investigated. I review a quantum solution to the Landau problem, and evaluate
the coordinate commutator in a truncated state space of Landau levels.
Restriction to the lowest Landau level reproduces the well known commutator of
planar coordinates. Inclusion of a finite number of Landau levels yields a
matrix generalization.


title: Efficient Synthesis of Linear Reversible Circuits

abstract:
  In this paper we consider circuit synthesis for n-wire linear reversible
circuits using the C-NOT gate library. These circuits are an important class of
reversible circuits with applications to quantum computation. Previous
algorithms, based on Gaussian elimination and LU-decomposition, yield circuits
with O(n^2) gates in the worst-case. However, an information theoretic bound
suggests that it may be possible to reduce this to as few as O(n^2/log n)
gates.
  We present an algorithm that is optimal up to a multiplicative constant, as
well as Theta(log n) times faster than previous methods. While our results are
primarily asymptotic, simulation results show that even for relatively small n
our algorithm is faster and yields more efficient circuits than the standard
method. Generically our algorithm can be interpreted as a matrix decomposition
algorithm, yielding an asymptotically efficient decomposition of a binary
matrix into a product of elementary matrices.


title: Speakable and Unspeakable, Past and Future

abstract:
  This chapter is based on a talk given at the Science and Ultimate Reality
meeting in March, 2002, in honour of John Archibald Wheeler. In it, I discuss
some questions related to what can and cannot be said about the history of a
quantum mechanical system. Relying heavily on the weak- measurement formalism
of Aharonov and coworkers, I argue that there is much to be learned about a
system based both on its preparation and on subsequent postselection. This is
illustrated with examples from a number of past, present, and future
experiments from our lab, ranging from tests of quantum "paradoxes" to studies
of nonlocality to non-deterministic implementations of logic operations on
quantum information. The connection between weak measurements and generalized
probability theory is discussed, along with some of the counterintuitive
features of these "probabilities." Conclusions are for the most part left to
the reader.


title:
Moving Atom-Field Interaction: Correction to Casimir-Polder Effect from
  Coherent Back-action

abstract:
  The Casimir-Polder force is an attractive force between a polarizable atom
and a conducting or dielectric boundary. Its original computation was in terms
of the Lamb shift of the atomic ground state in an electromagnetic field (EMF)
modified by boundary conditions along the wall and assuming a stationary atom.
We calculate the corrections to this force due to a moving atom, demanding
maximal preservation of entanglement generated by the moving atom-conducting
wall system. We do this by using non-perturbative path integral techniques
which allow for coherent back-action and thus can treat non-Markovian
processes. We recompute the atom-wall force for a conducting boundary by
allowing the bare atom-EMF ground state to evolve (or self-dress) into the
interacting ground state. We find a clear distinction between the cases of
stationary and adiabatic motions. Our result for the retardation correction for
adiabatic motion is up to twice as much as that computed for stationary atoms.
We give physical interpretations of both the stationary and adiabatic atom-wall
forces in terms of alteration of the virtual photon cloud surrounding the atom
by the wall and the Doppler effect.


title:
Generation of photon pairs using polarization-dependent two-photon
  absorption

abstract:
  We propose a new method for generating photon pairs from coherent light using
polarization-dependent two-photon absorption. We study the photon statistics of
two orthogonally polarized modes by solving a master equation, and show that
when we prepare a coherent state in one polarization mode, photon pairs are
created in the other mode. The photon pairs have the same frequency as that of
the incident light.


title: Quantum error correction for continuously detected errors

abstract:
  We show that quantum feedback control can be used as a quantum error
correction process for errors induced by weak continuous measurement. In
particular, when the error model is restricted to one, perfectly measured,
error channel per physical qubit, quantum feedback can act to perfectly protect
a stabilizer codespace. Using the stabilizer formalism we derive an explicit
scheme, involving feedback and an additional constant Hamiltonian, to protect
an ($n-1$)-qubit logical state encoded in $n$ physical qubits. This works for
both Poisson (jump) and white-noise (diffusion) measurement processes. In
addition, universal quantum computation is possible in this scheme. As an
example, we show that detected-spontaneous emission error correction with a
driving Hamiltonian can greatly reduce the amount of redundancy required to
protect a state from that which has been previously postulated [e.g., Alber
\emph{et al.}, Phys. Rev. Lett. 86, 4402 (2001)].


title: Algebra for generalised quantum observables

abstract:
  Generalised observables (POM observables) are necessary for representing all
possible measurements on a quantum system. Useful algebraic operations such as
addition and multiplication are defined for these observables, recovering many
advantages of the more restrictive Hermitian operator formalism. Examples
include new uncertainty relations and metrics, and optical phase applications.


title: Entanglement, local measurements, and symmetry

abstract:
  A definition of entanglement in terms of local measurements is discussed.
Viz, the maximum entanglement corresponds to the states that cause the highest
level of quantum fluctuations in all local measurements determined by the
dynamic symmetry group of the system. A number of examples illustrating this
definition is considered.


title:
On the path integration for the potential barrier $V_{0}\cosh
  ^{-2}(\omega x)$

abstract:
  The propagator associated to the potential barrier $V=V_{0}\cosh ^{-2}(\omega
x)$ is obtained by solving path integrals. The method of delta functionals
based on canonical and other transformations is used to reduce the path
integral for this potential into a path integral for the Morse potential
problem. The dimensional extension technique is seen to be essential for
performing the multiple integral representation of the propagator. The
correctly normalized scattering wave functions and the scattering function are
derived. To test the method employed, the free particle and the $\delta
-$function barrier are considered as limiting cases.


title:
Electron Wave Function in the Field of a One Dimensional Irregular
  Layered Structure

abstract:
  A method is proposed to find the wave function of an electron moving
infinitely in the field of an arbitrary 1D layer structure with two different
homogeneous semi-infinite boundaries. It is shown that in general the problem
reduces to solution of a set of two linear difference equations. The proposed
approach is discussed on a base of two cases: a structure of periodically
placed identical rectangular potentials and a non-ordered structure with
certain distortion of periodicity and potential identity.


title: Quantum limit of deterministic theories

abstract:
  We show that the quantum linear harmonic oscillator can be obtained in the
large $N$ limit of a classical deterministic system with SU(1,1) dynamical
symmetry. This is done in analogy with recent work by G.'t Hooft who
investigated a deterministic system based on SU(2). Among the advantages of our
model based on a non--compact group is the fact that the ground state energy is
uniquely fixed by the choice of the representation.


title: Atom spin squeezing in a double lambda system

abstract:
  The interaction of classical and quantized electromagnetic fields with an
ensemble of atoms in an optical cavity is considered. Four fields drive a
double-lambda level scheme in the atoms, consisting of a pair of lambda systems
sharing the same set of lower levels. Two of the fields produce maximum
coherence, rho12 = -1/2, between the ground state sublevels 1 and 2. This
pumping scheme involves equal intensity fields that are resonant with both the
one and two-photon transitions of the lambda system. There is no steady-state
absorption of these fields, implying that the fields induce a type
electromagnetically-induced transparency (EIT) in the medium. An additional
pair of fields interacting with the second lambda system, combined with the EIT
fields, leads to squeezing of the atom spin associated with the ground state
sublevels. Our method involves a new mechanism for creating steady-state spin
squeezing using an optical cavity. As the cooperativity parameter C is
increased, the optimal squeezing varies as C^{-1/3}. For experimentally
accessible values of C, squeezing as large as 90% can be achieved.


title: Transition from Quantum to Classical Information in a Superfluid

abstract:
  Whereas the entropy of any deterministic classical system described by a
principle of least action is zero, one can assign a "quantum information" to
quantum mechanical degree of freedom equal to Hausdorff area of the deviation
from a classical path. This raises the question whether superfluids carry
quantum information. We show that in general the transition from the classical
to quantum behavior depends on the probing length scale, and occurs for
microscopic length scales, except when the interactions between the particles
are very weak. This transition explains why, on macroscopic length scales,
physics is described by classical equations.


title: Spin squeezing and pairwise entanglement for symmetric multiqubit states

abstract:
  We show that spin squeezing implies pairwise entanglement for arbitrary
symmetric multiqubit states. If the squeezing parameter is less than or equal
to 1, we demonstrate a quantitative relation between the squeezing parameter
and the concurrence for the even and odd states. We prove that the even states
generated from the initial state with all qubits being spin down, via the
one-axis twisting Hamiltonian, are spin squeezed if and only if they are
pairwise entangled. For the states generated via the one-axis twisting
Hamiltonian with an external transverse field for any number of qubits greater
than 1 or via the two-axis counter-twisting Hamiltonian for any even number of
qubits, the numerical results suggest that such states are spin squeezed if and
only if they are pairwise entangled.


title: Dynamical aspects of quantum entanglement for coupled mapping systems

abstract:
  We investigate how the dynamical production of quantum entanglement for
weakly coupled mapping systems is influenced by the chaotic dynamics of the
corresponding classical system. We derive a general perturbative formula for
the entanglement production rate which is defined by using the linear entropy
of the subsystem. This formula predicts that {\it the increment of the strength
of chaos does not enhance the production rate of entanglement} when the
coupling is weak enough and the subsystems are strongly chaotic. The prediction
is confirmed by numerical experiments for coupled kicked tops and rotors. We
also discuss the entanglement production using the Husimi representation of the
reduced density matrix.


title: Entanglement generation in continuously coupled parametric generators

abstract:
  We investigate a compact source of entanglement. This device is composed of a
pair of linearly coupled nonlinear waveguides operating by means of degenerate
parametric downconversion. For the vacuum state at the input the generalized
squeeze variance and logarithmic negativity are used to quantify the amount of
nonclassicality and entanglement of output beams. Squeezing and entanglement
generation for various dynamical regimes of the device are discussed.


title: Continuous variable entanglement by radiation pressure

abstract:
  We show that the radiation pressure of an intense optical field impinging on
a perfectly reflecting vibrating mirror is able to entangle in a robust way the
first two optical sideband modes. Under appropriate conditions, the generated
entangled state is of EPR type [A. Einstein, {\it et al.}, Phys. Rev. {\bf 47},
777 (1935)].


title:
An efficient numerical method for calculating the entanglement of
  formation of arbitrary mixed quantum states of any dimension

abstract:
  We present a conjugate gradient method for calculating the entanglement of
formation of arbitrary mixed quantum states of any dimension and with any
bipartite division of the Hilbert space. The development of the gradient used
by the algorithm, its implications for the number of states required in the
optimal decomposition, and the way that conjugate gradient minimization has
been adapted for this particular problem are outlined. We have found that the
algorithm exhibits linear convergence for general mixed states, and that it
correctly reproduces the known results for pairs of qubits and for isotropic
states. The results of an example application of the code are discussed:
calculating the entanglement of formation of a Psi+ Bell state of two qutrits
when one of those qutrits is subject to various decoherence channels. The
results for qutrits are contrasted with those for qubits: for the types of
decoherence considered here, qutrit entanglement appears to be more robust than
qubit entanglement.


title:
Classicality and anticlassicality measures of pure and mixed quantum
  states

abstract:
  We introduce a simple measure of "classicality" of pure and mixed quantum
states as a maximum value of the Hilbert-Schmidt "scalar products" between the
renormalized statistical operators of the state concerned and all displaced
thermal states. Choosing Fock states as the reference set, we introduce the
measure of "anticlassicality". Both measures are illustrated for the Fock,
coherent phase, and generic mixed Gaussian states. Gaussian states are shown to
be the closest to thermal states possessing the same degree of quantum purity.
On the contrary, Fock states appear to be more close to mixed thermal states
than to pure coherent states.


title: Ordered Quantization and the Ehrenfest Time Scale

abstract:
  We propose a prescription to quantize classical monomials in terms of
symmetric and ordered expansions of non-commuting operators of a bosonic
theory. As a direct application of such quantization rules, we quantize a
classically time evolved function
  $\mathcal{O}(q,p,t)$, and calculate its expectation value in coherent states.
The result can be expressed in terms of the application of a classical operator
which performs a {\em Gaussian smoothing} of the original function
$\mathcal{O}$ evaluated at the center of the coherent state. This scheme
produces a natural semi-classical expansion for the quantum expectation values
at a short time scale. Moreover, since the classical Liouville evolution of a
Gaussian probability density gives the {\bf same} form for the classical
statistical mean value, we can calculate the first order correction in $\hbar$
entirely from the associated classical time evolved function. This allows us to
write a general expression for the Ehrenfest time in terms of the departure of
the centroid of the quantum distribution from the classical trajectory provided
we start with an initially coherent state for each subsystem. In order to
illustrate this approach, we have calculated analytically the Ehrenfest time of
a model with $N$ coupled non-linear oscillators with non-linearity of even
order.


title:
Theory of four-wave mixing and accompanying dissociation and population
  transfer controlled with laser-induced continuum structures

abstract:
  A theory is developed and applied to the study of opportunities and specific
features of coherent control of four-wave mixing as well as of the accompanying
processes in the continuous-wave regime, which involve transitions between
bound and free quantum states. Such opportunities become feasible through
constructive and destructive interference of quantum pathways. Two coupling
schemes of practical importance are investigated. In the first, a ladder energy
level scheme, fully-resonant sum-frequency nonlinear-optical generation of
short-wavelength radiation driven by several strong fields is investigated. The
relaxation processes as well as absorption of the fundamental and generated
radiations, which play an important role, are taken into consideration. It is
shown that the generation output can be considerably increased through the
appropriate adjustment of several laser-induced continuum structures. In the
second, a folded scheme, a possible control of two-photon dissociation
(Lambda-scheme) using auxiliary laser radiation applied to the adjacent
bound-free transition (V-configuration) is investigated. Besides dissociation,
the proposed method enables one to control population transfer between two
upper discreet levels via the lower-energy dissociation continuum, while direct
transition between these states is not allowed. The opportunities of
manipulating these processes as well as of four-wave-mixing-based spectroscopy
are explored both analytically and through a numerical simulation for Na_2
dimers.


title: On Computational Power of Quantum Branching Programs

abstract:
  In this paper we study a model of a Quantum Branching Program (QBP) and
investigate its computational power. We prove a general lower bound on the
width of read-once QBPs, which we show to be almost tight on certain symmetric
function.


title: Theory of an Entanglement Laser

abstract:
  We consider the creation of polarization entangled light from parametric
down- conversion driven by an intense pulsed pump inside a cavity. The
multi-photon states produced are close approximations to singlet states of two
very large spins. A criterion is derived to quantify the entanglement of such
states. We study the dynamics of the system in the presence of losses and other
imperfections, concluding that the creation of strongly entangled states with
photon numbers up to a million seems achievable.


title:
Characterization of the Positivity of the Density Matrix in Terms of the
  Coherence Vector Representation

abstract:
  A parameterization of the density operator, a coherence vector
representation, which uses a basis of orthogonal, traceless, Hermitian matrices
is discussed. Using this parameterization we find the region of permissible
vectors which represent a density operator. The inequalities which specify the
region are shown to involve the Casimir invariants of the group. In particular
cases, this allows the determination of degeneracies in the spectrum of the
operator. The identification of the Casimir invariants also provides a method
of constructing quantities which are invariant under {\it local} unitary
operations. Several examples are given which illustrate the constraints
provided by the positivity requirements and the utility of the coherence vector
parameterization.


title: Semiclassical approaches to controlling chemical reaction dynamics

abstract:
  We propose to use semiclassical methods to treat laser control problems of
chemical reaction dynamics. Our basic strategy is as follows: Laser-driven
chemical reactions are considered to consist of two processes. One is the
wavepacket propagation on an adiabatic potential energy surface (PES), and the
other is the electronic transition between PES's. Because the latter process is
mathematically equivalent to nonadiabatic transitions between Floquet (dressed)
states, we can control such a process using the semiclassical Zhu-Nakamura
theory for nonadiabatic transitions. For the former process, we incorporate
semiclassical propagation methods such as the Herman-Kluk propagator into
optimization procedures like optimal control theory. We show some numerical
examples for our strategies. We also develop a semiclassical direct algorithm
to treat the adiabatic propagation and nonadiabatic transitions as a whole.


title: Einstein-Podolsky-Rosen correlations and Galilean transformations

abstract:
  In this paper we calculate with full details Einstein-Podolsky-Rosen spin
correlations in the framework of nonrelativistic quantum mechanics. We consider
the following situation: two-particle state is prepared (we consider separately
distinguishable and identical particles and take into account the space part of
the wave function) and two observers in relative motion measure the spin
component of the particle along given directions. The measurements are
performed in bounded regions of space (detectors), not necessarily
simultaneously. The resulting correlation function depends not only on the
directions of spin measurements but also on the relative velocity of the
observers.


title:
Treating the Independent Set Problem by 2D Ising Interactions with
  Adiabatic Quantum Computing

abstract:
  We construct a nearest-neighbor Hamiltonian whose ground states encode the
solutions to the NP-complete problem INDEPENDENT SET in cubic planar graphs.
The Hamiltonian can be easily simulated by Ising interactions between adjacent
particles on a 2D rectangular lattice. We describe the required pulse
sequences. Our methods could help to implement adiabatic quantum computing by
physically reasonable Hamiltonians like short-range interactions.


title: Quantum Tomography

abstract:
  This is the draft version of a review paper which is going to appear in
"Advances in Imaging and Electron Physics"


title: Dynamical Criterion for Quantum Chaos: Entropy Production in Subsystems

abstract:
  We examine the conjecture that entropy production in subsystems of a given
system can be used as a dynamical criterion for quantum chaos in the latter.
Numerical results are presented for finite dimensional spin systems as also for
the quantum baker's map. Of especial importance is the power spectrum of the
entropy production which gets progressively more and more broad-banded as the
degree of correlation in the Hamiltonian matrix is made to decrease.


title: Quantum teleportation using three-particle entanglement

abstract:
  We investigate the teleportation of a quantum state using a three-particle
entangled W state. We compare and contrast our results with those in Ref.[11]
where a three-particle entangled GHZ state was used. The effects of white noise
on the average teleportation fidelities are also studied.


title: General Entanglement Breaking Channels

abstract:
  This paper studies the class of stochastic maps, or channels, whose action
(when tensored with the identity) on an entangled state always yields a
separable state. Such maps have a canonical form introduced by Holevo. Such
maps are called entanglement breaking, and can always be written in a canonical
form introduced by Holevo. Some special classes of these maps are considered
and several equivalent characterizations given.
  Since the set of entanglement-breaking trace-preserving maps is convex, it
can be described by its extreme points. The only extreme points of the set of
completely positive trace preserving maps which are also entanglement breaking
are those known as classical quantum or CQ. However, for d > 2 the set of
entanglement breaking maps has additional extreme points which are not extreme
CQ maps.


title: Qubit Entanglement Breaking Channels

abstract:
  This paper continues the study of stochastic maps, or channels, which break
entanglement. We give a detailed description of entanglement-breaking qubit
channels, and show that such maps are precisely the convex hull of those known
as classical-quantum channels. We also review the complete positivity
conditions in a canonical parameterization and show how they lead to
entanglement-breaking conditions.


title:
Optimum Probe Parameters for Entangling Probe in Quantum Key
  Distribution

abstract:
  For the four-state protocol of quantum key distribution, optimum sets of
probe parameters are calculated for the most general unitary probe in which
each individual transmitted photon is made to interact with the probe so that
the signal and the probe are left in an entangled state, and projective
measurement by the probe, made subsequent to projective measurement by the
legitimate receiver, yields information about the signal state. The probe
optimization is based on maximizing the Renyi information gain by the probe on
corrected data for a given error rate induced by the probe in the legitimate
receiver. An arbitrary angle is included between the nonorthogonal linear
polarization states of the signal photons. Two sets of optimum probe parameters
are determined which both correspond to the same optimization. Also, a larger
set of optimum probe parameters is found than was known previously for the
standard BB84 protocol. A detailed comparison is made between the complete and
incomplete optimizations, and the latter simpler optimization is also made
complete. Also, the process of key distillation from the quantum transmission
in quantum key distribution is reviewed, with the objective of calculating the
secrecy capacity of the four-state protocol in the presence of the
eavesdropping probe. Emphasis is placed on information leakage to the probe.


title: Probability in decoherent histories

abstract:
  The decoherent (consistent) histories formalism has been proposed as a means
of eliminating measurements as a fundamental concept in quantum mechanics. In
this formalism, probabilities can be assigned to any description which
satisfies a particular consistency condition. The formalism, however, admits
incompatible descriptions which cannot be combined, unlike classical physics.
This seems to leave an ambiguity in the choice of the description. I argue that
this ambiguity is removed by considering the observer as a physical system.


title: Solution of scaling quantum networks

abstract:
  We show that all scaling quantum graphs are explicitly integrable, i.e. any
one of their spectral eigenvalues $E_n$ is computable analytically, explicitly,
and individually for any given $n$. This is surprising, since quantum graphs
are excellent models of quantum chaos [see, e.g., T. Kottos and H. Schanz,
Physica E {\bf 9}, 523 (2001)].


title: Confined Quantum Time of Arrivals

abstract:
  We show that formulating the quantum time of arrival problem in a segment of
the real line suggests rephrasing the quantum time of arrival problem to
finding states that evolve to unitarily collapse at a given point at a definite
time. For the spatially confined particle, we show that the problem admits a
solution in the form of an eigenvalue problem of a compact and self-adjoint
time of arrival operator derived by a quantization of the classical time of
arrival, which is canonically conjugate with the Hamiltonian in closed subspace
of the Hilbert space.


title:
Coherent pulse implementations of quantum cryptography protocols
  resistant to photon number splitting attacks

abstract:
  A new class of quantum cryptography (QC) protocols that are robust against
the most general photon number splitting attacks in a weak coherent pulse
implementation has been recently proposed. In this article we give a quite
exhaustive analysis of several eavesdropping attacks on these schemes. The
eavesdropper (Eve) is supposed to have unlimited technological power while the
honest parties (Alice and Bob) use present day technology, in particular an
attenuated laser as an approximation of a single-photon source. They exploit
the nonorthogonality of quantum states for decreasing the information
accessible to Eve in the multi-photon pulses accidentally produced by the
imperfect source. An implementation of some of these protocols using present
day technology allow for a secure key distribution up to distances of $\sim$
150 km. We also show that strong-pulse implementations, where a strong pulse is
included as a reference, allow for key distribution robust against photon
number splitting attacks.


title: Coherent control with broadband squeezed vacuum

abstract:
  We report the experimental demonstration of coherent control with high power,
broadband squeezed vacuum. Although incoherent and exhibiting the statistics of
a thermal noise, broadband squeezed vacuum is shown to induce certain
two-photon interactions as a coherent ultrashort pulse with the same spectral
bandwidth. Utilizing pulse-shaping techniques we coherently control the
sum-frequency generation of broadband squeezed vacuum over a range of two
orders of magnitude. Coherent control of two-photon interactions with broadband
squeezed vacuum can potentially obtain spectral resolutions and extinction
ratios that are practically unattainable with coherent pulses.

categories: quant-ph physics.atom-ph physics.class-ph physics.optics


title:
Quantum nonlocality in the presence of superselection rules and data
  hiding protocols

abstract:
  We consider a quantum system subject to superselection rules, for which
certain restrictions apply to the quantum operations that can be implemented.
It is shown how the notion of quantum-nonlocality has to be redefined in the
presence of superselection rules: there exist separable states that cannot be
prepared locally and exhibit some form of nonlocality. Moreover, the notion of
local distinguishability in the presence of classical communication has to be
altered. This can be used to perform quantum information tasks that are
otherwise impossible. In particular, this leads to the introduction of perfect
quantum data hiding protocols, for which quantum communication (eventually in
the form of a separable but nonlocal state) is needed to unlock the secret.


title: Entanglement in The Second Quantization Formalism

abstract:
  We study properties of entangled systems in the (mainly non-relativistic)
second quantization formalism. This is then applied to interacting and
non-interacting bosons and fermions and the differences between the two are
discussed. We present a general formalism to show how entanglement changes with
the change of modes of the system. This is illustrated with examples such as
the Bose condensation and the Unruh effect. It is then shown that a
non-interacting collection of fermions at zero temperature can be entangled in
spin providing that their distances do not exceed the inverse Fermi wavenumber.
Beyond this distance all bipartite entanglement vanishes, although classical
correlations still persist. We compute the entanglement of formation as well as
the mutual information for two spin-correlated electrons as a function of their
distance. The analogous non-interacting collection of bosons displays no
entanglement in the internal degrees of freedom. We show how to generalize our
analysis of the entanglement in the internal degrees of freedom to an arbitrary
number of particles.


title: P.A.M. Dirac and the Discovery of Quantum Mechanics

abstract:
  This colloquium summarizes Dirac's contributions to the discovery of quantum
mechanics before he invented his relativistic wave equation.

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


title:
Experimental observation of four-photon entanglement from
  down-conversion

abstract:
  We observe polarization-entanglement between four photons produced from a
single down-conversion source. The non-classical correlations between the
measurement results violate a generalized Bell inequality for four qubits. The
characteristic properties and its easy generation with high interferometric
contrast make the observed four-photon state well-suited for implementing
advanced quantum communication schemes such as multi-party quantum key
distribution, secret sharing and telecloning.


title: Maximally-Disordered Distillable Quantum States

abstract:
  We explore classical to quantum transition of correlations by studying the
quantum states located just outside of the classically-correlated-states-only
neighborhood of the maximally mixed state (the largest separable ball (LSB)).
We show that a natural candidate for such states raises the possibility of a
layered transition, i.e., an annular region comprising only classical and the
classical-like bound entangled states, followed by free or distillable
entanglement. Surprisingly, we find the transition to be abrupt for bipartite
systems: distillable states emerge arbitrarily close to the LSB. For
multipartite systems, while the radius of the LSB remains unknown, we determine
the radius of the largest undistillable ball. Our results also provide an upper
bound on how noisy shared entangled states can be for executing quantum
information processing protocols.


title: Reduction of the Wavepacket: How Long Does it Take?

abstract:
  We show that the ``reduction of the wavepacket'' caused by the interaction
with the environment occurs on a timescale which is typically many orders of
magnitude shorter than the relaxation timescale $\tau$. In particular, we show
that in a system interacting with a ``canonical'' heat bath of harmonic
oscillators decorrelation timescale of two pieces of the wave-packet separated
by $N$ thermal de Broglie wavelengths is approximately $\tau/N^2$. Therefore,
in the classical limit $\hbar \to 0$ dynamical reversibility $(\tau \to
\infty)$ is compatible with ``instantaneous'' coherence loss.


title:
Predictions of the hydrodynamic interpretation of quantum mechanics
  compared with quantum electrodynamics for low energy bremsstrahlung

abstract:
  It is shown that the hydrodynamic interpretation of a charged quantum
particle leads to a different theoretical prediction for low energy
bremsstrahlung than does quantum electrodynamics (QED). In the calculations,
the electromagnetic fields are treated classically in the hydrodynamic case,
but are quantized in QED. Calculations show the hydrodynamic model to have a
different and more sensitive dependence on the size and shape of the radiating
particle's wave packet then does QED. In particular it is shown that
bremsstrahlung is sometimes greatly reduced when the force acting on the
particle is localized to a volume small compared to the particle's wave packet.
QED exhibits no such reduction. Therefore it is possible to test this effect
experimentally.
  An experiment is proposed. It involves an electron microscope with a Wien
filter for producing monochromatic beam electrons and an accurate energy
measurement of the particle after passing through a local force field.


title: Nonlinear Jaynes-Cummings model of atom-field interaction

abstract:
  Interaction of a two-level atom with a single mode of electromagnetic field
including Kerr nonlinearity for the field and intensity-dependent atom-field
coupling is discussed. The Hamiltonian for the atom-field system is written in
terms of the elements of a closed algebra, which has
  SU(1,1) and Heisenberg-Weyl algebras as limiting cases. Eigenstates and
eigenvalues of the Hamiltonian are constructed.
  With the field being in a coherent state initially, the dynamical behaviour
of atomic-inversion, field-statistics and uncertainties in the field
quadratures are studied. The appearance of nonclassical features during the
evolution of the field is shown. Further, we explore the overlap of initial and
time-evolved field states.


title: Concepts and methods in the theory of open quantum systems

abstract:
  The central physical concepts and mathematical techniques used in the theory
of open quantum systems are reviewed. Particular emphasis is laid on the
interrelations of apparently different approaches. Starting from the
appropriate characterization of the quantum statistical ensembles naturally
arising in the description of open quantum systems, the corresponding dynamical
evolution equations are derived for the Markovian as well as for the
non-Markovian case.


title: Sub-Poissonian statistics in order-to-chaos transition

abstract:
  We study the phenomena at the overlap of quantum chaos and nonclassical
statistics for the time-dependent model of nonlinear oscillator. It is shown in
the framework of Mandel Q-parameter and Wigner function that the statistics of
oscillatory excitation number is drastically changed in order-to chaos
transition. The essential improvement of sub-Poissonian statistics in
comparison with an analogous one for the standard model of driven anharmonic
oscillator is observed for the regular operational regime. It is shown that in
the chaotic regime the system exhibits the range of sub- and super-Poissonian
statistics which alternate one to other depending on time intervals. Unusual
dependence of the variance of oscillatory number on the external noise level
for the chaotic dynamics is observed.


title: Consistency of the Shannon entropy in quantum experiments

abstract:
  The consistency of the Shannon entropy, when applied to outcomes of quantum
experiments, is analysed. It is shown that the Shannon entropy is fully
consistent and its properties are never violated in quantum settings, but
attention must be paid to logical and experimental contexts. This last remark
is shown to apply regardless of the quantum or classical nature of the
experiments.


title: How To Treat An N-Level System : A Proposal

abstract:
  In this paper we propose a Hamiltonian of the n-level system by making use of
generalized Pauli matrices.