title:
Uncertainty, entropy and decoherence of the damped harmonic oscillator
  in the Lindblad theory of open quantum systems

abstract:
  In the framework of the Lindblad theory for open quantum systems, expressions
for the density operator, von Neumann entropy and effective temperature of the
damped harmonic oscillator are obtained. The entropy for a state characterized
by a Wigner distribution function which is Gaussian in form is found to depend
only on the variance of the distribution function. We give a series of
inequalities, relating uncertainty to von Neumann entropy and linear entropy.
We analyze the conditions for purity of states and show that for a special
choice of the diffusion coefficients, the correlated coherent states (squeezed
coherent states) are the only states which remain pure all the time during the
evolution of the considered system. These states are also the most stable under
evolution in the presence of the environment and play an important role in the
description of environment induced decoherence.


title: Toward the Collapse of State

abstract:
  The basic concepts of classical mechanics are given in the operator form.
Then, the hybrid systems approach, with the operator formulation of both
quantum and classical sector, is applied to the case of an ideal nonselective
measurement. It is found that the dynamical equation, consisting of the
Schr\"odinger and Liouville dynamics, produces noncausal evolution when the
initial state of measured system and measuring apparatus is chosen to be as it
is demanded in discussions regarding the problem of measurement. Nonuniqueness
of possible realizations of transition from pure noncorrelated to mixed
correlated state is analyzed in details. It is concluded that collapse of state
is the only possible way of evolution of physical systems in this case.


title: Probabilistic teleportation and entanglement matching

abstract:
  Teleportation may be taken as sending and extracting quantum information
through quantum channels. In this report, it is shown that to get the maximal
probability of exact teleportation through partially entangled quantum
channels, the sender (Alice) need only to operate a measurement which satisfy
an ``entanglement matching'' to this channel. An optimal strategy is also
provided for the receiver (Bob) to extract the quantum information by adopting
general evolutions.


title: Distillability and partial transposition in bipartite systems

abstract:
  We study the distillability of a certain class of bipartite density operators
which can be obtained via depolarization starting from an arbitrary one. Our
results suggest that non-positivity of the partial transpose of a density
operator is not a sufficient condition for distillability, when the dimension
of both subsystems is higher than two.


title: Motion of a particle and the vacuum

abstract:
  We propose the deterministic dynamics of a free particle in a physical
vacuum, which is considered as a discrete (quantum) medium. The motion of the
particle is studied taking into account its interactions with the medium. It is
assumed that this interaction results in the appearance of special virtual
excitations, called "inertons," in the vacuum medium in the surroundings of the
canonical particle. The solution of the equation of motion shows that a cloud
of inertons oscillates around the particle with amplitude $\Lambda=\lambda
v/c$, where $\lambda$ is the de Broglie wavelength, v is the initial velocity
of the particle, and c is the initial velocity of the inertons (velocity of
light). This oscillating nature of motion is also applied to the particle, and
the de Broglie wavelength $\lambda$ becomes the amplitude of spacial
oscillations. The oscillation frequency $\nu$ is given by the relation
$E=h\nu$. The connection of the present model with orthodox nonrelativistic
wave mechanics is analyzed.


title: Quantum State Reconstruction Using Atom Optics

abstract:
  We present a novel technique in which the total internal quantum state of an
atom may be reconstructed via the measurement of the momentum transferred to an
atom following its interaction with a near resonant travelling wave laser beam.
We present the first such measurement and demonstrate the feasibility of the
technique.


title:
Quantum stochastic resonance in driven spin-boson system with stochastic
  limit approximation

abstract:
  After a brief review of stochastic limit approximation with spin-boson system
from physical points of view, amplification phenomenon-stochastic resonance
phenomenon-in driven spin-boson system is observed which is helped by the
quantum white noise introduced through the stochastic limit approximation. The
shift in frequency of the system due to the interaction with the
environment-Lamb shift-has an important role in these phenomena.


title: Evidence for Bound Entangled States with Negative Partial Transpose

abstract:
  We exhibit a two-parameter family of bipartite mixed states $\rho_{bc}$, in a
$d\otimes d$ Hilbert space, which are negative under partial transposition
(NPT), but for which we conjecture that no maximally entangled pure states in
$2\otimes 2$ can be distilled by local quantum operations and classical
communication (LQ+CC). Evidence for this undistillability is provided by the
result that, for certain states in this family, we cannot extract entanglement
from any arbitrarily large number of copies of $\rho_{bc}$ using a projection
on $2\otimes 2$. These states are canonical NPT states in the sense that any
bipartite mixed state in any dimension with NPT can be reduced by LQ+CC
operations to an NPT state of the $\rho_{bc}$ form. We show that the main
question about the distillability of mixed states can be formulated as an open
mathematical question about the properties of composed positive linear maps.


title: Decoherence via Dynamical Casimir Effect

abstract:
  We derive a master equation for a mirror interacting with the vacuum field
via radiation pressure. The dynamical Casimir effect leads to decoherence of a
'Schroedinger cat' state in a time scale that depends on the degree of
'macroscopicity' of the state components, and which may be much shorter than
the relaxation time scale. Coherent states are selected by the interaction as
pointer states.


title: Two-state teleportation

abstract:
  Quantum teleportation with additional a priori information about the input
state achieves higher fidelity than teleportation of a completely unknown
state. However, perfect teleportation of two non-orthogonal input states
requires the same amount of entanglement as perfect teleportation of an unknown
state, namely one ebit. We analyse how well two-state teleportation can be
achieved using every degree of pure-state entanglement, and discuss the
fidelity of `teleportation' that can be achieved with only classical
communication but no shared entanglement. A two-state telecloning scheme is
constructed.


title: Measuring quantum state overlaps of traveling optical fields

abstract:
  We propose a detection scheme for measuring the overlap of the quantum state
of a weakly excited traveling-field mode with a desired reference quantum
state, by successive mixing the signal mode with modes prepared in coherent
states and performing photon-number measurements in an array of beam splitters.
To illustrate the scheme, we discuss the measurement of the quantum phase and
the detection of Schrodinger-cat-like states.


title: Criteria for Continuous-Variable Quantum Teleportation

abstract:
  We derive an experimentally testable criterion for the teleportation of
quantum states of continuous variables. This criterion is especially relevant
to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where
an input-output fidelity of $0.58 \pm 0.02$ was achieved for optical coherent
states. Our derivation demonstrates that fidelities greater than 1/2 could not
have been achieved through the use of a classical channel alone; quantum
entanglement was a crucial ingredient in the experiment.


title:
Entangling Dipole-Dipole Interactions and Quantum Logic in Optical
  Lattices

abstract:
  We study a means of creating multiparticle entanglement of neutral atoms
using pairwise controlled dipole-dipole interactions in a three dimensional
optical lattice. For tightly trapped atoms the dipolar interaction energy can
be much larger than the photon scattering rate, and substantial coherent
evolution of the two-atom state can be achieved before decoherence occurs.
Excitation of the dipoles can be made conditional on the atomic states,
allowing for deterministic generation of entanglement. We derive selection
rules and a figure-of-merit for the dipole-dipole interaction matrix elements,
for alkali atoms with hyperfine structure and trapped in well localized center
of mass states. Different protocols are presented for implementing two-qubits
quantum logic gates such as the controlled-phase and swap gate. We analyze the
fidelity of our gate designs, imperfect due to decoherence from cooperative
spontaneous emission and coherent couplings outside the logical basis. Outlines
for extending our model to include the full molecular interactions potentials
are discussed.


title:
A Self Assembled Nanoelectronic Quantum Computer Based on the Rashba
  Effect in Quantum Dots

abstract:
  Quantum computers promise vastly enhanced computational power and an uncanny
ability to solve classically intractable problems. However, few proposals exist
for robust, solid state implementation of such computers where the quantum
gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I
present a new approach whereby a complete computer with nanoscale gates might
be self-assembled using chemical synthesis. Specifically, I demonstrate how to
self-assemble the fundamental unit of this quantum computer - a 2-qubit
universal quantum controlled-NOT gate - based on two exchange coupled
multilayered quantum dots. Then I show how these gates can be wired using
thiolated conjugated molecules as electrical connectors. A qubit is encoded in
the ground state of a quantum dot spin-split by the Rashba interaction.
Arbitrary qubit rotations are effected by bringing the spin splitting energy in
a target quantum dot in resonance with a global ac magnetic field by applying a
potential pulse of appropriate amplitude and duration to the dot. The
controlled dynamics of the 2-qubit controlled-NOT operation (XOR) can be
realized by exploiting the exchange coupling with the nearest neighboring dot.
A complete prescription for initialization of the computer and data
input/output operations is presented.


title: Almost-Everywhere Superiority for Quantum Computing

abstract:
  Simon as extended by Brassard and H{\o}yer shows that there are tasks on
which polynomial-time quantum machines are exponentially faster than each
classical machine infinitely often. The present paper shows that there are
tasks on which polynomial-time quantum machines are exponentially faster than
each classical machine almost everywhere.


title: Relativistic quantum coin tossing

abstract:
  A relativistic quantum information exchange protocol is proposed allowing two
distant users to realize ``coin tossing'' procedure. The protocol is based on
the point that in relativistic quantum theory reliable distinguishing between
the two orthogonal states generally requires a finite time depending on the
structure of these states.


title: Locally curved quantum layers

abstract:
  We consider a quantum particle constrained to a curved layer of a constant
width built over an infinite smooth surface. We suppose that the latter is a
locally deformed plane and that the layer has the hard-wall boundary. Under
this assumptions we prove that the particle Hamiltonian possesses geometrically
induced bound states.


title: A realist view of the electron: recent advances and unsolved problems

abstract:
  In view of experimentally obtainable resolutions, equal to the Compton
wavelength of an electron, the conventional interpretation of quantum mechanics
no longer seems to provide a sufficiently subtle tool. Based on the intrinsic
properties of extended particles we propose a new theory, which allows to
describe fundamental processes with unlimited precision at the microlevel. It
is shown how this framework combines classical electrodynamics and quantum
mechanics in a single and consistent picture. An analysis of single measurement
problems reveals that the theory is suitable to remove some of the most
striking paradoxes in quantum mechanics, which are found to originate from
obscuring statistical effects with physical reasoning. A possible origin of the
infinity problems in relativistic quantum fields is found by analyzing electron
accelerations due to photon absorption processes. The current state of the
theory and existing problems are discussed briefly.


title: On mechanisms that enforce complementarity

abstract:
  In a recent publication Luis and Sanchez-Soto arrive at the conclusion that
complementarity is universally enforced by random classical phase kicks. We
disagree. One could just as well argue that quantum entanglement is the
universal mechanism. Both claims of universality are unjustified, however.


title: Refined Factorizations of Solvable Potentials

abstract:
  A generalization of the factorization technique is shown to be a powerful
algebraic tool to discover further properties of a class of integrable systems
in Quantum Mechanics. The method is applied in the study of radial oscillator,
Morse and Coulomb potentials to obtain a wide set of raising and lowering
operators, and to show clearly the connection that link these systems.


title: Maximum predictive power and the superposition principle

abstract:
  Recently, there has been a discussion on the origin of the quantum
probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et
al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which
is a slightly reformulated version of a paper published in Int.J.Theor.Phys.
33, 171 (1994), points out the follwoing: To an experimenter the world is a
persistent stream of discrete data. All that is certain is that with each
observation he/she knows more than before, simply because he/she can now answer
the question "Which of the possible outcomes have you just registered?", while
this was not possible before the observation. One can ask whether this
relentless increase of information entails a specific structure. In particular,
how must different observations be related in order to ensure that predictions
become ever more accurate, the more past observations serve as input? This
leads to the quantum rule for adding the complex square roots of probabilities,
and not to adding the probabilities themselves, as classical probability would
have it.


title: The Photon-Box Bohr-Einstein Debate Demithologized

abstract:
  The legendary discussion between Einstein and Bohr concerning the photon box
experiment is critically analyzed. It is shown that Einstein's argument is
flawed and Bohr's reply is wrong.


title: Measuring the entanglement of bipartite pure states

abstract:
  The problem of the experimental determination of the amount of entanglement
of a bipartite pure state is addressed. We show that measuring a single
observable does not suffice to determine the entanglement of a given unknown
pure state of two particles. Possible minimal local measuring strategies are
discussed and a comparison is made on the basis of their best achievable
precision.


title: Description of isolated macroscopic systems inside quantum mechanics

abstract:
  For an isolated macrosystem classical state parameters $\zeta(t)$ are
introduced inside a quantum mechanical treatment. By a suitable mathematical
representation of the actual preparation procedure in the time interval
$[T,t_0]$ a statistical operator is constructed as a solution of the Liouville
von Neumann equation, exhibiting at time $t$ the state parameters $\zeta(t')$,
$t_0\leq t' \leq t$, and {\it preparation parameters} related to times $T \leq
t'\leq t_0$. Relation with Zubarev's non-equilibrium statistical operator is
discussed. A mechanism for memory loss is investigated and time evolution by a
semigroup is obtained for a restricted set of relevant observables, slowly
varying on a suitable time scale.


title: High-Fidelity Teleportation of Independent Qubits

abstract:
  Quantum teleportation is one of the essential primitives of quantum
communication. We suggest that any quantum teleportation scheme can be
characterized by its efficiency, i.e. how often it succeeds to teleport, its
fidelity, i.e. how well the input state is reproduced at the output, and by its
insensitivity to cross talk, i.e. how well it rejects an input state that is
not intended to teleport. We discuss these criteria for the two teleportation
experiments of independent qubits which have been performed thus far. In the
first experiment (Nature {\bf 390},575 (1997)) where the qubit states were
various different polarization states of photons, the fidelity of teleportation
was as high as 0.80 $\pm$ 0.05 thus clearly surpassing the limit of 2/3 which
can, in principle, be obtained by a direct measurement on the qubit and
classical communication. This high fidelity is confirmed in our second
experiment (Phys. Rev. Lett. {\bf 80}, 3891 (1998)), demonstrating entanglement
swapping, that is, realizing the teleportation of a qubit which itself is still
entangled to another one. This experiment is the only one up to date that
demonstrates the teleportation of a genuine unknown quantum state.


title:
Scattering of relativistic particles by a Coulomb field in two
  dimensions

abstract:
  The scattering of relativistic Dirac particles by a Coulomb field $\pm
Ze^2/r$ in two dimensions is studied and the scattering amplitude is obtained
as a partial wave series. For small $Z$ the series can be summed up
approximately to give a closed form. The result, though being aproximate,
exhibites some nonperturbative feature and cannot be obtained from perturbative
quantum electrodynamics at the tree level.


title:
Critical visibility for N-particle Greenberger-Horne-Zeilinger
  correlations to violate local realism

abstract:
  A sequence of Bell inequalities for N-particle systems, which involve three
settings of each of the local measuring apparatuses, is derived. For
Greenberger-Horne-Zeilinger states, quantum mechanics violates these
inequalities by factors exponentially growing with N. The threshold
visibilities of the multiparticle sinusoidal interference fringes, for which
local realistic theories are ruled out, decrease as (2/3)^N.


title:
Quantum information processing in localized modes of light within a
  photonic band-gap material

abstract:
  The single photon occupation of a localized field mode within an engineered
network of defects in a photonic band-gap (PBG) material is proposed as a unit
of quantum information (qubit). Qubit operations are mediated by
optically-excited atoms interacting with these localized states of light as the
atoms traverse the connected void network of the PBG structure. We describe
conditions under which this system can have independent qubits with
controllable interactions and very low decoherence, as required for quantum
computation.


title:
Relations Between Low-lying Quantum Wave Functions and Solutions of the
  Hamilton-Jacobi Equation

abstract:
  We discuss a new relation between the low lying Schroedinger wave function of
a particle in a one-dimentional potential V and the solution of the
corresponding Hamilton-Jacobi equation with -V as its potential. The function V
is $\geq 0$, and can have several minina (V=0). We assume the problem to be
characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller
quantum tunneling parameter $\epsilon$ between these different minima.
Expanding either the wave function or its energy as a formal double power
series in $g^{-1}$ and $\epsilon$, we show how the coefficients of
$g^{-m}\epsilon^n$ in such an expansion can be expressed in terms of definite
integrals, with leading order term determined by the classical solution of the
Hamilton-Jacobi equation. A detailed analysis is given for the particular
example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.


title: Optimal Quantum Cloning via Stimulated Emission

abstract:
  We show that optimal universal quantum cloning can be realized via stimulated
emission. Universality of the cloning procedure is achieved by choosing systems
that have appropriate symmetries. We first discuss a scheme based on stimulated
emission in certain three-level-systems, e.g. atoms in a cavity. Then we
present a way of realizing optimal universal cloning based on stimulated
parametric down-conversion. This scheme also implements the optimal universal
NOT operation.


title: Reduced phase space quantization

abstract:
  We examine two singular Lagrangian systems with constraints which apparently
reduce the phase space to a 2-dimensional sphere and a 2-dimensional
hyperboloid. Rigorous constraint analysis by Dirac's method, however, gives
2-dimensional open disc and an infinite plane with a hole in the centre
respectively as the reduced phase spaces. Upon canonical quantisation the
classical constraints show up as restrictions on the Hilbert space.


title: Generalized Algebraic Bargmann - Darboux Transformations

abstract:
  Algebraic Bargmann and Darboux transformations for equations of a more
general form than the Schr\"odinger ones with an additional functional
dependence h(r) in the right-hand side of equations are constructed. The
suggested generalized transformations turn into the Bargmann and Darboux
transformations for both fixed and variable values of energy and an angular
momentum.


title: Barrier Penetration for Supersymmetric Shape-Invariant Potentials

abstract:
  Exact reflection and transmission coefficients for supersymmetric
shape-invariant potentials barriers are calculated by an analytical
continuation of the asymptotic wave functions obtained via the introduction of
new generalized ladder operators. The general form of the wave function is
obtained by the use of the F-matrix formalism of Froman and Froman which is
related to the evolution of asymptotic wave function coefficients.


title: Geometric quantum computation with NMR

abstract:
  The experimental realisation of the basic constituents of quantum information
processing devices, namely fault-tolerant quantum logic gates, requires
conditional quantum dynamics, in which one subsystem undergoes a coherent
evolution that depends on the quantum state of another subsystem. In
particular, the subsystem may acquire a conditional phase shift. Here we
consider a novel scenario in which this phase is of geometric rather than
dynamical origin. As the conditional geometric (Berry) phase depends only on
the geometry of the path executed it is resilient to certain types of errors,
and offers the potential of an intrinsically fault-tolerant way of performing
quantum gates. Nuclear Magnetic Resonance (NMR) has already been used to
demonstrate both simple quantum information processing and Berry's phase. Here
we report an NMR experiment which implements a conditional Berry phase, and
thus a controlled phase shift gate. This constitutes the first elementary
geometric quantum computation.


title:
Kirchhoff's Rule for Quantum Wires. II: The Inverse Problem with
  Possible Applications to Quantum Computers

abstract:
  In this article we continue our investigations of one particle quantum
scattering theory for Schroedinger operators on a set of connected (idealized
one-dimensional) wires forming a graph with an arbitrary number of open ends.
The Hamiltonian is given as minus the Laplace operator with suitable linear
boundary conditions at the vertices (the local Kirchhoff law). In ``Kirchhoff's
rule for quantum wires'' [J. Phys. A: Math. Gen. 32, 595 - 630 (1999)] we
provided an explicit algebraic expression for the resulting (on-shell) S-matrix
in terms of the boundary conditions and the lengths of the internal lines and
we also proved its unitarity. Here we address the inverse problem in the
simplest context with one vertex only but with an arbitrary number of open
ends. We provide an explicit formula for the boundary conditions in terms of
the S-matrix at a fixed, prescribed energy. We show that any unitary $n\times
n$ matrix may be realized as the S-matrix at a given energy by choosing
appropriate (unique) boundary conditions. This might possibly be used for the
design of elementary gates in quantum computing. As an illustration we
calculate the boundary conditions associated to the unitary operators of some
elementary gates for quantum computers and raise the issue whether in general
the unitary operators associated to quantum gates should rather be viewed as
scattering operators instead of time evolution operators for a given time
associated to a quantum mechanical Hamiltonian.


title: Scattering of short laser pulses from trapped fermions

abstract:
  We investigate the scattering of intense short laser pulses off trapped cold
fermionic atoms. We discuss the sensitivity of the scattered light to the
quantum statistics of the atoms. The temperature dependence of the scattered
light spectrum is calculated. Comparisons are made with a system of classical
atoms who obey Maxwell-Boltzmann statistics. We find the total scattering
increases as the fermions become cooler but eventually tails off at very low
temperatures (far below the Fermi temperature). At these low temperatures the
fermionic degeneracy plays an important role in the scattering as it inhibits
spontaneous emission into occupied energy levels below the Fermi surface. We
demonstrate temperature dependent qualitative changes in the differential and
total spectrum can be utilized to probe quantum degeneracy of trapped Fermi gas
when the total number of atoms are sufficiently large $(\geq 10^6)$. At smaller
number of atoms, incoherent scattering dominates and it displays weak
temperature dependence.


title:
Semiclassical approximation to the partition function of a particle in D
  dimensions

abstract:
  We use a path integral formalism to derive the semiclassical series for the
partition function of a particle in D dimensions. We analyze in particular the
case of attractive central potentials, obtaining explicit expressions for the
fluctuation determinant and for the semiclassical two-point function in the
special cases of the harmonic and single-well quartic anharmonic oscillators.
The specific heat of the latter is compared to precise WKB estimates. We
conclude by discussing the possible extension of our results to field theories.

categories: quant-ph cond-mat.stat-mech hep-ph hep-th


title: Evaluation of heating effects on atoms trapped in an optical trap

abstract:
  We solve a stochastic master equation based on the theory of Savard et al.
[T.A. Savard, K.M. O'Hara and J.E. Thomas, Phys. Rev. A 56, R1095 (1997)] for
heating arising from fluctuations in the trapping laser intensity. We compare
with recent experiments of Ye et. al. [J. Ye, D.W. Vernooy and H.J. Kimble,
Trapping of single atoms in cavity QED, quant-ph/9908007, Phys. Rev. Lett.
(1999 in press)], and find good agreement with the experimental measurements of
the distribution of trap occupancy times. The major cause of trap loss arises
from the broadening of the energy distribution of the trapped atom, rather than
the mean heating rate, which is a very much smaller effect.


title: Entangled Coherent State Qubits in an Ion Trap

abstract:
  We show how entangled qubits can be encoded as entangled coherent states of
two-dimensional centre-of-mass vibrational motion for two ions in an ion trap.
The entangled qubit state is equivalent to the canonical Bell state, and we
introduce a proposal for entanglement transfer from the two vibrational modes
to the electronic states of the two ions in order for the Bell state to be
detected by resonance fluorescence shelving methods.


title:
Strengthening the Bell Theorem: conditions to falsify local realism in
  an experiment

abstract:
  The two-particle correlation obtained from the quantum state used in the Bell
inequality is sinusoidal, but the standard Bell inequality only uses two pairs
of settings and not the whole sinusoidal curve. The highest to-date visibility
of an explicit model reproducing sinusoidal fringes is 2/pi. We conjecture from
a numerical approach presented in this paper that the highest possible
visibility for a local hidden variable model reproducing the sinusoidal
character of the quantum prediction for the two-particle Bell-type interference
phenomena is 1/sqrt2. In addition, the approach can be applied directly to
experimental data.


title: Quantum Reed-Solomon Codes

abstract:
  After a brief introduction to both quantum computation and quantum error
correction, we show how to construct quantum error-correcting codes based on
classical BCH codes. With these codes, decoding can exploit additional
information about the position of errors. This error model - the quantum
erasure channel - is discussed. Finally, parameters of quantum BCH codes are
provided.


title: Quantum BCH Codes


title: Cyclic Quantum Error-Correcting Codes and Quantum Shift Registers

abstract:
  We transfer the concept of linear feed-back shift registers to quantum
circuits. It is shown how to use these quantum linear shift registers for
encoding and decoding cyclic quantum error-correcting codes.


title: A Free Particle on a Circle with Point Interaction

abstract:
  The quantum dynamics of a free particle on a circle with point interaction is
described by a U(2) family of self-adjoint Hamiltonians. We provide a
classification of the family by introducing a number of subfamilies and thereby
analyze the spectral structure in detail. We find that the spectrum depends on
a subset of U(2) parameters rather than the entire U(2) needed for the
Hamiltonians, and that in particular there exists a subfamily in U(2) where the
spectrum becomes parameter-independent. We also show that, in some specific
cases, the WKB semiclassical approximation becomes exact (modulo phases) for
the system.


title: Bell's inequalities for states with positive partial transpose

abstract:
  We study violations of n particle Bell inequalities (as developed by Mermin
and Klyshko) under the assumption that suitable partial transposes of the
density operator are positive. If all transposes with respect to a partition of
the system into p subsystems are positive, the best upper bound on the
violation is 2^((n-p)/2). In particular, if the partial transposes with respect
to all subsystems are positive, the inequalities are satisfied. This is
supporting evidence for a recent conjecture by Peres that positivity of partial
transposes could be equivalent to existence of local classical models.


title: Why Two Qubits Are Special

abstract:
  We analyze some special properties of a system of two qubits, and in
particular of the so-called Bell basis for this system, which have played an
important role in recent papers on entanglement of qubits. In particular, we
show which of these properties may be generalized to higher dimension. We give
a general construction for bases of maximally entangled vectors in any
dimension, but show that none of the properties related to complex conjugation
in Bell basis can be realized for higher dimensional analogs.


title:
Comparison between quantum and classical dynamics in the effective
  action formalism

abstract: No abstract available


title: On the concept of EPR states and their structure

abstract:
  In this paper the notion of an EPR state for the composite S of two quantum
systems S1, S2, relative to S2 and a set O of bounded observables of S2, is
introduced in the spirit of classical examples of Einstein-Podolsky-Rosen and
Bohm. We restrict ourselves mostly to EPR states of finite norm. The main
results are contained in Theorem 3,4,5,6 in section III and imply that if the
EPR states of finite norm relative to (S2, O) exist, then the elements of O
have discrete probability distributions and the Von Neuman algebra generated by
O is essentially inbeddable inside S1 by an antiunitary map. The EPR states
then correspond to the different imbeddings and certain additional parameters,
and are explicitely given by formulae which generalize the famous example of
Bohm. If O generates all bounded observables, S2 must be of finite dimension
and can be imbedded inside S1 by an antiunitary map, and the EPR states
relative to S2 are then in canonical bijection with the different imbeddings of
S2 inside S1; moreover they are given by formulae which are exactly those of
the generalized Bohm states. The notion of EPR states of infinite norm is also
explored and it is shown that the original state of Einstein-Podolsky-Rosen can
be realized as a renormalized limit of EPR states of finite quantum systems
considered by Weyl, Schwinger and many others. Finally, a family of states of
infinite norm generalizing the Einstein-Podolsky-Rosen example is explicitly
given.


title: On the Theory of Quantum Secret Sharing

abstract:
  I present a variety of results on the theory of quantum secret sharing. I
show that any mixed state quantum secret sharing scheme can be derived by
discarding a share from a pure state scheme, and that the size of each share in
a quantum secret sharing scheme must be at least as large as the size of the
secret. I show that the only constraints on the existence of quantum secret
sharing schemes with general access structures are monotonicity (if a set is
authorized, so are larger sets) and the no-cloning theorem. I also discuss some
aspects of sharing classical secrets using quantum states. In this situation,
the size of each share can sometimes be half the size of the classical secret.


title: Quantum chaos in quantum Turing machines

abstract:
  We investigate a 2-spin quantum Turing architecture, in which discrete local
rotations \alpha_m of the Turing head spin alternate with quantum controlled
NOT-operations. We demonstrate that a single chaotic parameter input \alpha_m
leads to a chaotic dynamics in the entire Hilbert-space.


title: Note on Coherent States and Adiabatic Connections, Curvatures

abstract:
  We give a possible generalization to the example in the paper of Zanardi and
Rasetti (quant-ph/9904011). For this generalized one explicit forms of
adiabatic connection, curvature and etc. are given.


title: Controlled quantum evolutions and transitions

abstract:
  We study the nonstationary solutions of Fokker-Planck equations associated to
either stationary or nonstationary quantum states. In particular we discuss the
stationary states of quantum systems with singular velocity fields. We
introduce a technique that allows to realize arbitrary evolutions ruled by
these equations, to account for controlled quantum transitions. The method is
illustrated by presenting the detailed treatment of the transition
probabilities and of the controlling time-dependent potentials associated to
the transitions between the stationary, the coherent, and the squeezed states
of the harmonic oscillator. Possible extensions to anharmonic systems and mixed
states are briefly discussed and assessed.


title:
WKB and MAF Quantization Rules for Spatially Confined Quantum Mechanical
  Systems

abstract:
  A formalism is developed to obtain the energy eigenvalues of spatially
confined quantum mechanical systems in the framework of The usual WKB and MAF
methods. The technique is applied to three different cases,viz one dimensional
Harmonic Oscillators,Quartic Oscillators and a boxed-in charged particle in
electric field.


title: Quantum secure identification using entanglement and catalysis

abstract:
  I consider the use of entanglement between two parties to enable one to
authenticate her identity to another over a quantum communication channel.
Exploiting the phenomenon of entanglement-catalyzed transformations between
pure states gives a potentially reusable entangled identification token. In
analyzing this, I consider the independently interesting problem of the best
possible approximation to a given pure entangled state realizable using local
actions and classical communication by parties sharing a different entangled
state.


title: Entanglement Between Bose-Einstein Condensates

abstract:
  For a Bose condensate in a double-well potential or with two
Josephson-coupled internal states, the condensate wavefunction is a
superposition. Here we consider coupling two such Bose condensates, and suggest
the existence of a joint condensate wavefunction, which is in general a
superposition of all products of the bases condensate wavefunctions of the two
condensates. The corresponding many-body state is a product of such superposed
wavefunctions, with appropriate symmetrization. These states may be potentially
useful for quantum computation. There may be robustness and stability due to
macroscopic occupation of a same single particle state. The nonlinearity of the
condensate wavefunction due to particle-particle interaction may be utilized to
realize nonlinear quantum computation, which was suggested to be capable of
solving NP-complete problems.


title:
Particle Propagator in Elementary Quantum Mechanics: a New Path Integral
  Derivation

abstract:
  This paper suggests a new way to compute the path integral for simple quantum
mechanical systems. The new algorithm originated from previous research in
string theory. However, its essential simplicity is best illustrated in the
case of a free non relativistic particle, discussed here, and can be
appreciated by most students taking an introductory course in Quantum
Mechanics. Indeed, the emphasis is on the role played by the {\it entire family
of classical trajectories} in terms of which the path integral is computed
exactly using a functional representation of the Dirac delta-distribution. We
argue that the new algorithm leads to a deeper insight into the connection
between classical and quantum systems, especially those encountered in high
energy physics.


title: Implementation of a three-quantum-bit search algorithm

abstract:
  We report the experimental implementation of Grover's quantum search
algorithm on a quantum computer with three quantum bits. The computer consists
of molecules of $^{13}$C-labeled CHFBr$_2$, in which the three weakly coupled
spin-1/2 nuclei behave as the bits and are initialized, manipulated, and read
out using magnetic resonance techniques. This quantum computation is made
possible by the introduction of two techniques which significantly reduce the
complexity of the experiment and by the surprising degree of cancellation of
systematic errors which have previously limited the total possible number of
quantum gates.


title: An intrinsic limitation on the size of quantum database

abstract:
  It is found that Grover's quantum search algorithm is not robust against
phase inversion and Hadmard transformation inaccuracies. Imperfect phase
inversions and Hadmard-Walsh transformations in Grover's quantum search
algorithm lead to reductions in the maximum probability of the marked state and
affect the efficiency of the algorithm. even in the absence of decoherence.
Given the degrees of inaccuracies, we find that to guarantee half rate of
success, the size of the database should be in the order of $O({1 \over
\delta^2})$, where $\delta$ is the uncertainty.


title: EPR states for von Neumann algebras

abstract:
  In a recent paper [quant-ph/9910066], Arens and Varadarajan gave a
characterization of what they call EPR-states on a bipartite composite quantum
system. By definition, such states imply perfect correlation between suitable
pairs of observables in the two subsystems, and the task is to determine all
such correlated pairs for a given state. In this note the argument is shortened
and simplified, and at the same time extended to observables in general von
Neumann algebras, which naturally arise in quantum field theory.


title: Popper's experiment and the Copenhagen interpretation

abstract:
  Popper conceived an experiment whose analysis led to a result that he deemed
absurd. Popper wrote that his reasoning was based on the Copenhagen
interpretation and therefore invalidated the latter. Actually, Popper's
argument involves counterfactual reasoning and violates Bohr's complementarity
principle. The absurdity of Popper's result only confirms Bohr's approach.


title: Transition Radiation and the Origin of Sonoluminescence

abstract:
  It has been shown by Liberati et al. [quant-ph/9904013] that a dielectric
medium with a time-dependent refractive index may produce photons. We point out
that a free electric charge which interacts with such a medium will emit
quantum mechanically modified transition radiation in which an arbitrary odd
number of photons will be present. Excited atomic electrons will also exhibit a
similarly modified emission spectrum. This effect may be directly observable in
connection with sonoluminescence.


title:
Purification of impure density operators and the recovery of
  entanglements

abstract:
  The need to retain the relative phases in quantum mechanics implies an
addition law parametrized by a phase of two density operators required for the
purification of a density matrix. This is shown with quantum tomography and the
Wigner function. Entanglement is determined in terms of phase dependent
multiplication.


title: A Quantum to Classical Phase Transition in Noisy Quantum Computers

abstract:
  The fundamental problem of the transition from quantum to classical physics
is usually explained by decoherence, and viewed as a gradual process. The study
of entanglement, or quantum correlations, in noisy quantum computers implies
that in some cases the transition from quantum to classical is actually a phase
transition. We define the notion of entanglement length in $d$-dimensional
noisy quantum computers, and show that a phase transition in entanglement
occurs at a critical noise rate, where the entanglement length transforms from
infinite to finite. Above the critical noise rate, macroscopic classical
behavior is expected, whereas below the critical noise rate, subsystems which
are macroscopically distant one from another can be entangled.
  The macroscopic classical behavior in the super-critical phase is shown to
hold not only for quantum computers, but for any quantum system composed of
macroscopically many finite state particles, with local interactions and local
decoherence, subjected to some additional conditions.
  This phenomenon provides a possible explanation to the emergence of classical
behavior in such systems. A simple formula for an upper bound on the
entanglement length of any such system in the super-critical phase is given,
which can be tested experimentally.


title:
Representation of the Resonances of a Relativistic Quantum Field
  Theoretical Model in Lax-Phillips Scattering Theory

abstract:
  We apply the quantum Lax-Phillips scattering theory to a relativistically
covariant quantum field theoretical form of the (soluble) Lee model. We
construct the translation representations with the help of the wave operators,
and show that the resulting Lax-Phillips $S$-matrix is an inner function (the
Lax-Phillips theory is essentially a theory of translation invariant
subspaces). We then discuss the non-relativistic limit of this theory, and show
that the resulting kinematic relations coincide with the conditions required
for the Galilean description of a decaying system.


title:
Marginal and correlation distribution functions in the squeezed-states
  representation

abstract:
  Here we consider the Husimi function P for the squeezed states and calculate
the marginal and correlation distribution functions when P is projected onto
the photon number states. According to the value of the squeezing parameter one
verifies the occurence of oscillations and beats as already appointed in the
literature. We verify that these phenomena are entirely contained in the
correlation function. In particular, we show that since Husimi and its marginal
distribution functions satisfy partial differential equations where the squeeze
parameter plays the role of time, the solutions (the squeezed functions
obtained from initial unsqueezed functions) can be expressed by means of
kernels responsible for the propagation of squeezing. From the calculational
point of view, this method presents advantages for calculating the marginal
distribution functions (compared to a direct integration over one of the two
phase-space variables of P) since one can use the symmetry properties of the
differential equations.


title: Detection devices in entanglement-based optical state preparation

abstract:
  We study the use of detection devices in entanglement-based state
preparation. In particular we consider optical detection devices such as
single-photon sensitivity detectors, single-photon resolution detectors and
detector cascades (with an emphasis on the performance of realistic detectors).
We develop an extensive theory for the use of these devices. In
entanglement-based state preparation we perform measurements on subsystems, and
we therefore need precise bounds on the distinguishability of these
measurements (this is fundamentally different from, e.g., tomography, where an
ensemble of identical states is used to determine probability distributions,
etc.). To this end, we introduce the confidence of preparation, which may also
be used to quantify the performance of detection devices in entanglement-based
preparation. We give a general expression for detector cascades of arbitrary
size for the detection up to two photons. We show that, contrary to the general
belief, cascading does not give a practical advantage over detectors with
single-photon resolution in entanglement-based state preparation.


title: Universal homodyne tomography with a single local oscillator

abstract:
  We propose a general method for measuring an arbitrary observable of a
multimode electromagnetic field using homodyne detection with a single local
oscillator. In this method the local oscillator scans over all possible linear
combinations of the modes. The case of two modes is analyzed in detail and the
feasibility of the measurement is studied on the basis of Monte-Carlo
simulations. We also provide an application of this method in tomographic
testing of the GHZ state.


title: The Holevo bound and Landauer's principle

abstract:
  Landauer's principle states that the erasure of information generates a
corresponding amount of entropy in the environment. We show that Landauer's
principle provides an intuitive basis for Holevo bound on the classical
capacity of a quantum channel.


title:
Unconditionally Secure Commitment of a Certified Classical Bit is
  Impossible

abstract:
  In a secure bit commitment protocol involving only classical physics, A
commits either a 0 or a 1 to B. If quantum information is used in the protocol,
A may be able to commit a state of the form $\alpha \ket{0} + \beta \ket{1}$.
If so, she can also commit mixed states in which the committed bit is entangled
with other quantum states under her control. We introduce here a quantum
cryptographic primitive, {\it bit commitment with a certificate of
classicality} (BCCC), which differs from standard bit commitment in that it
guarantees that the committed state has a fixed classical value. We show that
no unconditionally secure BCCC protocol based on special relativity and quantum
theory exists. We also propose complete definitions of security for quantum and
relativistic bit commitment.


title: Localization of Eigenstates & Mean Wehrl Entropy

abstract:
  Dynamics of a periodically time dependent quantum system is reflected in the
features of the eigenstates of the Floquet operator. Of the special importance
are their localization properties quantitatively characterized by the
eigenvector entropy, the inverse participation ratio or the eigenvector
statistics. Since these quantities depend on the choice of the eigenbasis, we
suggest to use the overcomplete basis of coherent states, uniquely determined
by the classical phase space. In this way we define the mean Wehrl entropy of
eigenvectors of the Floquet operator and demonstrate that this quantity is
useful to describe quantum chaotic systems.


title: An Universal Quantum Network - Quantum CPU

abstract:
  An universal quantum network which can implement a general quantum computing
is proposed. In this sense, it can be called the quantum central processing
unit (QCPU). For a given quantum computing, its realization of QCPU is just its
quantum network. QCPU is standard and easy-assemble because it only has two
kinds of basic elements and two auxiliary elements. QCPU and its realizations
are scalable, that is, they can be connected together, and so they can
construct the whole quantum network to implement the general quantum algorithm
and quantum simulating procedure.


title: Quantum CPU and Quantum Simulating

abstract:
  Making use of an universal quantum network or QCPU proposed by me [6], some
special quantum networks for simulating some quantum systems are given out.
Specially, it is obtained that the quantum network for the time evolution
operator which can simulate, in general, Schr\"odinger equation.


title: Quantum CPU and Quantum Algorithm

abstract:
  Making use of an universal quantum network -- QCPU proposed by
me\upcite{My1}, it is obtained that the whole quantum network which can
implement some the known quantum algorithms including Deutsch algorithm,
quantum Fourier transformation, Shor's algorithm and Grover's algorithm.


title: Testing operational phase concepts in quantum optics

abstract:
  An experimental comparison of several operational phase concepts is
presented. In particular, it is shown that statistically motivated evaluation
of experimental data may lead to a significant improvement in phase fitting
upon the conventional Noh, Fouge'res and Mandel procedure. The analysis is
extended to the asymptotic limit of large intensities, where a strong evidence
in favor of multi--dimensional estimation procedures has been found.


title:
Security against individual attacks for realistic quantum key
  distribution

abstract:
  I prove the security of quantum key distribution against individual attacks
for realistic signals sources, including weak coherent pulses and
downconversion sources. The proof applies to the BB84 protocol with the
standard detection scheme (no strong reference pulse). I obtain a formula for
the secure bit rate per time slot of an experimental setup which can be used to
optimize the performance of existing schemes for the considered scenario.


title: Nonlinear Optics and Quantum Entanglement of Ultra-Slow Single Photons

abstract:
  Two light pulses propagating with ultra-slow group velocities in a coherently
prepared atomic gas exhibit dissipation-free nonlinear coupling of an
unprecedented strength. This enables a single-photon pulse to coherently
control or manipulate the quantum state of the other. Processes of this kind
result in generation of entangled states of radiation field and open up new
prospectives for quantum information processing.


title: Quantum Cryptography using larger alphabets

abstract:
  Like all of quantum information theory, quantum cryptography is traditionally
based on two level quantum systems. In this letter, a new protocol for quantum
key distribution based on higher dimensional systems is presented. An
experimental realization using an interferometric setup is also proposed.
Analyzing this protocol from the practical side, one finds an increased key
creation rate while keeping the initial laser pulse rate constant. Analyzing it
for the case of intercept/resend eavesdropping strategy, an increased error
rate is found compared to two dimensional systems, hence an advantage for the
legitimate users to detect an eavesdropper.


title: Quantum Mechanics as a Principle Theory

abstract:
  I show how quantum mechanics, like the theory of relativity, can be
understood as a 'principle theory' in Einstein's sense, and I use this notion
to explore the approach to the problem of interpretation developed in my book
Interpreting the Quantum World (Cambridge: Cambridge University Press, 1999).


title:
Revised Proof of the Uniqueness Theorem for 'No Collapse'
  Interpretations of Quantum Mechanics

abstract:
  We show that the Bub-Clifton uniqueness theorem for 'no collapse'
interpretations of quantum mechanics (Studies in the History and Philosophy of
Modern Physics 27, 181-219 (1996)) can be proved without the 'weak
separability' assumption.


title:
Statistical Properties and Algebraic Characteristics of Quantum
  Superpositions of Negative Binomial States

abstract:
  We introduce new kinds of states of quantized radiation fields, which are the
superpositions of negative binomial states. They exhibit remarkable
non-classical properties and reduce to Schr\"odinger cat states in a certain
limit. The algebras involved in the even and odd negative binomial states turn
out to be generally deformed oscillator algebras. It is found that the even and
odd negative binomial states satisfy a same eigenvalue equation with a same
eigenvalue and they can be viewed as two-photon nonlinear coherent states. Two
methods of generating such states are proposed.


title:
Approximate transformations and robust manipulation of bipartite pure
  state entanglement

abstract:
  We analyze approximate transformations of pure entangled quantum states by
local operations and classical communication, finding explicit conversion
strategies which optimize the fidelity of transformation. These results allow
us to determine the most faithful teleportation strategy via an initially
shared partially entangled pure state. They also show that procedures for
entanglement manipulation such as entanglement catalysis [Jonathan and Plenio,
Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states
involved, and motivate the notion of non-local fidelity, which quantifies the
difference in the entangled properties of two quantum states.


title: Quantum gates using two-electron states of triple quantum dot

abstract:
  Quantum computation using electron spins in three coupled dot with different
size is proposed. By using the energy selectivity of both photon assisted
tunneling and spin rotation of electrons, logic gates are realized by static
and rotational magnetic field and resonant optical pulses. Possibility of
increasing the number of quantum bits using the energy selectivity is also
discussed.


title: Control of Wave Packet Revivals Using Geometric Phases

abstract:
  Wave packets in a system governed by a Hamiltonian with a generic nonlinear
spectrum typically exhibit both full and fractional revivals. It is shown that
the latter can be eliminated by inducing suitable geometric phases in the
states, by varying the parameters in the Hamiltonian cyclically with a period
T. Further, with the introduction of this natural time step T, the occurrence
of near revivals can be mapped onto that of Poincar\'{e} recurrences in an
irrational rotation map of the circle. The distinctive recurrence time
statistics of the latter can thus serve as a clear signature of the dynamics of
wave packet revivals.


title: Quantum revivals, geometric phases and circle map recurrences

abstract:
  Revivals of the coherent states of a deformed, adiabatically and cyclically
varying oscillator Hamiltonian are examined. The revival time distribution is
exactly that of Poincar\'{e} recurrences for a rotation map: only three
distinct revival times can occur, with specified weights. A link is thus
established between quantum revivals and recurrences in a coarse-grained
discrete-time dynamical system.


title: Stroboscopic theory of atomic statistics in the micromaser

abstract:
  We study the statistics of the atoms emerging from the cavity of a micromaser
in a dynamical, discrete-time `stroboscopic' description which takes into
account the measurements made, in general, with imperfect efficiencies, on the
states of the outcoming atoms. Inverted atoms enter stochastically, in general,
with a binomial distribution in discrete time; but we also consider the
continuous-time limit of this input statistics which is Poissonian. We envisage
two alternative experimental procedures: one of these is to consider a fixed
number N of atoms pumped into the cavity and subsequently leaving it to undergo
state detection; the other is to consider input of the excited atoms and their
subsequent detection and collection in a fixed time t. We consider, in
particular, the steady state behaviors achieved in the two limits, N ->
infinity and t -> infinity, as well as the approaches to these two limits.
Although these limits are the same for the state of the cavity field, they are
not the same, in general, for the observable outcoming atom statistics. We
evaluate, in particular, Mandel's Q-parameters $Q_{e}$ $(Q_{g})$ for outcoming
atoms detected in their excited states (ground states), for both N -> infinity
and t -> infinity, as functions of $N_{ex} = RT_{c}$: R is the mean rate of
entry for the incoming atoms and $T_c$ is the cavity damping time. The behavior
of these atomic Q-parameters is compared with that parameter for the cavity
field.


title:
Perturbative Calculation of the Adiabatic Geometric Phase and Particle
  in a Well with Moving Walls

abstract:
  We use the Rayleigh-Schr\"odinger perturbation theory to calculate the
corrections to the adiabatic geometric phase due to a perturbation of the
Hamiltonian. We show that these corrections are at least of second order in the
perturbation parameter. As an application of our general results we address the
problem of the adiabatic geometric phase for a one-dimensional particle which
is confined to an infinite square well with moving walls.


title:
Propagation of squeezed radiation through amplifying or absorbing random
  media

abstract:
  We analyse how nonclassical features of squeezed radiation (in particular the
sub-Poissonian noise) are degraded when it is transmitted through an amplifying
or absorbing medium with randomly located scattering centra. Both the cases of
direct photodetection and of homodyne detection are considered. Explicit
results are obtained for the dependence of the Fano factor (the ratio of the
noise power and the mean current) on the degree of squeezing of the incident
state, on the length and the mean free path of the medium, the temperature, and
on the absorption or amplification rate.


title:
Unambiguous state discrimination in quantum cryptography with weak
  coherent states

abstract:
  The use of linearly independent signal states in realistic implementations of
quantum key distribution (QKD) enables an eavesdropper to perform unambiguous
state discrimination. We explore quantitatively the limits for secure QKD
imposed by this fact taking into account that the receiver can monitor to some
extend the photon number statistics of the signals even with todays standard
detection schemes. We compare our attack to the beamsplitting attack and show
that security against beamsplitting attack does not necessarily imply security
against the attack considered here.


title: On Rotating a Qubit

abstract:
  The state function of a quantum object is undetermined with respect to its
phase. This indeterminacy does not matter if it is global, but what if the
components of the state have unknown relative phases? Can useful computations
be performed in spite of this local indeterminacy? We consider this question in
relation to the problem of the rotation of a qubit and examine its broader
implications for quantum computing.


title: Quantum probability from a geometrical interpretation of a wave function

abstract:
  The probabilistic prediction of quantum theory is mystery. I solved the
mystery by a geometrical interpretation of a wave function. This suggests the
unification between quantum theory and the theory of relativity. This suggests
Many-Worlds Interpretation is true, too.


title: The Large Time Behaviour in Quantum Field Theory and Quantum Chaos

abstract:
  An exact general formula for the matrix elements of the evolution operator in
quantum theory is established. The formul ("ABC-formula") has the form
<U(t)>=exp(At+B+C(t)). The constants A and B and the decreasing function C(t)
are computed in perturbation theory. The ABC-formula is valid for a general
class of Hamiltonians used in statistical physics and quantum field theory. The
formula includes the higher order corrections to the well known
Weisskopf-Wigner approximation and to the stochastic (van Hove) limit which are
widely used in considerations of problems of radiation, decay, quantum
decoherence, derivation of master and kinetic equations etc. The function C(t)
admits an interpretation as an analogue of the autocorrelation function
describing quantum chaos for the quantum baker's map.

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


title: On the Phases Structure of the Micromaser System

abstract:
  We investigate, in an exact manner, the phase structure of the micromaser
system in terms of the physical parameters at hand like the atom cavity transit
time, the atom-photon frequency detuning, the number of thermal photons and the
probability for a pump atom to be in its excited state. Phase diagrams are
mapped out for various values of the physical parameters. At sufficiently large
values of the detuning, we find a ``twinkling'' mode of the micromaser system.
A correlation length is used to study fluctuations close to the various phase
transitions.


title:
Van Hove's "\lambda^2 t" limit in nonrelativistic and relativistic
  field-theoretical models

abstract:
  Van Hove's "\lambda^2 t" limiting procedure is analyzed in some interesting
quantum field theoretical cases, both in nonrelativistic and relativistic
models. We look at the deviations from a purely exponential behavior in a decay
process and discuss the subtle issues of state preparation and initial time.


title:
Mirrorless oscillation based on resonantly enhanced 4-wave mixing:
  All-order analytic solutions

abstract:
  The phase transition to mirrorless oscillation in resonantly enhanced
four-wave mixing in double-$\Lambda$ systems are studied analytically for the
ideal case of infinite lifetimes of ground-state coherences. The stationary
susceptibilities are obtained in all orders of the generated fields and
analytic solutions of the coupled nonlinear differential equations for the
field amplitudes are derived and discussed.


title: High-Temperature Expansions of Bures and Fisher Information Priors

abstract:
  For certain infinite and finite-dimensional thermal systems, we obtain ---
incorporating quantum-theoretic considerations into Bayesian thermostatistical
investigations of Lavenda --- high-temperature expansions of priors over
inverse temperature beta induced by volume elements ("quantum Jeffreys' priors)
of Bures metrics. Similarly to Lavenda's results based on volume elements
(Jeffreys' priors) of (classical) Fisher information metrics, we find that in
the limit beta -> 0, the quantum-theoretic priors either conform to Jeffreys'
rule for variables over [0,infinity], by being proportional to 1/beta, or to
the Bayes-Laplace principle of insufficient reason, by being constant. Whether
a system adheres to one rule or to the other appears to depend upon its number
of degrees of freedom.


title:
Perturbation method with triangular propagators and anharmonicities of
  intermediate strength

abstract:
  I propose a new version of the Rayleigh - Schr\"{o}dinger perturbation
method. It admits a lower triangular matrix in place of the usual diagonal
propagator. Illustrated on rational anharmonicities
polynomial}(x)/polynomial}(x), treated as perturbations of (quasi-)exact
anharmonic oscilators. In this sense the method works in an
intermediate-coupling regime and bridges the gap between the weak- and
strong-coupling expansions.


title: A Comment on Fisher Information and Quantum Algorithms

abstract:
  We show that Grover's algorithm defines a geodesic in quantum Hilbert space
with the Fubini-Study metric. From statistical point of view Grover's algorithm
is characterized by constant Fisher's function. Quantum algorithms changing
complexity class as Shor's factorization does not preserve constant Fisher's
information. An adiabatic quantum factorization algorithm in non polynomial
time is presented to exemplify the result.


title: Quantum Instantons and Quantum Chaos

abstract:
  Based on a closed form expression for the path integral of quantum transition
amplitudes, we suggest rigorous definitions of both, quantum instantons and
quantum chaos. As an example we compute the quantum instanton of the double
well potential.


title: Measuring Quantum State in Phase Space

abstract:
  In this thesis we present a direct scheme for measuring quasidistribution
functions of light. This scheme, based on photon counting, is derived from a
simple relation linking the Wigner function with photon statistics. We develop
a full multimode theory of the scheme, and show that the principle of the
measurement can be straightforwardly generalized to the detection of the
multimode radiation. We also discuss practical aspects of the scheme, including
statistical error, non-unit detection efficiency, and imperfect interference
visibility. Next, we report experimental realization of the scheme, and present
measurements of the Wigner function for several quantum states of light.
Finally, we study the general problem of statistical uncertainty in
quantum-optical photodetection measurements.


title: Dynamical mass shift for a partially reflecting moving mirror

abstract:
  We consider the vacuum fluctuations contribution to the mass of a mirror in
an exactly soluble partially reflecting moving mirror model. Partial
reflectivity is accounted for by a repulsive delta-type potential localized
along the mirror trajectory. The mirror's mass is explicitly found as an
integral functional of the mirror's past trajectory.


title: Exactly Solvable Model of Quantum Spin Interacting with Spin Environment

abstract:
  An exactly solvable model of a quantum spin interacting with a spin
environment is considered. The interaction is chosen to be such that the state
of the environment is conserved. The reduced density matrix of the spin is
calculated for arbitrary coupling strength and arbitrary time. The stationary
state of the spin is obtained explicitely in the $t \to \infty$ limit.


title: Counting Cold Collisions

abstract:
  We have experimentally explored a novel possibility to study exoergic cold
atomic collisions. Trapping of small countable atom numbers in a shallow
magneto-optical trap and monitoring of their temporal dynamics allows us to
directly observe isolated two-body atomic collisions and provides detailed
information on loss statistics. A substantial fraction of such cold collisional
events has been found to result in the loss of one atom only. We have also
observed for the first time a strong optical suppression of ground-state
hyperfine-changing collisions in the trap by its repump laser field.


title: Semiclassical analysis of level widths for one-dimensional potentials

abstract:
  We present a semiclassical study of level widths for a class of
one-dimensional potentials in the presence of an ohmic environment. Employing
an expression for the dipole matrix element in terms of the Fourier transform
of the classical path we obtain the level widths within the Golden rule
approximation. It is found that for potentials with an asymptotic power-law
behavior, which may in addition be limited by an infinite wall, the width that
an eigenstate of the isolated system acquires due to the coupling to the
environment is proportional to its quantum number.


title: Rank Two Bipartite Bound Entangled States Do Not Exist

abstract:
  We explore the relation between the rank of a bipartite density matrix and
the existence of bound entanglement. We show a relation between the rank,
marginal ranks, and distillability of a mixed state and use this to prove that
any rank n bound entangled state must have support on no more than an n \times
n Hilbert space. A direct consequence of this result is that there are no
bipartite bound entangled states of rank two. We also show that a separability
condition in terms of a quantum entropy inequality is associated with the above
results. We explore the idea of how many pure states are needed in a mixture to
cancel the distillable entanglement of a Schmidt rank n pure state and provide
a lower bound of n-1. We also prove that a mixture of a non-zero amount of any
pure entangled state with a pure product state is distillable.


title: Opposite momenta lead to opposite directions

abstract:
  When a particle decays into two fragments, the wavefunctions of the latter
are spherical shells with expanding radii. In spite of this spherical symmetry,
the two particles can be detected only in opposite directions.


title: The Rate of Optimal Purification procedures

abstract:
  Purification is a process in which decoherence is partially reversed by using
several input systems which have been subject to the same noise. The purity of
the outputs generally increases with the number of input systems, and decreases
with the number of required output systems. We construct the optimal quantum
operations for this task, and discuss their asymptotic behaviour as the number
of inputs goes to infinity. The rate at which output systems may be generated
depends crucially on the type of purity requirement. If one tests the purity of
the outputs systems one at a time, the rate is infinite: this fidelity may be
made to approach 1, while at the same time the number of outputs goes to
infinity arbitrarily fast. On the other hand, if one also requires the
correlations between outputs to decrease, the rate is zero: if fidelity with
the pure product state is to go to 1, the number of outputs per input goes to
zero. However, if only a fidelity close to 1 is required, the optimal purifier
achieves a positive rate, which we compute.


title: Quantum mechanical spectral engineering by scaling intertwining

abstract:
  Using the concept of spectral engineering we explore the possibilities of
building potentials with prescribed spectra offered by a modified intertwining
technique involving operators which are the product of a standard first-order
intertwiner and a unitary scaling. In the same context we study the iterations
of such transformations finding that the scaling intertwining provides a
different and richer mechanism in designing quantum spectra with respect to
that given by the standard intertwining


title: The Schrodinger Equation From a Quadratic Hamiltonian System

abstract:
  We regard the real and imaginary parts of the Schrodinger wave function as
canonical conjugate variables.With this pair of conjugate variables and some
other 2n pairs, we construct a quadratic Hamiltonian density. We then show that
the Schrodinger Equation follows from the Hamilton's Equation of motion when
the Planck frequency is much larger than the characteristic frequencies of the
Hamiltonian system. The Hamiltonian and the normal mode solutions coincide,
respectively, with the energy expectation value and the energy eigenstates of
the corresponding quantum mechanical system.


title: Quantum Trajectory in Multi-Dimensional Non-Linear System

abstract:
  We discuss quantum dynamics in multi-dimensional non-linear systems. It is
well-known that wave functions are localized in a kicked rotor model. However,
coupling with other degrees of freedom breaks the localization. In order to
clarify the difference, we describe the quantum dynamics by deterministic rigid
trajectories, which are accompanied with the de Broglie-Bohm interpretation of
quantum mechanics, instead of wave functions. A bundle of quantum trajectories
are repulsive through quantum potential and flow never to go across each other.
We show that, according to the degrees of freedom, this same property appears
differently.


title:
A New Class of Adiabatic Cyclic States and Geometric Phases for
  Non-Hermitian Hamiltonians

abstract:
  For a T-periodic non-Hermitian Hamiltonian H(t), we construct a class of
adiabatic cyclic states of period T which are not eigenstates of the initial
Hamiltonian H(0). We show that the corresponding adiabatic geometric phase
angles are real and discuss their relationship with the conventional complex
adiabatic geometric phase angles. We present a detailed calculation of the new
adiabatic cyclic states and their geometric phases for a non-Hermitian analog
of the spin 1/2 particle in a precessing magnetic field.


title: A novel SO(3) picture for quantum searching

abstract:
  An SO(3) picture of the generalized Grover's quantum searching algorithm,with
arbitrary unitary transformation and with arbitrary phase rotations, is
constructed. In this picture, any quantum search operation is a rotation in a 3
dimensional space. Exact formulas for the rotation angle and rotational axis
are given. The probability of finding the marked state is just $(z+1)/2$, where
z is the z-component of the state vector. Exact formulas for this probability
is easily obtained. The phase matching requirement and the failure of algorithm
when phase mismatches are clearly explained.


title: Filtering Number States of the Vibrational Motion of an Ion

abstract:
  We propose a scheme to generate number states (and specific superpositions of
them) of the vibrational motion of a trapped ion. In particular, we show that
robust to noise qubits can be generated with arbitrary amplitudes.


title:
A new approach to perturbation theory for a Dirac particle in a central
  field

abstract:
  The explicit semiclassical treatment of logarithmic perturbation theory for
the bound-state problem within the framework of the Dirac equation is
developed. Avoiding disadvantages of the standard approach in the description
of exited states, new handy recursion formulae with the same simple form both
for ground and exited states have been obtained. As an example, the
perturbation expansions for the energy eigenvalues for the Yukawa potential
containing the vector part as well as the scalar component are considered.


title: Motion of vortex lines in quantum mechanics

abstract:
  Exact analytic solutions of the time dependent Schrodinger equation are
produced that exhibit a variety of vortex structures. The qualitative analysis
of the motion of vortex lines is presented and various types of vortex behavior
are identified. Vortex creation and annihilation and vortex interactions are
illustrated in the special cases of the free motion, the motion in the harmonic
potential, and in the constant magnetic field. Similar analysis of the vortex
motions is carried out also for a relativistic wave equation.


title: Optimal estimation of two-qubit pure-state entanglement

abstract:
  We present optimal measuring strategies for the estimation of the
entanglement of unknown two-qubit pure states and of the degree of mixing of
unknown single-qubit mixed states, of which N identical copies are available.
The most general measuring strategies are considered in both situations, to
conclude in the first case that a local, although collective, measurement
suffices to estimate entanglement, a non-local property, optimally.


title: Distinguishability of States and von Neumann Entropy

abstract:
  Consider an ensemble of pure quantum states |\psi_j>, j=1,...,n taken with
prior probabilities p_j respectively. We show that it is possible to increase
all of the pairwise overlaps |<\psi_i|\psi_j>| i.e. make each constituent pair
of the states more parallel (while keeping the prior probabilities the same),
in such a way that the von Neumann entropy S is increased, and dually, make all
pairs more orthogonal while decreasing S. We show that this phenomenon cannot
occur for ensembles in two dimensions but that it is a feature of almost all
ensembles of three states in three dimensions. It is known that the von Neumann
entropy characterises the classical and quantum information capacities of the
ensemble and we argue that information capacity in turn, is a manifestation of
the distinguishability of the signal states. Hence our result shows that the
notion of distinguishability within an ensemble is a global property that
cannot be reduced to considering distinguishability of each constituent pair of
states.


title:
Hydrogen atom as an eigenvalue problem in 3D spaces of constant
  curvature and minimal length

abstract:
  An old result of A.F. Stevenson [Phys. Rev.} 59, 842 (1941)] concerning the
Kepler-Coulomb quantum problem on the three-dimensional (3D) hypersphere is
considered from the perspective of the radial Schr\"odinger equations on 3D
spaces of any (either positive, zero or negative) constant curvature. Further
to Stevenson, we show in detail how to get the hypergeometric wavefunction for
the hydrogen atom case. Finally, we make a comparison between the ``space
curvature" effects and minimal length effects for the hydrogen spectrum


title:
Constructing quantum error-correcting codes for p^m-state systems from
  classical error-correcting codes

abstract:
  We generalize the construction of quantum error-correcting codes from
GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how
to determine the error from a syndrome. Finally we discuss a systematic
construction of quantum codes with efficient decoding algorithms.


title: SWKB Quantization Rules for Bound States in Quantum Wells

abstract:
  In a recent paper by Gomes and Adhikari (J.Phys B30 5987(1997)) a matrix
formulation of the Bohr-Sommerfield quantization rule has been applied to the
study of bound states in one dimension quantum wells. Here we study these
potentials in the frame work of supersymmetric WKB (SWKB) quantization
approximation and find that SWKB quantization rule is superior to the modified
Bohr-Sommerfield or WKB rules as it exactly reproduces the eigenenergies.


title: Qubit and Entanglement assisted Optimal Entanglement Concentration

abstract:
  We present two method for optimal entanglement concentration from pure
entangled states by local actions only. However a prior knowledge of the
Schmidt coefficients is required. The first method is optimally efficient only
when a finite ensemble of pure entangled states are available whereas the
second method realizes the single pair optimal concentration probability. We
also propose an entanglement assisted method which is again optimally efficient
even for a single pair. We also discuss concentrating entanglement from
N-partite cat like states.


title:
First-order interference of nonclassical light emitted spontaneously at
  different times

abstract:
  We study first-order interference in spontaneous parametric down-conversion
generated by two pump pulses that do not overlap in time. The observed
modulation in the angular distribution of the signal detector counting rate can
only be explained in terms of a quantum mechanical description based on
biphoton states. The condition for observing interference in the signal channel
is shown to depend on the parameters of the idler radiation.


title: NMR spectroscopy and computing beyond myth and fiction

abstract: Only craziness I am ashamed about.


title: Faster Than Light Communication

abstract:
  This paper has been withdrawn by the author, due a crucial error in the main
idea.


title:
Creating a low-dimensional quantum gas using dark states in an inelastic
  evanescent-wave mirror

abstract:
  We discuss an experimental scheme to create a low-dimensional gas of
ultracold atoms, based on inelastic bouncing on an evanescent-wave mirror.
Close to the turning point of the mirror, the atoms are transferred into an
optical dipole trap. This scheme can compress the phase-space density and can
ultimately yield an optically-driven atom laser. An important issue is the
suppression of photon scattering due to ``cross-talk'' between the mirror
potential and the trapping potential. We propose that for alkali atoms the
photon scattering rate can be suppressed by several orders of magnitude if the
atoms are decoupled from the evanescent-wave light. We discuss how such dark
states can be achieved by making use of circularly-polarized evanescent waves.


title: Quantum Zeno effect in a probed downconversion process

abstract:
  The distorsion of a spontaneous downconvertion process caused by an auxiliary
mode coupled to the idler wave is analyzed. In general, a strong coupling with
the auxiliary mode tends to hinder the downconversion in the nonlinear medium.
On the other hand, provided that the evolution is disturbed by the presence of
a phase mismatch, the coupling may increase the speed of downconversion. These
effects are interpreted as being manifestations of quantum Zeno or anti-Zeno
effects, respectively, and they are understood by using the dressed modes
picture of the device. The possibility of using the coupling as a nontrivial
phase--matching technique is pointed out.


title: Recovery of entanglement lost in entanglement manipulation

abstract:
  When an entangled state is transformed into another one with probability one
by local operations and classical communication, the quantity of entanglement
decreases. This letter shows that entanglement lost in the manipulation can be
partially recovered by an auxiliary entangled pair. As an application, a
maximally entangled pair can be obtained from two partially entangled pairs
with probability one. Finally, this recovery scheme reveals a fundamental
property of entanglement relevant to the existence of incomparable states.


title:
A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann
  Algebras as the Base Category

abstract:
  We extend the topos-theoretic treatment given in previous papers of assigning
values to quantities in quantum theory, and of related issues such as the
Kochen-Specker theorem. This extension has two main parts: the use of von
Neumann algebras as a base category (Section 2); and the relation of our
generalized valuations to (i) the assignment to quantities of intervals of real
numbers, and (ii) the idea of a subobject of the coarse-graining presheaf
(Section 3).


title: Optimal Measurements of Spin Direction

abstract:
  The accuracy of a measurement of the spin direction of a spin-s particle is
characterised, for arbitrary half-integral s. The disturbance caused by the
measurement is also characterised. The approach is based on that taken in
several previous papers concerning joint measurements of position and momentum.
As in those papers, a distinction is made between the errors of retrodiction
and prediction. Retrodictive and predictive error relationships are derived.
The POVM describing the outcome of a maximally accurate measurement process is
investigated. It is shown that, if the measurement is retrodictively optimal,
then the distribution of measured values is given by the initial state SU(2)
Q-function. If the measurement is predictively optimal, then the distribution
of measured values is related to the final state SU(2) P-function. The general
form of the unitary evolution operator producing an optimal measurement is
characterised.


title: Kochen-Specker theorem and experimental test on hidden variables

abstract:
  A recent proposal to experimentally test quantum mechanics against
noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is
shown to be related with the smallest proof of the Kochen-Specker theorem
currently known [Phys. Lett. A 212, 183 (1996)]. This proof contains eighteen
yes-no questions about a four-dimensional physical system, combined in nine
mutually incompatible tests. When these tests are considered as tests about a
two-part two-state system, then quantum mechanics and non-contextual hidden
variables make the same predictions for eight of them, but make different
predictions for the ninth. Therefore, this ninth test would allow us to
discriminate between quantum mechanics and noncontextual hidden-variable
theories in a (gedanken) single run experiment.


title:
Nonlocality without inequalities has not been proved for maximally
  entangled states

abstract:
  Two approaches to extend Hardy's proof of nonlocality without inequalities to
maximally entangled states of bipartite two-level systems are shown to fail. On
one hand, it is shown that Wu and co-workers' proof [Phys. Rev. A 53, R1927
(1996)] uses an effective state which is not maximally entangled. On the other
hand, it is demonstrated that Hardy's proof cannot be generalized by the
replacement of one of the four von Neumann measurements involved in the
original proof by a generalized measurement to unambiguously discriminate
between non-orthogonal states.


title: Comment on "Non-contextual hidden variables and physical measurements"

abstract:
  Kent's conclusion that ``non-contextual hidden variable theories cannot be
excluded by theoretical arguments of the Kochen-Specker type once the
imprecision in real world experiments is taken into account'' [Phys. Rev. Lett.
83, 3755 (1999)], is criticized. The Kochen-Specker theorem just points out
that it is impossible even conceive a hidden variable model in which the
outcomes of all measurements are pre-determined; it does not matter if these
measurements are performed or not, or even if these measurements can be
achieved only with finite precision.


title: Quantum key distribution without alternative measurements

abstract:
  Entanglement swapping between Einstein-Podolsky-Rosen (EPR) pairs can be used
to generate the same sequence of random bits in two remote places. A quantum
key distribution protocol based on this idea is described. The scheme exhibits
the following features. (a) It does not require that Alice and Bob choose
between alternative measurements, therefore improving the rate of generated
bits by transmitted qubit. (b) It allows Alice and Bob to generate a key of
arbitrary length using a single quantum system (three EPR pairs), instead of a
long sequence of them. (c) Detecting Eve requires the comparison of fewer bits.
(d) Entanglement is an essential ingredient. The scheme assumes reliable
measurements of the Bell operator.


title: Semiclassical Approximation for Periodic Potentials

abstract:
  We derive the semiclassical WKB quantization condition for obtaining the
energy band edges of periodic potentials. The derivation is based on an
approach which is much simpler than the usual method of interpolating with
linear potentials in the regions of the classical turning points. The band
structure of several periodic potentials is computed using our semiclassical
quantization condition.


title:
Irrelevance of photon events distinguishability in a class of Bell
  experiments

abstract:
  We show that the possibility of distinguishing between single and two photon
detection events, usually not met in the actual experiments, is not a necessary
requirement for the proof that the experiments of Alley and Shih [Phys. Rev.
Lett. 61, 2921 (1988)], and Ou and Mandel [Phys. Rev. Lett. 61, 50 (1988)], are
modulo fair sampling assumption, valid tests of local realism. We also give the
critical parameters for the experiments to be unconditional tests of local
realism, and show that some other interesting phenomena (involving bosonic type
particle indistinguishability) can be observed during such tests.


title: Faster than light Bell telephone of Michalski transmits only noise

abstract:
  Motivated by pedagogical reasons we pinpoint the mistake in the recent claim,
in quant-ph/9911016, that faster than light communication is possible.


title: Geometric Phase, Hannay's Angle, and an Exact Action Variable

abstract:
  Canonical structure of a generalized time-periodic harmonic oscillator is
studied by finding the exact action variable (invariant). Hannay's angle is
defined if closed curves of constant action variables return to the same curves
in phase space after a time evolution. The condition for the existence of
Hannay's angle turns out to be identical to that for the existence of a
complete set of (quasi)periodic wave functions. Hannay's angle is calculated,
and it is shown that Berry's relation of semiclassical origin on geometric
phase and Hannay's angle is exact for the cases considered.


title:
Geometric phases in the simple harmonic and perturbative Mathieu's
  oscillator systems

abstract:
  Geometric phases of simple harmonic oscillator system are studied. Complete
sets of "eigenfunctions" are constructed, which depend on the way of choosing
classical solutions. For an eigenfunction, two different motions of the
probability distribution function (pulsation of the width and oscillation of
the center) contribute to the geometric phase which can be given in terms of
the parameters of classical solutions. The geometric phase for a general wave
function is also given. If a wave function has a parity under the inversion of
space coordinate, then the geometric phase can be defined under the evolution
of half of the period of classical motions. For the driven case, geometric
phases are given in terms of Fourier coefficients of the external force. The
oscillator systems whose classical equation of motion is Mathieu's equation are
perturbatively studied, and the first term of nonvanishing geometric phase is
calculated.


title: Evolution of fermionic systems as an expectation over Poisson processes

abstract:
  We derive an exact probabilistic representation for the evolution of a
Hubbard model with site- and spin-dependent hopping coefficients and
site-dependent interactions in terms of an associated stochastic dynamics of a
collection of Poisson processes.

categories: quant-ph cond-mat hep-lat math-ph math.MP


title: An application of two photon entangled states to quantum metrology

abstract:
  Besides many interesting application to the study of foundations of quantum
mechanics, entangled state are now assuming a large relevance for some
practical application. In particular, we discuss most recent results obtained
in our laboratory on the use of two photons entangled states produced in
parametric down conversion for absolute quantum efficiency calibration of
photodetectors, in photon counting regime.


title: An Operator Formulation of Classical Mechanics and Semiclassical Limit

abstract:
  The generalized h-dependent operator algebra is defined ($0\leq h \leq h_o$).
For h= h_o it becomes equivalent to the quantum mechanical algebra of
observables and for h=0 it is equivalent to the classical one. We show this by
proposing how the main features of both mechanics can be defined in operator
form.


title: Controlling Magneto-Optical Rotation via Atomic COherences

abstract:
  An isotropic medium, having magnetic sublevels, when subjected to a magnetic
field or an electromagnetic field can induce anisotropy in the medium; and as a
result the plane of polarization of the probe field can rotate. Therefore the
rotation due to the magnetic field alone, can be {\em controlled efficiently}
with use of a coherent field. We show, using a control field, significant
enhancement of the magneto-optical rotation and demonstrate the possibility of
realizing {\em magneto-optical switch}.


title:
Quantum Key Distribution using Two Coherent States of Light and their
  Superposition

abstract:
  Quantum mechanical complementarity ensures the security of the
key-distribution scheme reported by Brassard and Bennet in 1984 (BB84), but
does not prohibit use of multi-photons as a signal carrier. We describe a novel
BB84 scheme in which two nearly orthogonal coherent states carry the key, and
the superposition of these states (cat states) protects the communication
channel from eavesdropping. Information leakage to eavesdroppers can be
determined from the visibility of the interferential fringes in the
distribution of the outcome when a certain quadrature component is measured
through homodyne detection. The effect of channel loss and detector
inefficiency is discussed.


title: Optical Bell Measurement by Fock Filtering

abstract:
  We describe a nonlinear interferometric setup to perform a complete optical
Bell measurement, i.e. to unambigously discriminate the four polarization
entangled EPR-Bell photon pairs. The scheme is robust against detector
inefficiency.


title: Quantum Statistical Mechanics on a Quantum Computer

abstract:
  We describe a quantum algorithm to compute the density of states and thermal
equilibrium properties of quantum many-body systems. We present results
obtained by running this algorithm on a software implementation of a 21-qubit
quantum computer for the case of an antiferromagnetic Heisenberg model on
triangular lattices of different size.


title: Quantum Spin Dynamics and Quantum Computation

abstract:
  We describe a simulation method for a quantum spin model of a generic,
general purpose quantum computer. The use of this quantum computer simulator is
illustrated through several implementations of Grover's database search
algorithm. Some preliminary results on the stability of quantum algorithms are
presented.


title:
Greenberger-Horne-Zeilinger paradoxes with symmetric multiport beam
  splitters

abstract:
  In a gedankenexperiment N particles in a generalized GHZ-type beam entangled
state (each particle can be in one of M beams) are fed into N symmetric 2M-port
beam splitters (spatially separated). Correlation functions for such a process
(using the Bell numbers value assignment approach) reveal a remarkable
symmetry. For N=M+1 greater or equal to 4 a series of GHZ paradoxes are shown.


title: Coloring the rational quantum sphere and the Kochen-Specker theorem

abstract:
  We review and extend recent findings of Godsil and Zaks, who published a
constructive coloring of the rational unit sphere with the property that for
any orthogonal tripod formed by rays extending from the origin of the points of
the sphere, exactly one ray is red, white and black. They also showed that any
consistent coloring of the real sphere requires an additional color. We discuss
some of the consequences for the Kochen-Specker theorem.


title: Quantum Computer Emulator

abstract:
  We describe a quantum computer emulator for a generic, general purpose
quantum computer. This emulator consists of a simulator of the physical
realization of the quantum computer and a graphical user interface to program
and control the simulator. We illustrate the use of the quantum computer
emulator through various implementations of the Deutsch-Jozsa and Grover's
database search algorithm.


title: Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers

abstract:
  An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is
performed by computing Bloch and Husimi projections. The eigenstate analysis is
combined with the calculation of absorption bands of asymmetric dimer
configurations constituted by monomers with nonidentical excitation energies
and optical transition matrix elements. Absorption bands with regular and
irregular fine structures are obtained and related to the transition from the
coexistence to a mixing of adiabatic branches in the spectrum. It is shown that
correlations between spin states allow for an interpolation between absorption
bands for different optical asymmetries.


title: Cheat Sensitive Quantum Bit Commitment

abstract:
  We define cheat sensitive cryptographic protocols between mistrustful parties
as protocols which guarantee that, if either cheats, the other has some nonzero
probability of detecting the cheating. We give an example of an unconditionally
secure cheat sensitive non-relativistic bit commitment protocol which uses
quantum information to implement a task which is classically impossible; we
also describe a simple relativistic protocol.


title:
Classification of multi-qubit mixed states: separability and
  distillability properties

abstract:
  We give a complete, hierarchic classification for arbitrary multi-qubit mixed
states based on the separability properties of certain partitions. We introduce
a family of N-qubit states to which any arbitrary state can be depolarized.
This family can be viewed as the generalization of Werner states to multi-qubit
systems. We fully classify those states with respect to their separability and
distillability properties. This provides sufficient conditions for
nonseparability and distillability for arbitrary states.


title: Entanglement swapping with PDC sources

abstract:
  We show that the possibility of distinguishing between single and two photon
detection events is not a necessary requirement for the proof that recent
operational realization of entanglement swapping cannot find a local realistic
description. We propose a simple modification of the experiment, which gives a
richer set of interesting phenomena.


title: Orthogonality and Boundary Conditions in Quantum Mechanics

abstract:
  One-dimensional particle states are constructed according to orthogonality
conditions, without requiring boundary conditions. Free particle states are
constructed using Dirac's delta function orthogonality conditions. The states
(doublets) depend on two quantum numbers: energy and parity. With the aid of
projection operators the particles are confined to a constrained region, in a
way similar to the action of an infinite well potential. From the resulting
overcomplete basis only the mutually orthogonal states are selected. Four
solutions are found, corresponding to different non-commuting Hamiltonians.
Their energy eigenstates are labeled with the main quantum number n and parity
"+" or "-". The energy eigenvalues are functions of n only. The four cases
correspond to different boundary conditions: (I) the wave function vanishes on
the boundary, (II) the derivative of the wavefunction vanishes on the
boundary,(III) periodic (symmetric) boundary conditions, (IV) periodic
(antisymmetric)boundary conditions . Among the four cases, only solution (III)
forms a complete basis in the sense that any function in the constrained
region, can be expanded with it. By extending the boundaries of the constrained
region to infinity, only solution (III) converges uniformly to the free
particle states. Orthogonality seems to be a more basic requirement than
boundary conditions. By using projection operators, confinement of the particle
to a definite region can be achieved in a conceptually simple and unambiguous
way, and physical operators can be written so that they act only in the
confined region.