title: The quantum bit commitment: a complete classification of protocols

abstract:
  This paper addresses the controversy between Mayers, Lo and Chau on one side,
and Yuen on the opposite side, on whether there exist or not unconditionally
secure protocols. For such purpose, a complete classification of all possible
bit commitment protocols is given, including all possible cheating attacks. For
the simplest class of protocols (non-aborting and with complete and perfect
verification), it is shown how naturally a game-theoretical situation arises.
For these protocols, bounds for the cheating probabilities are derived, which
turn out to be different from those given in the impossibility proof. The whole
classification and analysis has been carried out using a "finite open system"
approach. The discrepancy with the impossibility proof is explained on the
basis of the implicit adoption of a "closed system approach"--equivalent to
modeling the commitment as performed by two fixed machines interacting
unitarily in a overall "closed system". However, it is shown that the closed
system approach for the classification of commitment protocols unavoidably
leads to infinite dimensions, which then invalidate the continuity argument at
the basis of the impossibility proof.


title:
Realization of a resonant non-linear phase flip in cavity quantum
  electrodynamics

abstract:
  Optical nonlinearities sensitive to individual photons may be extremely
useful as elements in quantum logic circuits for photonic qubits. A much cited
example is the work of Turchette et al. [Phys. Rev. Lett. 75, 4710 (1995)], in
which a phase shift of about 10 degrees was reported. To improve this result,
we propose a single sided cavity geometry with minimal cavity losses. It should
then be possible to achieve a nonlinear phase shift of 180 degrees.


title:
Heun Functions and the energy spectrum of a charged particle on a sphere
  under magnetic field and Coulomb force

abstract:
  We study the competitive action of magnetic field, Coulomb repulsion and
space curvature on the motion of a charged particle. The three types of
interaction are characterized by three basic lengths: l_{B} the magnetic
length, l_{0} the Bohr radius and R the radius of the sphere. The energy
spectrum of the particle is found by solving a Schr\"odinger equation of the
Heun type, using the technique of continued fractions. It displays a rich set
of functioning regimes where ratios \frac{R}{l_{B}} and \frac{R}{l_{0}} take
definite values.


title: Time-local master equations: influence functional and cumulant expansion

abstract:
  The non-Markovian behaviour of open quantum systems interacting with a
reservoir can often be described in terms of a time-local master equation
involving a time-dependent generator which is not in Lindblad form. A
systematic perturbation expansion of the generator is obtained either by means
of van Kampen's method of ordered cumulants or else by use of the
Feynman-Vernon influence functional technique. Both expansions are demonstrated
to yield equivalent expressions for the generator in all orders of the
system-reservor coupling. Explicit formulae are derived for the second and the
fourth order generator in terms of the influence functional.


title: Two photon interference and optical free induction decay

abstract:
  The two photon interference phenomenon is theoretically investigated for the
general situations with an arbitrary input two photon state with and without
photon polarization. For the case without polarization, the
necessary-sufficient condition for the destructive interference of coincidence
counting is given as the symmetric pairing of photons in the light pulses. For
both case it is shown that the "dip" in coincidence curve can be understood in
terms of the free induction decay mechanism. This observation predicts the
destructive interference phenomenon to occur even for certain cases with
separable input two photon state, but it can only be explained in terms of "the
two photon (not two photons)interference ".


title: LOCC protocols for entanglement transformations

abstract:
  We construct the protocols to achieve probabilistic and deterministic
entanglement transformations for bipartite pure states by means of local
operations and classical communication. A new condition on pure contraction
transformations is provided.


title:
New results concerning the $so(2,1)$ treatment for the hypergeometric
  Natanzon potentials

abstract:
  The $so(2,1)$ analysis for the bound state sector of the hypergeometric
Natanzon potentials (HNP) is extended to the scattering sector by considering
the continuous series of the $so(2,1)$ algebra. As a result a complete
algebraic treatment of the HNP by means of the $so(2,1)$ algebra is achieved.
  In the bound state sector we discuss a set of satellite potentials which
arises from the action of the $so(2,1)$ generators. It is shown that the set of
new potentials are not related to the one obtained by means of SUSYQM or of the
potential algebra approach using the $so(2,2)$ algebra.


title:
$so(2,1)$ scattering via Euclidean Connection for the Natanzon
  Hypergeometric Potentials

abstract:
  The $so(2,1)$ Euclidean Connection formalism is used to calculate the $S$
matrix for the Hypergeometric Natanzon Potentials ($HNP$).


title:
Physical limitations on quantum nonlocality in the detection of gamma
  photons emitted from positron/electron annihilation

abstract:
  Recent experimental measurements of the time interval between detection of
the two photons emitted in positron/electron annihilation have indicated that
collapse of the spatial part of the photon's wavefunction, due to detection of
the other photon, does not occur. Although quantum nonlocality actually occurs
in photons produced through parametric down-conversion, the recent experiments
give strong evidence against measurement-induced instantaneous
spatial-localization of high-energy gamma photons. A new quantum-mechanical
analysis of the EPR problem is presented which may help to explain the observed
differences between photons produced through parametric down-conversion and
photons produced through positron/electron annihilation. The results are found
to concur with the recent experiments involving gamma photons.


title: Comparison of Entropies in the Light of Separability

abstract:
  This paper has been withdrawn by the author(s) in the light of several other
works available and due to a misunderstanding in the authorships.


title: On numerical integration of coupled Korteweg-de Vries System

abstract:
  We introduce a numerical method for general coupled Korteweg-de Vries
systems. The scheme is valid for solving Cauchy problems for arbitrary number
of equations with arbitrary constant coefficients. The numerical scheme takes
its legality by proving its stability and convergence which gives the
conditions and the appropriate choice of the grid sizes. The method is applied
to Hirota-Satsuma (HS) system and compared with its known explicit solution
investigating the influence of initial conditions and grid sizes on accuracy.
We also illustrate the method to show the effects of constants with a
transition to the non-integrable case.


title: Analytical study of four-wave mixing with large atomic coherence

abstract:
  Four-wave mixing in resonant atomic vapors based on maximum coherence induced
by Stark-chirped rapid adiabatic passage (SCRAP) is investigated theoretically.
We show the advantages of a coupling scheme involving maximum coherence and
demonstrate how a large atomic coherence between a ground and an highly excited
state can be prepared by SCRAP. Full analytic solutions of the field
propagation problem taking into account pump field depletion are derived. The
solutions are obtained with the help of an Hamiltonian approach which in the
adiabatic limit permits to reduce the full set of Maxwell-Bloch equations to
simple canonical equations of Hamiltonian mechanics for the field variables. It
is found that the conversion efficiency reached is largely enhanced if the
phase mismatch induced by linear refraction is compensated. A detailed analysis
of the phase matching conditions shows, however, that the phase mismatch
contribution from the Kerr effect cannot be compensated simultaneously with
linear refraction contribution. Therefore, the conversion efficiency in a
coupling scheme involving maximum coherence prepared by SCRAP is high, but not
equal to unity.


title: Uncertainty characteristics of generalized quantum measurements

abstract:
  The effects of any quantum measurement can be described by a collection of
measurement operators {M_m} acting on the quantum state of the measured system.
However, the Hilbert space formalism tends to obscure the relationship between
the measurement results and the physical properties of the measured system. In
this paper, a characterization of measurement operators in terms of measurement
resolution and disturbance is developed. It is then possible to formulate
uncertainty relations for the measurement process that are valid for arbitrary
input states. The motivation of these concepts is explained from a quantum
communication viewpoint. It is shown that the intuitive interpretation of
uncertainty as a relation between measurement resolution and disturbance
provides a valid description of measurement back action. Possible applications
to quantum cryptography, quantum cloning, and teleportation are discussed.


title:
There is no unmet requirement of optical coherence for
  continuous-variable quantum teleportation

abstract:
  It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903
(2001)] that continuous-variable quantum teleportation at optical frequencies
has not been achieved because the source used (a laser) was not `truly
coherent'. Here I show that `true coherence' is always illusory, as the concept
of absolute time on a scale beyond direct human experience is meaningless. A
laser is as good a clock as any other, even in principle, and this objection to
teleportation experiments is baseless.


title: Relativistic entanglement and Bell's inequality

abstract:
  In this paper, the Lorentz transformation of entangled Bell states seen by a
moving observer is studied. The calculated Bell observable for 4 joint
measurements turns out to give a universal value,
$<\hat{a}\otimes\vec{b}>+<\hat{a}\otimes\vec{b}'>+\lang
le\hat{a}'\otimes\vec{b}>
-<\hat{a}'\otimes\vec{b}'>=\frac{2}{\sqrt{2-\beta^2}}(1+\sqrt{1-\be ta^2})$,
where $\hat{a}, \hat{b}$ are the relativistic spin observables derived from the
Pauli-Lubanski pseudo vector and $\beta=\frac{v}{c}$.
  We found that the degree of violation of the Bell's inequality is decreasing
with increasing velocity of the observer and the Bell's inequality is satisfied
in the ultra-relativistic limit where the boost speed reaches the speed of
light.


title:
Pseudo-unitary symmetry and the Gaussian pseudo-unitary ensemble of
  random matrices

abstract:
  Employing the currently discussed notion of pseudo-Hermiticity, we define a
pseudo-unitary group. Further, we develop a random matrix theory which is
invariant under such a group and call this ensemble of pseudo-Hermitian random
matrices as the pseudo-unitary ensemble. We obtain exact results for the
nearest-neighbour level spacing distribution for (2 X 2) PT-symmetric
Hamiltonian matrices which has a novel form, s log (1/s) near zero spacing.
This shows a level repulsion in marked distinction with an algebraic form in
the Wigner surmise. We believe that this paves way for a description of varied
phenomena in two-dimensional statistical mechanics, quantum chromodynamics, and
so on.


title: Protocols for entanglement transformations of bipartite pure states

abstract:
  We present a general theoretical framework for both deterministic and
probabilistic entanglement transformations of bipartite pure states achieved
via local operations and classical communication. This framework unifies and
greatly simplifies previous works. A necessary condition for ``pure
contraction'' transformations is given. Finally, constructive protocols to
achieve both probabilistic and deterministic entanglement transformations are
presented.


title:
Experimental and Theoretical Investigation of the Lateral Casimir Force
  Between Corrugated Surfaces

abstract:
  The lateral Casimir force acting between a sinusoidally corrugated gold plate
and sphere was calculated and measured. The experimental setup was based on the
atomic force microscope specially adapted for the measurement of the lateral
Casimir force. The measured force oscillates sinusoidally as a function of the
phase difference between the two corrugations. Both systematic and random
errors are analysed and a lateral force amplitude of $3.2\times 10^{-13} $N was
measured at a separation distance of 221 nm with a resulting relative error 24%
at a 95% confidence probability. The dependence of the measured lateral force
amplitude on separation was investigated and shown to be consistent with the
inverse fourth power distance dependence. The complete theory of the lateral
Casimir force is presented including finite conductivity and roughness
corrections. The obtained theoretical dependence was analysed as a function of
surface separation, corrugation amplitudes, phase difference, and plasma
wavelength of a metal. The theory was compared with the experimental data and
shown to be in good agreement. The constraints on hypothetical Yukawa-type
interactions following from the measurements of the lateral Casimir force are
calculated. The possible applications of the lateral vacuum forces to
nanotechnology are discussed.


title: Remote state preparation and teleportation in phase space

abstract:
  Continuous variable remote state preparation and teleportation are analyzed
using Wigner functions in phase space. We suggest a remote squeezed state
preparation scheme between two parties sharing an entangled twin beam, where
homodyne detection on one beam is used as a conditional source of squeezing for
the other beam. The scheme works also with noisy measurements, and provide
squeezing if the homodyne quantum efficiency is larger than 50%. Phase space
approach is shown to provide a convenient framework to describe teleportation
as a generalized conditional measurement, and to evaluate relevant degrading
effects, such the finite amount of entanglement, the losses along the line, and
the nonunit quantum efficiency at the sender location.


title: Quantum ground-mode computation with static gates

abstract:
  We develop a computation model for solving Boolean networks by implementing
wires through quantum ground-mode computation and gates through identities
following from angular momentum algebra and statistics. Gates are represented
by three-dimensional (triplet) symmetries due to particle indistinguishability
and are identically satisfied throughout computation being constants of the
motion. The relaxation of the wires yields the network solutions. Such gates
cost no computation time, which is comparable with that of an easier Boolean
network where all the gate constraints implemented as constants of the motion
are removed. This model computation is robust with respect to decoherence and
yields a generalized quantum speed-up for all NP problems.


title: Stochastic Schroedinger Equations with General Complex Gaussian Noises

abstract:
  Within the framework of stochastic Schroedinger equations, we show that the
correspondence between statevector equations and ensemble equations is
infinitely many to one, and we discuss the consequences. We also generalize the
results of [Phys. Lett. A 224, p. 25 (1996)] to the case of more general
complex Gaussian noises and analyze the two important cases of purely real and
purely imaginary stochastic processes.


title: Quantum computing with spatially delocalized qubits

abstract:
  We analyze the operation of quantum gates for neutral atoms with qubits that
are delocalized in space, i.e., the computational basis states are defined by
the presence of a neutral atom in the ground state of one out of two trapping
potentials. The implementation of single qubit gates as well as a controlled
phase gate between two qubits is discussed and explicit calculations are
presented for rubidium atoms in optical microtraps. Furthermore, we show how
multi-qubit highly entangled states can be created in this scheme.


title: Towards quantum superpositions of a mirror

abstract:
  We propose a scheme for creating quantum superposition states involving of
order $10^{14}$ atoms via the interaction of a single photon with a tiny
mirror. This mirror, mounted on a high-quality mechanical oscillator, is part
of a high-finesse optical cavity which forms one arm of a Michelson
interferometer. By observing the interference of the photon only, one can study
the creation and decoherence of superpositions involving the mirror. All
experimental requirements appear to be within reach of current technology.


title:
The entanglement of indistinguishable particles shared between two
  parties

abstract:
  Using an operational definition we quantify the entanglement, $E_P$, between
two parties who share an arbitrary pure state of $N$ indistinguishable
particles. We show that $E_P \leq E_M$, where $E_M$ is the bipartite
entanglement calculated from the mode-occupation representation. Unlike $E_M$,
$E_P$ is {\em super-additive}. For example, $E_P =0$ for any single-particle
state, but the state $\ket{1}\ket{1}$, where both modes are split between the
two parties, has $E_P = 1/2$. We discuss how this relates to quantum
correlations between particles, for both fermions and bosons.


title: Analytical and numerical solution of coupled KdV-MKdV system

abstract:
  The matrix 2x2 spectral differential equation of the second order is
considered on x in ($-\infty,+\infty$). We establish elementary Darboux
transformations covariance of the problem and analyze its combinations. We
select a second covariant equation to form Lax pair of a coupled KdV-MKdV
system. The sequence of the elementary Darboux transformations of the
zero-potential seed produce two-parameter solution for the coupled KdV-MKdV
system with reductions. We show effects of parameters on the resulting
solutions (reality, singularity). A numerical method for general coupled
KdV-MKdV system is introduced. The method is based on a difference scheme for
Cauchy problems for arbitrary number of equations with constants coefficients.
We analyze stability and prove the convergence of the scheme which is also
tested by numerical simulation of the explicit solutions.


title: Probabilistic Quantum Teleportation

abstract:
  We consider a generalized quantum teleportation protocol for an unknown qubit
using non-maximally entangled state as a shared resource. Without recourse to
local filtering or entanglement concentration, using standard Bell-state
measurement and classical communication one cannot teleport the state with unit
fidelity and unit probability. We show that using non-maximally entangled
measurements one can teleport an unknown state with unit fidelity albeit with
reduced probability, hence probabilistic teleportation. We also give a
generalized protocol for entanglement swapping using non-maximally entangled
states.


title: Quantum information science and complex quantum systems

abstract:
  What makes quantum information science a science? This paper explores the
idea that quantum information science may offer a powerful approach to the
study of complex quantum systems.


title:
Transient Dynamics in Magnetic Force Microscopy for a Single-Spin
  Measurement

abstract:
  We analyze a single-spin measurement using a transient process in magnetic
force microscopy (MFM) which could increase the maximum operating temperature
by a factor of Q (the quality factor of the cantilever) in comparison with the
static Stern-Gerlach effect. We obtain an exact solution of the master
equation, which confirms this result. We also discuss the conditions required
to create a macroscopic Schrodinger cat state in the cantilever.


title: Solution to the King's Problem in prime power dimensions

abstract:
  It is shown how to ascertain the values of a complete set of mutually
complementary observables of a prime power degree of freedom by generalizing
the solution in prime dimensions given by Englert and Aharonov [Phys. Lett.
A284, 1-5 (2001)].


title: Delay time and tunneling transient phenomena

abstract:
  Analytic solutions to the time-dependent Schr\"odinger equation for cutoff
wave initial conditions are used to investigate the time evolution of the
transmitted probability density for tunneling. For a broad range of values of
the potential barrier opacity $\alpha$, we find that the probability density
exhibits two evolving structures. One refers to the propagation of a {\it
forerunner} related to a {\it time domain resonance} [Phys. Rev. A {\bf 64},
0121907 (2001)], while the other consists of a semiclassical propagating
wavefront. We find a regime where the {\it forerunners} are absent,
corresponding to positive {\it time delays}, and show that this regime is
characterized by opacities $\alpha < \alpha_c$. The critical opacity $\alpha_c$
is derived from the analytical expression for the {\it delay time}, that
reflects a link between transient effects in tunneling and the {\it delay time}


title:
Transient tunneling effects of resonance doublets in triple barrier
  systems

abstract:
  Transient tunneling effects in triple barrier systems are investigated by
considering a time-dependent solution to the Schr\"{o}dinger equation with a
cutoff wave initial condition. We derive a two-level formula for incidence
energies $E$ near the first resonance doublet of the system. Based on that
expression we find that the probability density along the internal region of
the potential, is governed by three oscillation frequencies: one of them refers
to the well known Bohr frequency, given in terms of the first and second
resonance energies of the doublet, and the two others, represent a coupling
with the incidence energy $E$. This allows to manipulate the above frequencies
to control the tunneling transient behavior of the probability density in the
short-time regime


title: Quantum-wave evolution in a step potential barrier

abstract:
  By using an exact solution to the time-dependent Schr\"{o}dinger equation
with a point source initial condition, we investigate both the time and spatial
dependence of quantum waves in a step potential barrier. We find that for a
source with energy below the barrier height, and for distances larger than the
penetration length, the probability density exhibits a {\it forerunner}
associated with a non-tunneling process, which propagates in space at exactly
the semiclassical group velocity. We show that the time of arrival of the
maximum of the {\it forerunner} at a given fixed position inside the potential
is exactly the traversal time, $\tau$. We also show that the spatial evolution
of this transient pulse exhibits an invariant behavior under a rescaling
process. This analytic property is used to characterize the evolution of the
{\it forerunner}, and to analyze the role played by the time of arrival,
$3^{-1/2}\tau$, found recently by Muga and B\"{u}ttiker [Phys. Rev. A {\bf 62},
023808 (2000)].


title:
Limit theorems and absorption problems for quantum random walks in one
  dimension

abstract:
  In this paper we consider limit theorems, symmetry of distribution, and
absorption problems for two types of one-dimensional quantum random walks
determined by 2 times 2 unitary matrices using our PQRS method. The one type
was introduced by Gudder in 1988, and the other type was studied intensively by
Ambainis et al. in 2001. The difference between both types of quantum random
walks is also clarified.


title:
The role of the buildup oscillations on the speed of resonant tunneling
  diodes

abstract:
  The fastest tunneling response in double barrier resonant structures is
investigated by considering explicit analytic solutions of the time dependent
Schr\"{o}dinger equation. For cutoff initial plane waves, we find that the
earliest tunneling events consist on the emission of a series of propagating
pulses of the probability density governed by the buildup oscillations in the
quantum well. We show that the fastest tunneling response comes from the
contribution of incident carriers at energies different from resonance, and
that its relevant time scale is given by $\tau_r=\pi \hbar /| E-\epsilon | $,
where $\epsilon $ is the resonance energy and $E$ is the incidence energy.


title: Radiation damping and decoherence in quantum electrodynamics

abstract:
  The processes of radiation damping and decoherence in Quantum Electrodynamics
are studied from an open system's point of view. Employing functional
techniques of field theory, the degrees of freedom of the radiation field are
eliminated to obtain the influence phase functional which describes the reduced
dynamics of the matter variables. The general theory is applied to the dynamics
of a single electron in the radiation field. From a study of the wave packet
dynamics a quantitative measure for the degree of decoherence, the decoherence
function, is deduced. The latter is shown to describe the emergence of
decoherence through the emission of bremsstrahlung caused by the relative
motion of interfering wave packets. It is argued that this mechanism is the
most fundamental process in Quantum Electrodynamics leading to the destruction
of coherence, since it dominates for short times and because it is at work even
in the electromagnetic field vacuum at zero temperature. It turns out that
decoherence trough bremsstrahlung is very small for single electrons but
extremely large for superpositions of many-particle states.


title: Binary communication in entangled channels

abstract:
  We analyze optical binary communication assisted by entanglement and show
that: i) ideal entangled channels have smaller error probability than ideal
single-mode coherent channels if the photon number of the channel is larger
than one; ii) realistic entangled channels with heterodyne receivers have
smaller error probability than ideal single-mode coherent channels if the
photon number of the channel is larger than a threshold of about five photons.


title:
Quantum entanglement with acousto-optic modulators: 2-photon beatings
  and Bell experiments with moving beamsplitters

abstract:
  We present an experiment testing quantum correlations with frequency shifted
photons. We test Bell inequality with 2-photon interferometry where we replace
the beamsplitters by acousto-optic modulators, which are equivalent to moving
beamsplitters. We measure the 2-photon beatings induced by the frequency
shifts, and we propose a cryptographic scheme in relation. Finally, setting the
experiment in a relativistic configuration, we demonstrate that the quantum
correlations are not only independent of the distance but also of the time
ordering between the two single-photon measurements.


title:
Cole-Hopf Like Transformation for a Class of Coupled Nonlinear
  Schroedinger Equations

abstract:
  In this paper we consider a class of coupled nonlinear Schroedinger equations
for the fields $\psi_i$ containing complex nonlinearities, that has been
obtained by requiring that the norms $|\psi_i|^2$ are conserved densities. For
this class of equations we introduce a Cole-Hopf like transformation, whose
effect is to reduce the complex nonlinearities into real ones, this way
reducing the continuity equations of the system to the standard bilinear form.
Some examples are presented to illustrate the applicability of the method.
  Pacs numbers: 03.50.-z, 03.65.-w, 11.30.Na, 11.40.Dw
  Keywords: Coupled nonlinear Schroedinger equations, Cole-Hopf transformation,
Nonlinear transformations.


title: Quantum theory from four of Hardy's axioms

abstract:
  In a recent paper [e-print quant-ph/0101012], Hardy has given a derivation of
"quantum theory from five reasonable axioms." Here we show that Hardy's first
axiom, which identifies probability with limiting frequency in an ensemble, is
not necessary for his derivation. By reformulating Hardy's assumptions, and
modifying a part of his proof, in terms of Bayesian probabilities, we show that
his work can be easily reconciled with a Bayesian interpretation of quantum
probability.


title: Response to Horton and Dewdney

abstract:
  There are some points in the reply of Horton et al.
[http://stacks.iop.org/JPhysA/35/7963] to my comment [quant-ph/0202140] on
their paper [quant-ph/0103114] which I cannot let stand without a response. I
provide here some clarification of how much I proved about the set of points
where their law of motion is ill-defined.


title: Induced vortex tunneling in a superconducting wire

abstract:
  We consider induced topological transitions in a wire made from cylindrical
superconducting film. During a transition, a pulse of electric current causes
transport of a virtual vortex-antivortex pair around the cylinder. We consider
both the instanton approach, in which the transition is viewed as motion of
vortices in the Euclidean time, and the real-time dual formulation, in which
vortices are described by a fundamental quantum field. The instanton approach
is convenient to discuss effects of the environment, while in the dual
formulation we show that there exists a potentially useful adiabatic regime, in
which the probability to create a real vortex pair is exponentially suppressed,
but the total transport of the vortex number can be of order one.


title: Quantum Certificate Complexity

abstract:
  Given a Boolean function f, we study two natural generalizations of the
certificate complexity C(f): the randomized certificate complexity RC(f) and
the quantum certificate complexity QC(f). Using Ambainis' adversary method, we
exactly characterize QC(f) as the square root of RC(f). We then use this result
to prove the new relation R0(f) = O(Q2(f)^2 Q0(f) log n) for total f, where R0,
Q2, and Q0 are zero-error randomized, bounded-error quantum, and zero-error
quantum query complexities respectively. Finally we give asymptotic gaps
between the measures, including a total f for which C(f) is superquadratic in
QC(f), and a symmetric partial f for which QC(f) = O(1) yet Q2(f) = Omega(n/log
n).


title: Space-time transformation for superluminal signaling

abstract:
  We analyze the possible implication of the existence of superluminal
signaling for space-time structure. A new space-time transformation for
superluminal signaling is presented based on the superluminal synchrony method.
We argue that Lorentz transformation should be replaced by the new
transformation in case of the existence of superluminal signaling. Furthermore,
we discuss the possible existence of absolute frame, and give a possible
practical method to probe it.


title:
Engineering QND measurements for continuous variable quantum information
  processing

abstract:
  A novel scheme to realize the whole class of quantum nondemolition (QND)
measurements of a field quadrature is suggested. The setup requires linear
optical components and squeezers, and allows optimal QND measurements of
quadratures, which minimize the information gain versus state disturbance
trade-off.


title:
Experimental study of the spatial distribution of quantum correlations
  in a confocal Optical Parametric Oscillator

abstract:
  We study experimentally the spatial distribution of quantum noise in the twin
beams produced by a type II Optical Parametric Oscillator operating in a
confocal cavity above threshold. The measured intensity correlations are at the
same time below the standard quantum limit and not uniformly distributed inside
the beams. We show that this feature is an unambiguous evidence for the
multimode and nonclassical character of the quantum state generated by the
device.


title: Information dynamics in cavity QED

abstract:
  A common experimental setup in cavity quantum electrodynamics (QED) consists
of a single two-level atom interacting with a single mode of the
electromagnetic field inside an optical cavity. The cavity is externally driven
and the output is continuously monitored via homodyne measurements. We derive
formulas for the optimal rates at which these measurements provide information
about (i) the quantum state of the system composed of atom and electromagnetic
field, and (ii) the coupling strength between atom and field. We find that the
two information rates are anticorrelated.


title: Floquet Analysis of Atom Optics Tunneling Experiments

abstract:
  Dynamical tunneling has been observed in atom optics experiments by two
groups. We show that the experimental results are extremely well described by
time-periodic Hamiltonians with momentum quantized in units of the atomic
recoil. The observed tunneling has a well defined period when only two Floquet
states dominate the dynamics. Beat frequencies are observed when three Floquet
states dominate. We find frequencies which match those observed in both
experiments. The dynamical origin of the dominant Floquet states is identified.


title:
On a loss of information in a transition from quantum to a
  quasi-classical regime

abstract:
  By defining information entropy in terms of probabilities densities
$|\Psi|^2$ ($\Psi$ is a wave function in the coordinate representation) it is
explicitly shown how a loss of quantum information occurs in a transition from
a quantum to a quasi-classical regime.


title:
Universal quantum gates based on a pair of orthogonal cyclic states:
  Application to NMR systems

abstract:
  We propose an experimentally feasible scheme to achieve quantum computation
based on a pair of orthogonal cyclic states. In this scheme, quantum gates can
be implemented based on the total phase accumulated in cyclic evolutions. In
particular, geometric quantum computation may be achieved by eliminating the
dynamic phase accumulated in the whole evolution. Therefore, both dynamic and
geometric operations for quantum computation are workable in the present
theory. Physical implementation of this set of gates is designed for NMR
systems. Also interestingly, we show that a set of universal geometric quantum
gates in NMR systems may be realized in one cycle by simply choosing specific
parameters of the external rotating magnetic fields. In addition, we
demonstrate explicitly a multiloop method to remove the dynamic phase in
geometric quantum gates. Our results may provide useful information for the
experimental implementation of quantum logical gates.


title:
An Analysis of Mutual Communication between Qubits by Capacitive
  Coupling

abstract:
  A behavior of a two qubit system coupled by the electric capacitance has been
studied quantum mechanically. We found that the interaction is essentially the
same as the one for the dipole-dipole interaction; i.e., qubit-qubit coupling
of the NMR quantum gate. Therefore a quantum gate could be constructed by the
same operation sequence for the NMR device if the coupling is small enough. The
result gives an information to the effort of development of the devices
assuming capacitive coupling between qubits.


title: Quantum Iterated Function Systems

abstract:
  Iterated functions system (IFS) is defined by specifying a set of functions
in a classical phase space, which act randomly on an initial point. In an
analogous way, we define a quantum iterated functions system (QIFS), where
functions act randomly with prescribed probabilities in the Hilbert space. In a
more general setting a QIFS consists of completely positive maps acting in the
space of density operators. We present exemplary classical IFSs, the invariant
measure of which exhibits fractal structure, and study properties of the
corresponding QIFSs and their invariant states.


title: Reduced density matrices of oscillator systems

abstract:
  We study the evolution of an oscillator interacting via the most general
bilinear coupling (with time-independent coefficients) with an ``environment''
consisting of a set of other harmonic oscillators. We are mainly interested in
a possibility of using the Fokker-Planck equation to describe this evolution.
Studying different interaction Hamiltonians, we show that unambiguous reduction
to the Fokker-Planck equation is possible only within the framework of the so
called rotating-wave approximation. As special cases we consider in detail the
evolution of two coupled oscillators and relaxation of a charged oscillator in
a uniform magnetic field.


title:
About the use of entanglement in the optical implementation of quantum
  information processing

abstract:
  We review some applications of entanglement to improve quantum measurements
and communication, with the main focus on the optical implementation of quantum
information processing. The evolution of continuos variable entangled states in
active optical fibers is also analyzed.


title:
Comment on "Deterministic Single-Photon Source for Distributed Quantum
  Networking" by Kuhn, Hennrich, and Rempe

abstract:
  I comment on the experiment to realize an "on-demand," reversible
single-photon source by Kuhn, Hennrich, and Rempe [Phys. Rev. Lett. 89, 067901
(2002)].


title: Non-dispersive wave packets in periodically driven quantum systems

abstract:
  With the exception of the harmonic oscillator, quantum wave-packets usually
spread as time evolves. We show here that, using the nonlinear resonance
between an internal frequency of a system and an external periodic driving, it
is possible to overcome this spreading and build non-dispersive (or
non-spreading) wave-packets which are well localized and follow a classical
periodic orbit without spreading. From the quantum mechanical point of view,
the non-dispersive wave-packets are time periodic eigenstates of the Floquet
Hamiltonian, localized in the nonlinear resonance island. We discuss the
general mechanism which produces the non-dispersive wave-packets, with emphasis
on simple realization in the electronic motion of a Rydberg electron driven by
a microwave field. We show the robustness of such wavepackets for a model
one-dimensional as well as for realistic three dimensional atoms. We consider
their essential properties such as the stability versus ionization, the
characteristic energy spectrum and long lifetimes. The requirements for
experiments aimed at observing such non-dispersive wave-packets are also
considered. We also discuss other related phenomena in atomic and molecular
physics as well as possible further extensions of the theory.


title: Interferometer-Type Structures for Guided Atoms

abstract:
  We experimentally demonstrate interferometer-type guiding structures for
neutral atoms based on dipole potentials created by micro-fabricated optical
systems. As a central element we use an array of atom waveguides being formed
by focusing a red-detuned laser beam with an array of cylindrical microlenses.
Combining two of these arrays, we realize X-shaped beam splitters and more
complex systems like the geometries for Mach-Zehnder and Michelson-type
interferometers for atoms.


title: Entanglement as Internal Constraint

abstract:
  Our investigation aims to study the specific role played by entanglement in
the quantum computation process, by elaborating an entangled spin model
developed within the 'hidden measurement approach' to quantum mechanics. We
show that an arbitrary tensor product state for the entity consisting of two
entangled qubits can be described in a complete way by a specific internal
constraint between the ray and density states of the two qubits. For the
individual qubits we use a sphere model representation, which is a
generalization of the Bloch or Pauli representation, where also the collapse
and noncollapse measurements are represented. We identify a parameter r in
[0,1], arising from the Schmidt diagonal decomposition, that is a measure of
the amount of entanglement, such that for r = 0 the system is in the singlet
state with 'maximal' entanglement, and for r = 1 the system is in a pure
product state.


title:
Quantum Zeno and anti-Zeno effects by indirect measurement with finite
  errors

abstract:
  We study the quantum Zeno effect and the anti-Zeno effect in the case of
`indirect' measurements, where a measuring apparatus does not act directly on
an unstable system, for a realistic model with finite errors in the
measurement. A general and simple formula for the decay rate of the unstable
system under measurement is derived. In the case of a Lorentzian form factor,
we calculate the full time evolutions of the decay rate, the response of the
measuring apparatus, and the probability of errors in the measurement. It is
shown that not only the response time but also the detection efficiency plays a
crucial role. We present the prescription for observing the quantum Zeno and
anti-Zeno effects, as well as the prescriptions for avoiding or calibrating
these effects in general experiments.


title: Proposing a new approach to implementing Fuzzy Systems

abstract: This paper has been withdrawn.


title:
Disentangling and broadcasting an entangled state simultaneously by
  asymmetric cloning

abstract:
  We construct a quantum machine which, by using asymmetric cloner, deals with
disentangling and broadcasting entanglement in a single unitary evolution. The
attainable maximum value of the scaling parameter $s$ for disentangling is
identical to that obtained in previous works. The fidelity of the cloning state
with respect to the input entangled state is state-dependent.


title:
Optimal Sizes of Dielectric Microspheres for Cavity QED with Strong
  Coupling

abstract:
  The whispering gallery modes (WGMs) of quartz microspheres are investigated
for the purpose of strong coupling between single photons and atoms in cavity
quantum electrodynamics (cavity QED). Within our current understanding of the
loss mechanisms of the WGMs, the saturation photon number, n, and critical atom
number, N, cannot be minimized simultaneously, so that an "optimal" sphere size
is taken to be the radius for which the geometric mean, (n x N)^(1/2), is
minimized. While a general treatment is given for the dimensionless parameters
used to characterize the atom-cavity system, detailed consideration is given to
the D2 transition in atomic Cesium (852nm) using fused-silica microspheres, for
which the maximum coupling coefficient g/(2*pi)=750MHz occurs for a sphere
radius a=3.63microns corresponding to the minimum for n=6.06x10^(-6). By
contrast, the minimum for N=9.00x10^(-6) occurs for a sphere radius of
a=8.12microns, while the optimal sphere size for which (n x N)^(1/2) is
minimized occurs at a=7.83microns. On an experimental front, we have fabricated
fused-silica microspheres with radii a=10microns and consistently observed
quality factors Q=0.8x10^(7). These results for the WGMs are compared with
corresponding parameters achieved in Fabry-Perot cavities to demonstrate the
significant potential of microspheres as a tool for cavity QED with strong
coupling.


title: Streaming Caused by Impulse Acoustic Wave

abstract:
  Five eigenvectors of the linear thermoviscous flow over the homogeneous
background derived for the quasi-plane geometry of the flow. The corresponding
projectors are calculated and applied to get the nonlinear evolution equations
for the interacting vortical and acoustic modes. Equation on streaming cased by
arbitrary acoustic wave is specified. The correspondence to the known results
on streaming cased by quasi-periodic source is traced. The radiation acoustic
force is calculated for the mono-polar source.


title: Factorization and Entanglement in Quantum Systems

abstract:
  We discuss the question of entanglement versus separability of pure quantum
states in direct product Hilbert spaces and the relevance of this issue to
physics. Different types of separability may be possible, depending on the
particular factorization or split of the Hilbert space. A given orthonormal
basis set for a Hilbert space is defined to be of type (p,q) if p elements of
the basis are entangled and q are separable, relative to a given bi-partite
factorization of that space. We conjecture that not all basis types exist for a
given Hilbert space.


title: The Landau-Problem on the \theta-Deformed Two-Torus

abstract:
  We study the Landau-problem on the $\theta$-deformed two-torus and use
well-known projective modules to obtain perturbed spectra. For a strong
magnetic field B the problem can be restricted to one particular Landau-level.
First we represent generators of the algebra of the non-commutative torus as
finite dimensional matrices. A second approach leads to a reducible
representation with a $\theta$-dependent center. For a simple periodic
potential, the rational part of the Hofstadter-butterfly spectrum is obtained.


title:
Single-Spin Measurement and Decoherence in Magnetic Resonance Force
  Microscopy

abstract:
  We consider a simple version of a cyclic adiabatic inversion (CAI) technique
in magnetic resonance force microscopy (MRFM). We study the problem: What
component of the spin is measured in the CAI MRFM? We show that the
non-destructive detection of the cantilever vibrations provides a measurement
of the spin component along the effective magnetic field. This result is based
on numerical simulations of the Hamiltonian dynamics (the Schrodinger equation)
and the numerical solution of the master equation.


title:
Physical content of Heisenberg's uncertainty relation: Limitation and
  reformulation

abstract:
  Heisenberg's reciprocal relation between position measurement error and
momentum disturbance is rigorously proven under the assumption that those error
and disturbance are independent of the state of the measured object. A
generalization of Heisenberg's relation proven valid for arbitrary measurements
is proposed and reveals two distinct types of possible violations of
Heisenberg's relation.


title: Isotopic Dependence of the Casimir Force

abstract:
  We calculate the dependence of the Casimir force on the isotopic composition
of the interacting objects. This dependence arises from the subtle influence of
the nuclear masses on the electronic properties of the bodies. We discuss the
relevance of these results to current experiments utilizing the iso-electronic
effect to search at very short separations for new weak forces suggested by
various unification theories.


title:
Quantum Limits of Measurement and Computing Induced by Conservation Laws
  and Uncertainty Relations

abstract:
  A quantitative extension of the Wigner-Araki-Yanase theorem is obtained on
the limitation on precise, non-disturbing measurements of observables which do
not commute with additive conserved quantities, and applied to obtaining a
limitation on the accuracy of quantum computing with computational bases which
do not commute with angular momentum.


title: Decoherence in a quantum walk on the line

abstract:
  We have studied how decoherence affects a quantum walk on the line. As
expected, it is highly sensitive, consisting as it does of an extremely
delocalized particle. We obtain an expression for the rate at which the
standard deviation falls from the quantum value as decoherence increases and
show that it is proportional to the number of decoherence "events" occuring
during the walk.


title: Green's Function Approach to B.E. Condensation in the Alkali Atoms

abstract:
  A new scheme has been proposed to solve the B.E. condenstates in terms of
Green's function approach. It has been shown that the radial wave function of
two interacting atoms, moving in a common harmonic oscillator potential
modified by an effective interaction,satifies an integral equation whose kernel
is separable.The solution of the integral equation can be written in terms of
the harmonic oscillator wave functions. The ground state wave function of the
system can be written in terms of these solutions.
  PACS numbers:03.75Fi,02.60Cb,32.80Pj


title:
Algebras and universal quantum computations with higher dimensional
  systems

abstract:
  Here is discussed application of the Weyl pair to construction of universal
set of quantum gates for high-dimensional quantum system. An application of Lie
algebras (Hamiltonians) for construction of universal gates is revisited first.
It is shown next, how for quantum computation with qubits can be used
two-dimensional analog of this Cayley-Weyl matrix algebras, i.e. Clifford
algebras, and discussed well known applications to product operator formalism
in NMR, Jordan-Wigner construction in fermionic quantum computations. It is
introduced universal set of quantum gates for higher dimensional system
(``qudit''), as some generalization of these models. Finally it is briefly
mentioned possible application of such algebraic methods to design of quantum
processors (programmable gates arrays) and discussed generalization to quantum
computation with continuous variables.


title: Can Quantum Mechanics be Cleared from Conceptual Difficulties?

abstract:
  The major conceptual difficulties of quantum mechanics are analyzed. They
are: the notion "wave-particle", the probabilistic interpretation of the
Schroedinger wave \psi-function and hence the probability amplitude and its
phase, long-range action, Heisenberg's uncertainty principle, etc. The
probabilistic formalism is developed in the phase space, but not in the real
one. Elimination of the difficulties is likely if we are able to develop
quantum mechanics in the real space. Such a theory in fact can be constructed,
however, it should proceed from deepest first principles starting from the
notion of a 4D space-time, the notion of a massive particle in the space, the
principles of the motion of a particle, etc. The theory should be characterized
by short-range action that automatically means the introduction of a quantum
mechanical force. It is shown that the aforementioned force makes it evident
and, moreover, is able to appear on the macroscopic scale. A simple experiment,
the express test, which in fact proves the macroscopic manifestation of quantum
mechanical force, is proposed for the demonstration in the quantum curriculum.


title:
The statistics of the entanglement changes generated by the
  Hadamard-CNOT quantum circuit

abstract:
  We consider the change of entanglement of formation $\Delta E$ produced by
the Hadamard-CNOT circuit on a general (pure or mixed) state $\rho$ describing
a system of two qubits. We study numerically the probabilities of obtaining
different values of $\Delta E$, assuming that the initial state is randomly
distributed in the space of all states according to the product measure
recently introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998)
883].


title: Dynamical localization simulated on a few qubits quantum computer

abstract:
  We show that a quantum computer operating with a small number of qubits can
simulate the dynamical localization of classical chaos in a system described by
the quantum sawtooth map model. The dynamics of the system is computed
efficiently up to a time $t\geq \ell$, and then the localization length $\ell$
can be obtained with accuracy $\nu$ by means of order $1/\nu^2$ computer runs,
followed by coarse grained projective measurements on the computational basis.
We also show that in the presence of static imperfections a reliable
computation of the localization length is possible without error correction up
to an imperfection threshold which drops polynomially with the number of
qubits.


title: Local Hidden Variable Theories for Quantum States

abstract:
  While all bipartite pure entangled states violate some Bell inequality, the
relationship between entanglement and non-locality for mixed quantum states is
not well understood. We introduce a simple and efficient algorithmic approach
for the problem of constructing local hidden variable theories for quantum
states. The method is based on constructing a so-called symmetric
quasi-extension of the quantum state that gives rise to a local hidden variable
model with a certain number of settings for the observers Alice and Bob.


title: Open environments for quantum open systems

abstract:
  The majority of quantum open system models in the literature are simplistic
in the sense that they only explicitly account for that part of the environment
that directly interacts with the system of interest. A quantum open system with
an open environment is examined using the projection operator method in the
weak coupling limit. The openness of environment is modelled by nonunitary
evolution of the Lindblad form. Under certain conditions, the resulting master
equation for the system is insensitive to the initial state of the environment
and to initial entanglements between the system and environment for time scales
greater than the environment relaxation timescales. For the particular case of
an environment consisting of a harmonic oscillator bath, the resulting master
equations are demonstrated to have the algebraic form for completely positive
evolution. The open environment model is illustrated for the particular case of
a system linearly coupled to an oscillator bath.


title: The underlying digraph of a coined quantum random walk

abstract:
  We give a characterization of the line digraph of a regular digraph. We make
use of the characterization, to show that the underlying digraph of a coined
quantum random walk is a line digraph. We remark the connection between line
digraphs and in-split graphs in symbolic dynamics.


title: Continuous measurement with traveling wave probes

abstract:
  We consider the use of a traveling wave probe to continuously measure the
quantum state of an atom in free space. Unlike the more familiar cavity QED
geometry, the traveling wave is intrinsically a multimode problem. Using an
appropriate modal decomposition we determine the effective measurement strength
for different atom-field interactions and different initial states of the
field. These include the interaction of a coherent-state pulse with an atom,
the interaction of a Fock-state pulse with an atom, and the use of Faraday
rotation of a polarized laser probe to perform a QND measurement on an atomic
spin.


title: Exploring Noiseless Subsystems via Nuclear Magnetic Resonance

abstract:
  Noiseless subsystems offer a general and efficient method for protecting
quantum information in the presence of noise that has symmetry properties. A
paradigmatic class of error models displaying non-trivial symmetries emerges
under collective noise behavior, which implies a permutationally-invariant
interaction between the system and the environment. We describe experiments
demonstrating the preservation of a bit of quantum information encoded in a
three qubit noiseless subsystem for general collective noise. A complete set of
input states is used to determine the super-operator for the implemented
one-qubit process and to confirm that the fidelity of entanglement is improved
for a large, non-commutative set of engineered errors. To date, this is the
largest set of error operators that has been successfully corrected for by any
quantum code.


title: Quantum Time Arrows, Semigroups and Time-Reversal in Scattering

abstract:
  Two approaches toward the arrow of time for scattering processes have been
proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm,
involves preparations and registrations in laboratory operations and results in
two semigroups oriented in the forward direction of time. The other, employed
by the Brussels-Austin group, is more general, involving excitations and
de-excitations of systems, and apparently results in two semigroups oriented in
opposite directions of time. It turns out that these two time arrows can be
related to each other via Wigner's extensions of the spacetime symmetry group.
Furthermore, their are subtle differences in causality as well as the
possibilities for the existence and creation of time-reversed states depending
on which time arrow is chosen.


title:
Generation of Large Photon-Number Cat States using Linear Optics and
  Quantum Memory

abstract:
  A recursive method for producing path-entangled states of light is presented.
These states may find applications in quantum lithography and high-precision
interferometric measurements. The required resources are single-photon sources,
linear optics components, and photodetectors. Adding a quantum memory greatly
enhances the yield in comparison with the previously known schemes.


title: A single quantum cannot be teleported

abstract:
  Due to the Heisemberg uncertainty principle, it is impossible to design a
procedure which permits perfect cloning of an arbitrary, unknown "qubit" (the
spin or polarization state of a single quantum system)1,2. However, it is
believed that a perfect copying protocol can be achieved, at least in
principle, if the qubit to be copied is destroyed in the original system.
Quantum teleportation3,4 is supposed to allow for such a result. Here, this
belief is shown to be invalidated by a fundamental uncertainty about the number
of particles involved in any process, as predicted by Quantum Field Theory. As
a result, teleportation cannot provide an infallible copying procedure for the
single qubits, not even in the limit of perfect experimental sensitivities. The
no-cloning theorem1,2 can then be generalized to the case of destroying the
original. Teleportation remains an interesting statistical procedure, having an
unavoidable theoretical error at the percent level or few orders of magnitude
smaller, depending on the physical process that is used. Although it cannot be
made arbitrarily small, such an error is small enough to remain hidden in
present experiments.


title: Quantum cloning with continuous variables

abstract:
  Cloning machines, that is, transformations that achieve the best approximate
copying of a quantum state compatible with the no-cloning theorem, have been a
fundamental research topic over the last five years. This study is of
particular significance given the close connection between quantum cloning and
quantum cryptography: using an optimal cloner generally makes it possible to
obtain a tight bound on the best individual eavesdropping strategy in a quantum
cryptosystem. In this Chapter, the issue of cloning a continuous-variable
quantum system will be analyzed, and a Gaussian cloning transformation will be
introduced. This cloner, which copies equally well any two canonically
conjugate continuous variables, duplicates all coherent states with a same
fidelity (F=2/3). The optical implementation of this cloner and its extension
to N-to-M cloners will also be discussed. Finally, the use of this cloner for
the security assessment of a quantum key distribution scheme relying on
continuous (Gaussian) key carriers will be sketched.


title: Uncloneable Encryption

abstract:
  Quantum states cannot be cloned. I show how to extend this property to
classical messages encoded using quantum states, a task I call "uncloneable
encryption." An uncloneable encryption scheme has the property that an
eavesdropper Eve not only cannot read the encrypted message, but she cannot
copy it down for later decoding. She could steal it, but then the receiver Bob
would not receive the message, and would thus be alerted that something was
amiss. I prove that any authentication scheme for quantum states acts as a
secure uncloneable encryption scheme. Uncloneable encryption is also closely
related to quantum key distribution (QKD), demonstrating a close connection
between cryptographic tasks for quantum states and for classical messages.
Thus, studying uncloneable encryption and quantum authentication allows for
some modest improvements in QKD protocols. While the main results apply to a
one-time key with unconditional security, I also show uncloneable encryption
remains secure with a pseudorandom key. In this case, to defeat the scheme, Eve
must break the computational assumption behind the pseudorandom sequence before
Bob receives the message, or her opportunity is lost. This means uncloneable
encryption can be used in a non-interactive setting, where QKD is not
available, allowing Alice and Bob to convert a temporary computational
assumption into a permanently secure message.


title: Fidelity Decay Saturation Level for Initial Eigenstates

abstract:
  We show that the fidelity decay between an initial eigenstate state evolved
under a unitary chaotic operator and the same eigenstate evolved under a
perturbed operator saturates well before the 1/N limit, where $N$ is the size
of the Hilbert space, expected for a generic initial state. We provide a
theoretical argument and numerical evidence that, for intermediate perturbation
strengths, the saturation level depends quadratically on the perturbation
strength.


title: A Quantum Random Walk Search Algorithm

abstract:
  Quantum random walks on graphs have been shown to display many interesting
properties, including exponentially fast hitting times when compared with their
classical counterparts. However, it is still unclear how to use these novel
properties to gain an algorithmic speed-up over classical algorithms. In this
paper, we present a quantum search algorithm based on the quantum random walk
architecture that provides such a speed-up. It will be shown that this
algorithm performs an oracle search on a database of $N$ items with
$O(\sqrt{N})$ calls to the oracle, yielding a speed-up similar to other quantum
search algorithms. It appears that the quantum random walk formulation has
considerable flexibility, presenting interesting opportunities for development
of other, possibly novel quantum algorithms.


title:
Extending Heisenberg's measurement--disturbance relation to the
  twin-slit case

abstract:
  Heisenberg's position-measurement--momentum-disturbance relation is derivable
from the uncertainty relation $\sigma(q)\sigma(p) \geq \hbar/2$ only for the
case when the particle is initially in a momentum eigenstate. Here I derive a
new measurement--disturbance relation which applies when the particle is
prepared in a twin-slit superposition and the measurement can determine at
which slit the particle is present. The relation is $d \times \Delta p \geq
2\hbar/\pi$, where $d$ is the slit separation and $\Delta p=D_{M}(P_{f},P_{i})$
is the Monge distance between the initial $P_{i}(p)$ and final $P_{f}(p)$
momentum distributions.


title: Quantum statistics of ideal gases in confined space

abstract:
  In this paper, the effects of boundary and connectivity on ideal gases in
two-dimensional confined space and three-dimensional tubes are discussed in
detail based on the analytical result. The implication of such effects on the
mesoscopic system is also revealed.


title: Superpositions of SU(3) coherent states via a nonlinear evolution

abstract:
  We show that a nonlinear Hamiltonian evolution can transform an SU(3)
coherent state into a superposition of distinct SU(3) coherent states, with a
superposition of two SU(2) coherent states presented as a special case. A phase
space representation is depicted by projecting the multi-dimensional $Q$-symbol
for the state to a spherical subdomain of the coset space. We discuss
realizations of this nonlinear evolution in the contexts of nonlinear optics
and Bose--Einstein condensates.


title: An information-theoretic analysis of Grover's algorithm

abstract:
  Grover discovered a quantum algorithm for identifying a target element in an
unstructured search universe of N items in approximately square-root of N
queries to a quantum oracle, thus achieving a square-root speed-up over
classical algorithms. We present an information-theoretic analysis of Grover's
algorithm and show that the square-root speed-up is the best attainable result
using Grover's oracle.


title: Entanglement purification for Quantum Computation

abstract:
  We show that thresholds for fault-tolerant quantum computation are solely
determined by the quality of single-system operations if one allows for
d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one
logical qubit and additional auxiliary dimensions are used to create and purify
entanglement between systems. Physical, possibly probabilistic two-system
operations with error rates up to 2/3 are still tolerable to realize
deterministic high quality two-qubit gates on the logical qubits. The
achievable error rate is of the same order of magnitude as of the single-system
operations. We investigate possible implementations of our scheme for several
physical set-ups.


title:
Precession and interference in the Aharonov-Casher and scalar
  Aharonov-Bohm effect

abstract:
  The ideal scalar Aharonov-Bohm (SAB) and Aharonov-Casher (AC) effect involve
a magnetic dipole pointing in a certain fixed direction: along a purely time
dependent magnetic field in the SAB case and perpendicular to a planar static
electric field in the AC case. We extend these effects to arbitrary direction
of the magnetic dipole. The precise conditions for having nondispersive
precession and interference effects in these generalized set ups are delineated
both classically and quantally. Under these conditions the dipole is affected
by a nonvanishing torque that causes pure precession around the directions
defined by the ideal set ups. It is shown that the precession angles are in the
quantal case linearly related to the ideal phase differences, and that the
nonideal phase differences are nonlinearly related to the ideal phase
differences. It is argued that the latter nonlinearity is due the appearance of
a geometric phase associated with the nontrivial spin path. It is further
demonstrated that the spatial force vanishes in all cases except in the
classical treatment of the nonideal AC set up, where the occurring force has to
be compensated by the experimental arrangement. Finally, for a closed
space-time loop the local precession effects can be inferred from the
interference pattern characterized by the nonideal phase differences and the
visibilities. It is argued that this makes it natural to regard SAB and AC as
essentially local and nontopological effects.


title: Optimal approximate reversal of quantum operations on a single qubit

abstract:
  We demonstrate how insights gained from reformulating the problem of quantum
teleportation into one of reversing quantum operations, and designing optimum
completely positive maps for teleportation, can enable one to explore optimal
approximate reversal of quantum operations on a single qubit. In particular, we
show that the optimal approximate reversal of a generalized depolarizing
channel can be achieved using only unitary transformations. We also show that
for a quantum channel, which reveals some information about the input state,
extremal completely positive maps and not unitary transformations yield optimal
approximate reversal.


title: Combined Error Correction Techniques for Quantum Computing Architectures

abstract:
  Proposals for quantum computing devices are many and varied. They each have
unique noise processes that make none of them fully reliable at this time.
There are several error correction/avoidance techniques which are valuable for
reducing or eliminating errors, but not one, alone, will serve as a panacea.
One must therefore take advantage of the strength of each of these techniques
so that we may extend the coherence times of the quantum systems and create
more reliable computing devices. To this end we give a general strategy for
using dynamical decoupling operations on encoded subspaces. These encodings may
be of any form; of particular importance are decoherence-free subspaces and
quantum error correction codes. We then give means for empirically determining
an appropriate set of dynamical decoupling operations for a given experiment.
Using these techniques, we then propose a comprehensive encoding solution to
many of the problems of quantum computing proposals which use exchange-type
interactions. This uses a decoherence-free subspace and an efficient set of
dynamical decoupling operations. It also addresses the problems of
controllability in solid state quantum dot devices.


title: Tight Bell inequality for d-outcome measurements correlations

abstract:
  In this paper we prove that the inequality introduced by Collins, Gisin,
Linden, Massar and Popescu is tight, or in other words, it is a facet of the
convex polytope generated by all local-realistic joint probabilities of d
outcomes. This means that this inequality is optimal. We also show that, for
correlation functions generalized to deal with three-outcome measurements, the
satisfyability of this inequality is a necessary and sufficient condition for
the existence of a local-realistic model accounting for them.


title:
Comment on "Limits of the measurability of the local quantum
  electromagnetic-field amplitude"

abstract:
  It is argued that the findings of a recent reanalysis by Compagno and Persico
[Phys. Rev. A 57, 1595 (1998)] of the Bohr--Rosenfeld procedure for the
measurement of a single space-time-averaged component of the electromagnetic
field are incorrect when the field measurement time is shorter than that
required for light to traverse the measurement's test body. To this end, the
time-averaged "self-force" on the test body, assumed for simplicity to be of a
spherical shape, is evaluated in terms of a one-dimensional quadrature for the
general trajectory allowed for the test body by Compagno and Persico, and in
closed form for the limiting steplike trajectory used by Bohr and Rosenfeld.


title:
Bohr's Conception of the Quantum Mechanical State of a System and Its
  Role in the Framework of Complementarity

abstract:
  What Niels Bohr called the `epistemological lesson' of `complementarity' was
the result of reasoning analogically from the classical conception of a
mechanical state to a new quantum mechanical conception of an `object' in a
mechanical state. Bohr proposed to redefine the `objectivity' essential for
scientific description in terms of the epistemological demand for unambiguously
communicable descriptions of observational results, a move which has profound
consequences for how we can understand the concept of the quantum mechanical
state and the nature of the `system' which is `in' this state. Here it is
argued that the old notion of the `object' which is in a classical mechanical
state is drawn from a substance/property ontology derived from Aristotle's
analysis of categorical propositions. In moving to describing a system in a
quantum mechanical state, the system that is `in' such a state can no longer be
so regarded as a substance possessing properties. Bohr argues that the concept
refers to an interaction which has a feature of wholeness or `individuality'
that implies that the distinction between `object system' and `observing
system' is relative to the context of the description. This conclusion, in
turn, implies the need for a combination of complementary modes of description;
however, because of his reticence in making ontological claims, he failed to
develop this dimension of his new framework of complementarity.


title: Operation Time of Quantum Gates

abstract:
  We consider a quantum gate that complements the state of a qubit and then
adds to it an arbitrary phase shift. It is shown that the minimum operation
time of the gate is tau = (h/4E)(1+2 theta/pi), where h is Planck's constant, E
is the quantum-mechanical average energy, and theta is the phase shift modulo
pi.
  [We changed the name of a macro file to a more Windows-friendly one, and we
clarified the remark "Note that..." after equation (4).]


title: Quantum NP - A Survey

abstract:
  We describe Kitaev's result from 1999, in which he defines the complexity
class QMA, the quantum analog of the class NP, and shows that a natural
extension of 3-SAT, namely local Hamiltonians, is QMA complete. The result
builds upon the classical Cook-Levin proof of the NP completeness of SAT, but
differs from it in several fundamental ways, which we highlight. This result
raises a rich array of open problems related to quantum complexity, algorithms
and entanglement, which we state at the end of this survey. This survey is the
extension of lecture notes taken by Naveh for Aharonov's quantum computation
course, held in Tel Aviv University, 2001.


title:
Using unitary operations to preserve quantum states in the presence of
  relaxation

abstract:
  When a quantum system interacts with an external environment, it undergoes
the loss of quantum correlation (decoherence) and the loss of energy
(relaxation) and eventually all of the quantum information becomes classical.
Here we show a general principle to use unitary operations to establish and
preserve particular non-equilibrium states in arbitrary relaxing quantum
systems. We elucidate these concepts with examples of state preservation in
one-spin and two-spin entangled systems.


title: Solving the liar detection problem using the four-qubit singlet state

abstract:
  A method for solving the Byzantine agreement problem [M. Fitzi, N. Gisin, and
U. Maurer, Phys. Rev. Lett. 87, 217901 (2001)] and the liar detection problem
[A. Cabello, Phys. Rev. Lett. 89, 100402 (2002)] is introduced. The main
advantages of this protocol are that it is simpler and is based on a four-qubit
singlet state already prepared in the laboratory.


title: The four-qubit singlet state and decoherence-free subspaces

abstract: This paper has been withdrawn by the author.


title: Bell's inequality without alternative settings

abstract:
  A suitable generalized measurement described by a 4-element positive
operator-valued measure (POVM) on each particle of a two-qubit system in the
singlet state is, from the point of view of Einstein, Podolsky, and Rosen's
(EPR's) criterion of elements of reality, equivalent to a random selection
between two alternative projective measurements. It is shown that an
EPR-experiment with a fixed POVM on each particle provides a violation of
Bell's inequality without requiring local observers to choose between the
alternatives. This approach could be useful for designing a loophole-free test
of Bell's inequality.


title:
Kochen-Specker theorem for a single qubit using positive operator-valued
  measures

abstract:
  A proof of the Kochen-Specker theorem for a single two-level system is
presented. It employs five eight-element positive operator-valued measures and
a simple algebraic reasoning based on the geometry of the dodecahedron.


title: An implication in orthologic

abstract:
  We involve a certain propositional logic based on ortholattices. We
characterize the implicational reduct of such a logic and we show that its
algebraic counterpart is the so-called orthosemilattice. Properties of
congruences and congruence kernels of these algebras are described.


title: Supersymmetric Quantum Mechanics with a Point Singularity

abstract:
  We study the possibility of supersymmetry (SUSY) in quantum mechanics in one
dimension under the presence of a point singularity. The system considered is
the free particle on a line R or on the interval [-l, l] where the point
singularity lies at x = 0. In one dimension, the singularity is known to admit
a U(2) family of different connection conditions which include as a special
case the familiar one that arises under the Dirac delta-potential. Similarly,
each of the walls at x = l and x = -l admits a U(1) family of boundary
conditions including the Dirichlet and the Neumann boundary conditions. Under
these general connection/boundary conditions, the system is shown to possess an
N = 1 or N = 2 SUSY for various choices of the singularity and the walls, and
the SUSY is found to be `good' or `broken' depending on the choices made. We
use the supercharge which allows for a constant shift in the energy, and argue
that if the system is supersymmetric then the supercharge is self-adjoint on
states that respect the connection/boundary conditions specified by the
singularity.


title:
Measurement of the overlap between quantum states with the use of
  coherently addressed teleportation

abstract:
  We will show how to measure the overlap between photon polarization states
with the use of linear optics and postselection only. Our scheme is based on
quantum teleportation and succeeds with the probability of 1/8.


title:
Proposal to produce long-lived mesoscopic superpositions through an
  atom-driven field interaction

abstract:
  We present a proposal for the production of longer-lived mesoscopic
superpositions which relies on two requirements: parametric amplification and
squeezed vacuum reservoir for cavity-field states. Our proposal involves the
interaction of a two-level atom with a cavity field which is simultaneously
subjected to amplification processes.


title: Single-particle quantum tunneling in ionic traps

abstract:
  We describe a proposal to probe the quantum tunneling mechanism of an
individual ion trapped in a double-well electromagnetic potential. The
time-evolution of the probability of fluorescence measurement of the electronic
ground state is employed to characterize the single-particle tunneling
mechanism. The proposed scheme can be used to implement quantum information
devices.


title: Decoherence, fluctuations and Wigner function in neutron optics

abstract:
  We analyze the coherence properties of neutron wave packets, after they have
interacted with a phase shifter undergoing different kinds of statistical
fluctuations. We give a quantitative (and operational) definition of
decoherence and compare it to the standard deviation of the distribution of the
phase shifts. We find that in some cases the neutron ensemble is more coherent,
even though it has interacted with a wider (i.e. more disordered) distribution
of shifts. This feature is independent of the particular definition of
decoherence: this is shown by proposing and discussing an alternative
definition, based on the Wigner function, that displays a similar behavior. We
briefly discuss the notion of entropy of the shifts and find that, in general,
it does not correspond to that of decoherence of the neutron.


title: Secure communication using coherent states

abstract:
  We demonstrate that secure communication using coherent states is possible.
The optimal eavesdropping strategy for an M-ry ciphering scheme shows that the
minimum probability of error in a measurement for bit determination can be made
arbitrarily close to the pure guessing value P_e=1/2. This ciphering scheme can
be optically amplified without degrading the security level. New avenues are
open to secure communications at high speeds in fiber-optic or free-space
channels.


title: Towards single-atom detection on a chip

abstract:
  We investigate the optical detection of single atoms held in a microscopic
atom trap close to a surface. Laser light is guided by optical fibers or
optical micro-structures via the atom to a photo-detector. Our results suggest
that with present-day technology, micro-cavities can be built around the atom
with sufficiently high finesse to permit unambiguous detection of a single atom
in the trap with 10 $\mu$s of integration. We compare resonant and non-resonant
detection schemes and we discuss the requirements for detecting an atom without
causing it to undergo spontaneous emission.


title: Note on purifications of a qubit

abstract:
  This work provides a parametrization of the set of purifications of a 2x2
mixed state, and joint purifications (if any) of a given pair of mixed 2x2
states. The former is parametrized by SO(3, R), while the latter is
parametrized by SO(2,R), except when the 2x2 state is pure. Using this
parametrization some quantum information measures are obtained. In the process
it is shown how to solve one variation of the classical Procustes problem. The
appendix is devoted to the first step in extending this work to higher
dimensions.


title: An efficient quantum algorithm for the one-dimensional Burgers equation

abstract:
  We analyze one-dimensional classical and quantum microscopic lattice-gas
models governed by a lattice Boltzmann equation at the mesoscopic scale,
achieved by ensemble averaging over microscopic realizations. The models are
governed by the Burgers equation at the macroscopic scale, achieved by taking
the limit where the grid size and time step both approach zero and by
performing a perturbative Chapman-Enskog expansion. The quantum algorithm
exploiting superposition and entanglement is more efficient than the classical
one because the quantum algorithm requires less memory. Furthermore, its
viscosity can be made arbitrarily small.


title: An efficient and accurate quantum algorithm for the Dirac equation

abstract:
  An efficient quantum algorithm for the many-body three-dimensional Dirac
equation is presented. Its computational complexity is dominantly linear in the
number of qubits used to spatially resolve the 4-spinor wave function.


title: Tunneling time scale of under-the-barrier forerunners

abstract:
  Time-dependent analytical solutions to Schr\"{o}dinger's equation with
quantum shutter initial conditions are used to investigate the issue of the
tunneling time of forerunners in rectangular potential barriers. By using a
time-frequency analysis, we find the existence of a regime characterized by the
opacity of the barrier, where the maximum peak of a forerunner measured at the
barrier transmission edge $x=L$ corresponds to a genuine tunneling process. The
corresponding time scale represents the tunneling time of the forerunner
through the classically forbidden region.


title: Quantum Computation of Jones' Polynomials

abstract:
  It is a challenging problem to construct an efficient quantum algorithm which
can compute the Jones' polynomial for any knot or link obtained from platting
or capping of a $2n$-strand braid. We recapitulate the construction of
braid-group representations from vertex models. We present the eigenbases and
eigenvalues for the braiding generators and its usefulness in direct evaluation
of Jones' polynomial. The calculation suggests that it is possible to associate
a series of unitary operators for any braid word. Hence we propose a quantum
algorithm using these unitary operators as quantum gates acting on a $2n$ qubit
state. We show that the quantum computation gives Jones' polynomial for achiral
knots and links.


title:
Linear optical implementation of a single mode quantum filter and
  generation of multi-photon polarization entangled state

abstract:
  We propose a scheme to implement a single-mode quantum filter, which
selectively eliminates the one-photon state in a quantum state
$\alpha|0>+\beta|1>+\gamma|2>$. The vacuum state and the two photon state are
transmitted without any change. This scheme requires single-photon sources,
linear optical elements and photon detectors. Furthermore we demonstrate, how
this filter can be used to realize a two-qubit projective measurement and to
generate multi-photon polarization entangled states.


title: Nonstabilizer Quantum Codes from Abelian Subgroups of the Error Group

abstract:
  This paper is motivated by the computer-generated nonadditive ((5,6,2)) code
described in an article by Rains, Hardin, Shor and Sloane. We describe a theory
of non-stabilizer codes of which the nonadditive code of Rains et al is an
example. Furthermore, we give a general strategy of constructing good
nonstabilizer codes from good stabilizer codes and give some explicit
constructions and asymptotically good nonstabilizer codes. In fact, we
explicitly construct a family of distance 2 non-stabilizer codes over all
finite fields of which the ((5,6,2)) is an special example. More interestingly,
using our theory, we are also able to explicitly construct examples of
non-stablizer quantum codes of distance 3. Like in the case of stabilizer
codes, we can design fairly efficient encoding and decoding procedures.


title: There is no "first" quantization

abstract:
  The introduction of spinor and other massive fields by ``quantizing''
particles (corpuscles) is conceptually misleading. Only spatial fields must be
postulated to form the fundamental objects to be quantized (that is, to define
a formal basis for all quantum states), while apparent ``particles'' are a mere
consequence of decoherence. This conclusion is also supported by the nature of
gauge fields.


title:
Classical information capacities of some single qubit quantum noisy
  channels

abstract:
  By using the Holevo-Schumacher-Westmoreland (HSW) theorem and through solving
eigenvalues of states out from the quantum noisy channels directly, or with the
help of the Bloch sphere representation, or Stokes parametrization
representation, we investigate the classical information capacities of some
well-known quantum noisy channels.


title:
Operator-Schmidt decomposition of the quantum Fourier transform on C^N1
  tensor C^N2

abstract:
  Operator-Schmidt decompositions of the quantum Fourier transform on C^N1
tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be
completely degenerate when N1 is a factor of N2 and when N1>N2. The first known
special case, N1=N2=2^n, was computed by Nielsen in his study of the
communication cost of computing the quantum Fourier transform of a collection
of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis,
University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More
generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in
their study of strength measures of quantum operations. [M.A. Nielsen et. al,
(accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the
Schmidt decompositions presented here, it follows that in all cases the
communication cost of exact computation of the quantum Fourier transform is
maximal.


title:
Path integral for relativistic oscillators: model of the Klein-Gordon
  particle in AdS space

abstract:
  Explicit path integration is carried out for the Green's functions of special
relativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowski
space-time modeled by a Klein-Gordon particle in the universal covering
space-time of the anti-de Sitter static space-time. The energy spectrum
together with the normalized wave functions are obtained. In the
non-relativistic limit, the bound states of the one- and three-dimensional
ordinary oscillators are regained.


title:
The causal consciousness: presynaptic beta-neurexin promotes
  neuromediator release via vibrational multidimensional tunneling

abstract:
  Epiphenomenalism is shown to be absurd because the development of
consciousness must be explainable through natural selection. A detailed
neuromolecular basis of the neuromediator release is given and it is stressed
on the possible key point where the quantum mind could act, namely presynaptic
scaffold protein dynamics and detachment of the calcium sensor v-SNARE
synaptotagmin-1. The beta-neurexin molecules are tuned via fast propagating
solitons by the quantum coherent microtubule network so that the beta-neurexin
molecule thermal vibrations could promote or suppress conformational changes
via vibrational multidimensional tunneling, which drives synaptotagmin-1
detachment from the SNARE complex under calcium ion binding. Following the
synaptotagmin-1 detachment membrane fusion takes place in SNARE dependent
fashion and the presynaptic vesicle spills neuromediator in the synaptic cleft.
Thus the quantum transfer of information causally affects the neuromediator
release.


title: Violation of local realism vs detection efficiency

abstract:
  We put bounds on the minimum detection efficiency necessary to violate local
realism in Bell experiments. These bounds depends of simple parameters like the
number of measurement settings or the dimensionality of the entangled quantum
state. We derive them by constructing explicit local-hidden variable models
which reproduce the quantum correlations for sufficiently small detectors
efficiency.


title: Amherst Interpretation of Quantum Mechanics

abstract:
  This paper was withdrawn by the author. It turns out that similar ideas have
been presented before. The author apologizes.


title: Spin tomography

abstract:
  We propose a tomographic reconstruction scheme for spin states. The
experimental setup, which is a modification of the Stern-Gerlach scheme, can be
easily performed with currently available technology. The method is generalized
to multi-particle states, analyzing the spin 1/2 case for indistinguishable
particles. Some Monte Carlo numerical simulations are given to illustrate the
technique.


title:
Universal Formula for the Expectation Value of the Radial Operator under
  the Aharonov-Bohm Flux and the Coulomb Field

abstract:
  A useful and universal formula for the expectation value of the radial
operator in the presence of the Aharonov-Bohm flux and the Coulomb Field is
established. We find that the expectation value $< r^{\lambda}>$ $(-\infty \leq
\lambda \leq \infty)$ is greatly affected due to the non-local effect of the
magnetic flux although the Aharonov-Bohm flux does not have any dynamical
significance in classical mechanics. In particular, the quantum fluctuation
increases in the presence of the magnetic flux due to the Aharonov-Bohm effect.
In addition, the Virial theory in quantum mechanics is also constructed for the
spherically symmetric system under the Aharonov-Bohm effect.


title: Entanglement properties of composite quantum systems

abstract:
  We present here an overview of our work concerning entanglement properties of
composite quantum systems. The characterization of entanglement, i.e. the
possibility to assert if a given quantum state is entangled with others and how
much entangled it is, remains one of the most fundamental open questions in
quantum information theory. We discuss our recent results related to the
problem of separability and distillability for distinguishable particles,
employing the tool of witness operators. Finally, we also state our results
concerning quantum correlations for indistinguishable particles.


title: 'Algorithmic cooling' in a momentum state quantum computer

abstract:
  We describe a quantum computer based upon the coherent manipulation of
two-level atoms between discrete one-dimensional momentum states. Combinations
of short laser pulses with kinetic energy dependent free phase evolution can
perform the logical invert, exchange, CNOT and Hadamard operations on any
qubits in the binary representation of the momentum state, as well as
conditional phase inversion. These allow a binary right-rotation, which halves
the momentum distribution in a single coherent process. Fields for the coherent
control of atomic momenta may thus be designed as quantum algorithms.


title:
Entangled imaging and wave-particle duality: from the microscopic to the
  macroscopic realm

abstract:
  We formulate a theory for entangled imaging, which includes also the case of
a large number of photons in the two entangled beams. We show that the results
for imaging and for the wave-particle duality features, which have been
demonstrated in the microscopic case, persist in the macroscopic domain. We
show that the quantum character of the imaging phenomena is guaranteed by the
simultaneous spatial entanglement in the near and in the far field.


title:
Quantum nonlocality test for continuous-variable states with dichotomic
  observables

abstract:
  There have been theoretical and experimental studies on quantum nonlocality
for continuous variables, based on dichotomic observables. In particular, we
are interested in two cases of dichotomic observables for the light field of
continuous variables: One case is even and odd numbers of photons and the other
case is no photon and presence of photons. We analyze various observables to
give the maximum violation of Bell's inequalities for continuous-variable
states. We discuss an observable which gives the violation of Bell's inequality
for any entangled pure continuous variable state. However, it does not have to
be a maximally entangled state to give the maximal violation of Bell's
inequality. This is attributed to a generic problem of testing the quantum
nonlocality of an infinite-dimensional state using a dichotomic observable.


title: Defect band-gap structures for triggering single-photon emission

abstract:
  A 3D analysis of the spontaneous decay of a single dipole embedded in a
planar multilayer structure is given, with special emphasis on Kerr-tunable
photonic band-gap materials for single-photon emission on demand. It is shown
that the change in the density of states near a defect resonance is much more
pronounced than that one near the band edges. In particular, operation near the
band edge as suggested from a 1D analysis is little suited for controlling the
photon emission.


title: Explicit Solution of the Time Evolution of the Wigner Function

abstract:
  Previously, an explicit solution for the time evolution of the Wigner
function was presented in terms of auxiliary phase space coordinates which obey
simple equations that are analogous with, but not identical to, the classical
equations of motion. They can be solved easily and their solutions can be
utilized to construct the time evolution of the Wigner function. In this paper,
the usefulness of this explicit solution is demonstrated by solving a numerical
example in which the Wigner function has strong spatial and temporal variations
as well as regions with negative values. It is found that the explicit solution
gives a correct description of the time evolution of the Wigner function. We
examine next the pseudoparticle approximation which uses classical trajectories
to evolve the Wigner function. We find that the pseudoparticle approximation
reproduces the general features of the time evolution, but there are
deviations. We show how these deviations can be systematically reduced by
including higher-order correction terms in powers of $\hbar^2$.

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


title:
Fast quantum logic gates with trapped ions interacting with external
  laser and quantized cavity field beyond the Lamb-Dicke regime

abstract:
  A scheme to implement quantum logic gates by manipulating trapped ions
through interaction with monochromatic external laser field and quantized
cavity field, beyond the Lamb-Dicke regime, is presented. Characteristic times,
for implementing ionic state transitions using non-resont laser pulse or
quantized cavity field, shows a sharp decline for large Lamb-Dicke parameter
value of $\eta_{L}=\eta_{c}=0.2$, and is seen to decrease further with increase
in number of initial state vibrational quanta $m$.


title:
Violation of Bell's inequality: criterion for quantum communication
  complexity advantage

abstract:
  We prove that for every Bell's inequality and for a broad class of protocols,
there always exists a multi-party communication complexity problem, for which
the protocol assisted by states which violate the inequality is more efficient
than any classical protocol. Moreover, for that advantage Bell's inequality
violation is a necessary and sufficient criterion. Thus, violation of Bell's
inequalities has a significance beyond that of a non-optimal-witness of
non-separability.


title: Constraints on the mixing of states on bipartite quantum systems

abstract:
  We give necessary conditions for the mixing problem in bipartite case, which
are independent of eigenvalues and based on algebraic-geometric invariants of
the bipartite states. One implication of our results is that for some special
bipartite mixed states, only special mixed states in a measure zero set can be
used to mix to get them. The results indicate for many physical problems on
composite quantum systems the description based on majorization of eigenvalues
is not sufficient


title: On "Bell's inequality without alternative settings"

abstract:
  Cabello has recently (in quant-ph/0210081) observed that ``...an
EPR-experiment with a fixed POVM on each particle provides a violation of
Bell's inequality without requiring local observers to choose between the
alternatives.'' In this note I discuss the implications of this observation for
tests of locality.


title:
Characterizing the entanglement of symmetric many-particle spin-1/2
  systems

abstract:
  Analyzing the properties of entanglement in many-particle spin-1/2 systems is
generally difficult because the system's Hilbert space grows exponentially with
the number of constituent particles, $N$. Fortunately, it is still possible to
investigate many-particle entanglement when the state of the system possesses
sufficient symmetry. In this paper, we present a practical method for
efficiently computing various bipartite entanglement measures for states in the
symmetric subspace and perform these calculations for $N\sim 10^3$. By
considering all possible bipartite splits, we construct a picture of the
multiscale entanglement in large symmetric systems. In particular, we
characterize dynamically generated spin-squeezed states by comparing them to
known reference states (e.g., GHZ and Dicke states) and new families of states
with near-maximal bipartite entropy. We quantify the trade-off between the
degree of entanglement and its robustness to particle loss, emphasizing that
substantial entanglement need not be fragile.


title: Toward the spectral zone control

abstract:
  The desired shifts of the boundaries of spectral allowed zones of periodical
systems are demonstrated. In particular, the phenomenon of merging neighbor
allowed zones is exhibited and its simple explanation is given. It is also
shown how to change the additional fundamental spectral parameter, the degree
of exponential solution growth, at arbitrary given energy points inside the
forbidden zones. This allows one to control tunneling through fragments of
periodic structures at energies belonging to spectral gap. All the results are
based on the finite interval inverse eigenvalue problem which provides us with
complete sets of exactly solvable models. This is a radical extension
(continuous ! multiplicity) in comparison to the famous finite-gap models.


title:
Tunneling Time Distribution by means of Nelson's Quantum Mechanics and
  Wave-Particle Duality

abstract:
  We calculate a tunneling time distribution by means of Nelson's quantum
mechanics and investigate its statistical properties. The relationship between
the average and deviation of tunneling time suggests the exsistence of
``wave-particle duality'' in the tunneling phenomena.


title: Asymptotic Theory for Quantum Bose Systems with Many Degrees of Freedom

abstract:
  We construct asymptotic expansions of Laplace type for the time-dependent
quantum averages for Bose systems with many degrees of freedom, initially
populated in coherent states. These solutions are localized in phase space, and
they are different from the usual oscillating asymptotics for the
quasi-classical wave functions. These expansions are valid on any fixed time
interval, and caustics do not contribute to the asymptotics.