title: High coherent solid-state qubit from a pair of quantum dots

abstract:
  In this letter we propose a scheme to build up high coherent solid-state
quantum bit (qubit) from two coupled quantum dots. Quantum information is
stored in electron-hole pair state with the electron and hole locating in
different dots, and universal quantum gates involving any pair of qubits are
realized by effective coupling interaction via virtually exchanging cavity
photons.


title: Non-adiabatic geometric quantum computation with trapped ions

abstract:
  We propose a non-adiabatic scheme for geometric quantum computation with
trapped ions. By making use of the Aharonov-Anandan phase, the proposed scheme
not only preserves the globally geometric nature in quantum computation, but
also provides the advantage of non-adiabaticity that overcomes the problem of
slow evolution in the existing adiabatic schemes. Moreover, the present scheme
requires only two atomic levels in each ion, making it an appealing candidate
for quantum computation.


title: A new class of non-Hermitian Hamiltonians with real spectra

abstract:
  We construct a new class of non-Hermitian Hamiltonians with real spectra. The
Hamiltonians possess one explicitly known eigenfunction.


title: Holonomic quantum computation with neutral atoms

abstract:
  We propose an all-geometric implementation of quantum computation using
neutral atoms in cavity QED. We show how to perform generic single- and
two-qubit gates, the latter by encoding a two-atom state onto a single,
many-level atom. We compare different strategies to overcome limitations due to
cavity imperfections.


title: Quantum limits on phase-shift detection using multimode interferometers

abstract:
  Fundamental phase-shift detection properties of optical multimode
interferometers are analyzed. Limits on perfectly distinguishable phase shifts
are derived for general quantum states of a given average energy. In contrast
to earlier work, the limits are found to be independent of the number of
interfering modes. However, the reported bounds are consistent with the
Heisenberg limit. A short discussion on the concept of well-defined relative
phase is also included.


title: Quantum logic gates and maximally entangled states in microtraps

abstract:
  This paper has been withdrawn because the first author submitted the paper
without previously consulting the rest of the authors.


title: The Cosmic Digital Code and Quantum Mechanics

abstract:
  This paper posits that the cosmic digital code as the law of all physical
laws contains two mutually exclusive values: attachment space attaching to
object and detachment space detaching from object. However, the cosmic physical
system could not start with mutually exclusive attachment space and detachment
space at the same time in the beginning. The way out of this impasse is that
the complete cosmic system consists of both the cosmic physical system and the
unphysical cosmic digital code. The unphysical cosmic digital code allows the
coexistence of attachment space and detachment space at the same time. The
cosmic digital code behaves as gene in organism, and the cosmic physical system
behaves as organ. Under different conditions and times, different spaces in the
cosmic digital code are activated to generate different spaces in the cosmic
physical systems with different physical laws for different universes in the
multivese. All universes start from the primitive multiverse, which only has
attachment space attaching to 10D string without the four force fields. During
the big bang in our universe, detachment space emerged to detach particle from
its four force fields. Such detachment, however, cannot be completely and
permanently detached, because particle still attaches to its force fields. The
result is hybrid space, combining both attachment space and detachment space in
coherent state, such as particle and its force fields. Hybrid space is the
space for wavefunction whose probability density is proportional to attachment
space, and inversely proportional to detachment space. The collapse of
wavefunction in decoherent state is the separation of attachment space and
detachment space in such way that attachment space attaches to particle, and
detachment space separately detaches from all probability density.


title:
Practical creation and detection of polarization Bell states using
  parametric down-conversion

abstract:
  The generation and detection of maximally-entangled two-particle states,
`Bell states,' are crucial tasks in many quantum information protocols such as
cryptography and teleportation. Unfortunately, they require strong
inter-particle interactions lacking in optics. For this reason, it has not
previously been possible to perform complete Bell state determination in
optical systems. In this work, we show how a recently developed quantum
interference technique for enhancing optical nonlinearities can make efficient
Bell-state measurement possible. We also discuss weaknesses of the scheme
including why it cannot be used for unconditional quantum teleportation.


title:
Matching Weak Coupling and Quasiclassical Expansions For Dual QES
  Problems

abstract:
  Certain quasi-exactly solvable systems exhibit an energy reflection property
that relates the energy levels of a potential or of a pair of potentials. We
investigate two sister potentials and show the existence of this energy
reflection relationship between the two potentials. We establish a relationship
between the lowest energy edge in the first potential using the weak coupling
expansion and the highest energy level in the sister potential using a WKB
approximation carried out to higher order.


title: Quantum randomness emerging under gravitational nonlinearity

abstract:
  A scenario is outlined for quantum measurement, assuming that self-sustaining
classicality is the consequence of an attractive gravitational self-interaction
acting on massive bodies, and randomness arises already in the classical
domain. A simple solvable model is used to demonstrate that small quantum
systems influence big ones in a mean-field way, offering a natural route to
Born's probability rule.


title: About quantum mechanics interpretation

abstract:
  There is a certainty that the modern (Copenhagen's) interpretation of quantum
mechanics is correct. However, the some physicist had the opinion that the
modern quantum mechanics is a phenomenological theory. The suggested theory is
the new quantum mechanics interpretation that is entirely according to the
modern interpretation and gives a number of results, which naturally explain
the postulates of the modern quantum mechanics.


title: Trading quantum for classical resources in quantum data compression

abstract:
  We study the visible compression of a source E of pure quantum signal states,
or, more formally, the minimal resources per signal required to represent
arbitrarily long strings of signals with arbitrarily high fidelity, when the
compressor is given the identity of the input state sequence as classical
information. According to the quantum source coding theorem, the optimal
quantum rate is the von Neumann entropy S(E) qubits per signal.
  We develop a refinement of this theorem in order to analyze the situation in
which the states are coded into classical and quantum bits that are quantified
separately. This leads to a trade--off curve Q(R), where Q(R) qubits per signal
is the optimal quantum rate for a given classical rate of R bits per signal.
  Our main result is an explicit characterization of this trade--off function
by a simple formula in terms of only single signal, perfect fidelity encodings
of the source. We give a thorough discussion of many further mathematical
properties of our formula, including an analysis of its behavior for group
covariant sources and a generalization to sources with continuously
parameterized states. We also show that our result leads to a number of
corollaries characterizing the trade--off between information gain and state
disturbance for quantum sources. In addition, we indicate how our techniques
also provide a solution to the so--called remote state preparation problem.
Finally, we develop a probability--free version of our main result which may be
interpreted as an answer to the question: ``How many classical bits does a
qubit cost?'' This theorem provides a type of dual to Holevo's theorem, insofar
as the latter characterizes the cost of coding classical bits into qubits.


title: A theorem for the beam splitter entangler

abstract:
  It is conjectured that the an entanglement output states from a beam splitter
requires the nonclassicality in the input state(M.S. Kim, W. Son, V. Buzek and
P. L. Knight, Phys. Rev. A, 65, 032323(2002)). Here we give a proof for this
conjecture.


title: Wave packet dynamics and factorization of numbers

abstract:
  We connect three phenomena of wave packet dynamics: Talbot images, revivals
of a particle in a box and fractional revivals. The physical origin of these
effects is deeply rooted in phase factors which are quadratic in the quantum
number. We show that the characteristic structures in the time evolution of
these systems allow us to factorize large integers.


title: Quantify entanglement by concurrence hierarchy

abstract:
  We define the concurrence hierarchy as d-1 independent invariants under local
unitary transformations in d-level quantum system. The first one is the
original concurrence defined by Wootters et al in 2-level quantum system and
generalized to d-level pure quantum states case. We propose to use this
concurrence hierarchy as measurement of entanglement. This measurement does not
increase under local quantum operations and classical communication.


title:
Simple diamagnetic monotonicities for Schroedinger operators with
  inhomogeneous magnetic fields of constant direction

abstract:
  Under certain simplifying conditions we detect monotonicity properties of the
ground-state energy and the canonical-equilibrium density matrix of a spinless
charged particle in the Euclidean plane subject to a perpendicular, possibly
inhomogeneous magnetic field and an additional scalar potential. Firstly, we
point out a simple condition warranting that the ground-state energy does not
decrease when the magnetic field and/or the potential is increased pointwise.
Secondly, we consider the case in which both the magnetic field and the
potential are constant along one direction in the plane and give a genuine
path-integral argument for corresponding monotonicities of the density-matrix
diagonal and the absolute value of certain off-diagonals. Our results
complement to some degree results of M. Loss and B. Thaller [Commun. Math.
Phys. 186 (1997) 95] and L. Erdos [J. Math. Phys. 38 (1997) 1289].


title: Evolution of entanglement under echo dynamics

abstract:
  Echo dynamics and fidelity are often used to discuss stability in quantum
information processing and quantum chaos. Yet fidelity yields no information
about entanglement, the characteristic property of quantum mechanics. We study
the evolution of entanglement in echo dynamics. We find qualitatively different
behavior between integrable and chaotic systems on one hand and between random
and coherent initial states for integrable systems on the other. For the latter
the evolution of entanglement is given by a classical time scale. Analytic
results are illustrated numerically in a Jaynes Cummings model.


title: Energy and Efficiency of Adiabatic Quantum Search Algorithms

abstract:
  We present the results of a detailed analysis of a general, unstructured
adiabatic quantum search of a data base of $N$ items. In particular we examine
the effects on the computation time of adding energy to the system. We find
that by increasing the lowest eigenvalue of the time dependent Hamiltonian {\it
temporarily} to a maximum of $\propto \sqrt{N}$, it is possible to do the
calculation in constant time. This leads us to derive the general theorem which
provides the adiabatic analogue of the $\sqrt{N}$ bound of conventional quantum
searches. The result suggests that the action associated with the oracle term
in the time dependent Hamiltonian is a direct measure of the resources required
by the adiabatic quantum search.


title:
Realization of quantum operations on photonic qubits by linear optics
  and post-selection

abstract:
  One of the greatest difficulties in the applications of single photon
polarization states as qubits is the realization of controlled interactions
between two photons. Recently, it has been shown that such interactions can be
realized using only beam splitters and high efficiency photon detection by
post-selecting a well defined part of the results in the output. We analyze
these interactions and discuss schemes for qubit operations based on this
mechanism.


title: Center-of-mass motion in many-body theory of BEC

abstract:
  The method of generating a family of new solutions starting from any wave
function satisfying the nonlinear Schr\"odinger equation in a harmonic
potential proposed recently [ J. J. Garc\'{\i}a-Ripoll, V. M.
P\'erez-Garc\'{\i}a, and V. Vekslerchik, Phys. Rev. E {\bf 64}, 056602 (2001)]
is extended to many-body theory of mutually interacting particles. Our method
is based on a generalization of the displacement operator known in quantum
optics and results in the separation of the center of mass motion from the
internal dynamics of many-body systems. The center of mass motion is analyzed
for an anisotropic rotating trap and a region of instability for intermediate
rotational velocities is predicted.


title:
Quantum Nondemolition State Measurement via Atomic Scattering in Bragg
  Regime

abstract:
  We suggest a quantum nondemolition scheme to measure a quantized cavity field
state using scattering of atoms in general Bragg regime. Our work extends the
QND measurement of a cavity field from Fock state, based on first order Bragg
deflection [9], to any quantum state based on Bragg deflection of arbitrary
order. In addition a set of experimental parameters is provided to perform the
experiment within the frame work of the presently available technology.


title:
General realization of N=4 supersymmetric quantum mechanics and its
  applications

abstract:
  Based upon the general supercharges which involve not only generators C_j of
the Clifford algebra C(4,0) with positive metric, but also operators of third
order, C_j C_k C_l, the general form of N=4 supersymmetric quantum mechanics
(SSQM), which brings out the richer structures, is realized. Then from them, an
one-dimensional physical realization and a new multi-dimensional physical
realization of N=4 SSQM are respectively obtained by solving the constraint
conditions. As applications, N=4 dynamical superconformal symmetries, which
possess both the N=4 supersymmetries and the usual dynamical conformal
symmetries, are studied in detail by considering two simple superpotentials k/x
and \omega x, and their corresponding superalgebraic structures, which are
spanned by eight fermionic generators and six bosonic generators, are
established as well.


title:
Experimentally obtaining the Likeness of Two Unknown Quantum States on
  an NMR Quantum Information Processor

abstract:
  Recently quantum states discrimination has been frequently studied. In this
paper we study them from the other way round, the likeness of two quantum
states. The fidelity is used to describe the likeness of two quantum states.
Then we presented a scheme to obtain the fidelity of two unknown qubits
directly from the integral area of the spectra of the assistant qubit(spin) on
an NMR Quantum Information Processor. Finally we demonstrated the scheme on a
three-qubit quantum information processor. The experimental data are consistent
with the theoretical expectation with an average error of 0.05, which confirms
the scheme.


title: Improved discrimination of unitaries by entangled probes

abstract:
  We consider the problem of discriminating among a set of unitaries by means
of measurements performed on the state undergoing the transformation. We show
that use of entangled probes improves the discrimination in the two following
cases: i) for a set of unitaries that are the UIR of a group and, ii) for any
pair of transformations provided that multiple uses of the channel are allowed.


title:
Interference scheme to measure light-induced nonlinearities in
  Bose-Einstein condensates

abstract:
  Light-induced nonlinear terms in the Gross-Pitaevskii equation arise from the
stimulated coherent exchange of photons between two atoms. For atoms in an
optical dipole trap this effect depends on the spatial profile of the trapping
laser beam. Two different laser beams can induce the same trapping potential
but very different nonlinearities. We propose a scheme to measure light-induced
nonlinearities which is based on this observation.


title:
On the impossibility of distilling Gaussian states with Gaussian
  operations

abstract:
  We show that no distillation protocol for Gaussian quantum states exists that
relies on (i) arbitrary local unitary operations that preserve the Gaussian
character of the state and (ii) homodyne detection together with classical
communication and postprocessing by means of local Gaussian unitary operations
on two symmetric identically prepared copies. This is in contrast to the
finite-dimensional case, where entanglement can be distilled in an iterative
protocol using two copies at a time. The ramifications for the distribution of
Gaussian states over large distances will be outlined. We also comment on the
generality of the approach and sketch the most general form of a Gaussian local
operation with classical communication in a bipartite setting.


title:
On the Influence of the Unit Cell Type on the Wave Function in
  One-Dimensional Kronig-Penney Models

abstract:
  We study the influence of the different choice of unit cells on the Bloch
solutions of Schr\c{c}dinger equation for one-dimensional periodic Kronig-
Penney models with rectangular potential barriers or potential wells and
partially constant effectiv mass. We obtain generalized Kronig-Penney relations
for bulk states and exact expressions for the corresponding periodic parts of
the Bloch wave functions for the two possible choices of the matching
conditions in an unit cell. We show also that our analitic expressions reduce
to the well known expressions for the Kronig-Penney relations and Bloch waves
under constant effective mass and appropriate matching conditions.


title: Degree of entanglement in a quantum measurement process

abstract:
  We suggest a quantum measurement model in an ion trap which specifies the
probability distribution of two, distinct internal ground states of a trapped
four-level ion. The external degrees of motion of the four-level ion constitute
the meter which, in turn, is coupled to the environment by engineered
reservoirs. In a previous publication, a similar measurement model was employed
to test decoherence effects on quantum nonlocality in phase space on the basis
of coincidence measurements of the entangled system-meter scheme. Here, we
study the effects of decoherence on the entanglement of formation characterized
by the concurrence. The concurrence of the system enables to find the maximum
possible violation of the Bell inequality. Surprisingly, this model gives
illustrative insights into the question to what extend the Bell inequality can
be considered as a measure of entanglement.


title: Bell's Theorem Without Inequalitites for a Maximally Entangled State

abstract:
  A proof of Bell's theorem without inequalities for two maximally entangled
particles is proposed using the technique of quantum teleportation. It follows
Hardy's arguments for a non-maximally entangled state with the help of two
auxiliary particles without correlation. The present proof can be tested by
measurements with 100% probability.


title: Quantum Jumps, EEQT and the Five Platonic Fractals

abstract:
  It is shown that symmetric configurations of fuzzy spin direction detectors
generate, through quantum jumps, IFS fractals on the sphere S^2. The IFS
fractals can be also interpreted as resulting from applications of Lorentz
boosts to the projective light cone.


title:
High-fidelity teleportation of entanglements of running-wave field
  states

abstract:
  We describe a scheme for the teleportation of entanglements of zero- and
one-photon running-wave field states. In addition to linear optical elements,
Kerr nonlinearity is also employed so as to achieve a 100% probability of
success in the ideal case. A comprehensive phenomenological treatment of errors
in the domain of running-wave physics, for linear and nonlinear optical
elements, is also given, making it possible to calculate the fidelity of the
teleportation process. A strategy for carrying out the Bell-type measurement
which is able to probe the absorption of photons in the optical elements is
adopted. Such strategy, combined with usually small damping constants
characterizing the optical devices, results in a high fidelity for the
teleportation process. The feasibility of the proposed scheme relies on the
fact that the Kerr nonlinearity it demands can be achieved through the recently
reported ultraslow light propagation in cold atomic media [Phys. Rev. Lett. 84,
1419 (2000); Phys. Rev. A 65, 033833 (2002)].


title: Quantum Entanglement in Second-quantized Condensed Matter Systems

abstract:
  The entanglement between occupation-numbers of different single particle
basis states depends on coupling between different single particle basis states
in the second-quantized Hamiltonian. Thus in principle, interaction is not
necessary for occupation-number entanglement to appear. However, in order to
characterize quantum correlation caused by interaction, we use the eigenstates
of the single-particle Hamiltonian as the single particle basis upon which the
occupation-number entanglement is defined. Using the proper single particle
basis, we discuss occupation-number entanglement in important eigenstates,
especially ground states, of systems of many identical particles. The
discussions on Fermi systems start with Fermi gas, Hatree-Fock approximation,
and the electron-hole entanglement in excitations. The entanglement in a
quantum Hall state is quantified as -fln f-(1-f)ln(1-f), where f is the proper
fractional part of the filling factor. For BCS superconductivity, the
entanglement is a function of the relative momentum wavefunction of the Cooper
pair, and is thus directly related to the superconducting energy gap. For a
spinless Bose system, entanglement does not appear in the
Hatree-Gross-Pitaevskii approximation, but becomes important in the Bogoliubov
theory.


title:
Optical qubit generation by state truncation using an experimentally
  feasible scheme

abstract:
  Generation of arbitrary superposition of vacuum and one-photon states using
quantum scissors device (QSD) is studied. The device allows the preparation of
states by truncating an input coherent light. Optimum values of the intensity
of the coherent light for the generation of any desired state using the
experimentally feasible QSD scheme are found.


title:
Super-poissonian photon statistics and correlations between pump and
  probe fields in Electromagnetically Induced Transparency

abstract:
  We have measured the photon statistics of pump and probe beams after
interaction with Rb atoms in a situation of Electromagnetically Induced
Transparency. Both fields present super-poissonian statistics and their
intensities become correlated, in good qualitative agreement with theoretical
predictions in which both fields are treated quantum-mechanically. The
intensity correlations measured are a first step towards the observation of
entanglement between the fields.


title: Controlling quantum entanglement through photocounts

abstract:
  We present a protocol to generate and control quantum entanglement between
the states of two subsystems (the system ${\cal S}$) by making measurements on
a third subsystem (the monitor ${\cal M}$), interacting with ${\cal S}$. For
the sake of comparison we consider first an ideal, or instantaneous projective
measurement, as postulated by von Neumann. Then we compare it with the more
realistic or generalized measurement procedure based on photocounting on ${\cal
M}$. Further we consider that the interaction term (between ${\cal S}$ and
${\cal M}$) contains a quantum nondemolition variable of ${\cal S}$ and discuss
the possibility and limitations for reconstructing the initial state of ${\cal
S}$ from information acquired by photocounting on ${\cal M}$.


title: Discrete teleportation protocol of continuum spectra field states

abstract:
  A discrete protocol for teleportation of superpositions of coherent states of
optical cavity fields is presented. Displacement and parity operators are
unconventionally used in Bell-like measurement for field states.


title: Lower bound for a class of weak quantum coin flipping protocols

abstract:
  We study the class of protocols for weak quantum coin flipping introduced by
Spekkens and Rudolph (quant-ph/0202118). We show that, for any protocol in this
class, one party can win the coin flip with probability at least $1/\sqrt{2}$.


title: Continuous Variable Quantum Cryptography - beating the 3 dB loss limit

abstract:
  We demonstrate that secure quantum key distribution systems based on
continuous variables implementations can operate beyond the apparent 3 dB loss
limit that is implied by the beam splitting attack . The loss limit was
established for standard minimum uncertainty states such as coherent states. We
show that by an appropriate postselection mechanism we can enter a region where
Eve's knowledge falls behind the information shared between Alice and Bob even
in the presence of substantial losses.


title: Efficient Classical Simulation of Optical Quantum Circuits

abstract:
  We identify a broad class of physical processes in an optical quantum circuit
that can be efficiently simulated on a classical computer: this class includes
unitary transformations, amplification, noise, and measurements. This
simulatability result places powerful constraints on the capability to realize
exponential quantum speedups as well as on inducing an optical nonlinear
transformation via linear optics, photodetection-based measurement and
classical feedforward of measurement results, optimal cloning, and a wide range
of other processes.


title: Anomalous transparency for near-top Bloch states of periodic potential

abstract:
  In the paper are considered stationary (Bloch) states of a particle, in the
field of periodic biparabolic type potential. It is shown that while the
particle's energy decreases in limits of a single energy band, the probability
of the particle to be in barrier-type region of periodic potential increases,
in contrary to the expected decreasing. This ''anomalous'' behavior is more
pronounced for the near-top bands and monotonically decreases for the higher or
lower ones.


title:
Integrals over Products of Distributions and Coordinate Independence of
  Zero-Temperature Path Integrals

abstract:
  In perturbative calculations of quantum-statistical zero-temperature path
integrals in curvilinear coordinates one encounters Feynman diagrams involving
multiple temporal integrals over products of distributions, which are
mathematically undefined. In addition, there are terms proportional to powers
of Dirac delta-functions at the origin coming from the measure of path
integration. We give simple rules for integrating products of distributions in
such a way that the results ensure coordinate independence of the path
integrals. The rules are derived by using equations of motion and partial
integration, while keeping track of certain minimal features originating in the
unique definition of all singular integrals in $1 - \epsilon$ dimensions. Our
rules yield the same results as the much more cumbersome calculations in 1-
epsilon dimensions where the limit epsilon --> 0 is taken at the end. They also
agree with the rules found in an independent treatment on a finite time
interval.


title: Wavepacket and its collapse

abstract:
  The notions of wavepacket and collapse are discussed and a local-realistic
interpretation of Berkeley experiment is done.


title: Gaussian transformations and distillation of entangled Gaussian states

abstract:
  We prove that it is impossible to distill more entanglement from a single
copy of a two-mode bipartite entangled Gaussian state via LOCC Gaussian
operations. More generally, we show that any hypothetical distillation protocol
for Gaussian states involving only Gaussian operations would be a deterministic
protocol. Finally, we argue that the protocol considered by Eisert et al.
[quant-ph/0204052] is the optimum Gaussian distillation protocol for two copies
of entangled Gaussian states.


title:
Generation of two-mode nonclassical states and a quantum phase gate
  operation in trapped ion cavity QED

abstract:
  We propose a scheme to generate nonclassical states of a quantum system,
which is composed of the one-dimensional trapped ion motion and a single cavity
field mode. We show that two-mode SU(2) Schr\"odinger-cat states, entangled
coherent states, two-mode squeezed vacuum states and their superposition can be
generated. If the vibration mode and the cavity mode are used to represent
separately a qubit, a quantum phase gate can be implemented.


title:
Quantum optical versus quantum Brownian motion master-equation in terms
  of covariance and equilibrium properties

abstract:
  Structures of quantum Fokker-Planck equations are characterized with respect
to the properties of complete positivity, covariance under symmetry
transformations and satisfaction of equipartition, referring to recent
mathematical work on structures of unbounded generators of covariant quantum
dynamical semigroups. In particular the quantum optical master-equation and the
quantum Brownian motion master-equation are shown to be associated to
$\mathrm{U(1)}$ and $\mathrm{R}$ symmetry respectively. Considering the motion
of a Brownian particle, where the expression of the quantum Fokker-Planck
equation is not completely fixed by the aforementioned requirements, a recently
introduced microphysical kinetic model is briefly recalled, where a quantum
generalization of the linear Boltzmann equation in the small energy and
momentum transfer limit straightforwardly leads to quantum Brownian motion.


title:
Polarization-squeezed light formation in a medium with electronic Kerr
  nonlinearity

abstract:
  We analyze the formation of polarization-squeezed light in a medium with
electronic Kerr nonlinearity. Quantum Stokes parameters are considered and the
spectra of their quantum fluctuations are investigated. It is established that
the frequency at which the suppression of quantum fluctuations is the greatest
can be controlled by adjusting the linear phase difference between pulses. We
shown that by varying the intensity or the nonlinear phase shift per photon for
one pulse, one can effectively control the suppression of quantum fluctuations
of the quantum Stokes parameters.


title:
Photon counting schemes and performance of non-deterministic nonlinear
  gates in linear optics

abstract:
  The performance of nondeterministic nonlinear gates in linear optics relies
on the photon counting scheme being employed and the efficiencies of the
detectors in such schemes. We assess the performance of the nonlinear sign
gate, which is a critical component of linear optical quantum computing, for
two standard photon counting methods: the double detector array and the visible
light photon counter. Our analysis shows that the double detector array is
insufficient to provide the photon counting capability for effective
nondeterministic nonlinear transformations, and we determine the gate fidelity
for both photon counting methods as a function of detector efficiencies.


title: Approximate Master Equations for Atom Optics

abstract:
  In the field of atom optics, the basis of many experiments is a two level
atom coupled to a light field. The evolution of this system is governed by a
master equation. The irreversible components of this master equation describe
the spontaneous emission of photons from the atom. For many applications, it is
necessary to minimize the effect of this irreversible evolution. This can be
achieved by having a far detuned light field. The drawback of this regime is
that making the detuning very large makes the timestep required to solve the
master equation very small, much smaller than the timescale of any significant
evolution. This makes the problem very numerically intensive. For this reason,
approximations are used to simulate the master equation which are more
numerically tractable to solve. This paper analyses four approximations: The
standard adiabatic approximation; a more sophisticated adiabatic approximation
(not used before); a secular approximation; and a fully quantum dressed-state
approximation. The advantages and disadvantages of each are investigated with
respect to accuracy, complexity and the resources required to simulate. In a
parameter regime of particular experimental interest, only the sophisticated
adiabatic and dressed-state approximations agree well with the exact evolution.


title:
Exploiting the Difference in Probability Calculation between Quantum and
  Probabilistic Computations

abstract:
  The main purpose of this paper is to show that we can exploit the difference
($l_1$-norm and $l_2$-norm) in the probability calculation between quantum and
probabilistic computations to claim the difference in their space efficiencies.
It is shown that there is a finite language $L$ which contains sentences of
length up to $O(n^{c+1})$ such that: ($i$) There is a one-way quantum finite
automaton (qfa) of $O(n^{c+4})$ states which recognizes $L$. ($ii$) However, if
we try to simulate this qfa by a probabilistic finite automaton (pfa)
\textit{using the same algorithm}, then it needs $\Omega(n^{2c+4})$ states. It
should be noted that we do not prove real lower bounds for pfa's but show that
if pfa's and qfa's use exactly the same algorithm, then qfa's need much less
states.


title:
Self-induced transparency and giant nonlinearity in doped photonic
  crystals

abstract:
  Photonic crystals doped with resonant atoms allow for uniquely advantageous
nonlinear modes of optical propagation: (a) Self-induced transparency (SIT)
solitons and multi-dimensional localized "bullets" propagating at photonic band
gap frequencies. These modes can exist even at ultraweak intensities (few
photons) and therefore differ substantially either from solitons in
Kerr-nonlinear photonic crystals or from SIT solitons in uniform media. (b)
Cross-coupling between pulses exhibiting electromagnetically induced
transparency (EIT) and SIT gap solitons. We show that extremely strong
correlations (giant cross-phase modulation) can be formed between the two
pulses. These features may find applications in high-fidelity classical and
quantum optical communications.


title: On states, channels and purification

abstract:
  In this note we introduce purification for a pair $(\rho,\Phi),$ where $\rho
$ is a quantum state and $\Phi $ is a channel, which allows in particular a
natural extension of the properties of related information quantities (such as
mutual and coherent informations) to the channels with arbitrary input and
output spaces.


title:
Non-Perturbative Renormalization Group Analysis of the Ohmic Quantum
  Dissipation

abstract:
  We analyze quantum tunneling with the Ohmic dissipation by the
non-perturbative renormalization group method. We calculate the localization
susceptibility to evaluate the critical dissipation for the quantum-classical
transition, and find considerably larger critical dissipation compared to the
previous semi-classical arguments.


title: A Relativistic Extension of Event-Enhanced Quantum Theory

abstract:
  In this paper, we develop a formalism describing in a relativistic way a
system which consists of a classical and a quantum part being coupled. The
formalism models one particle with spin 1/2 and it is a possible relativistic
extension of the Event-Enhanced Quantum Theory. We postulate a covariant
algorithm which plays the role of the standard reduction postulate in
non-relativistic quantum mechanics. Furthermore, we present an algorithm to
simulate detections of the particle.


title: Towards Quantum Mechanism of Sensory Transduction

abstract:
  In this communication the nonlinear wave equations is proposed to describe
classical exitations in microtubules. Double-periodic solution of this equation
is considered as classical background for quantum excitations.


title:
A Simple Method of Calculating Commutators in Hamilton System with
  Mathematica Software

abstract:
  As a powerful tool in scientific computation, Mathematica offers us algebraic
computation, but it does not provide functions to directly calculate
commutators in quantum mechanics. Different from present software packets to
deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one
simple method of calculating the commutator in quantum mechanics is put forward
and is demonstrated by an example calculating SO(4) dynamical symmetry in 3
dimensions Coulomb potential. This method does not need to develop software
packets but rather to directly write program in Mathematica. It is based on the
connection between commutator in quantum mechanics and Poisson bracket in
classical mechanics to perform calculations. Both the length and the running
time of this example are very short, which demonstrates that this method is
simple and effective in scientific research. Moreover, this method is used to
calculate any commutator in Hamilton system in principle. In the end some
deficiencies and applications are discussed.


title: Properties of a beam splitter entangler with Gaussian input states

abstract:
  An explicit formula is given for the quantity of entanglement in the output
state of a beam splitter, given the squeezed vacuum states input in each mode.


title: The Effect of Stochastic Noise on Quantum State Transfer

abstract:
  We consider the effect of classical stochastic noise on control laser pulses
used in a scheme for transferring quantum information between atoms, or quantum
dots, in separate optical cavities via an optical connection between cavities.
We develop a master equation for the dynamics of the system subject to
stochastic errors in the laser pulses, and use this to evaluate the sensitivity
of the transfer process to stochastic pulse shape errors for a number of
different pulse shapes. We show that under certain conditions, the sensitivity
of the transfer to the noise depends on the pulse shape, and develop a method
for determining a pulse shape that is minimally sensitive to specific errors.


title:
Jordan blocks and Gamow-Jordan eigenfunctions associated to a double
  pole of the S-matrix

abstract:
  An accidental degeneracy of resonances gives rise to a double pole in the
scattering matrix, a double zero in the Jost function and a Jordan chain of
length two of generalized Gamow-Jordan eigenfunctions of the radial
Schroedinger equation. The generalized Gamow-Jordan eigenfunctions are basis
elements of an expansion in bound and resonant energy eigenfunctions plus a
continuum of scattering wave functions of complex wave number. In this
biorthonormal basis, any operator which is a regular function of the
Hamiltonian is represented by a complex matrix which is diagonal except for a
Jordan block of rank two. The occurrence of a double pole in the Green's
function, as well as the non-exponential time evolution of the Gamow-Jordan
generalized eigenfunctions are associated to the Jordan block in the complex
energy representation.


title:
The characterization of Gaussian operations and Distillation of Gaussian
  States

abstract:
  We characterize the class of all physical operations that transform Gaussian
states to Gaussian states. We show that this class coincides with that of all
operations which can be performed on Gaussian states using linear optical
elements and homodyne measurements. For bipartite systems we characterize the
processes which can be implemented by local operations and classical
communication, as well as those that can be implemented using positive partial
transpose preserving maps. As an application, we show that Gaussian states
cannot be distilled by local Gaussian operations and classical communication.
We also define and characterize positive (but not completely positive) Gaussian
maps.


title: An entanglement measure based on the capacity of dense coding

abstract:
  An asymptotic entanglement measure for any bipartite states is derived in the
light of the dense coding capacity optimized with respect to local quantum
operations and classical communications. General properties and some examples
with explicit forms of this entanglement measure are investigated.


title: Maximum Speedup in Quantum Search : O(1) Running Time

abstract:
  Recently the continuous time algorithm based on the generalized quantum
search Hamiltonian was presented. In this letter, we consider the running time
of the generalized quantum search Hamiltonian. We provide the surprising result
that the maximum speedup of quantum search in the generalized Hamiltonian is
the O(1) running time regardless of the number of total states. It seems to
violate the proof of Zalka that the quadratic speedup is optimal in quantum
search. However the argurment of Giovannetti et al. that a quantum speedup
comes from the interaction between subsystems(or, equivalently entanglement)
(and is concerned with the Margolus and Levitin theorem) supports our result.


title: The Wave Function: It or Bit?

abstract:
  Schroedinger's wave function shows many aspects of a state of incomplete
knowledge or information ("bit"): (1) it is usually defined on a space of
classical configurations, (2) its generic entanglement is, therefore, analogous
to statistical correlations, and (3) it determines probabilities of measurement
outcomes. Nonetheless, quantum superpositions (such as represented by a wave
function) define individual physical states ("it"). This conceptual dilemma may
have its origin in the conventional operational foundation of physical
concepts, successful in classical physics, but inappropriate in quantum theory
because of the existence of mutually exclusive operations (used for the
definition of concepts). In contrast, a hypothetical realism, based on concepts
that are justified only by their universal and consistent applicability, favors
the wave function as a description of (thus nonlocal) physical reality. The
(conceptually local) classical world then appears as an illusion, facilitated
by the phenomenon of decoherence, which is consistently explained by the very
entanglement that must dynamically arise in a universal wave function.

categories: quant-ph gr-qc physics.ed-ph physics.pop-ph


title:
Resonant nonlinear optics in coherently prepared media: full analytic
  solutions

abstract:
  We derive analytic solution for pulsed frequency conversion based on
electromagnetically induced transparency (EIT) or maximum coherence in resonant
atomic vapors. In particular drive-field and coherence depletion are taken into
account. The solutions are obtained with the help of an Hamiltonian approach
which in the adiabatic limit allows to reduce the full set of Maxwell-Bloch
equations to simple canonical equations of Hamiltonian mechanics for the field
variables. Adiabatic integrals of motion can be obtained and general
expressions for the spatio-temporal evolution of field intensities derived.
Optimum conditions for maximum conversion efficiency are identified and the
physical mechanism of nonlinear conversion in the limit of drive-field and
coherence depletion discussed.


title: The continuum problem and reality

abstract:
  Set-theoretical, physical, and intuitive notions of continuum are compared.
It is shown that the independence of the continuum hypothesis determines status
and properties of the set of intermediate cardinality. The intermediate set is
a hierarchy of non-equivalent infinite sets. Its description consist of
autonomous theories. In particular, quantum mechanics, classical mechanics, and
geometrical optics should be regarded as components of the complete description
of the intermediate set. The intermediate sets may be produced as a result of a
fission of a continuous interval. The simplest schemes of the fission are
considered. Some analogy with the Standard Model is pointed out.


title: Subdynamics of relevant observables: a field theoretical approach

abstract:
  An approach to the description of subdynamics inside non-relativistic quantum
field theory is presented, in which the notions of relevant observable, time
scale and complete positivity of the time evolution are stressed. A scattering
theory derivation of the subdynamics of a microsystem interacting through
collisions with a macrosystem is given, leading to a master-equation expressed
in terms of the operator-valued dynamic structure factor, a two-point
correlation function which compactly takes the statistical mechanics properties
of the macrosystem into account. For the case of a free quantum gas the dynamic
structure factor can be exactly calculated and in the long wavelength limit a
Fokker-Planck equation for the description of quantum dissipation and in
particular quantum Brownian motion is obtained, where peculiar corrections due
to quantum statistics can be put into evidence.


title: On the communication cost of entanglement transformations

abstract:
  We study the amount of communication needed for two parties to transform some
given joint pure state into another one, either exactly or with some fidelity.
Specifically, we present a method to lower bound this communication cost even
when the amount of entanglement does not increase. Moreover, the bound applies
even if the initial state is supplemented with unlimited entanglement in the
form of EPR pairs, and the communication is allowed to be quantum mechanical.
  We then apply the method to the determination of the communication cost of
asymptotic entanglement concentration and dilution. While concentration is
known to require no communication whatsoever, the best known protocol for
dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462,
1999], requires a number of bits to be exchanged which is of the order of the
square root of the number of EPR pairs. Here we prove a matching lower bound of
the same asymptotic order, demonstrating the optimality of the Lo-Popescu
protocol up to a constant factor and establishing the existence of a
fundamental asymmetry between the concentration and dilution tasks.
  We also discuss states for which the minimal communication cost is
proportional to their entanglement, such as the states recently introduced in
the context of ``embezzling entanglement'' [W. van Dam and P. Hayden,
quant-ph/0201041].


title: Renyi-entropic bounds on quantum communication

abstract:
  In this article we establish new bounds on the quantum communication
complexity of distributed problems. Specifically, we consider the amount of
communication that is required to transform a bipartite state into another,
typically more entangled, state. We obtain lower bounds in this setting by
studying the Renyi entropy of the marginal density matrices of the distributed
system.
  The communication bounds on quantum state transformations also imply lower
bounds for the model of communication complexity where the task consists of the
the distributed evaluation of a function f(x,y). Our approach encapsulates
several known lower bound methods that use the log-rank or the von Neumann
entropy of the density matrices involved. The technique is also effective for
proving lower bounds on problems involving a promise or for which the "hard"
distributions of inputs are correlated. As examples, we show how to prove a
nearly tight bound on the bounded-error quantum communication complexity of the
inner product function in the presence of unlimited amounts of EPR-type
entanglement and a similarly strong bound on the complexity of the shifted
quadratic character problem.


title: Dissipation and decoherence in photon interferometry

abstract:
  The propagation of polarized photons in optical media can be effectively
modeled by means of quantum dynamical semigroups. These generalized time
evolutions consistently describe phenomena leading to loss of phase coherence
and dissipation originating from the interaction with a large, external
environment. High sensitive experiments in the laboratory can provide stringent
bounds on the fundamental energy scale that characterizes these non-standard
effects.


title: Property lattices for independent quantum systems

abstract:
  We consider the description of two independent quantum systems by a complete
atomistic ortho-lattice (cao-lattice) L. It is known that since the two systems
are independent, no Hilbert space description is possible, i.e. $L\ne P(H)$,
the lattice of closed subspaces of a Hilbert space (theorem 1). We impose five
conditions on L. Four of them are shown to be physically necessary. The last
one relates the orthogonality between states in each system to the
ortho-complementation of L. It can be justified if one assumes that the
orthogonality between states in the total system induces the
ortho-complementation of L. We prove that if L satisfies these five conditions,
then L is the separated product proposed by Aerts in 1982 to describe
independent quantum systems (theorem 2). Finally, we give strong arguments to
exclude the separated product and therefore our last condition. As a
consequence, we ask whether among the ca-lattices that satisfy our first four
basic necessary conditions, there exists an ortho-complemented one different
from the separated product.


title:
A tight lower bound on the classical communication cost of entanglement
  dilution

abstract:
  Entanglement concentration requires no classical communication, but the best
prior art result for diluting to N copies of a partially entangled state
requires an amount of communication on the order of sqrt(N) bits. Our main
result is to prove this prior art result optimal up to a constant factor; any
procedure for creating N partially entangled states from singlets requires
Omega(sqrt(N)) bits of classical communication. Previously not even a constant
bound was known for approximate entanglement transforms.
  We also prove a lower bound on the inefficiency of the process: to dilute
singlets to N copies of a partially entangled state, the entropy of
entanglement must decrease by Omega(sqrt(N)).


title: Quantum relays and noise suppression using linear optics

abstract:
  Probabilistic quantum non-demolition (QND) measurements can be performed
using linear optics and post-selection. Here we show how QND devices of this
kind can be used in a straightforward way to implement a quantum relay, which
is capable of extending the range of a quantum cryptography system by
suppressing the effects of detector noise. Unlike a quantum repeater, a quantum
relay system does not require entanglement purification or the ability to store
photons.


title: Calculation of entanglement for continious variable states

abstract:
  In this paper, we present a general formula for obtaining the reduced density
opeator for any biparticle pure entangled state. Using this formula, we derive,
in a compact form, the explicit formula of the entanglement for any bipartical
pure entangled Gaussian state. In the case of Gaussian states, the criteria of
separabelity can be naturely obtained by the formula. For non-Gaussian states,
we also show the usefulness of the method presented in this paper.


title: One-parameter nonrelativistic supersymmetry for microtubules

abstract:
  The one-parameter nonrelativistic supersymmetry of Mielnik [J. Math. Phys.
25, 3387 (1984)] is applied to the simple supersymmetric model of Caticha
[Phys. Rev. A 51, 4264 (1995)] in the form used by Rosu [Phys. Rev. E 55, 2038
(1997)] for microtubules. By this means, we introduce Montroll double-well
potentials with singularities that move along the positive or negative
traveling direction depending on the sign of the free parameter of Mielnik's
method. Possible interpretations of the singularity are either microtubule
associated proteins (motors) or structural discontinuities in the arrangement
of the tubulin molecules


title: Topologically coupled energy bands in molecules

abstract:
  We propose a concrete application of the Atiyah-Singer index formula in
molecular physics, giving the exact number of levels in energy bands, in terms
of vector bundles topology. The formation of topologically coupled bands is
demonstrated. This phenomenon is expected to be present in many quantum
systems.


title:
Molecular Quantum Computing by an Optimal Control Algorithm for Unitary
  Transformations

abstract:
  Quantum computation is based on implementing selected unitary transformations
which represent algorithms. A generalized optimal control theory is used to
find the driving field that generates a prespecified unitary transformation.
The approach is illustrated in the implementation of one and two qubits gates
in model molecular systems.


title: High-order inertial phase shifts for time-domain atom interferometers

abstract:
  High-order inertial phase shifts are calculated for time-domain atom
interferometers. We obtain closed-form analytic expressions for these shifts in
accelerometer, gyroscope, optical clock and photon recoil measurement
configurations. Our analysis includes Coriolis, centrifugal, gravitational, and
gravity gradient-induced forces. We identify new shifts which arise at levels
relevant to current and planned experiments.


title:
Direct measurement of optical quasidistribution functions: multimode
  theory and homodyne tests of Bell's inequalities

abstract:
  We develop a multimode theory of direct homodyne measurements of quantum
optical quasidistribution functions. We demonstrate that unbalanced homodyning
with appropriately shaped auxiliary coherent fields allows one to sample
point-by-point different phase space representations of the electromagnetic
field. Our analysis includes practical factors that are likely to affect the
outcome of a realistic experiment, such as non-unit detection efficiency,
imperfect mode matching, and dark counts. We apply the developed theory to
discuss feasibility of observing a loophole-free violation of Bell's
inequalities by measuring joint two-mode quasidistribution functions under
locality conditions by photon counting. We determine the range of parameters of
the experimental setup that enable violation of Bell's inequalities for two
states exhibiting entanglement in the Fock basis: a one-photon Fock state
divided by a 50:50 beam splitter, and a two-mode squeezed vacuum state produced
in the process of non-degenerate parametric down-conversion.


title: Causal Quantum Theory and the Collapse Locality Loophole

abstract:
  Causal quantum theory is an umbrella term for ordinary quantum theory
modified by two hypotheses: state vector reduction is a well-defined process,
and strict local causality applies. The first of these holds in some versions
of Copenhagen quantum theory and need not necessarily imply practically
testable deviations from ordinary quantum theory. The second implies that
measurement events which are spacelike separated have no non-local
correlations. To test this prediction, which sharply differs from standard
quantum theory, requires a precise theory of state vector reduction.
  Formally speaking, any precise version of causal quantum theory defines a
local hidden variable theory. However, causal quantum theory is most naturally
seen as a variant of standard quantum theory. For that reason it seems a more
serious rival to standard quantum theory than local hidden variable models
relying on the locality or detector efficiency loopholes.
  Some plausible versions of causal quantum theory are not refuted by any Bell
experiments to date, nor is it obvious that they are inconsistent with other
experiments. They evade refutation via a neglected loophole in Bell experiments
-- the {\it collapse locality loophole} -- which exists because of the possible
time lag between a particle entering a measuring device and a collapse taking
place. Fairly definitive tests of causal versus standard quantum theory could
be made by observing entangled particles separated by $\approx 0.1$ light
seconds.


title: Squeezing concentration for Gaussian states with unknown parameter

abstract:
  A continuous-variable analog of the Deutsch's distillation protocol locally
operating with two copies of the same Gaussian state is suggested.
Irrespectively of the impossibility of Gaussian state distillation, we reveal
that this protocol is able to perform a squeezing concentration of the Gaussian
states with {\em unknown} displacement. Since this operation cannot be
implemented using only single copy of the state, it is a new application of the
distillation protocol which utilizes two copies of the same Gaussian state.


title: Nonlinearity without Superluminality

abstract:
  Quantum theory is compatible with special relativity. In particular, though
measurements on entangled systems are correlated in a way that cannot be
reproduced by local hidden variables, they cannot be used for superluminal
signalling. As Czachor, Gisin and Polchinski pointed out, this is not true for
general nonlinear modifications of the Schroedinger equation. Excluding
superluminal signalling has thus been taken to rule out most nonlinear versions
of quantum theory. The no superluminal signalling constraint has also been used
for alternative derivations of the optimal fidelities attainable for imperfect
quantum cloning and other operations.
  These results apply to theories satisfying the rule that their predictions
for widely separated and slowly moving entangled systems can be approximated by
non-relativistic equations of motion with respect to a preferred time
coordinate. This paper describes a natural way in which this rule might fail to
hold. In particular, it is shown that quantum readout devices which display the
values of localised pure states need not allow superluminal signalling,
provided that the devices display the values of the states of entangled
subsystems as defined in a non-standard, but natural, way. It follows that any
locally defined nonlinear evolution of pure states can be made consistent with
Minkowski causality.


title: Deconstructing Dense Coding

abstract:
  The remarkable transmission of two bits of information via a single qubit
entangled with another at the destination, is presented as an expansion of the
unremarkable classical circuit that transmits the bits with two direct
qubit-qubit couplings between source and destination


title: A Bell Telegraph

abstract:
  We show a device with which, apparently, information (in the form of a
"slash-dot" code) is instantly transmitted via Bell state collapse, over
arbitrary distance. We show then why the device does not actually work, and
discuss about the "no Bell telephone" statement. We discuss also about the
troublesome relationship between the Copenhagen interpretation and special
relativity. In particular, we advocate the interpretation that the "state
space" cannot be a description of the state of the object studied alone, but
that the observer is inextricably involved even if no measurement is taking
place.


title:
Non-local Quantum Electrodynamics. II. Possibility of correlated
  2n-photon absorption in gases leading to VERY High frequency spontaneous
  emission and Very high order Harmonic Generation

abstract:
  In a recent work [Mod. Phys. Lett A13, p-1265 (1998)] we expounded a
non-local Quantum Electrodynamics (QED) which predicted a linear two-photon
absorption by an atom placed in a laser field of appropriate intensity and
frequency. In this paper we extend our earlier work to show that the theory
allows for linear 2n-photon absorption by gaseous matter where, under suitable
conditions, n may literally run upto thousands. The consequences of this
extension of the theory are outlined and predictions are made which may be
verified in laboratories.


title: State transformations after quantum fuzzy measurements

abstract:
  Using a standard fuzzification procedure and the dynamical map in Heisenberg
picture, a new expression for the state transformation after a fuzzy filter
measurement, subject to covariance conditions, was obtained and some
calculations were done to distinguish its properties from the those of the
usual solution.


title:
Quantum Cryptography Using Einstein-Podolsky-Rosen Correlations of
  Continuous Variables

abstract:
  Quantum cryptography with the predetermined key was experimentally realized
using Einstein-Podolsky-Rosen(EPR) correlations of continuously bright optical
beams. Only one of two EPR correlated beams is transmitted with the signals
modulated on quadrature phases and amplitudes, and the other one is retained by
the authorized receiver. The modulated small signals are totally submerged in
the large quantum noise of the signal beam, therefore nobody except the
authorized receiver can decode the signals. Usability of imperfect quantum
correlation, high transmission and detection efficiencies, and security
provided by quantum mechanics are the favorable features of the presented
scheme.


title: Phase equivalent chains of Darboux transformations in scattering theory

abstract:
  We propose a procedure based on phase equivalent chains of Darboux
transformations to generate local potentials satisfying the radial
Schr\"odinger equation and sharing the same scattering data. For potentials
related by a chain of transformations an analytic expression is derived for the
Jost function. It is shown how the same system of $S$-matrix poles can be
differently distributed between poles and zeros of a Jost function which
corresponds to different potentials with equal phase shifts. The concept of
shallow and deep phase equivalent potentials is analyzed in connection with
distinct distributions of poles. It is shown that phase equivalent chains do
not violate the Levinson theorem. The method is applied to derive a shallow and
a family of deep phase equivalent potentials describing the $^1S_0$ partial
wave of the nucleon-nucleon scattering.


title:
Simulating decoherence behavior of a system in entangled state using
  nuclear magnetic resonance

abstract:
  By choosing H nucleus in Carbon-13 labelled trichloroethylene as one qubit
environment, and two C nuclei as a two-qubit system, we have simulated quantum
decoherence when the system lies in an entangled state using nuclear magnetic
resonance (NMR). Decoupling technique is used to trace over the environment
degrees of freedom. Experimental results show agreements with the theoretical
predictions. Our experiment scheme can be generalized to the case that
environment is composed of multiple qubits.


title:
Non-Abelian linear Boltzmann equation and quantum correction to Kramers
  and Smoluchowski equation

abstract:
  A quantum linear Boltzmann equation is proposed, constructed in terms of the
operator-valued dynamic structure factor of the macroscopic system the test
particle is interacting with. Due to this operator structure it is a
non-Abelian linear Boltzmann equation and when expressed through the Wigner
function it allows for a direct comparison with the classical one. Considering
a Brownian particle the corresponding Fokker-Planck equation is obtained in a
most direct way taking the limit of small energy and momentum transfer. A
typically quantum correction to the Kramers equation thus appears, describing
diffusion in position and further implying a correction to Einstein's diffusion
coefficient in the high temperature and friction limit in which Smoluchowski
equation emerges.


title: Phase Transitions in Quantum Pattern Recognition

abstract:
  With the help of quantum mechanics one can formulate a model of associative
memory with optimal storage capacity. I generalize this model by introducing a
parameter playing the role of an effective temperature. The corresponding
thermodynamics provides criteria to tune the efficiency of quantum pattern
recognition. I show that the associative memory undergoes a phase transition
from a disordered high-temperature phase with no correlation between input and
output to an ordered, low-temperature phase with minimal input-output Hamming
distance.


title: Local indistinguishability and LOCC monotones

abstract:
  We provide a method for checking indistinguishability of a set of
multipartite orthogonal states by local operations and classical communication
(LOCC). It bases on the principle of nonincreasing of entanglement under LOCC.
This method originates from the one introduced by Ghosh \emph{et al.} (Phys.
Rev. Lett. \textbf{87}, 5807 (2001) (quant-ph/0106148)), though we deal with
{\emph pure} states. In the bipartite case, our method is operational, although
we do not know whether it can always detect local indistinguishability. We
apply our method to show that an arbitrary complete multipartite orthogonal
basis is indistinguishable if it contains at least one entangled state. We also
show that probabilistic distinguishing is possible for full basis if and only
if all vectors are product. We employ our method to prove local
indistinguishability in a very interesting example akin to "nonlocality without
entanglement".


title: Topological Features in Ion Trap Holonomic Computation

abstract:
  Topological features in quantum computing provide controllability and noise
error avoidance in the performance of logical gates. While such resilience is
favored in the manipulation of quantum systems, it is very hard to identify
topological features in nature. This paper proposes a scheme where holonomic
quantum gates have intrinsic topological features. An ion trap is employed
where the vibrational modes of the ions are coherently manipulated with lasers
in an adiabatic cyclic way producing geometrical holonomic gates. A crucial
ingredient of the manipulation procedures is squeezing of the vibrational
modes, which effectively suppresses exponentially any undesired fluctuations of
the laser amplitudes, thus making the gates resilient to control errors.


title: Quantum information processing in bosonic lattices

abstract:
  We consider a class of models of self-interacting bosons hopping on a
lattice. We show that properly tailored space-temporal coherent control of the
single-body coupling parameters allows for universal quantum computation in a
given sector of the global Fock space. This general strategy for encoded
universality in bosonic systems has in principle several candidates for
physical implementation.


title:
The Schwinger SU(3) construction - I: Multiplicity problem and relation
  to induced representations

abstract:
  The Schwinger oscillator operator representation of SU(3) is analysed with
particular reference to the problem of multiplicity of irreducible
representations. It is shown that with the use of an $Sp(2,R)$ unitary
representation commuting with the SU(3) representation, the infinity of
occurrences of each SU(3) irreducible representation can be handled in complete
detail. A natural `generating representation' for SU(3), containing each
irreducible representation exactly once, is identified within a subspace of the
Schwinger construction; and this is shown to be equivalent to an induced
representation of SU(3).


title:
The Schwinger SU(3) Construction - II: Relations between Heisenberg-Weyl
  and SU(3) Coherent States

abstract:
  The Schwinger oscillator operator representation of SU(3), studied in a
previous paper from the representation theory point of view, is analysed to
discuss the intimate relationships between standard oscillator coherent state
systems and systems of SU(3) coherent states. Both SU(3) standard coherent
states, based on choice of highest weight vector as fiducial vector, and
certain other specific systems of generalised coherent states, are found to be
relevant. A complete analysis is presented, covering all the oscillator
coherent states without exception, and amounting to SU(3) harmonic analysis of
these states.


title: An quantum approach of measurement based on the Zurek's triple model

abstract:
  In a close form without referring the time-dependent Hamiltonian to the total
system, a consistent approach for quantum measurement is proposed based on
Zurek's triple model of quantum decoherence [W.Zurek, Phys. Rev. D 24, 1516
(1981)]. An exactly-solvable model based on the intracavity system is dealt
with in details to demonstrate the central idea in our approach: by peeling off
one collective variable of the measuring apparatus from its many degrees of
freedom, as the pointer of the apparatus, the collective variable de-couples
with the internal environment formed by the effective internal variables, but
still interacts with the measured system to form a triple entanglement among
the measured system, the pointer and the internal environment. As another
mechanism to cause decoherence, the uncertainty of relative phase and its
many-particle amplification can be summed up to an ideal entanglement or an
Shmidt decomposition with respect to the preferred basis.


title: Bell inequality for quNits with binary measurements

abstract:
  We present a generalized Bell inequality for two entangled quNits. On one
quNit the choice is between two standard von Neumann measurements, whereas for
the other quNit there are $N^2$ different binary measurements. These binary
measurements are related to the intermediate states known from eavesdropping in
quantum cryptography. The maximum violation by $\sqrt{N}$ is reached for the
maximally entangled state. Moreover, for N=2 it coincides with the familiar
CHSH-inequality.


title: Quantum Dynamics as a Stochastic Process

abstract:
  We study the classical motion of a particle subject to a stochastic force. We
then present a perturbative schema for the associated Fokker-Planck equation
where, in the limit of a vanishingly small noise source, a consistent dynamical
model is obtained. The resulting theory is similar to Quantum Mechanics, having
the same field equations for probability measures, the same operator structure
and symmetric ordering of operators. The model is valid for general
electromagnetic interaction as well as many body systems with mutual
interactions of general nature.


title: Quantum secret sharing based on reusable GHZ states as secure carriers

abstract:
  We introduce a protocol for quantum secret sharing based on reusable
entangled states. The entangled state between the sender and the receiver acts
only as a carrier to which data bits are entangled by the sender and
disentangled from it by the receivers, all by local actions of simple gates.
  We also show that the interception by Eve or the cheating of one of the
receivers introduces a quantum bit error rate (QBER) larger than
  25 percent which can be detected by comparing a subsequence of the bits.


title: The Energy Density in the Casimir Effect

abstract:
  We compute the expectations of the squares of the electric and magnetic
fields in the vacuum region outside a half-space filled with a uniform
dispersive dielectric. We find a positive energy density of the electromagnetic
field which diverges at the interface despite the inclusion of dispersion in
the calculation. We also investigate the mean squared fields and the energy
density in the vacuum region between two parallel half-spaces. Of particular
interest is the sign of the energy density. We find that the energy density is
described by two terms: a negative position independent (Casimir) term, and a
positive position dependent term with a minimum value at the center of the
vacuum region. We argue that in some cases, including physically realizable
ones, the negative term can dominate in a given region between the two
half-spaces, so the overall energy density can be negative in this region.


title: Focusing Vacuum Fluctuations II

abstract:
  The quantization of the scalar and electromagnetic fields in the presence of
a parabolic mirror is further developed in the context of a geometric optics
approximation. We extend results in a previous paper to more general
geometries, and also correct an error in one section of that paper. We
calculate the mean squared scalar and electric fields near the focal line of a
parabolic cylindrical mirror. These quantities are found to grow as inverse
powers of the distance from the focus. We give a combination of analytic and
numerical results for the mean squared fields. In particular, we find that the
mean squared electric field can be either negative or positive, depending upon
the choice of parameters. The case of a negative mean squared electric field
corresponds to a repulsive Van der Waals force on an atom near the focus, and
to a region of negative energy density. Similarly, a positive value corresponds
to an attractive force and a possibility of atom trapping in the vicinity of
the focus.


title:
Reverse reconciliation protocols for quantum cryptography with
  continuous variables

abstract:
  We introduce new quantum key distribution protocols using quantum continuous
variables, that are secure against individual attacks for any transmission of
the optical line between Alice and Bob. In particular, it is not required that
this transmission is larger than 50 %. Though squeezing or entanglement may be
helpful, they are not required, and there is no need for quantum memories or
entanglement purification. These protocols can thus be implemented using
coherent states and homodyne detection, and they may be more efficient than
usual protocols using quantum discrete variables.


title: Coherent States and Duality

abstract:
  We formulate a relation between quantum-mechanical coherent states and
complex-differentiable structures on the classical phase space ${\cal C}$ of a
finite number of degrees of freedom. Locally-defined coherent states
parametrised by the points of ${\cal C}$ exist when there is an almost complex
structure on ${\cal C}$. When ${\cal C}$ admits a complex structure, such
coherent states are globally defined on ${\cal C}$. The picture of quantum
mechanics that emerges allows to implement duality transformations.


title: Unversality of decoherence in the macroworld

abstract:
  We consider environment induced decoherence of quantum superpositions to
mixtures in the limit in which that process is much faster than any competing
one generated by the Hamiltonian $H_{\rm sys}$ of the isolated system. This
interaction dominated decoherence limit has previously not found much attention
even though it is of importance for the emergence of classical behavior in the
macroworld, since it will always be the relevant regime for large enough
separations between superposed wave packets. The usual golden-rule treatment
then does not apply but we can employ a short-time expansion for the free
motion while keeping the interaction $H_{\rm int}$ in full. We thus reveal
decoherence as a universal short-time phenomenon largely independent of the
character of the system as well as the bath. Simple analytical expressions for
the decoherence time scales are obtained in the limit in which decoherence is
even faster than any timescale emerging from the reservoir Hamiltonian $H_{\rm
res}$.


title: Solving Single and Many-body Quantum Problems: A Novel Approach

abstract:
  A unified approach, for solving a wide class of single and many-body quantum
problems, commonly encountered in literature is developed based on a recently
proposed method for finding solutions of linear differential equations. Apart
from dealing with exactly and quasi-exactly solvable problems, the present
approach makes transparent various properties of the familiar orthogonal
polynomials and also the construction of their respective ladder operators. We
illustrate the procedure for finding the approximate eigenvalues and
eigenfunctions of non-exactly solvable problems.


title: Mode structure and photon number correlations in squeezed quantum pulses

abstract:
  The question of efficient multimode description of optical pulses is studied.
We show that a relatively very small number of nonmonochromatic modes can be
sufficient for a complete quantum description of pulses with Gaussian
quadrature statistics. For example, a three-mode description was enough to
reproduce the experimental data of photon number correlations in optical
solitons [S. Spalter et al., Phys. Rev. Lett. 81, 786 (1998)]. This approach is
very useful for a detailed understanding of squeezing properties of soliton
pulses with the main potential for quantum communication with continuous
variables. We show how homodyne detection and/or measurements of photon number
correlations can be used to determine the quantum state of the multi-mode
field. We also discuss a possible way of physical separation of the
nonmonochromatic modes.


title:
Evolution of Gaussian Wave Packet and Nonadiabatic Geometrical Phase for
  the time-dependent Singular Oscillator

abstract:
  The geometrical phase of a time-dependent singular oscillator is obtained in
the framework of Gaussian wave packet. It is shown by a simple geometrical
approach that the geometrical phase is connected to the classical nonadiabatic
Hannay angle of the generalized harmonic oscillator.


title:
Dissipative Systems and Objective Description: Quantum Brownian Motion
  as an Example

abstract:
  A structure of generator of a quantum dynamical semigroup for the dynamics of
a test particle interacting through collisions with the environment is
considered, which has been obtained from a microphysical model. The related
master-equation is shown to go over to a Fokker-Planck equation for the
description of Brownian motion at quantum level in the long wavelength limit.
The structure of this Fokker-Planck equation is expressed in this paper in
terms of superoperators, giving explicit expressions for the coefficient of
diffusion in momentum in correspondence with two cases of interest for the
interaction potential. This Fokker-Planck equation gives an example of a
physically motivated generator of quantum dynamical semigroup, which serves as
a starting point for the theory of measurement continuous in time, allowing for
the introduction of trajectories in quantum mechanics. This theory had in fact
already been applied to the problem of Brownian motion referring to similar
phenomenological structures obtained only on the basis of mathematical
requirements.


title: About quantum mechanics interpretation II

abstract:
  In the previous paper (quant-ph/0204037) we proved that the quantum mechanics
not only has statistic interpretation, but also the specific electromagnetic
form. Here, from this point of view we show that all the formal particularities
of Dirac's equation have also the known electromagnetic sense.


title:
Markovian Behaviour and Constrained Maximization of the Entropy in
  Chaotic Quantum Systems

abstract:
  The separation of the Schr\"{o}dinger equation into a Markovian and an
interference term provides a new insight in the quantum dynamics of classically
chaotic systems. The competition between these two terms determines the
localized or diffusive character of the dynamics. In the case of the Kicked
Rotor, we show how the constrained maximization of the entropy implies
exponential localization.


title: State permutations from manipulation of near level-crossings

abstract:
  We discuss some systematic methods for implementing state manipulations in
systems formally similar to chains of a few spins with nearest-neighbor
interactions, arranged such that there are strong and weak scales of coupling
links. States are permuted by means of bias potentials applied to a few
selected sites. This generic structure is then related to an atoms-in-a-cavity
model that has been proposed in the literature as a way of achieving a
decoherence free subspace. A new method using adiabatically varying laser
detuning to implement a CNOT gate in this model is proposed.


title: Dirac's Quantization of Maxwell's Theory on Non-Commutative Spaces

abstract:
  Dirac's quantization of the Maxwell theory on non-commutative spaces has been
considered. First class constraints were found which are the same as in
classical electrodynamics. The gauge covariant quantization of the non-linear
equations of electromagnetic fields on non-commutative spaces were studied. We
have found the extended Hamiltonian which leads to equations of motion in the
most general gauge covariant form. As a special case, the gauge fixing approach
on the basis of Dirac's brackets has been investigated. The problem of the
construction of the wave function and physical observables have been discussed.


title: Einstein-Podolsky-Rosen correlation seen from moving observers

abstract:
  Within the framework of relativistic quantum theory, we consider the
Einstein-Podolsky-Rosen (EPR) gedanken-experiment in which measurements of the
spin are performed by moving observers. We find that the perfect
anti-correlation in the same direction between the EPR pair no longer holds in
the observers' frame. This does not imply a breakdown of the non-local
correlation. We explicitly show that the observers must measure the spin in
appropriately chosen different directions in order to observe the perfect
anti-correlation. This fact should be taken into account in utilizing the
entangled state in quantum communication by moving observers.


title: Canonically conjugate pairs and phase operators

abstract:
  For quantum mechanics on a lattice the position (``particle number'')
operator and the quasi-momentum (``phase'') operator obey canonical commutation
relations (CCR) only on a dense set of the Hilbert space. We compare exact
numerical results for a particle in simple potentials on the lattice with the
expectations, when the CCR are assumed to be strictly obeyed. Only for
sufficiently smooth eigenfunctions this leads to reasonable results. In the
long time limit the use of the CCR can lead to a qualitativel wrong dynamics
even if the initial state is in the dense set.


title: Entangling two-level atoms by spontaneous emission

abstract:
  It is shown that the dissipation due to spontaneous emission can entangle two
closely separated two-level atoms.


title: Generalized model-independent approach to intrinsic decoherence

abstract:
  A formalism is presented to express decoherence both in the markovian and
nonmarkovian regimes and both dissipative and nondissipative in isolated
systems. The main physical hypothesis, already contained in the literature,
amounts to allowing some internal parameters of the system to evolve in a
random fashion. This formalism may also be applicable to open quantum systems.


title:
Demonstration of Feed-Forward Control for Linear Optics Quantum
  Computation

abstract:
  One of the main requirements in linear optics quantum computing is the
ability to perform single-qubit operations that are controlled by classical
information fed forward from the output of single photon detectors. These
operations correspond to pre-determined combinations of phase corrections and
bit-flips that are applied to the post-selected output modes of
non-deterministic quantum logic devices. Corrections of this kind are required
in order to obtain the correct logical output for certain detection events, and
their use can increase the overall success probability of the devices. In this
paper, we report on the experimental demonstration of the use of this type of
feed-forward system to increase the probability of success of a simple
non-deterministic quantum logic operation from approximately 1/4 to 1/2. This
logic operation involves the use of one target qubit and one ancilla qubit
which, in this experiment, are derived from a parametric down-conversion photon
pair. Classical information describing the detection of the ancilla photon is
fed-forward in real-time and used to alter the quantum state of the output
photon. A fiber optic delay line is used to store the output photon until a
polarization-dependent phase shift can be applied using a high speed Pockels
cell.


title:
Asymptotic Relative Entropy of Entanglement for Orthogonally Invariant
  States

abstract:
  For a special class of bipartite states we calculate explicitly the
asymptotic relative entropy of entanglement $E_R^\infty$ with respect to states
having a positive partial transpose (PPT). This quantity is an upper bound to
distillable entanglement. The states considered are invariant under rotations
of the form $O\otimes O$, where $O$ is any orthogonal matrix. We show that in
this case $E_R^\infty$ is equal to another upper bound on distillable
entanglement, constructed by Rains. To perform these calculations, we have
introduced a number of new results that are interesting in their own right: (i)
the Rains bound is convex and continuous; (ii) under some weak assumption, the
Rains bound is an upper bound to $E_R^\infty$; (iii) for states for which the
relative entropy of entanglement $E_R$ is additive, the Rains bound is equal to
$E_R$.


title: Autocompensating Quantum Cryptography

abstract:
  Quantum cryptographic key distribution (QKD) uses extremely faint light
pulses to carry quantum information between two parties (Alice and Bob),
allowing them to generate a shared, secret cryptographic key. Autocompensating
QKD systems automatically and passively compensate for uncontrolled time
dependent variations of the optical fiber properties by coding the information
as a differential phase between orthogonally-polarized components of a light
pulse sent on a round trip through the fiber, reflected at mid-course using a
Faraday mirror. We have built a prototype system based on standard telecom
technology that achieves a privacy-amplified bit generation rate of ~1000
bits/s over a 10-km optical fiber link. Quantum cryptography is an example of
an application that, by using quantum states of individual particles to
represent information, accomplishes a practical task that is impossible using
classical means.


title: Universal quantum computing based on monodromy representations

abstract:
  A model of quantum computing is presented, based on properties of connections
with a prescribed monodromy group on holomorphic vector bundles over bases with
nontrivial topology. Such connections with required properties appear in the
WZW-models, in which moreover the corresponding n-point correlation functions
are sections of appropriate bundles which are holomorphic with respect to the
connection.


title: The Anti-Vaxjo Interpretation of Quantum Mechanics

abstract:
  In this note, I try to accomplish two things. First, I fulfill Andrei
Khrennikov's request that I comment on his "Vaxjo Interpretation of Quantum
Mechanics," contrasting it with my own present view of the subject matter.
Second, I try to paint an image of the hopeful vistas an information-based
conception of quantum mechanics indicates.


title: Deterministic Single-Photon Source for Distributed Quantum Networking

abstract:
  A sequence of single photons is emitted on demand from a single three-level
atom strongly coupled to a high-finesse optical cavity. The photons are
generated by an adiabatically driven stimulated Raman transition between two
atomic ground states, with the vacuum field of the cavity stimulating one
branch of the transition, and laser pulses deterministically driving the other
branch. This process is unitary and therefore intrinsically reversible, which
is essential for quantum communication and networking, and the photons should
be appropriate for all-optical quantum information processing.


title: Random Walk and Diffusion on a Smash Line Algebra

abstract:
  Working withing the framework of Hopf algebras, a random walk and the
associated diffusion equation are constructed on a space that is algebraically
described as the merging of the real line algebra with the anyonic line
algebra. Technically this merged structure is a smash algebra, namely an
algebra resulting by a braided tensoring of real with anyonic line algebras.
  The motivation of introducing the smashing results from the necessity of
having non commuting increments in the random walk. Based on the
observable-state duality provided by the underlying Hopf structure, the
construction is cast into two dual forms: one using functionals determined by
density probability functions and the other using the associated Markov
transition operator. The ensuing diffusion equation is shown to possess
triangular matrix realization.
  The study is completed by the incorporation of Hamiltonian dynamics in the
above random walk model, and by the construction of the dynamical equation
obeyed by statistical moments of the problem for generic entangled density
functions.


title: Quantum computers in phase space

abstract:
  We represent both the states and the evolution of a quantum computer in phase
space using the discrete Wigner function. We study properties of the phase
space representation of quantum algorithms: apart from analyzing important
examples, such as the Fourier Transform and Grover's search, we examine the
conditions for the existence of a direct correspondence between quantum and
classical evolutions in phase space. Finally, we describe how to directly
measure the Wigner function in a given phase space point by means of a
tomographic method that, itself, can be interpreted as a simple quantum
algorithm.


title:
Discrete Wigner functions and the phase space representation of quantum
  teleportation

abstract:
  We present a phase space description of the process of quantum teleportation
for a system with an $N$ dimensional space of states. For this purpose we
define a discrete Wigner function which is a minor variation of previously
existing ones. This function is useful to represent composite quantum system in
phase space and to analyze situations where entanglement between subsystems is
relevant (dimensionality of the space of states of each subsystem is
arbitrary). We also describe how a direct tomographic measurement of this
Wigner function can be performed.


title: Relativistic, Causal Description of Quantum Entanglement

abstract:
  A possible causal solution to the problem of providing a spacetime
description of the transmission of signals in quantum entangled states is
described using a `bimetric' spacetime structure, in which the quantum
entanglement measurements alter the structure of spacetime. Possible
experimental tests to verify the suggested spacetime interpretation of quantum
entangled states are proposed.


title:
The relative entropy of entanglement of Schmidt correlated states and
  distillation

abstract:
  We show that a mixed state $\rho=\sum_{mn}a_{mn}|m> < n|$ can be realized by
an ensemble of pure states $\{p_{k}, |\phi_{k} > \}$ where
$|\phi_{k}>=\sum_{m}\sqrt{a_{mm}}e^{i\theta_{m}^{k}}|m>$. Employing this form,
we discuss the relative entropy of entanglement of Schmidt correlated states.
Also, we calculate the distillable entanglement of a class of mixed states.


title: A stronger no-cloning theorem

abstract:
  It is well known that (non-orthogonal) pure states cannot be cloned so one
may ask: how much or what kind of additional (quantum) information is needed to
supplement one copy of a quantum state in order to be able to produce two
copies of that state by a physical operation? For classical information, no
supplementary information is required. However for pure quantum
(non-orthogonal) states, we show that the supplementary information must always
be as large as it can possibly be i.e. the clone must be able to be generated
from the additional information alone, independently of the first (given) copy.


title: Ion Trap Proposal for Quantum Search

abstract:
  In this letter, we show that the laser Hamiltonian can perform the quantum
search. We also show that the process of quantum search is a resonance between
the initial state and the target state, which implies that Nature already has a
quantum search system to use a transition of energy. In addition, we provide
the particular scheme to implement the quantum search algorithm based on a
trapped ion.


title:
Einstein-Podolsky-Rosen Correlations of Spin Measurements in Two Moving
  Inertial Frames

abstract:
  The formula for the correlation function of spin measurements of two
particles in two moving inertial frames is derived within Lorentz-covariant
quantum-mechanics formulated in the absolute synchronization framework. The
results are the first exact Einstein-Podolsky-Rosen correlation functions
obtained for Lorentz-covariant quantum-mechanical system in moving frames under
physically acceptable conditions, i.e., taking into account the localization of
the particles during the detection and using the spin opeartor with proper
transformation properties under the action of the Lorentz group. Some special
cases and approximations of the calculated correlation function are given. The
resulting correlation function can be used as a basis for a proposal of a
decisive experiment for a possible existence of a quantum-mechanical preferred
frame.


title: Quantum Tunneling

abstract:
  This article is a slightly expanded version of the talk I delivered at the
Special Plenary Session of the 46-th Annual Meeting of the Israel Physical
Society (Technion, Haifa, May 11, 2000) dedicated to Misha Marinov. In the
first part I briefly discuss quantum tunneling, a topic which Misha cherished
and to which he was repeatedly returning through his career. My task was to
show that Misha's work had been deeply woven in the fabric of today's theory.
The second part is an attempt to highlight one of many facets of Misha's human
portrait. In the 1980's, being a refusenik in Moscow, he volunteered to teach
physics under unusual circumstances. I present recollections of people who were
involved in this activity.


title:
Climbing Mount Scalable: Physical-Resource Requirements for a Scalable
  Quantum Computer

abstract:
  The primary resource for quantum computation is Hilbert-space dimension.
Whereas Hilbert space itself is an abstract construction, the number of
dimensions available to a system is a physical quantity that requires physical
resources. Avoiding a demand for an exponential amount of these resources
places a fundamental constraint on the systems that are suitable for scalable
quantum computation. To be scalable, the effective number of degrees of freedom
in the computer must grow nearly linearly with the number of qubits in an
equivalent qubit-based quantum computer.


title: ''Active'' Teleportation of a Quantum Bit

abstract:
  We report the experimental realization of the ''active'' quantum
teleportation (QST) of a one-particle entangled qubit. This demonstration
completes the original QST protocol and renders it available for actual
implementation in quantum computation networks. It is accomplished by
implementing a 8m optical delay line and a single-photon triggered fast
Electro-Optic Pockels cell. A large value of teleportation ''fidelity'' was
attained: F = (90 +/- 2)%. Our work follows the line recently suggested by H.
W. Lee and J. Kim, Phys. Rev. A 63, 012305 (2000) and E.Knill, R.Laflamme and
G.Milburn Nature 409: 46 (2001).


title:
Largest separable balls around the maximally mixed bipartite quantum
  state

abstract:
  For finite-dimensional bipartite quantum systems, we find the exact size of
the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of
separable (unentangled) matrices around the identity matrix. This implies a
simple and intutively meaningful geometrical sufficient condition for
separability of bipartite density matrices: that their purity $\tr \rho^2$ not
be too large. Theoretical and experimental applications of these results
include algorithmic problems such as computing whether or not a state is
entangled, and practical ones such as obtaining information about the existence
or nature of entanglement in states reached by NMR quantum computation
implementations or other experimental situations.


title: Integral equation of quantum stochastic process

abstract:
  To describe stochastic quantum processes I propose an integral equation of
Volterra type which is not generally transformable to any differential one. The
process is a composition of ordinary quantum evolution which admits presence of
a quantum bath and reductions to pure states. It is proved that generically
solutions stabilize asymptotically for $t\to +\infty$ to a universal limit -
the projection onto the state with maximal available entropy. A number of
typical methods of finding solutions of the equation are proposed.


title: Stochastic quantum process

abstract:
  I propose to treat quantum evolution as a stochastic process consisting from
a sequence of doubly stochastic matrices, which naturally arise in the
generalized quantum evolution. Then it is proved that the law of non-decreasing
entropy is fulfilled and that the law characterizes doubly stochastic matrices.
Finally, an application of the model to support the generalized second law of
black hole thermodynamics and a relation to the quantum histories formulation
of quantum physics appear.


title: Degree of entanglement for two qubits

abstract:
  In this paper, we present a measure to quantify the degree of entanglement
for two qubits in a pure state.


title: Comment on "Entropy and Wigner function"

abstract:
  In a recent paper [PRE 62, 4665 (2000)] (quant-ph/0203102) Manfredi and Feix
proposed an alternative definition of quantum entropy based on Wigner
phase-space distribution functions and discussed its properties. They proposed
also some simple rules to construct positive-definite Wigner functions which
are crucial in their discussion. We show, however, that the main results
obtained and their discussion are incorrect.