title: Entanglement of a Multiparticle Schroedinger Cat State

abstract:
  We characterize the degree of entanglement of a subsystem of $k$ particles in
a $N$-two level system ($k\leq N/2$) initially prepared in a mesoscopic
superposition $|\psi>=\int d\theta f(\theta) (|\phi_{1}(\theta)>^{\otimes
N}+|\phi_{2}(\theta)>^{\otimes N})$, where $f(\theta)$ is a gaussian or a delta
function, subject to the time evolution described by a dephasing channel.
Negativity is used as a measure of entanglement for such system. For an
arbitrary number of particles $N$, numerical results are given for the full
time evolution up to ten particles. Analytical results are obtained for short
times and asymptotic time regimes. We show that negativity is initially
proportional to the square root of the product of the number of particles in
each partition, the overlap ${|<\phi_1(\theta)|\phi_2(\theta)>|}^2$ and the
coupling to the environment. Asymptotically, negativity tends to zero, a
necessary condition for separability.


title:
Optical-fiber source of polarization-entangled photon pairs in the
  1550nm telecom band

abstract:
  We present a fiber based source of polarization-entangled photon pairs that
is well suited for quantum communication applications in the 1550nm band of
standard fiber-optic telecommunications. Polarization entanglement is created
by pumping a nonlinear-fiber Sagnac interferometer with two time-delayed
orthogonally-polarized pump pulses and subsequently removing the time
distinguishability by passing the parametrically scattered signal-idler photon
pairs through a piece of birefringent fiber. Coincidence detection of the
signal-idler photons yields biphoton interference with visibility greater than
90%, while no interference is observed in direct detection of either the signal
or the idler photons. All four Bell states can be prepared with our setup and
we demonstrate violations of CHSH form of Bell's inequalities by up to 10
standard deviations of measurement uncertainty.


title: Non-gaussian statistics from individual pulses of squeezed light

abstract:
  We describe the observation of a degaussification protocol that maps
individual pulses of squeezed light onto non-Gaussian states. This effect is
obtained by sending a small fraction of the squeezed vacuum beam onto an
avalanche photodiode, and by conditioning the single-shot homodyne detection of
the remaining state upon the photon-counting events. The experimental data
provides a clear evidence of phase-dependent non-Gaussian statistics. This
protocol is closely related to the first step of an entanglement distillation
procedure for continuous variables.


title:
Pulsed homodyne measurements of femtosecond squeezed pulses generated by
  single-pass parametric deamplification

abstract:
  A new scheme is described for pulsed squeezed light generation using
femtosecond pulses parametrically deamplified through a single pass in a thin
(0.1mm) potassium niobate KNbO3 crystal, with a significant deamplification of
about -3dB. The quantum noise of each individual pulse is registered in the
time domain using a single-shot homodyne detection operated with femtosecond
pulses and the best squeezed quadrature variance was measured to be 1.87 dB
below the shot noise level. Such a scheme provides the basic ressource for
time-resolved quantum communication protocols.


title:
Generation of nonlinear coherent states in a coherently pumped
  micromaser under intensity-dependent Jaynes-Cummings model

abstract:
  In this paper the possibility of generating nonlinear coherent states of the
radiation field in a micromaser is explored. It is shown that these states can
be provided in a lossless micromaser cavity under the weak Jaynes-Cummings
interaction with intensity-dependent coupling of large number of individually
injected two-level atoms in a coherent superposition of the upper and lower
states. In particular, we show that the so-called nonlinear squeezed vacuum and
nonlinear squeezed first excited states, as well as the even and odd nonlinear
coherent states can be generated in the presence of two-photon transitions.


title:
Dynamical properties of a two-level atom in three variants of the
  two-photon q-deformed Jaynes-Cummings model

abstract:
  Temporal evolution of atomic properties including the population inversion
and quantum fluctuations of atomic dipole variables are discussed in three
various variants of two-photon q-deformed Jaynes-Cummings model.With the the
field initially being in three different types of q-deformed coherent
states,the quantum collapse and revival effects as well as atomic diploe
squeezing are studied for both on-and off-resonant atom-field interaction.
Particularly, it is shown that for nonzero detuning the atomic inversion
exhibits superstructures which are absent in the non-deformed Jaynes-Cummings
model and the dipole squeezing may be enhanced.


title:
Implementation of Shor's Algorithm on a Linear Nearest Neighbour Qubit
  Array

abstract:
  Shor's algorithm, which given appropriate hardware can factorise an integer
$N$ in a time polynomial in its binary length $L$, has arguable spurred the
race to build a practical quantum computer. Several different quantum circuits
implementing Shor's algorithm have been designed, but each tacitly assumes that
arbitrary pairs of qubits within the computer can be interacted. While some
quantum computer architectures possess this property, many promising proposals
are best suited to realising a single line of qubits with nearest neighbour
interactions only. In light of this, we present a circuit implementing Shor's
factorisation algorithm designed for such a linear nearest neighbour
architecture. Despite the interaction restrictions, the circuit requires just
$2L+4$ qubits and to first order requires $8L^{4}$ gates arranged in a circuit
of depth $32L^{3}$ -- identical to first order to that possible using an
architecture that can interact arbitrary pairs of qubits.


title: From Heisenberg to Goedel via Chaitin

abstract:
  In 1927 Heisenberg discovered that the ``more precisely the position is
determined, the less precisely the momentum is known in this instant, and vice
versa''. Four years later G\"odel showed that a finitely specified, consistent
formal system which is large enough to include arithmetic is incomplete. As
both results express some kind of impossibility it is natural to ask whether
there is any relation between them, and, indeed, this question has been
repeatedly asked for a long time. The main interest seems to have been in
possible implications of incompleteness to physics. In this note we will take
interest in the {\it converse} implication and will offer a positive answer to
the question: Does uncertainty imply incompleteness? We will show that
algorithmic randomness is equivalent to a ``formal uncertainty principle''
which implies Chaitin's information-theoretic incompleteness. We also show that
the derived uncertainty relation, for many computers, is physical. In fact, the
formal uncertainty principle applies to {\it all} systems governed by the wave
equation, not just quantum waves. This fact supports the conjecture that
uncertainty implies randomness not only in mathematics, but also in physics.


title: Comment on "Experimental realization of a three-qubit entangled W state"

abstract:
  Recently Eibl et al. [PRL 92, 077901 (2004)] reported the experimental
observation of the three-photon polarization-entangled W state. In this Comment
we point out that, actually, the particular measurements involved in the
experiment testing Mermin's inequality cannot be used for the verification of
the existence of genuinely quantal tripartite correlations in the observed
state, and therefore this state cannot conclusively be identified with the W
state.


title: Quantum adiabatic optimization and combinatorial landscapes

abstract:
  In this paper we analyze the performance of the Quantum Adiabatic Evolution
algorithm on a variant of Satisfiability problem for an ensemble of random
graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We
introduce a set of macroscopic parameters (landscapes) and put forward an
ansatz of universality for random bit flips. We then formulate the problem of
finding the smallest eigenvalue and the excitation gap as a statistical
mechanics problem. We use the so-called annealing approximation with a
refinement that a finite set of macroscopic variables (versus only energy) is
used, and are able to show the existence of a dynamic threshold
$\gamma=\gamma_d$ starting with some value of K -- the number of variables in
each clause. Beyond dynamic threshold, the algorithm should take exponentially
long time to find a solution. We compare the results for extended and
simplified sets of landscapes and provide numerical evidence in support of our
universality ansatz. We have been able to map the ensemble of random graphs
onto another ensemble with fluctuations significantly reduced. This enabled us
to obtain tight upper bounds on satisfiability transition and to recompute the
dynamical transition using the extended set of landscapes.


title: The concept of Existence and the derivation of a Quantum Force

abstract:
  We define a new dynamical variable, the relative existence e, in terms of
space and time. Taking it as a generalized positional coordinate, we show that
for conservative systems the canonically conjugated momentum is identified as
the classical force. Applying Wilson-Sommerfeld-Bohr's quantum conditions for a
conditionally periodic motion, we derive an expression for the quantum force, F
= hbar k f_e, where k is the wave number and f_e is the characteristic
frequency of the system. Applying Dirac's method to the Poisson Brackets
involving existence and force, we obtain the uncertainty relation Delta e Delta
F >= hbar/2. The force quantization may have already been observed in
stimulated bichromatic optical force experiments, used to deflect, decelerate
and manipulate laser-cooled atomic beams.


title: Detector Efficiency Limits on Quantum Improvement

abstract:
  Although the National Institute of Standards and Technology has measured the
intrinsic quantum efficiency of Si and InGaAs APD materials to be above 98 % by
building an efficient compound detector, commercially available devices have
efficiencies ranging between 15 % and 75 %. This means bandwidth, dark current,
cost, and other factors are more important than quantum efficiency for existing
applications. This paper systematically examines the generic detection process,
lays out the considerations needed for designing detectors for non-classical
applications, and identifies the ultimate physical limits on quantum
efficiency.


title: Constructing finite dimensional codes with optical continuous variables

abstract:
  We show how a qubit can be fault-tolerantly encoded in the
infinite-dimensional Hilbert space of an optical mode. The scheme is efficient
and realizable with present technologies. In fact, it involves two travelling
optical modes coupled by a cross-Kerr interaction, initially prepared in
coherent states, one of which is much more intense than the other. At the exit
of the Kerr medium, the weak mode is subject to a homodyne measurement and a
quantum codeword is conditionally generated in the quantum fluctuations of the
intense mode.


title: The Effect of a Magnetic Flux Line in Quantum Theory

abstract:
  The nonloclal exchange of the conserved, gauge invariant quantity
$e^{\frac{i}{\hbar} (p_{k}-\frac{e}{c}A_{k})L^{k}}, L^{k}=const., k=1,2$
between the charged particle and the magnetic flux line (in the $k=3$
direction), is responsible for the Aharonov-Bohm effect. This exchange occurs
at a definite time, before the wavepackets are brought together to interfere,
and can be verified experimentally.


title:
State Transfer instead of Teleportation in Measurement-based Quantum
  Computation

abstract:
  Quantum measurement is universal for quantum computation. The model of
quantum computation introduced by Nielsen and further developed by Leung relies
on a generalized form of teleportation. In order to simulate any n-qubit
unitary transformation with this model, 4 auxiliary qubits are required.
Moreover Leung exhibited a universal family of observables composed of 4
two-qubit measurements. We introduce a model of quantum computation via
measurements only, relying on state transfer: state transfer only retains the
part of teleportation which is necessary for computating. In order to simulate
any n-qubit unitary transformation with this new model, only one auxiliary
qubit is required. Moreover we exhibit a universal family of observables
composed of 3 one-qubit measurements and only one two-qubit measurement. This
model improves those of Nielsen and Leung in terms of both the number of
auxiliary qubits and the number of two-qubit measurements required for quantum
universality. In both cases, the minimal amounts of necessary resources are now
reached: one auxiliary qubit (because measurement is destructive) and one
two-qubit measurement (for creating entanglement).


title:
A Theory of Concepts and Their Combinations II: A Hilbert Space
  Representation

abstract:
  The sets of contexts and properties of a concept are embedded in the complex
Hilbert space of quantum mechanics. States are unit vectors or density
operators, and contexts and properties are orthogonal projections. The way
calculations are done in Hilbert space makes it possible to model how context
influences the state of a concept. Moreover, a solution to the combination of
concepts is proposed. Using the tensor product, a procedure for describing
combined concepts is elaborated, providing a natural solution to the pet fish
problem. This procedure allows the modeling of an arbitrary number of combined
concepts. By way of example, a model for a simple sentence containing a
subject, a predicate and an object, is presented.


title: Periodic Potentials and Supersymmetry

abstract:
  We review the current status of one dimensional periodic potentials and also
present several new results. It is shown that using the formalism of
supersymmetric quantum mechanics, one can considerably enlarge the limited
class of analytically solvable one-dimensional periodic potentials. Further,
using the Landen transformations as well as cyclic identities for Jacobi
elliptic functions discovered by us recently, it is shown that a linear
superposition of Lam\'e (as well as associated Lam\'e) potentials are also
analytically solvable. Finally, using anti-isospectral transformations, we also
obtain a class of analytically solvable, complex, PT-invariant, periodic
potentials having real band spectra.


title:
A Theory of Concepts and Their Combinations I: The Structure of the Sets
  of Contexts and Properties

abstract:
  We propose a theory for modeling concepts that uses the
state-context-property theory (SCOP), a generalization of the quantum
formalism, whose basic notions are states, contexts and properties. This theory
enables us to incorporate context into the mathematical structure used to
describe a concept, and thereby model how context influences the typicality of
a single exemplar and the applicability of a single property of a concept. We
introduce the notion `state of a concept' to account for this contextual
influence, and show that the structure of the set of contexts and of the set of
properties of a concept is a complete orthocomplemented lattice. The structural
study in this article is a preparation for a numerical mathematical theory of
concepts in the Hilbert space of quantum mechanics that allows the description
of the combination of concepts (see quant-ph/0402205)


title:
Deterministic Controlled-NOT gate for single-photon two-qubit quantum
  logic

abstract:
  We demonstrate a robust implementation of a deterministic linear-optical
Controlled-NOT (CNOT) gate for single-photon two-qubit quantum logic. A
polarization Sagnac interferometer with an embedded 45$^{\circ}$-oriented dove
prism is used to enable the polarization control qubit to act on the momentum
(spatial) target qubit of the same photon. The CNOT gate requires no active
stabilization because the two spatial modes share a common path, and it is used
to entangle the polarization and momentum qubits.


title: Long-range entanglement generation via frequent measurements

abstract:
  A method is introduced whereby two non-interacting quantum subsystems, that
each interact with a third subsystem, are entangled via repeated projective
measurements of the state of the third subsystem. A variety of physical
examples are presented. The method can be used to establish long range
entanglement between distant parties in one parallel measurement step, thus
obviating the need for entanglement swapping.


title: Zeno era and non-decaying subspaces for multilevel Friedrichs model

abstract:
  We study the short-time and medium-time behavior of the survival probability
of decaying states in the framework of the $N$-level Friedrichs model. The
degenerated and nearly degenerated systems are discussed in detail. We show
that in these systems decay can be considerably slowed down or even stopped by
appropriate choice of initial conditions. We analyze the behaviour of the
multilevel system within the so-called Zeno era. We examine and compare two
different definitions of the Zeno time. We demonstrate that the Zeno era can be
considerably enlarged by proper choice of the system parameters.


title: Stationary entanglement induced by dissipation

abstract:
  The dynamics of two two-level dipole-dipole interacting atoms coupled to a
common electromagnetic bath and closely located inside a lossy cavity, is
reported. Initially injecting only one excitation in the two atoms-cavity
system, loss mechanisms asymptotically drive the matter sample toward a
stationary maximally entangled state. The role played by the closeness of the
two atoms with respect to such a cooperative behaviour is carefully discussed.
Stationary radiation trapping effects are found and transparently interpreted.


title: Active and Passive Quantum Erasers for Neutral Kaons

abstract:
  Quantum marking and quantum erasure are discussed for the neutral kaon
system. Contrary to other two-level systems, strangeness and lifetime of a
neutral kaon state can be alternatively measured via an "active" or a "passive"
procedure. This offers new quantum erasure possibilities. In particular, the
operation of a quantum eraser in the "delayed choice" mode is clearly
illustrated.


title: Stable single photon source in near infrared

abstract:
  Owing to their unsurpassed photostability, defects in solids may be ideal
candidates for single photon sources. Here we report on generation of single
photons by optical excitation of a yet unexplored defect in diamond, the
nickel-nitrogen complex (NE8) centre. The most striking feature of the defect
is its emission bandwidth of 1.2 nm at room temperature. The emission
wavelength of the defect is around 800 nm, which is suitable for telecom
fibres. In addition, in this spectral region little background light from the
diamond bulk material is detected. Consequently, a high contrast in
antibunching measurements is achieved.


title:
Large two-atom two-photon vacuum Rabi oscillations in a high quality
  cavity

abstract:
  We predict large cooperative effect involving two atom two photon vacuum Rabi
oscillations in a high quality cavity. The two photon emission occurs as a
result of simultaneous de-excitation of both atoms with two photon resonance
condition $\omega_1+\omega_2\approx \omega_a+\omega_b$, where $\omega_1$,
$\omega_2$ are the atomic transition frequencies and $\omega_a$, $\omega_b$ are
the frequencies of the emitted photons. The actual resonance condition depends
on the vacuum Rabi couplings. The effect can be realized either with identical
atoms in a bimodal cavity or with nonidentical atoms in a single mode cavity.


title:
Search for optimum labeling schemes in qubit systems for Quantum
  Information processing by NMR

abstract:
  Optimal labeling schemes lead to efficient experimental protocols for quantum
information processing by nuclear magnetic resonance (NMR). A systematic
approach of finding optimal labeling schemes for a given computation is
described here. The scheme is described for both quadrupolar systems and
spin-1/2 systems. Finally, one of the optimal labeling scheme has been used to
experimentally implement a quantum full-adder in a 4-qubit system by NMR, using
the technique of transition selective pulses.


title:
The Construction of Some Important Classes of Generalized Coherent
  states: The Nonlinear Coherent States Method

abstract:
  Considering some important classes of generalized coherent states known in
literature, we demonstrated that all of them can be created via conventional
fashion, i.e. the "lowering operator eigen-state" and the "displacement
operator" techniques using the {\it "nonlinear coherent states"} approach. As a
result we obtained a {\it "unified method"} to construct a large class of
coherent states which already have been introduced by different prescriptions.


title:
Geometric quantum computation and multi-qubit entanglement with
  superconducting charge qubits inside a cavity

abstract:
  We analyze a new scheme for quantum information processing, with
superconducting charge qubits coupled through a cavity mode, in which quantum
manipulations are insensitive to the state of the cavity. We illustrate how to
physically implement universal quantum computation as well as multi-qubit
entanglement based on unconventional geometric phase shifts in this scalable
solid-state system. Some quantum error-correcting codes can also be easily
constructed using the same technique. In view of the gate dependence on just
global geometric features and the insensitivity to the state of cavity modes,
the proposed quantum operations may result in high-fidelity quantum information
processing.


title: Path integrals from classical momentum paths

abstract:
  The path integral formulation of quantum mechanics constructs the propagator
by evaluating the action S for all classical paths in coordinate space. A
corresponding momentum path integral may also be defined through Fourier
transforms in the endpoints. Although these momentum path integrals are
especially simple for several special cases, no one has, to my knowledge, ever
formally constructed them from all classical paths in momentum space. I show
that this is possible because there exists another classical mechanics based on
an alternate classical action R. Hamilton's Canonical equations result from a
variational principle in both S and R. S uses fixed beginning and ending
spatial points while R uses fixed beginning and ending momentum points. This
alternative action's classical mechanics also includes a Hamilton-Jacobi
equation. I also present some important points concerning the beginning and
ending conditions on the action necessary to apply a Canonical transformation.
These properties explain the failure of the Canonical transformation in the
phase space path integral. It follows that a path integral may be constructed
from classical position paths using S in the coordinate representation or from
classical momentum paths using R in the momentum representation. Several
example calculations are presented that illustrate the simplifications and
practical advantages made possible by this broader view of the path integral.
In particular, the normalized amplitude for a free particle is found without
using the Schrodinger equation, the internal spin degree of freedom is simply
and naturally derived, and the simple harmonic oscillator is calculated.

categories: quant-ph math-ph math.MP physics.class-ph


title:
Ultracold atoms confined in rf-induced two-dimensional trapping
  potentials

abstract:
  We present the experimental implementation of a new trap for cold atoms
proposed by O. Zobay and B. M. Garraway. It relies on adiabatic potentials for
atoms dressed by a rf field in an inhomogeneous magnetic field. This trap is
well suited to confine atoms tightly along one direction to produce a
two-dimensional atomic gas. We transferred ultracold atoms into this trap,
starting either from thermal samples or Bose--Einstein condensates. In the
latter case, technical noise during the loading stage caused heating and
prevented us from observing 2D BECs.


title:
Translation of Lueders' "Uber die Zustandsanderung durch den
  Messprozess"

abstract:
  A translation and discussion of G. Luders, Ann. Phys. (Leipzig) 8 322-328
(1951).


title: Explicit Form of Solution of Two Atoms Tavis-Cummings Model

abstract:
  In this paper we consider the two atoms Tavis--Cummings model and give an
explicit form to the solution of this model which will play a central role in
quantum computation based on atoms of laser--cooled and trapped linearly in a
cavity.
  We also present a problem of three atoms Tavis--Cummings model which is
related to the construction of controlled--controlled NOT operation (gate) in
quantum computation.


title: A Purification Scheme and Entanglement Distillations

abstract:
  A purification scheme which utilizes the action of repeated measurements on a
(part of a total) quantum system is briefly reviewed and is applied to a few
simple systems to show how it enables us to extract an entangled state as a
target pure state. The scheme is rather simple (e.g., we need not prepare a
specific initial state) and is shown to have wide applicability and
flexibility, and is able to accomplish both the maximal fidelity and
non-vanishing yield.


title: Quantum tunneling time

abstract:
  A simple model of a quantum clock is applied to the old and controversial
problem of how long a particle takes to tunnel through a quantum barrier. The
model I employ has the advantage of yielding sensible results for energy
eigenstates, and does not require the use of time-dependant wave packets.
Although the treatment does not forbid superluminal tunneling velocities, there
is no implication of faster-than-light signaling because only the transit
duration is measurable, not the absolute time of transit. A comparison is given
with the weak-measurement post-selection calculations of Steinberg.


title: The Pegg-Barnett oscillator and its supersymmetric generalization

abstract:
  The oscillator algebra of Pegg-Barnett (P-B) oscillator with a
finite-dimensional number-state space is investigated in this note. It is shown
that the Pegg-Barnett oscillator possesses the su($n$) Lie algebraic structure.
Additionally, we suggest a so-called supersymmetric P-B oscillator and discuss
the related topics such as the algebraic structure and particle occupation
number of supersymmetric P-B oscillator.


title: Non-Commutative Worlds

abstract:
  This paper shows how the forms of gauge theory, Hamiltonian mechanics and
quantum mechanics arise from a non-commutative framework for calculus and
differential geometry. Discrete calculus is seen to fit into this pattern by
reformulating it in terms of commutators. Differential geometry begins here,
not with the concept of parallel translation, but with the concept of a
physical trajectory and the algebra related to the Jacobi identity that governs
that trajectory. The paper discusses how Poisson brackets give rise to Jacobi
identity, and how Jacobi identity arises in combinatorial contexts, including
graph coloring and knot theory.
  The paper gives a highly sharpened derivation of results of Tanimura on the
consequences of commutators that generalize the Feynman-Dyson derivation of
electromagnetism, and a generalization of the original Feynman-Dyson result
that makes no assumptions about commutators. The latter result is a consequence
of the definitions of the derivations in a particular non-commutative world.
Our generalized version of electromagnetism sheds light on the orginal
Feynman-Dyson derivation, and has many discrete models.


title: Covariance of the Schr\"odinger equation under low velocity boosts

abstract:
  It is known that the Schroedinger equation is not covariant under Galilei
boosts, unless the phase of its solutions are shifted simultaneously. It is
argued that the phase shift is not a coordinate transformation, because it
depends on the mass of the Schroedinger particle. The phase shift also cannot
be derived from low speed Lorentz boost. It is proposed to extend the Galilei
boost with two terms of order v^2/c^2 to avoid these issues and to guarantee
covariance of the Schroedinger kinetic energy and momentum. The extensions
imply that proper time and relativity of simultaneity are essential features of
Schroedinger quantum mechanics.


title: Relativistically invariant quantum information

abstract:
  We show that quantum information can be encoded into entangled states of
multiple indistinguishable particles in such a way that any inertial observer
can prepare, manipulate, or measure the encoded state independent of their
Lorentz reference frame. Such relativistically invariant quantum information is
free of the difficulties associated with encoding into spin or other degrees of
freedom in a relativistic context.


title: A Geometric Diagram of Separable States

abstract:
  This paper present a geometric diagram of a separable state: If a mixed state
$\sigma $ is separable, there are $2^{nS(\sigma)}$ linearly independant product
vectors which span the same Hilbert space as the $2^{nS(\sigma)}$ ``likely''
strings of $\sigma ^{\otimes n}$ do. This diagram results in a criterion for
separability which is strictly stronger than the inorder criterion in [M.A.
Nielsen and J. Kempe, Phys. Rev. Lett. 86, 5184 (2001)]. This means that the
number of product bases of states of a system has close link to the nonlocality
of the system.


title: Bound entanglement provides convertibility of pure entangled states

abstract:
  I show that two distant parties can transform pure entangled states to
arbitrary pure states by stochastic local operations and classical
communication (SLOCC) at the single copy level, if they share bound entangled
states. This is the effect of bound entanglement since this entanglement
processing is impossible by SLOCC alone. Similar effect of bound entanglement
occurs in three qubits where two incomparable entangled states of GHZ and W can
be inter-converted. In general multipartite settings composed by $N$ distant
parties, all $N$-partite pure entangled states are inter-convertible by SLOCC
with the assistance of bound entangled states with positive partial transpose.


title: Quantum fluctuations and life

abstract:
  There have been many claims that quantum mechanics plays a key role in the
origin and/or operation of biological organisms, beyond merely providing the
basis for the shapes and sizes of biological molecules and their chemical
affinities. These range from the suggestion by Schrodinger that quantum
fluctuations produce mutations, to the conjecture by Hameroff and Penrose that
quantum coherence in microtubules is linked to consciousness. I review some of
these claims in this paper, and discuss the serious problem of decoherence. I
advance some further conjectures about quantum information processing in
bio-systems. Some possible experiments are suggested.


title: Completely-Positive Non-Markovian Decoherence

abstract:
  We propose an effective Hamiltonian approach to investigate decoherence of a
quantum system in a non-Markovian reservoir, naturally imposing the complete
positivity on the reduced dynamics of the system. The formalism is based on the
notion of an effective reservoir, i.e., certain collective degrees of freedom
in the reservoir that are responsible for the decoherence. As examples for
completely positive decoherence, we present three typical decoherence processes
for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects
of the non-Markovian decoherence are compared to the Markovian decoherence.


title: Path integral in a magnetic field using the Trotter product formula

abstract:
  The derivation of the Feynman path integral based on the Trotter product
formula is extended to the case where the system is in a magnetic field.


title: On the Cyclotomic Quantum Algebra of Time Perception

abstract:
  I develop the idea that time perception is the quantum counterpart to time
measurement. Phase-locking and prime number theory were proposed as the
unifying concepts for understanding the optimal synchronization of clocks and
their 1/f frequency noise. Time perception is shown to depend on the
thermodynamics of a quantum algebra of number and phase operators already
proposed for quantum computational tasks, and to evolve according to a
Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum
model for prime numbers. The picture that emerges is a unique perception state
above a critical temperature and plenty of them allowed below, which are
parametrized by the symmetry group for the primitive roots of unity. Squeezing
of phase fluctuations close to the phase transition temperature may play a role
in memory encoding and conscious activity.


title: Compatibility and probability

abstract:
  A review of various definitions of "compatibility" expressed in terms of
ordinary probability, and a discussion of the occurrence of incompatibility
(and the related phenomenon of interference) in non-quantal probabilistic
systems.


title: Complementarity relations for multi-qubit systems

abstract:
  We derive two complementarity relations that constrain the individual and
bipartite properties that may simultaneously exist in a multi-qubit system. The
first expression, valid for an arbitrary pure state of n qubits, demonstrates
that the degree to which single particle properties are possessed by an
individual member of the system is limited by the bipartite entanglement that
exists between that qubit and the remainder of the system. This result implies
that the phenomenon of entanglement sharing is one specific consequence of
complementarity. The second expression, which holds for an arbitrary state of
two qubits, pure or mixed, quantifies a tradeoff between the amounts of
entanglement, separable uncertainty, and single particle properties that are
encoded in the quantum state. The separable uncertainty is a natural measure of
our ignorance about the properties possessed by individual subsystems, and may
be used to completely characterize the relationship between entanglement and
mixedness in two-qubit systems. The two-qubit complementarity relation yields a
useful geometric picture in which the root mean square values of local
subsystem properties act like coordinates in the space of density matrices, and
suggests possible insights into the problem of interpreting quantum mechanics.


title: Universal Quantum Computation through Control of Spin-Orbit Coupling

abstract:
  We propose a method for quantum computation which uses control of spin-orbit
coupling in a linear array of single electron quantum dots. Quantum gates are
carried out by pulsing the exchange interaction between neighboring electron
spins, including the anisotropic corrections due to spin-orbit coupling.
Control over these corrections, even if limited, is sufficient for universal
quantum computation over qubits encoded into pairs of electron spins. The
number of voltage pulses required to carry out either single qubit rotations or
controlled-Not gates scales as the inverse of a dimensionless measure of the
degree of control of spin-orbit coupling.


title:
Experimental demonstration of entanglement-enhanced classical
  communication over a quantum channel with correlated noise

abstract:
  We present an experiment demonstrating entanglement-enhanced classical
communication capacity of a quantum channel with correlated noise. The channel
is modelled by a fiber optic link exhibiting random birefringence that
fluctuates on a time scale much longer than the temporal separation between
consecutive uses of the channel. In this setting, introducing entanglement
between two photons travelling down the fiber allows one to encode reliably up
to one bit of information into their joint polarization degree of freedom. When
no quantum correlations between two separate uses of the channel are allowed,
this capacity is reduced by a factor of more than three. We demonstrated this
effect using a fiber-coupled source of entagled photon pairs based on
spontaneous parametric down-conversion, and a linear-optics Bell state
measurement.


title:
Universal Quantum Computation with ideal Clifford gates and noisy
  ancillas

abstract:
  We consider a model of quantum computation in which the set of elementary
operations is limited to Clifford unitaries, the creation of the state
$|0\rangle$ computational basis. In addition, we allow the creation of a
one-qubit ancilla in a mixed state $\rho$, which should be regarded as a
parameter of the model. Our goal is to determine for which $\rho$ universal
quantum computation (UQC) can be efficiently simulated. To answer this
question, we construct purification protocols that consume several copies of
$\rho$ and produce a single output qubit with higher polarization. The
protocols allow one to increase the polarization only along certain "magic"
directions. If the polarization of $\rho$ along a magic direction exceeds a
threshold value (about 65%), the purification asymptotically yields a pure
state, which we call a magic state. We show that the Clifford group operations
combined with magic states preparation are sufficient for UQC. The connection
of our results with the Gottesman-Knill theorem is discussed.


title:
The entanglement of Heisenberg chain with next-nearest-neighbor
  interaction

abstract:
  The features of the concurrences of the nearest-neighbor and the
next-nearest-neighbor sites for one-dimensional Heisenberg model with the
next-nearest-neighbor interaction are studied both at the ground state and
finite temperatures respectively. Both concurrences are found to exhibit
different behaviors at the ground state, which is clarified from the point of
view of the correlation function. The threshold temperature with respective to
different number of sites and the thermal concurrences of the system up to 12
sites are studied numerically.


title: Quantum mechanics and the equivalence principle

abstract:
  A quantum particle moving in a gravitational field may penetrate the
classically forbidden region of the gravitational potential. This raises the
question of whether the time of flight of a quantum particle in a gravitational
field might deviate systematically from that of a classical particle due to
tunnelling delay, representing a violation of the weak equivalence principle. I
investigate this using a model quantum clock to measure the time of flight of a
quantum particle in a uniform gravitational field, and show that a violation of
the equivalence principle does not occur when the measurement is made far from
the turning point of the classical trajectory. I conclude with some remarks
about the strong equivalence principle in quantum mechanics.


title:
Applications of Electromagnetically Induced Transparency to Quantum
  Information Processing

abstract:
  We provide a broad outline of the requirements that should be met by
components produced for a Quantum Information Technology (QIT) industry, and we
identify electromagnetically induced transparency (EIT) as potentially key
enabling science toward the goal of providing widely available few-qubit
quantum information processing within the next decade. As a concrete example,
we build on earlier work and discuss the implementation of a two-photon
controlled phase gate and a one-photon phase gate using the approximate Kerr
nonlinearity provided by EIT. We rigorously the dependence of the performance
of these gates on atomic dephasing and field detuning and intensity, and we
calculate the optimum parameters needed to apply a pi phase shift in a gate of
a given fidelity. Although high-fidelity gate operation will be difficult to
achieve with realistic system dephasing rates, the moderate fidelities that we
believe will be needed for few-qubit QIT seem much more obtainable.


title: The effect of focusing on polarization qubits

abstract:
  When a photon with well-defined polarization and momentum passes through a
focusing device, these properties are no longer well defined. Their loss is
captured by describing polarization by a 3x3 effective density matrix. Here we
show that the effective density matrix corresponds to the actual photodetection
model and we provide a simple formula to calculate it in terms of classical
fields. Moreover, we explore several possible experimental consequences of the
"longitudinal" term: limits on single-photon detection efficiency,
polarization-dependent atomic transitions rates and the implications on quantum
information processing.


title: Quantum recurrences versus stability

abstract:
  Consequences of quantum recurrences on the stability of a broad class of
dynamical systems is presented.


title: Fermionic Linear Optics Revisited

abstract:
  We provide an alternative view of the efficient classical simulatibility of
fermionic linear optics in terms of Slater determinants. We investigate the
generic effects of two-mode measurements on the Slater number of fermionic
states. We argue that most such measurements are not capable (in conjunction
with fermion linear optics) of an efficient exact implementation of universal
quantum computation. Our arguments do not apply to the two-mode parity
measurement, for which exact quantum computation becomes possible, see
quant-ph/0401066.


title:
Multimode Interference: Identifying Channels and Ridges in Quantum
  Probability Distributions

abstract:
  The multimode interference technique is a simple way to study the
interference patterns found in many quantum probability distributions. We
demonstrate that this analysis not only explains the existence of so-called
"quantum carpets," but can explain the spatial distribution of channels and
ridges in the carpets. With an understanding of the factors that govern these
channels and ridges we have a limited ability to produce a particular pattern
of channels and ridges by carefully choosing the weighting coefficients c_{n} .
We also use these results to demonstrate why fractional revivals of initial
wavepackets are themselves composed of many smaller packets.


title: Cavity cooling of a single atom

abstract:
  All conventional methods to laser-cool atoms rely on repeated cycles of
optical pumping and spontaneous emission of a photon by the atom. Spontaneous
emission in a random direction is the dissipative mechanism required to remove
entropy from the atom. However, alternative cooling methods have been proposed
for a single atom strongly coupled to a high-finesse cavity; the role of
spontaneous emission is replaced by the escape of a photon from the cavity.
Application of such cooling schemes would improve the performance of atom
cavity systems for quantum information processing. Furthermore, as cavity
cooling does not rely on spontaneous emission, it can be applied to systems
that cannot be laser-cooled by conventional methods; these include molecules
(which do not have a closed transition) and collective excitations of Bose
condensates, which are destroyed by randomly directed recoil kicks. Here we
demonstrate cavity cooling of single rubidium atoms stored in an intracavity
dipole trap. The cooling mechanism results in extended storage times and
improved localization of atoms. We estimate that the observed cooling rate is
at least five times larger than that produced by free-space cooling methods,
for comparable excitation of the atom.


title: Dynamical Origin of Quantum Probabilities

abstract:
  We study the origin of the Born probability rule rho = |psi|^2 in the de
Broglie-Bohm pilot-wave formulation of quantum theory. It is argued that
quantum probabilities arise dynamically, and have a status similar to thermal
probabilities in ordinary statistical mechanics. This is illustrated by
numerical simulations for a two-dimensional system. We show that a simple
initial ensemble with a non-standard distribution rho not= |psi|^2 of particle
positions evolves towards the quantum distribution to high accuracy. The
relaxation process rho --> |psi|^2 is quantified in terms of a coarse-grained
H-function (equal to minus the relative entropy of rho with respect to
|psi|^2), which is found to decrease approximately exponentially over time,
with a time constant that accords with a simple theoretical estimate.


title: Nature and Measure of Entanglement in Quantum Phase Transitions

abstract:
  Characterizing and quantifying quantum correlations in states of
many-particle systems is at the core of a full understanding of phase
transitions in matter. In this work, we continue our investigation of the
notion of generalized entanglement [Barnum et al. Phys. Rev. A 68, 032308
(2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum
state relative to an observable set. For the algebra of local observables on
multi-qubit systems, the resulting local purity measure is equivalent to a
recently introduced global entanglement measure [Meyer and Wallach, J. Math.
Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of
Lie-algebraic purity is exploited to identify and characterize the quantum
phase transitions present in two exactly solvable models: the
Lipkin-Meshkov-Glick model, and the spin-1/2 anisotropic XY model in a
transverse magnetic field. For the latter, we argue that a natural fermionic
observable-set arising after the Jordan-Wigner transformation, better
characterizes the transition than alternative measures based on qubits. This
illustrates the usefulness of going beyond the standard subsystem-based
framework while providing a global disorder parameter for this model. Our
results show how generalized entanglement leads to useful tools for
distinguishing between the ordered and disordered phases in the case of broken
symmetry quantum phase transitions. Additional implications and possible
extensions of concepts to other systems of interest in condensed matter physics
are also discussed.


title: An Unconditionally Secure Quantum Bit Commitment Scheme

abstract:
  This paper has been withdrawn by the authors,because the proposed protocol is
still coverd by the no-go theorem of Mayers, Lo and Chau. We thank H-K. Lo and
HF Chau for helpful correspondences.


title: Nondeterministic Recursion with Quantum Units (I-V)

abstract:
  In this paper are discussed some formal properties of quantum devices
necessary for implementation of nondeterministic Turing machine.


title:
Uncertainty Relations (UR) Have Nothing to do with Quantum Mechanics
  (QM)

abstract:
  Uncertainty relations are shown to have nothing specific for quantum
mechanics, being the general property valid for arbitrary function. A wave
function of a particle having precisely defined position and momentum in QM
simultaneously is demonstrated. Interference on two slits in a screen is shown
to exist in classical mechanics. A nonlinear classical system of equations
replacing QM Schr\"odinger equation is suggested. This approach is shown to
have nothing in common with Bohmian mechanics.


title: Spin and Statistics in Galilean Covariant Field Theory

abstract:
  The existence of a possible connection between spin and statistics is
explored within the framework of Galilean covariant field theory. To this end
fields of arbitrary spin are constructed and admissible interaction terms
introduced. By explicitly solving such a model in the two particle sector it is
shown that no spin and statistics connection can be established.


title:
Comment on "A mathematical theorem as a basis for the second law:
  Thomson's formulation applied to equilibruim"

abstract:
  A.E. Allahverdyan and Th. M. Nieuwenhuizen [1] in their paper "A mathematical
theorem as a basis for the second law: Thomson's formulation applied to
equilibriium" present a proof of the second law of thermodynamics based on
quantum mechanics. In this comment on their paper I offer a counterexample to
their proof.


title: Improved algorithm for quantum separability and entanglement detection

abstract:
  Determining whether a quantum state is separable or entangled is a problem of
fundamental importance in quantum information science. It has recently been
shown that this problem is NP-hard. There is a highly inefficient `basic
algorithm' for solving the quantum separability problem which follows from the
definition of a separable state. By exploiting specific properties of the set
of separable states, we introduce a new classical algorithm that solves the
problem significantly faster than the `basic algorithm', allowing a feasible
separability test where none previously existed e.g. in 3-by-3-dimensional
systems. Our algorithm also provides a novel tool in the experimental detection
of entanglement.


title: On the distributed compression of quantum information

abstract:
  We consider the problem of distributed compression for correlated quantum
sources. The classical version of this problem was solved by Slepian and Wolf,
who showed that distributed compression could take full advantage of redundancy
in the local sources created by the presence of correlations. We show that, in
general, this is not the case for quantum sources by proving a lower bound on
the rate sum for irreducible sources of product states which is stronger than
the one given by a naive application of Slepian-Wolf. Nonetheless, strategies
taking advantage of correlation do exist for some special classes of quantum
sources. For example, Devetak and Winter demonstrated the existence of such a
strategy when one of the sources is classical. Here we find optimal non-trivial
strategies for a different extreme, sources of Bell states. In addition, we
illustrate how distributed compression is connected to other problems in
quantum information theory, including information-disturbance questions,
entanglement distillation and quantum error correction.


title:
Entanglement as an Observer-Dependent Concept: An Application to Quantum
  Phase Transitions

abstract:
  This paper addresses the following main question: Do we have a theoretical
understanding of entanglement applicable to a full variety of physical
settings? It is clear that not only the assumption of distinguishability, but
also the few-subsystem scenario, are too narrow to embrace all possible
physical settings. In particular, the need to go beyond the traditional
subsystem-based framework becomes manifest when one tries to apply the
conventional concept of entanglement to the physics of matter, since the
constituents of a quantum many-body system are indistinguishable particles. We
shall discuss here a notion of generalized entanglement, which can be applied
to any operator language (fermions, bosons, spins, etc.) used to describe a
physical system and which includes the conventional entanglement settings
introduced to date in a unified fashion. This is realized by noticing that
entanglement is an observer-dependent concept, whose properties are determined
by the expectations of a distinguished set of observables without reference to
a preferred subsystem decomposition, i.e., it depends on the physically
relevant point of view. This viewpoint depends in turn upon the relationship
between different sets of observables that determine our ability to control the
system of interest. Indeed, the extent to which entanglement is present depends
on the observables used to measure a system and describe its states. This
represents a most conspicuous advantage as will be highlighted by the
condensed-matter application we will discuss.


title: Entanglement beyond subsystems

abstract:
  We present a notion of generalized entanglement which goes beyond the
conventional definition based on quantum subsystems. This is accomplished by
directly defining entanglement as a property of quantum states relative to a
distinguished set of observables singled out by Physics. While recovering
standard entanglement as a special case, our notion allows for substantially
broader generality and flexibility, being applicable, in particular, to
situations where existing tools are not directly useful.


title: Finiteness of the universe and computation beyond Turing computability

abstract:
  We clarify the confusion, misunderstanding and misconception that the
physical finiteness of the universe, if the universe is indeed finite, would
rule out all hypercomputation, the kind of computation that exceeds the Turing
computability, while maintaining and defending the validity of Turing
computation and the Church-Turing thesis.


title: Quantum Digital Signature based on Quantum One-way Functions

abstract:
  A quantum digital signature protocol based on quantum mechanics is proposed
in this paper. The security of the protocol relies on the existence of quantum
one-way functions by quantum information theorem. This protocol involves a
so-called arbitrator who validates and authenticates the signed message. In
this protocol, we use privacy key algorithm to ensure the security of quantum
information on channel and use quantum public keys to sign message. To
guarantee the authenticity of the message, a family of quantum stabilizer codes
are employed. Our protocol presents a novel method to construct ultimately
secure digital system in future secure communication.


title: Free particle states from Geometry

abstract:
  In this short paper I discuss how conformal geometric algebra models for
euclidean and minkowski targetspaces determine the allowed quantum mechanical
statespaces for free particles. I explicitly treat 2-dimensional euclidean
space and (1+1)-dimensional spacetime.


title: Quantum implementation of elementary arithmetic operations

abstract:
  Quantum computation has received great attention in recent years for its
possible application to difficult problem in classical calculation. Despite the
experimental problems of implementing quantum devices, theoretical physicists
have tried to conceive some implementations for quantum algorithms. We present
here some explicit schemes for executing elementary arithmetic operations.


title:
Creating Steady Atom-Molecule Entanglement by Demkov-Kunike Type
  Non-adiabatic Transition

abstract:
  We, based on the photoassociation of fermion atoms into bosonic molecules,
propose a scheme to create the steady entanglement between the atom state and
the molecule state inside an optical lattice. The stability of entanglement
state is guaranteed by sweeping the frequency of Ramman laser beam through
resonance according to the second Demkov-Kunike (DK2) nonadiabatic transition
model\cite{DK,models}. The probability amplitude of each components can be
precisely controlled by adjusting the sweeping parameter.


title: Regularization of the Coulomb scattering problem

abstract:
  Exact solutions of the Schr\"odinger equation for the Coulomb potential are
used in the scope of both stationary and time-dependent scattering theories in
order to find the parameters which define regularization of the Rutherford
cross-section when the scattering angle tends to zero but the distance r from
the center remains fixed. Angular distribution of the particles scattered in
the Coulomb field is investigated on the rather large but finite distance r
from the center. It is shown that the standard asymptotic representation of the
wave functions is not available in the case when small scattering angles are
considered. Unitary property of the scattering matrix is analyzed and the
"optical" theorem for this case is discussed. The total and transport
cross-sections for scattering of the particle by the Coulomb center proved to
be finite values and are calculated in the analytical form. It is shown that
the considered effects can be essential for the observed characteristics of the
transport processes in semiconductors which are defined by the electron and
hole scattering in the fields of the charged impurity centers.


title:
Quantum Models of Mind: Are They Compatible with Environment
  Decoherence?

abstract:
  We criticize the Hameroff Penrose model in the context of quantum brain model
by gravitational collapse orchestrated objective reduction, orch. OR, assumed
by Penrose, and we propose instead that the decoherence process is caused by
interaction with the environment. We consider it useful to exploit this
possibility because of the growing importance of decoherence theory in quantum
measurement, and also because quantum mechanics can be applied to brain study
independently of the Hameroff Penrose model for mind and consciousness. Our
conclusion is that the Hameroff Penrose model is not compatible with
decoherence, but nevertheless quantum brain can still be considered if we
replace gravitational collapse orch .OR with decoherence.


title: Scalable quantum computation in systems with Bose-Hubbard dynamics

abstract:
  Several proposals for quantum computation utilize a lattice type architecture
with qubits trapped by a periodic potential. For systems undergoing many body
interactions described by the Bose-Hubbard Hamiltonian, the ground state of the
system carries number fluctuations that scale with the number of qubits. This
process degrades the initialization of the quantum computer register and can
introduce errors during error correction. In an earlier manuscript we proposed
a solution to this problem tailored to the loading of cold atoms into an
optical lattice via the Mott Insulator phase transition. It was shown that by
adding an inhomogeneity to the lattice and performing a continuous measurement,
the unit filled state suitable for a quantum computer register can be
maintained. Here, we give a more rigorous derivation of the register fidelity
in homogeneous and inhomogeneous lattices and provide evidence that the
protocol is effective in the finite temperature regime.


title: Improved Quantum Cost for n-bit Toffoli Gates

abstract:
  We present an n-bit Toffoli gate quantum circuit based on the realization
proposed by Barenco, where some of the Toffoli gates in their construction are
replaced with Peres gates. This results in a significant cost reduction. Our
main contribution is a quantum circuit which simulates the (m+1)-bit Toffoli
gate with 32m-96 elementary quantum gates and one garbage bit which is passed
unchanged. This paper is a corrected and expanded version of our recent journal
publication.


title: Quantum Hamilton-Jacobi analysis of PT symmetric Hamiltonians

abstract:
  We apply the quantum Hamilton-Jacobi formalism, naturally defined in the
complex domain, to a number of complex Hamiltonians, characterized by discrete
parity and time reversal (PT) symmetries and obtain their eigenvalues and
eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials
are analyzed and the subtle differences, in the singularity structures of their
quantum momentum functions, are pointed out. The role of the PT symmetry in the
complex domain is also illustrated.


title:
Classical Extensions, Classical Representations and Bayesian Updating in
  Quantum Mechanics

abstract:
  I review the formalism of classical extensions of quantum mechanics
introduced by Beltrametti and Bugajski, and compare it to the classical
representations discussed e.g. by Busch, Hellwig and Stulpe and recently used
by Fuchs in his discussion of quantum mechanics in terms of standard quantum
measurements. I treat the problem of finding Bayesian analogues of the state
transition associated with measurement in the canonical classical extension as
well as in the related 'uniform' classical representation. In the classical
extension, the analogy is extremely good.


title: Quantum Identification of Boolean Oracles

abstract:
  The oracle identification problem (OIP) is, given a set $S$ of $M$ Boolean
oracles out of $2^{N}$ ones, to determine which oracle in $S$ is the current
black-box oracle. We can exploit the information that candidates of the current
oracle is restricted to $S$. The OIP contains several concrete problems such as
the original Grover search and the Bernstein-Vazirani problem. Our interest is
in the quantum query complexity, for which we present several upper and lower
bounds. They are quite general and mostly optimal: (i) The query complexity of
OIP is $O(\sqrt{N\log M \log N}\log\log M)$ for {\it any} $S$ such that $M =
|S| > N$, which is better than the obvious bound $N$ if $M < 2^{N/\log^{3}N}$.
(ii) It is $O(\sqrt{N})$ for {\it any} $S$ if $|S| = N$, which includes the
upper bound for the Grover search as a special case. (iii) For a wide range of
oracles ($|S| = N$) such as random oracles and balanced oracles, the query
complexity is $\Theta(\sqrt{N/K})$, where $K$ is a simple parameter determined
by $S$.


title: Coherent backscattering of light by atoms in the saturated regime

abstract:
  We present the first calculation of coherent backscattering with inelastic
scattering by saturated atoms. We consider the scattering of a
quasi-monochromatic laser pulse by two distant atoms in free space. By
restricting ourselves to scattering of two photons, we employ a perturbative
approach, valid up to second order in the incident laser intensity. The
backscattering enhancement factor is found to be smaller than two (after
excluding single scattering), indicating a loss of coherence between the doubly
scattered light emitted by both atoms. Since the undetected photon carries
information about the path of the detected photon, the coherence loss can be
explained by a which-path argument, in analogy with a double-slit experiment.


title: Criteria for unconditional entanglement purification

abstract:
  We show that the fidelity result of advantage distillation (Bennett et al,
Phys. Rev. Lett., 76, 722(1996)) is not only for the product state of raw
pairs, it is actually correct with whatever form of state of raw pairs. We then
give a general theorem for unconditional entanglement purification. This
theorem lists the conditions on which the fidelity result of a purification
protocol keeps unchanged from product form of raw-pair state and arbitrary form
of raw-pair state. Using this theorem, we find that all existing purification
puricfication can work for arbitrary initial state of raw pairs.


title: Comment on 'Grover Search with Pairs of Trapped Ions'

abstract:
  In this brief comment on `Grover search with pairs of trapped Ions' [Phys.
Rev. A 63, 052308, (2001)], we show that Grover's algorithm may be performed
exactly using the gate set given provided that small changes are made to the
gate sequence. An analytic expression for the probability of success of
Grover's algorithm for any unitary operator, U, instead of Hadamard is
presented.


title: The twistor geometry of three-qubit entanglement

abstract:
  A geometrical description of three qubit entanglement is given. A part of the
transformations corresponding to stochastic local operations and classical
communication on the qubits is regarded as a gauge degree of freedom. Entangled
states can be represented by the points of the Klein quadric ${\cal Q}$ a space
known from twistor theory. It is shown that three-qubit invariants are
vanishing on special subspaces of ${\cal Q}$. An invariant vanishing for the
$GHZ$ class is proposed. A geometric interpretation of the canonical
decomposition and the inequality for distributed entanglement is also given.


title: Driven chaotic mesoscopic systems, dissipation and decoherence

abstract:
  Driven chaotic systems are of interest in mesoscopic physics, as well as in
nuclear, atomic and molecular physics. Such systems [coordinates $(Q,P)$]$ tend
to absorb energy. This irreversible effect is known as dissipation. "Driving"
means that a parameter $x$ is changed in time. More generally, $x$ may be a
dynamical variable. In such case the interaction of $(x,p)$ with the
environmental degrees of freedom $(Q,P)$ leads to dephasing as well as to
dissipation. We introduce a general framework for the analysis of dissipation
and dephasing, and we clarify the tight connection to recent studies of quantum
irreversibility (also referred to as "Loschmidt echo" or as the "fidelity" of
quantum computation). Specific model systems that will be presented are:
particle in a box driven by moving a wall, and particle in a box/ring driven by
electro-motive-force. These two examples are related to studies of nuclear
friction and mesoscopic conductance.


title: Demonstration of an all-optical quantum controlled-NOT gate

abstract:
  The promise of tremendous computational power, coupled with the development
of robust error-correcting schemes, has fuelled extensive efforts to build a
quantum computer. The requirements for realizing such a device are confounding:
scalable quantum bits (two-level quantum systems, or qubits) that can be well
isolated from the environment, but also initialized, measured and made to
undergo controllable interactions to implement a universal set of quantum logic
gates. The usual set consists of single qubit rotations and a controlled-NOT
(CNOT) gate, which flips the state of a target qubit conditional on the control
qubit being in the state 1. Here we report an unambiguous experimental
demonstration and comprehensive characterization of quantum CNOT operation in
an optical system. We produce all four entangled Bell states as a function of
only the input qubits' logical values, for a single operating condition of the
gate. The gate is probabilistic (the qubits are destroyed upon failure), but
with the addition of linear optical quantum non-demolition measurements, it is
equivalent to the CNOT gate required for scalable all-optical quantum
computation.


title: Concurrence of mixed bipartite quantum states in arbitrary dimensions

abstract:
  We derive a lower bound for the concurrence of mixed bipartite quantum
states, valid in arbitrary dimensions. As a corollary, a weaker, purely
algebraic estimate is found, which detects mixed entangled states with positive
partial transpose.


title:
Continuous variable quantum key distribution using polarization encoding
  and post selection

abstract:
  We present an experimental demonstration of a quantum key distribution
protocol using coherent polarization states. Post selection is used to ensure a
low error rate and security against beam splitting attacks even in the presence
of high losses. Signal encoding and readout in polarization bases avoids the
difficult task of sending a local oscillator with the quantum channel. This
makes our setup robust and easy to implement. A shared key was established for
losses up to 64%.


title: On the Optimal Mean Photon Number for Quantum Cryptography

abstract:
  The optimal mean photon number (mu) for quantum cryptography is the average
photon number per transmitted pulse that results in the highest delivery rate
of distilled cryptographic key bits, given a specific system scenario and set
of assumptions about Eve's capabilities. Although many experimental systems
have employed a mean photon number (mu) of 0.1 in practice, several research
teams have pointed out that this value is somewhat arbitrary. In fact, various
optimal values for mu have been described in the literature.
  In this paper we offer a detailed analytic model for an experimental,
fiber-based quantum cryptographic system, and an explicit set of reasonable
assumptions about Eve's current technical capabilities. We explicitly model
total system behavior ranging from physical effects to the results of quantum
cryptographic protocols such as error correction and privacy amplification. We
then derive the optimal photon number (mu) for this system in a range of
scenarios. One interesting result is that mu of approximately 1.1 is optimal
for a wide range of realistic, fiber-based QKD systems; in fact, it provides
nearly 10 times the distilled throughput of systems that employ a more
conventional mu = 0.1, without any adverse affect on system security, as judged
against a set of reasonable assumptions about Eve's current capabilities.


title: Quantum walks on graphs and quantum scattering theory

abstract:
  We discuss a particular kind of quantum walk on a general graph. We affix two
semi-infinite lines to a general finite graph, which we call tails. On the
tails, the particle making the walk simply advances one unit at each time step,
so that its behavior there is analogous to free propagation We are interested
in how many steps it will take the particle, starting on one tail and
propagating through the graph (where its propagation is not free), to emerge
onto the other tail. The probability to make such a walk in n steps and the
hitting time for such a walk can be expressed in terms of the transmission
amplitude for the graph, which is one element of its S matrix. Demonstrating
this necessitates a study of the analyticity properties of the transmission and
reflection amplitudes of a graph. We show that the graph can have bound states
that cannot be accessed by a particle entering the graph from one of its tails.
Time-reversal invariance of a quantum walk is defined and used to show that the
transmission amplitudes for the particle entering the graph from different
directions are the same if the walk is time-reversal invariant.


title: Contradictions of the quantum scattering theory

abstract:
  The standard scattering theory (SST) in non relativistic quantum mechanics
(QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to
calculate scattering probability without introduction of a finite volume is
discussed. Substantiation of SST in textbooks with the help of wave packets is
shown to be incomplete. A complete theory of wave packets scattering on a fixed
center is presented, and its similarity to the plane wave scattering is
demonstrated. The neutron scattering on a monatomic gas is investigated, and
several problems are pointed out. A catastrophic ambiguity of the cross section
is revealed, and a way to resolve this ambiguity is discussed.


title: Non-additivity of quantum capacity for multiparty communication channels

abstract:
  We investigate multiparty communication scenarios where information is sent
from several sender to several receivers. We establish a relation between the
quantum capacity of multiparty communication channels and their distillability
properties which enables us to show that the quantum capacity of such channels
is not additive.


title:
Computational Indistinguishability between Quantum States and Its
  Cryptographic Application

abstract:
  We introduce a computational problem of distinguishing between two specific
quantum states as a new cryptographic problem to design a quantum cryptographic
scheme that is "secure" against any polynomial-time quantum adversary. Our
problem, QSCDff, is to distinguish between two types of random coset states
with a hidden permutation over the symmetric group of finite degree. This
naturally generalizes the commonly-used distinction problem between two
probability distributions in computational cryptography. As our major
contribution, we show that QSCDff has three properties of cryptographic
interest: (i) QSCDff has a trapdoor; (ii) the average-case hardness of QSCDff
coincides with its worst-case hardness; and (iii) QSCDff is computationally at
least as hard as the graph automorphism problem in the worst case. These
cryptographic properties enable us to construct a quantum public-key
cryptosystem, which is likely to withstand any chosen plaintext attack of a
polynomial-time quantum adversary. We further discuss a generalization of
QSCDff, called QSCDcyc, and introduce a multi-bit encryption scheme that relies
on similar cryptographic properties of QSCDcyc.


title: Geometric Phases for Mixed States during Cyclic Evolutions

abstract:
  The geometric phases of cyclic evolutions for mixed states are discussed in
the framework of unitary evolution. A canonical one-form is defined whose line
integral gives the geometric phase which is gauge invariant. It reduces to the
Aharonov and Anandan phase in the pure state case. Our definition is consistent
with the phase shift in the proposed experiment [Phys. Rev. Lett. \textbf{85},
2845 (2000)] for a cyclic evolution if the unitary transformation satisfies the
parallel transport condition. A comprehensive geometric interpretation is also
given. It shows that the geometric phases for mixed states share the same
geometric sense with the pure states.


title: Improved Bounds for the Approximate QFT

abstract:
  It has previously been established that the logarithmic-depth approximate
quantum Fourier transform (AQFT) provides a suitable replacement for the
regular QFT in many quantum algorithms. Since the AQFT is less accurate by
definition, polynomially many more applications of the AQFT are required to
achieve the original accuracy. However, in many quantum algorithms, the smaller
size of the AQFT circuit yields a net improvement over using the QFT.
  This paper presents a more thorough analysis of the AQFT circuit, which leads
to the surprising conclusion that for sufficiently large input sizes, the
difference between the QFT and the logarithmic-depth AQFT is negligible. In
effect, the AQFT can be used as an direct replacement for the QFT, yielding
improvements in any application which does not require exact quantum
computation.


title: A quantum channel with additive minimum output entropy

abstract:
  We give a direct proof of the additivity of the minimum output entropy of a
particular quantum channel which breaks the multiplicativity conjecture. This
yields additivity of the classical capacity of this channel, a result obtained
by a different method by Matsumoto and Yura [quant-ph/0306009]. Our proof
relies heavily upon certain concavity properties of the output entropy which
are of independent interest.


title:
Characterization of distillability of entanglement in terms of positive
  maps

abstract:
  A necessary and sufficient condition for 1-distillability is formulated in
terms of decomposable positive maps. As an application we provide insight into
why all states violating the reduction criterion map are distillable and
demonstrate how to construct such maps in a systematic way. We establish a
connection between a number of existing results, which leads to an elementary
proof for the characterisation of distillability in terms of 2-positive maps.


title: Purity and State Fidelity of Quantum Channels via Hamiltonians

abstract:
  We associate to every quantum channel $T$ acting on a Hilbert space
$\mathcal{H}$ a pair of Hamiltonian operators over the symmetric subspace of
$\mathcal{H}^{\otimes 2}$. The expectation values of these Hamiltonians over
symmetric product states give either the purity or the pure state fidelity of
$T$. This allows us to analytically compute these measures for a wide class of
channels, and to identify states that are optimal with respect to these
measures.


title: Additivity properties of a Gaussian Channel

abstract:
  The Amosov-Holevo-Werner conjecture implies the additivity of the minimum
Re'nyi entropies at the output of a channel. The conjecture is proven true for
all Re'nyi entropies of integer order greater than two in a class of Gaussian
bosonic channel where the input signal is randomly displaced or where it is
coupled linearly to an external environment.


title: Quantum key distribution using polarized coherent states

abstract:
  We discuss a continuous variables method of quantum key distribution
employing strongly polarized coherent states of light. The key encoding is
performed using the variables known as Stokes parameters, rather than the field
quadratures. Their quantum counterpart, the Stokes operators $\hat{S}_i$
(i=1,2,3), constitute a set of non-commuting operators, being the precision of
simultaneous measurements of a pair of them limited by an uncertainty-like
relation. Alice transmits a conveniently modulated two-mode coherent state, and
Bob randomly measures one of the Stokes parameters of the incoming beam. After
performing reconciliation and privacy amplification procedures, it is possible
to distill a secret common key. We also consider a non-ideal situation, in
which coherent states with thermal noise, instead of pure coherent states, are
used for encoding.


title: Multi-Qubit Gates in Arrays Coupled by 'Always On' Interactions

abstract:
  Recently there has been interest in the idea of quantum computing without
control of the physical interactions between component qubits. This is highly
appealing since the 'switching' of such interactions is a principal difficulty
in creating real devices. It has been established that one can employ 'always
on' interactions in a one-dimensional Heisenberg chain, provided that one can
tune the Zeeman energies of the individual (pseudo-)spins. It is important to
generalize this scheme to higher dimensional networks, since a real device
would probably be of that kind. Such generalisations have been proposed, but
only at the severe cost that the efficiency of qubit storage must *fall*. Here
we propose the use of multi-qubit gates within such higher-dimensional arrays,
finding a novel three-qubit gate that can in fact increase the efficiency
beyond the linear model. Thus we are able to propose higher dimensional
networks that can constitute a better embodiment of the 'always on' concept - a
substantial step toward bringing this novel concept to full fruition.


title: Universal quantum data compression via gentle tomography

abstract:
  Quantum state tomography--the practice of estimating a quantum state by
performing measurements on it--is useful in a variety of contexts. We introduce
"gentle tomography" as a version of tomography that preserves the measured
quantum data. As an application of gentle tomography, we describe a simple
polynomial-time method for universal source coding.


title: Are all reversible computations tidy?

abstract:
  It has long been known that to minimise the heat emitted by a deterministic
computer during it's operation it is necessary to make the computation act in a
logically reversible manner\cite{Lan61}. Such logically reversible operations
require a number of auxiliary bits to be stored, maintaining a history of the
computation, and which allows the initial state to be reconstructed by running
the computation in reverse. These auxiliary bits are wasteful of resources and
may require a dissipation of energy for them to be reused. A simple procedure
due to Bennett\cite{Ben73} allows these auxiliary bits to be "tidied", without
dissipating energy, on a classical computer. All reversible classical
computations can be made tidy in this way. However, this procedure depends upon
a classical operation ("cloning") that cannot be generalised to quantum
computers\cite{WZ82}. Quantum computations must be logically reversible, and
therefore produce auxiliary qbits during their operation. We show that there
are classes of quantum computation for which Bennett's procedure cannot be
implemented. For some of these computations there may exist another method for
which the computation may be "tidied". However, we also show there are quantum
computations for which there is no possible method for tidying the auxiliary
qbits. Not all reversible quantum computations can be made "tidy". This
represents a fundamental additional energy burden to quantum computations. This
paper extends results in \cite{Mar01}.


title:
Influence of branch points in the complex plane on the transmission
  through double quantum dots

abstract:
  We consider single-channel transmission through a double quantum dot system
consisting of two single dots that are connected by a wire and coupled each to
one lead. The system is described in the framework of the S-matrix theory by
using the effective Hamiltonian of the open quantum system. It consists of the
Hamiltonian of the closed system (without attached leads) and a term that
accounts for the coupling of the states via the continuum of propagating modes
in the leads. This model allows to study the physical meaning of branch points
in the complex plane. They are points of coalesced eigenvalues and separate the
two scenarios with avoided level crossings and without any crossings in the
complex plane. They influence strongly the features of transmission through
double quantum dots.


title: Quantum dwell times

abstract:
  We put forward several inherently quantum characteristics of the dwell time,
and propose an operational method to detect them. The quantum dwell time is
pointed out to be a conserved quantity, totally bypassing Pauli's theorem.
Furthermore, the quantum dwell time in a region for one dimensional motion is
doubly degenerate. In presence of a potential barrier, the dwell time becomes
bounded, unlike the classical quantity. By using off-resonance coupling to a
laser we propose an operational method to measure the absorption by a complex
potential, and thereby the average time spent by an incoming atom in the laser
region.


title: Gate simulation and lower bounds on the simulation time

abstract:
  Unitary operations are the building blocks of quantum programs. Our task is
to design effcient or optimal implementations of these unitary operations by
employing the intrinsic physical resources of a given n-qubit system. The most
common versions of this task are known as Hamiltonian simulation and gate
simulation, where Hamiltonian simulation can be seen as an infinitesimal
version of the general task of gate simulation. We present a Lie-theoretic
approach to Hamiltonian simulation and gate simulation. From this, we derive
lower bounds on the time complexity in the n-qubit case, generalizing known
results to both even and odd n. To achieve this we develop a generalization of
the so-called magic basis for two-qubits. As a corollary, we note a connection
to entanglement measures of concurrence-type.


title: Covariant quantum measurements which maximize the likelihood

abstract:
  We derive the class of covariant measurements which are optimal according to
the maximum likelihood criterion. The optimization problem is fully resolved in
the case of pure input states, under the physically meaningful hypotheses of
unimodularity of the covariance group and measurability of the stability
subgroup. The general result is applied to the case of covariant state
estimation for finite dimension, and to the Weyl-Heisenberg displacement
estimation in infinite dimension. We also consider estimation with multiple
copies, and compare collective measurements on identical copies with the scheme
of independent measurements on each copy. A "continuous-variables" analogue of
the measurement of direction of the angular momentum with two anti-parallel
spins by Gisin and Popescu is given.


title: Probability tables

abstract:
  The idea of writing a table of probabilistic data for a quantum or classical
system, and of decomposing this table in a compact way, leads to a shortcut for
Hardy's formalism, and gives new perspectives on foundational issues.


title:
Modeling full adder in Ising spin quantum computer with 1000 qubits
  using quantum maps

abstract:
  The quantum adder is an essential attribute of a quantum computer, just as
classical adder is needed for operation of a digital computer. We model the
quantum full adder as a realistic complex algorithm on a large number of qubits
in an Ising-spin quantum computer. Our results are an important step toward
effective modeling of the quantum modular adder which is needed for Shor's and
other quantum algorithms. Our full adder has the following features: (i) The
near-resonant transitions with small detunings are completely suppressed, which
allows us to decrease errors by several orders of magnitude and to model a
1000-qubit full adder. (We add a 1000-bit number using 2001 spins.) (ii) We
construct the full adder gates directly as sequences of radio-frequency pulses,
rather than breaking them down into generalized logical gates, such as
Control-Not and one qubit gates. This substantially reduces the number of
pulses needed to implement the full adder. [The maximum number of pulses
required to add one bit (F-gate) is 15]. (iii) Full adder is realized in a
homogeneous spin chain. (iv) The phase error is minimized: the F-gates generate
approximately the same phase for different states of the superposition. (v)
Modeling of the full adder is performed using quantum maps instead of
differential equations. This allows us to reduce the calculation time to a
reasonable value.


title: Measurement-assisted Coherent Control

abstract:
  Two advantageous roles of the influence of measurement on a system subject to
coherent control are exposed using a five-level model system. In particular, a
continuous measurement of the population in a branch state in the Kobrak-Rice
extended stimulated Raman adiabatic passage scheme is shown to provide a
powerful means for controlling the population transfer branching ratio between
two degenerate target states. It is demonstrated that a measurement with a
large strength may be used to completely shut off the yield of one target state
and that the same measurement with a weak strength can dramatically enhance the
robustness of the controlled branching ratio against dephasing.


title: A remark about the Mermin-Squires Music Hall's inteludium

abstract:
  The Mermin-Squires Music Hall inteludium on the Einstein-Podolsky-Rosen
affair is analyzed by showing the fallacity of the One-Borel-Normality
Criterion and the necessity of replacing it with the more restrictive
Algorithmic-Randomness Criterion


title: The Importance of Being Unistochastic

abstract:
  A bistochastic matrix is a square matrix with positive entries such that rows
and columns sum to unity. A unistochastic matrix is a bistochastic matrix whose
matrix elements are the absolute values squared of a unitary matrix. We can now
ask questions such as when a given bistochastic matrix is unistochastic. I
review these questions: Why they are asked, why they are difficult to answer,
and what is known about them.


title:
Distillability and positivity of partial transposes in general quantum
  field systems

abstract:
  Criteria for distillability, and the property of having a positive partial
transpose, are introduced for states of general bipartite quantum systems. The
framework is sufficiently general to include systems with an infinite number of
degrees of freedom, including quantum fields. We show that a large number of
states in relativistic quantum field theory, including the vacuum state and
thermal equilibrium states, are distillable over subsystems separated by
arbitrary spacelike distances. These results apply to any quantum field model.
It will also be shown that these results can be generalized to quantum fields
in curved spacetime, leading to the conclusion that there is a large number of
quantum field states which are distillable over subsystems separated by an
event horizon.


title: Scalable Superconducting Architecture for Adiabatic Quantum Computation

abstract:
  A scalable superconducting architecture for adiabatic quantum computers is
proposed. The architecture is based on time-independent, nearest-neighbor
interqubit couplings: it can handle any problem in the class NP even in the
presence of measurement errors, noise, and decoherence. The implementation of
this architecture with superconducting persistent-current qubits and the
natural robustness of such an implementation to manufacturing imprecision and
decoherence are discussed.


title:
Bitwise Bell inequality violations for an entangled state involving 2N
  ions

abstract:
  Following on from previous work [J. A. Larsson, Phys. Rev. A 67, 022108
(2003)], Bell inequalities based on correlations between binary digits are
considered for a particular entangled state involving 2N trapped ions. These
inequalities involve applying displacement operations to half of the ions and
then measuring correlations between pairs of corresponding bits in the binary
representations of the number of centre-of-mass phonons of N particular ions.
It is shown that the state violates the inequalities and thus displays
nonclassical correlations. It is also demonstrated that it violates a Bell
inequality when the displacements are replaced by squeezing operations.


title: On quantum error-correction by classical feedback in discrete time

abstract:
  We consider the problem of correcting the errors incurred from sending
quantum information through a noisy quantum environment by using classical
information obtained from a measurement on the environment. For discrete time
Markovian evolutions, in the case of fixed measurement on the environment, we
give criteria for quantum information to be perfectly corrigible and
characterize the related feedback. Then we analyze the case when perfect
correction is not possible and, in the qubit case, we find optimal feedback
maximizing the channel fidelity.


title:
Transition from pure-state to mixed-state entanglement by random
  scattering

abstract:
  We calculate the effect of polarization-dependent scattering by disorder on
the degree of polarization-entanglement of two beams of radiation. Multi-mode
detection converts an initially pure state into a mixed state with respect to
the polarization degrees of freedom. The degree of entanglement decays
exponentially with the number of detected modes if the scattering mixes the
polarization directions and algebraically if it does not.


title: Solving the measurement problem: de Broglie-Bohm loses out to Everett

abstract:
  The quantum theory of de Broglie and Bohm solves the measurement problem, but
the hypothetical corpuscles play no role in the argument. The solution finds a
more natural home in the Everett interpretation.


title: Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

abstract:
  A complete orthonormal basis of N-qutrit unitary operators drawn from the
Pauli Group consists of the identity and 9^N-1 traceless operators. The
traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of
3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove
that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how
this result applies in specific cases. For two qutrits, the 80 traceless
operators partition into 10 MCS's. We prove that 4 of the corresponding basis
sets must be separable, while 6 must be totally entangled (and Bell-like). For
three qutrits, 728 operators partition into 28 MCS's with less rigid structure
allowing for the coexistence of separable, partially-entangled, and totally
entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur.
Every basis state is described by an N-digit trinary number consisting of the
eigenvalues of N observables constructed from the corresponding MCS.


title:
Continuous Weak Measurement and Nonlinear Dynamics in a Cold Spin
  Ensemble

abstract:
  A weak continuous quantum measurement of an atomic spin ensemble can be
implemented via Faraday rotation of an off-resonance probe beam, and may be
used to create and probe nonclassical spin states and dynamics. We show that
the probe light shift leads to nonlinearity in the spin dynamics and limits the
useful Faraday measurement window. Removing the nonlinearity allows a
non-perturbing measurement on the much longer timescale set by decoherence. The
nonlinear spin Hamiltonian is of interest for studies of quantum chaos and
real-time quantum state estimation.


title: Entropy production and fidelity for quantum many-body systems with noise

abstract:
  We study dynamical properties of systems with many interacting
Fermi-particles under the influence of static imperfections. Main attention is
payed to the time dependence of the Shannon entropy of wave packets, and to the
fidelity of the dynamics. Our question is how the entropy and fidelity are
sensitive to the noise. In our study, we use both random matrix models with
two-body interaction and dynamical models of a quantum computation. Numerical
data are compared with analytical predictions.


title:
The Green function for thermal waves induced by attosecond laser pulses
  in one and three dimensions

abstract:
  In this paper the solution of the hyperbolic Klein-Gordon thermal equation
are obtained and discussed. The analytical form of the solution - Green
functions are calculated for one and three dimensional cases. It is shown that
only in three dimensional case the undisturbed, with one value of the velocity,
thermal wave can be generated by attosecond laser pulses. The conductivity for
the space-time inside the atom is calculated and the value sigma_0=10^6
1/(Omega m) is obtained.
  Key words: Attosecond laser pulses; Klein-Gordon equation; Green functions.


title: Representation of SO(3) Group by a Maximally Entangled State

abstract:
  A representation of the SO(3) group is mapped into a maximally entangled two
qubit state according to literatures. To show the evolution of the entangled
state, a model is set up on an maximally entangled electron pair, two electrons
of which pass independently through a rotating magnetic field. It is found that
the evolution path of the entangled state in the SO(3) sphere breaks an odd or
even number of times, corresponding to the double connectedness of the SO(3)
group. An odd number of breaks leads to an additional $\pi$ phase to the
entangled state, but an even number of breaks does not. A scheme to trace the
evolution of the entangled state is proposed by means of entangled photon pairs
and Kerr medium, allowing observation of the additional $\pi$ phase.


title: Coherent quantum control of $\Lambda$-atoms through the stochastic limit

abstract:
  We investigate, using the stochastic limit method, the coherent quantum
control of a 3-level atom in $\Lambda$-configuration interacting with two laser
fields. We prove that, in the generic situation, this interaction entangles the
two lower energy levels of the atom into a single qubit, i.e. it drives at an
exponentially fast rate the atom to a stationary state which is a coherent
superposition of the two lower levels. By applying to the atom two laser fields
with appropriately chosen intensities, one can create, in principle, any
superposition of the two levels. Thus {\it relaxation} is not necessarily
synonymous of {\it decoherence}.


title:
Distinguishing quantum measurements of observables in terms of state
  transformers

abstract:
  The modern framework of state transformers, i. e., the first Kraus
representation of quantum measurement, is introduced and related both to the
known textbook concepts and to measurement-interaction evolution (the second
Kraus representation). In this framework the known kinds of measurements of
ordinary (as distinct from generalized) observables are distinguished by
necessary and sufficient conditions. Thus, repeatable,nonrepeatable, and ideal
measurements are characterized both algebraically and geometrically in terms of
polar factors of state transformers.


title: Analysis of Quantum Light Memory in Atomic Systems

abstract:
  We extend the theory to describe the quantum light memory in type atoms with
considering (lower levels coherency decay rate) and detuning for the probe and
the control fields. We obtain that with considering these parameters, group
velocity of the probe pulse does not tend to zero by turning off the control
field. We show that there are considerable decay for the probe pulse and the
stored information. Also, it is inferred that the light field does not tend to
zero when the control field is turned off. In addition, we obtain that in the
off-resonance case there is considerable distortion of the output light pulse
(with fast oscillations) that destroys the stored information. Then we present
the limitations on detuning (bandwidths) of the probe and the control fields to
achieve negligible distortion. We finally present the numerical calculations
and compare them with obtained analytical results.


title: Upper bounds on success probabilities in linear optics

abstract:
  We develop an abstract way of defining linear-optics networks designed to
perform quantum information tasks such as quantum gates. We will be mainly
concerned with the nonlinear sign shift gate, but it will become obvious that
all other gates can be treated in a similar manner. The abstract scheme is
extremely well suited for analytical as well as numerical investigations since
it reduces the number of parameters for a general setting. With that we show
numerically and partially analytically for a wide class of states that the
success probability of generating a nonlinear sign shift gate does not exceed
1/4 which to our knowledge is the strongest bound to date.


title:
Single-photon interference over 150-km transmission using silica-based
  integrated-optic interferometers for quantum cryptography

abstract:
  We have demonstrated single-photon interference over 150 km using
time-division interferometers for quantum cryptography, which were composed of
two integrated-optic asymmetric Mach-Zehnder interferometers, and balanced
gated-mode photon detectors. The observed fringe visibility was more than 80%
after 150-km transmission.


title: A note on continuous ensemble expansions of quantum states

abstract:
  Generalizing the notion of relative entropy, the difference between a priori
and a posteriori relative entropy for quantum systems is drawn. The former,
known as quantum relative entropy, is associated with quantum states
recognition. The latter -- a posteriori relative quantum entropy is shown to be
related with state reconstruction due to the following property: given a
density operator $\rho$, ensembles of pure states with Gibbs distribution with
respect to the defined distance are proved to represent the initial state
$\rho$ up to an amount of white noise (completely mixed state) which can be
made arbitrary small.


title: Spectral properties of the squeeze operator

abstract:
  We show that a single-mode squeeze operator S(z) being an unitary operator
with a purely continuous spectrum gives rise to a family of discrete real
generalized eigenvalues. These eigenvalues are closely related to the spectral
properties of S(z) and the corresponding generalized eigenvectors may be
interpreted as resonant states well known in the scattering theory. It turns
out that these states entirely characterize the action of S(z). This result is
then generalized to N-mode squeezing.


title: Quantum Walks and Reversible Cellular Automata

abstract:
  We investigate a connection between a property of the distribution and a
conserved quantity for the reversible cellular automaton derived from a
discrete-time quantum walk in one dimension. As a corollary, we give a detailed
information of the quantum walk.


title: Position and momentum observables on R and on R^3

abstract:
  We characterize all position and momentum observables on R and on R^3. We
study some of their operational properties and discuss their covariant joint
observables.