title:
A Constraint between Noncommutative Parameters of Quantum Theories in
  Noncommutative Space

abstract:
  In two-dimensional noncommutive space for the case of both position -
position and momentum - momentum noncommuting, a constraint between
noncommutative parameters is investigated. The related topic of guaranteeing
Bose - Einstein statistics in noncommutive space in the general case are
elucidated: Bose - Einstein statistics is guaranteed by the deformed Heisenberg
- Weyl algebra itself, independent of dynamics. A special character of a
dynamical system is represented by a constraint between noncommutative
parameters. The general feature of the constraint for any system is a direct
proportionality between noncommutative parameters with a proportional
coefficient depending on characteristic parameters of the system under study.
The constraint for a harmonic oscillator is illustrated.


title:
Cold Atom Physics Using Ultra-Thin Optical Fibers: Light-Induced Dipole
  Forces and Surface Interactions

abstract:
  The strong evanescent field around ultra-thin unclad optical fibers bears a
high potential for detecting, trapping, and manipulating cold atoms.
Introducing such a fiber into a cold atom cloud, we investigate the interaction
of a small number of cold Caesium atoms with the guided fiber mode and with the
fiber surface. Using high resolution spectroscopy, we observe and analyze
light-induced dipole forces, van der Waals interaction, and a significant
enhancement of the spontaneous emission rate of the atoms. The latter can be
assigned to the modification of the vacuum modes by the fiber.


title: Using quantum key distribution for cryptographic purposes: a survey

abstract:
  The appealing feature of quantum key distribution (QKD), from a cryptographic
viewpoint, is the ability to prove the information-theoretic security (ITS) of
the established keys. As a key establishment primitive, QKD however does not
provide a standalone security service in its own: the secret keys established
by QKD are in general then used by a subsequent cryptographic applications for
which the requirements, the context of use and the security properties can
vary. It is therefore important, in the perspective of integrating QKD in
security infrastructures, to analyze how QKD can be combined with other
cryptographic primitives. The purpose of this survey article, which is mostly
centered on European research results, is to contribute to such an analysis. We
first review and compare the properties of the existing key establishment
techniques, QKD being one of them. We then study more specifically two generic
scenarios related to the practical use of QKD in cryptographic infrastructures:
1) using QKD as a key renewal technique for a symmetric cipher over a
point-to-point link; 2) using QKD in a network containing many users with the
objective of offering any-to-any key establishment service. We discuss the
constraints as well as the potential interest of using QKD in these contexts.
We finally give an overview of challenges relative to the development of QKD
technology that also constitute potential avenues for cryptographic research.


title: Effects of imperfections for Shor's factorization algorithm

abstract:
  We study effects of imperfections induced by residual couplings between
qubits on the accuracy of Shor's algorithm using numerical simulations of
realistic quantum computations with up to 30 qubits. The factoring of numbers
up to N=943 show that the width of peaks, which frequencies allow to determine
the factors, grow exponentially with the number of qubits. However, the
algorithm remains operational up to a critical coupling strength $\epsilon_c$
which drops only polynomially with $\log_2 N$. The numerical dependence of
$\epsilon_c$ on $\log_2 N$ is explained by analytical estimates that allows to
obtain the scaling for functionality of Shor's algorithm on realistic quantum
computers with a large number of qubits.


title:
Strongly Correlated Two-Photon Transport in One-Dimensional Waveguide
  Coupled to A Two-Level System

abstract:
  We show that two-photon transport is strongly correlated in one-dimensional
waveguide coupled to a two-level system. The exact S-matrix is constructed
using a generalized Bethe-Ansatz technique. We show that the scattering
eigenstates of this system include a two-photon bound state that passes through
the two-level system as a composite single particle. Also, the two-level system
can induce effective attractive or repulsive interactions in space for photons.
This general procedure can be applied to the Anderson model as well.


title: Turning the Liar paradox into a metatheorem of Basic logic

abstract:
  We show that self-reference can be formalized in Basic logic by means of the
new connective @, called "entanglement". In fact, the property of
non-idempotence of the connective @ is a metatheorem, which states that a
self-entangled sentence loses its own identity. This prevents having
self-referential paradoxes in the corresponding metalanguage. In this context,
we introduce a generalized definition of self-reference, which is needed to
deal with the multiplicative connectives of substructural logics.


title:
Initializing a Quantum Register from Mott Insulator States in Optical
  Lattices

abstract:
  We propose and quantitatively develop two schemes to quickly and accurately
generate a stable initial configuration of neutral atoms in optical microtraps
by extraction from the Mott insulator state in optical lattices. We show that
thousands of atoms may be extracted and stored in the ground states of optical
microtrap arrays with one atom per trap in one operational process
demonstrating massive scalability. The failure probability during extraction in
the first scheme can be made sufficiently small (10^{-4}) to initialize a large
scale quantum register with high fidelity. A complementary faster scheme with
more extracted atoms but lower fidelity is also developed.


title: Quantum walks on quotient graphs

abstract:
  A discrete-time quantum walk on a graph is the repeated application of a
unitary evolution operator to a Hilbert space corresponding to the graph. If
this unitary evolution operator has an associated group of symmetries, then for
certain initial states the walk will be confined to a subspace of the original
Hilbert space. Symmetries of the original graph, given by its automorphism
group, can be inherited by the evolution operator. We show that a quantum walk
confined to the subspace corresponding to this symmetry group can be seen as a
different quantum walk on a smaller quotient graph. We give an explicit
construction of the quotient graph for any subgroup of the automorphism group
and illustrate it with examples. The automorphisms of the quotient graph which
are inherited from the original graph are the original automorphism group
modulo the subgroup used to construct it. We then analyze the behavior of
hitting times on quotient graphs. Hitting time is the average time it takes a
walk to reach a given final vertex from a given initial vertex. It has been
shown in earlier work [Phys. Rev. A {\bf 74}, 042334 (2006)] that the hitting
time can be infinite. We give a condition which determines whether the quotient
graph has infinite hitting times given that they exist in the original graph.
We apply this condition for the examples discussed and determine which quotient
graphs have infinite hitting times. All known examples of quantum walks with
fast hitting times correspond to systems with quotient graphs much smaller than
the original graph; we conjecture that the existence of a small quotient graph
with finite hitting times is necessary for a walk to exhibit a quantum
speed-up.


title: Eavesdropping of quantum communication from a non-inertial frame

abstract:
  We introduce a relativistic version of quantum encryption protocol by
considering two inertial observers who wish to securely transmit quantum
information encoded in a free scalar quantum field state forming Minkowski
particles. In a non-relativistic setting a certain amount of shared classical
resources is necessary to perfectly encrypt the state. We show that in the case
of a uniformly accelerated eavesdropper the communicating parties need to share
(asymptotically in the limit of infinite acceleration) just half of the
classical resources.


title: Asymptotically noise decoupling for Markovian open quantum systems

abstract:
  The noise decoupling problem is investigated for general N-level Markovian
open quantum systems. Firstly, the concept of Cartan decomposition of the Lie
algebra $su(N)$ is introduced as a tool of designing control Hamiltonians.
Next, under certain assumptions, it is shown that a part of variables of the
coherence vector of the system density matrix can be asymptotically decoupled
from the environmental noises. The resulting noise decoupling scheme is applied
to one-qubit, qutrit and two-qubit quantum systems, by which the coherence
evolution of the one-qubit and qutrit systems can always be asymptotically
preserved, while, for two-qubit systems, our findings indicate that evolution
of some variables can be preserved only for some initial states.


title:
First direct determination of the Boltzmann constant by an optical
  method

abstract:
  We have recorded the Doppler profile of a well-isolated rovibrational line in
the \nu2 band of 14NH3. Ammonia gas was placed in an absorption cell
thermalized by a water-ice bath. By extrapolating to zero pressure, we have
deduced the Doppler width which gives a first measurement of the Boltzmann
constant, kB, by laser spectroscopy. A relative uncertainty of 2x10-4 has been
obtained. The present determination should be significantly improved in the
near future and contribute to a new definition of the kelvin.


title: PT-Symmetric, Quasi-Exactly Solvable matrix Hamiltonians

abstract:
  Matrix quasi exactly solvable operators are considered and new conditions are
determined to test whether a matrix differential operator possesses one or
several finite dimensional invariant vector spaces. New examples of $2\times
2$-matrix quasi exactly solvable operators are constructed with the emphasis
set on PT-symmetric Hamiltonians.


title: Quantum theory: the role of microsystems and macrosystems

abstract:
  We stress the notion of statistical experiment, which is mandatory for
quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which
provides the most general framework to deal with statistical experiments giving
evidence for particles. In this approach particles appear as interaction
carriers between preparation and registration apparatuses. We further briefly
point out the more modern and versatile formalism of quantum theory, stressing
the relevance of probabilistic concepts in its formulation. At last we discuss
the role of macrosystems, focusing on quantum field theory for their
description and introducing for them objective state parameters.


title: Polarizability measurements in a molecule near-field interferometer

abstract:
  We apply near-field matter-wave interferometry to determine the absolute
scalar polarizability of the fullerenes C$_{60}$ and C$_{70}$. A key feature of
our experiment is the combination of good transmission and high spatial
resolution, gained by wide molecular beams passing through sub-micron gratings.
This allows to significantly facilitate the observation of field-dependent beam
shifts. We thus measure the polarizability to be $\alpha=88.9 \pm 0.9 \pm 5.1
  \rm \AA^{3}$ for C$_{60}$ and to $\alpha = 108.5 \pm 2.0 \pm 6.2 \rm \AA^{3}$
for C$_{70}$.


title: Coherent electron pair. Electromagnetic field

abstract:
  It is shown that relative coordinate and momentum of coherent electron pair
have the meaning of observables with the help of quadrupole and magnetic
moments. Distributions of quadrupole terms of scalar potential are shown. These
distributions have nonclassical properties.


title: Quantum Theory as Efficient Representation of Probabilistic Information

abstract:
  Quantum experiments yield random data. We show that the most efficient way to
store this empirical information by a finite number of bits is by means of the
vector of square roots of observed relative frequencies. This vector has the
unique property that its dispersion becomes invariant of the underlying
probabilities, and therefore invariant of the physical parameters. This also
extends to the complex square roots, and it remains true under a unitary
transformation. This reveals quantum theory as a theory for making predictions
which are as accurate as the input information, without any statistical loss.
Our analysis also suggests that from the point of view of information a
slightly more accurate theory than quantum theory should be possible.


title: Generation of EPR-entangled radiation through an atomic reservoir

abstract:
  We propose a scheme for generating two-mode squeezing in high-Q resonators
using a beam of atoms with random arrival times, which acts as a reservoir for
the field. The scheme is based on four-wave mixing processes leading to
emission into two cavity modes, which are resonant with the Rabi sidebands of
the atomic dipole transition, driven by a saturating classical field. At steady
state the cavity modes are in an Einstein-Podolski-Rosen (EPR) state, whose
degree of entanglement is controlled by the intensity and the frequency of the
transverse field. This scheme is robust against stochastic fluctuations in the
atomic beam, does not require atomic detection nor velocity selection, and can
be realized by presently available experimental setups with microwave
resonators.


title: Reduction of Quantum Phase Fluctuations Implies Antibunching of Photon

abstract:
  A clear physical meaning of the Carruthers-Nieto symmetric quantum phase
fluctuation parameter (U) has been provided in Susskind Glogower and Barnett
Pegg formalism of quantum phase and it is shown that the reduction of phase
fluctuation parameter U with respect to its coherent state value corresponds to
an antibunched state. Thus nonclassicality of a state may be manifested through
the phase fluctuation parameters. As examples, quantum phase fluctuations in
different optical processes, such as four wave mixing, six wave mixing and
second harmonic generation have been studied by using Carruthers-Nieto quantum
phase fluctuation parameters. The operators required for the calculation of
quantum phase fluctuations are expressed in closed analytical forms (up to
second order in coupling constant). It is also found that the reduction of
phase fluctuations compared to their initial values are possible in all three
cases which means nonclassical (antibunched) state exists in all these cases.


title:
Experimental Observation of Environment-induced Sudden Death of
  Entanglement

abstract:
  We demonstrate the difference between local, single-particle dynamics and
global dynamics of entangled quantum systems coupled to independent
environments. Using an all-optical experimental setup, we show that, while the
environment-induced decay of each system is asymptotic, quantum entanglement
may suddenly disappear. This "sudden death" constitutes yet another distinct
and counter-intuitive trait of entanglement.


title: On the normal ordering of multi-mode boson operators

abstract:
  In this article combinatorial aspects of normal ordering annihilation and
creation operators of a multi-mode boson system are discussed. The modes are
assumed to be coupled since otherwise the problem of normal ordering is reduced
to the corresponding problem of the single-mode case. To describe the normal
ordering in the multi-mode case for each mode a colour is introduced and
coloured contractions are considered. A depiction for coloured contractions via
coloured linear representations is given. In analogy to the single-mode case
associated coloured Stirling numbers are defined as coefficients appearing in
the process of normal ordering powers of the number operators. Several
properties of these coloured Stirling numbers are discussed.


title:
Phase Space Representations and Perturbation Theory for Continuous-time
  Histories

abstract:
  We consider two technical developments of the formalism of continuous-time
histories. First, we provide an explicit description of histories of the simple
harmonic oscillator on the classical histories phase space, comparing and
contrasting the Q, P and Wigner representations; we conclude that a
representation based on coherent states is the most appropriate. Second, we
demonstrate a generic method for implementing a perturbative approach for
interacting theories in the histories formalism, using the quartic anharmonic
oscillator. We make use of the identification of the closed-time path (CTP)
generating functional with the decoherence functional to develop a perturbative
expansion for the latter up to second order in the coupling constant. We
consider both configuration space and phase space histories.


title:
Some observations on two-way finite automata with quantum and classical
  states

abstract:
  {\it Two-way finite automata with quantum and classical states} (2qcfa's)
were introduced by Ambainis and Watrous. Though this computing model is more
restricted than the usual {\it two-way quantum finite automata} (2qfa's) first
proposed by Kondacs and Watrous, it is still more powerful than the classical
counterpart. In this note, we focus on dealing with the operation properties of
2qcfa's. We prove that the Boolean operations (intersection, union, and
complement) and the reversal operation of the class of languages recognized by
2qcfa's with error probabilities are closed; as well, we verify that the
catenation operation of such class of languages is closed under certain
restricted condition. The numbers of states of these 2qcfa's for the above
operations are presented. Some examples are included, and $\{xx^{R}|x\in
\{a,b\}^{*},#_{x}(a)=#_{x}(b)\}$ is shown to be recognized by 2qcfa with
one-sided error probability, where $x^{R}$ is the reversal of $x$, and
$#_{x}(a)$ denotes the $a$'s number in string $x$.


title:
The Bound of Entanglement of Superpositions with More Than Two
  Components

abstract:
  A bipartite quantum state (for two systems in any dimensions) can be
decomposed as a superposition of many components. For a superposition of more
than two components we prove that there is a bound of the entanglement of the
superposition state which can be expressed according to entanglements of its
component states. Especially, if the component states are mutually
bi-orthogonal, the entanglement of the superposition state can be exactly given
in terms of the entanglements of the states being superposed.


title:
Background Independent Quantum Mechanics, Metric of Quantum States, and
  Gravity: A Comprehensive Perspective

abstract:
  This paper presents a comprehensive perspective of the metric of quantum
states with a focus on the background independent metric structures. We also
explore the possibilities of geometrical formulations of quantum mechanics
beyond the quantum state space and Kahler manifold. The metric of quantum
states in the classical configuration space with the pseudo-Riemannian
signature and its possible applications are explored. On contrary to the common
perception that a metric for quantum state can yield a natural metric in the
configuration space with the limit when Planck constant vanishes, we obtain the
metric of quantum states in the configuration space without imposing this
limiting condition. Here, Planck constant is absorbed in the quantity like Bohr
radii. While exploring the metric structure associated with Hydrogen like atom,
we witness another interesting finding that the invariant lengths appear in the
multiple of Bohr radii.


title: Quantum Dynamics with Bohmian Trajectories

abstract:
  We describe the advantages and disadvantages of numerical methods when
Bohmian trajectory-grids are used for numerical simulations of quantum
dynamics. We focus on the crucial non crossing property of Bohmian
trajectories, which numerically must be paid careful attention to. Failure to
do so causes instabilities or leads to false simulations.


title:
Minimum detection efficiency for a loophole-free atom-photon Bell
  experiment

abstract:
  In Bell experiments, one problem is to achieve high enough photodetection to
ensure that there is no possibility of describing the results via a local
hidden-variable model. Using the Clauser-Horne inequality and a two-photon
non-maximally entangled state, a photodetection efficiency higher than 0.67 is
necessary. Here we discuss atom-photon Bell experiments. We show that, assuming
perfect detection efficiency of the atom, it is possible to perform a
loophole-free atom-photon Bell experiment whenever the photodetection
efficiency exceeds 0.50.


title: Thermal quantum electrodynamics of nonrelativistic charged fluids

abstract:
  The theory relevant to the study of matter in equilibrium with the radiation
field is thermal quantum electrodynamics (TQED). We present a formulation of
the theory, suitable for non relativistic fluids, based on a joint functional
integral representation of matter and field variables. In this formalism
cluster expansion techniques of classical statistical mechanics become
operative. They provide an alternative to the usual Feynman diagrammatics in
many-body problems which is not perturbative with respect to the coupling
constant. As an application we show that the effective Coulomb interaction
between quantum charges is partially screened by thermalized photons at large
distances. More precisely one observes an exact cancellation of the dipolar
electric part of the interaction, so that the asymptotic particle density
correlation is now determined by relativistic effects. It has still the
$r^{-6}$ decay typical for quantum charges, but with an amplitude strongly
reduced by a relativistic factor.


title:
A General Framework for Recursive Decompositions of Unitary Quantum
  Evolutions

abstract:
  Decompositions of the unitary group U(n) are useful tools in quantum
information theory as they allow one to decompose unitary evolutions into local
evolutions and evolutions causing entanglement. Several recursive
decompositions have been proposed in the literature to express unitary
operators as products of simple operators with properties relevant in
entanglement dynamics. In this paper, using the concept of grading of a Lie
algebra, we cast these decompositions in a unifying scheme and show how new
recursive decompositions can be obtained. In particular, we propose a new
recursive decomposition of the unitary operator on $N$ qubits, and we give a
numerical example.


title: Computation at a distance

abstract:
  We consider a model of computation motivated by possible limitations on
quantum computers. We have a linear array of n wires, and we may perform
operations only on pairs of adjacent wires. Our goal is to build a circuits
that perform specified operations spanning all n wires. We show that the
natural lower bound of n-1 on circuit depth is nearly tight for a variety of
problems, and we prove linear upper bounds for additional problems. In
particular, using only gates adding a wire (mod 2) into an adjacent wire, we
can realize any linear operation in GL_n(2) as a circuit of depth 5n. We show
that some linear operations require depth at least 2n+1.


title: Investigation of a single-photon source based on quantum interference

abstract:
  We report on an experimental investigation of a single-photon source based on
a quantum interference effect first demonstrated by Koashi, Matsuoka, and
Hirano [Phys. Rev. A 53, 3621 (1996)]. For certain types of measurement-based
quantum information processing applications this technique may be useful as a
high rate, but random, source of single photons.


title: Physical properties of the Schur complement of local covariance matrices

abstract:
  General properties of global covariance matrices representing bipartite
Gaussian states can be decomposed into properties of local covariance matrices
and their Schur complements. We demonstrate that given a bipartite Gaussian
state $\rho_{12}$ described by a $4\times 4$ covariance matrix \textbf{V}, the
Schur complement of a local covariance submatrix $\textbf{V}_1$ of it can be
interpreted as a new covariance matrix representing a Gaussian operator of
party 1 conditioned to local parity measurements on party 2. The connection
with a partial parity measurement over a bipartite quantum state and the
determination of the reduced Wigner function is given and an operational
process of parity measurement is developed. Generalization of this procedure to
a $n$-partite Gaussian state is given and it is demonstrated that the $n-1$
system state conditioned to a partial parity projection is given by a
covariance matrix such as its $2 \times 2$ block elements are Schur complements
of special local matrices.


title:
Scheme for remote implementation of partially unknown quantum operation
  of two qubits in cavity QED

abstract:
  By constructing the recovery operations of the protocol of remote
implementation of partially unknown quantum operation of two qubits [An Min
Wang: PRA, \textbf{74}, 032317(2006)], we present a scheme to implement it in
cavity QED. Long-lived Rydberg atoms are used as qubits, and the interaction
between the atoms and the field of cavity is a nonresonant one. Finally, we
analyze the experimental feasibility of this scheme.


title:
On Nondemolition Measurements of Photon Number: A Comment on
  quant-ph/0612031

abstract:
  Experimental results stated in quant-ph/0612031 are seminal: The authors have
realized nondemolition measurements of the photon number. As to the
interpretation of the results, it seems to be less than convincing: The
treatment of the system state and of the role of measurement is not compatible
with the conventional point of view. We propose an adequate treatment, in which
the experimental results are a manifestation of a partial Zeno effect (a
slowdown of relaxation).


title:
Noise resilience and entanglement evolution in two non-equivalent
  classes of quantum algorithms

abstract:
  The speed-up provided by quantum algorithms with respect to their classical
counterparts is at the origin of scientific interest in quantum computation.
However, the fundamental reasons for such a speed-up are not yet completely
understood and deserve further attention. In this context, the classical
simulation of quantum algorithms is a useful tool that can help us in gaining
insight. Starting from the study of general conditions for classical
simulation, we highlight several important differences between two
non-equivalent classes of quantum algorithms. We investigate their performance
under realistic conditions by quantitatively studying their resilience with
respect to static noise. This latter refers to errors affecting the inital
preparation of the register used to run an algorithm. We also compare the
evolution of the entanglement involved in the different computational
processes.


title: Information and measurement in generally covariant quantum theory

abstract:
  Due to the absence of an external, classical time variable, the probabilistic
predictions of covariant quantum theory are ambiguous when multiple
measurements are considered. Here, we introduce an information theoretic
framework to the covariant formalism, and use it to interpret the measurement
process. We find that the time ordering of measurements emerges as an entropy
relationship in the state of the observers, giving unique probabilities for
multiple measurements. This approach suggests a new, fully self-contained
probability interpretation for generally covariant quantum physics, which makes
use of a quantum mechanical description of the observer, in contrast to
standard quantum mechanics which assumes an external, classical observer.


title:
Factorization of Quantum Density Matrices According to Bayesian and
  Markov Networks

abstract:
  We show that any quantum density matrix can be represented by a Bayesian
network (a directed acyclic graph), and also by a Markov network (an undirected
graph). We show that any Bayesian or Markov net that represents a density
matrix, is logically equivalent to a set of conditional independencies
(symmetries) satisfied by the density matrix. We show that the d-separation
theorems of classical Bayesian and Markov networks generalize in a simple and
natural way to quantum physics. The quantum d-separation theorems are shown to
be closely connected to quantum entanglement. We show that the graphical rules
for d-separation can be used to detect pairs of nodes (or of node sets) in a
graph that are unentangled. CMI entanglement (a.k.a. squashed entanglement), a
measure of entanglement originally discovered by analyzing Bayesian networks,
is an important part of the theory of this paper.


title:
An explicit family of unitaries with exponentially minimal length Pauli
  geodesics

abstract:
  Recently, Nielsen et al have proposed a geometric approach to quantum
computation. They've shown that the size of the minimum quantum circuits
implementing a unitary U, up to polynomial factors, equals to the length of
minimal geodesic from identity I through U. They've investigated a large class
of solutions to the geodesic equation, called Pauli geodesics. They've raised a
natural question whether we can explicitly construct a family of unitaries U
that have exponentially long minimal length Pauli geodesics? We give a positive
answer to this question.


title: Zero modes of various graphene configurations from the index theorem

abstract:
  In this article we consider a graphene sheet that is folded in various
compact geometries with arbitrary topology described by a certain genus, $g$.
While the Hamiltonian of these systems is defined on a lattice one can take the
continuous limit. The obtained Dirac-like Hamiltonian describes well the low
energy modes of the initial system. Starting from first principles we derive an
index theorem that corresponds to this Hamiltonian. This theorem relates the
zero energy modes of the graphene sheet with the topology of the compact
lattice. For $g=0$ and $g=1$ these results coincide with the analytical and
numerical studies performed for fullerene molecules and carbon nanotubes while
for higher values of $g$ they give predictions for more complicated molecules.


title: Signatures for generalized macroscopic superpositions

abstract:
  We develop criteria sufficient to enable detection of macroscopic coherence
where there are not just two macroscopically distinct outcomes for a pointer
measurement, but rather a spread of outcomes over a macroscopic range. The
criteria provide a means to distinguish a macroscopic quantum description from
a microscopic one based on mixtures of microscopic superpositions of
pointer-measurement eigenstates. The criteria are applied to Gaussian-squeezed
and spin-entangled states.


title: Factorizing Numbers with the Gauss Sum Technique: NMR Implementations

abstract:
  Several physics-based algorithms for factorizing large number were recently
published. A notable recent one by Schleich et al. uses Gauss sums for
distinguishing between factors and non-factors. We demonstrate two NMR
techniques that evaluate Gauss sums and thus implement their algorithm. The
first one is based on differential excitation of a single spin magnetization by
a cascade of RF pulses. The second method is based on spatial averaging and
selective refocusing of magnetization for Gauss sums corresponding to factors.
All factors of 16637 and 52882363 are successfully obtained.


title: Exact solution of Schrodinger equation for Pseudoharmonic potential

abstract:
  Exact solution of Schrodinger equation for the pseudoharmonic potential is
obtained for an arbitrary angular momentum. The energy eigenvalues and
corresponding eigenfunctions are calculated by Nikiforov-Uvarov method.
Wavefunctions are expressed in terms of Jacobi polynomials. The energy
eigenvalues are calculated numerically for some values of l and n with n<5 for
some diatomic molecules.


title: Roughness suppression via rapid current modulation on an atom chip

abstract:
  We present a method to suppress the potential roughness of a wire-based,
magnetic atom guide: modulating the wire current at a few tens of kHz, the
potential roughness, which is proportional to the wire current, averages to
zero. Using ultra-cold $^{87}{\rm Rb}$ clouds, we show experimentally that
modulation reduces the roughness by at least of a factor five without
measurable heating or atom loss. This roughness suppression results in a
dramatic reduction of the damping of center of mass oscillations.


title: Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion

abstract:
  We present a method of simulating the Dirac equation in 3+1 dimensions for a
free spin-1/2 particle in a single trapped ion. The Dirac bispinor is
represented by four ionic internal states, and position and momentum of the
Dirac particle are associated with the respective ionic variables. We show also
how to simulate the simplified 1+1 case, requiring the manipulation of only two
internal levels and one motional degree of freedom. Moreover, we study relevant
quantum-relativistic effects, like the Zitterbewegung and Klein's paradox, the
transition from massless to massive fermions, with the relativistic and
nonrelativistic limits, via the tuning of controllable experimental parameters.


title:
Two-Mode Squeezed States and Entangled States of Two Mechanical
  Resonators

abstract:
  We study a device consisting of a dc-SQUID with two sections of its loop
acting as two mechanical resonators. An analog of the parametric
down-conversion process in quantum optics can be realized with this device. We
show that a two-mode squeezed state can be generated for two overdamped
mechanical resonators, where the damping constants of the two mechanical
resonators are larger than the coupling strengths between the dc-SQUID and the
two mechanical resonators. Thus we show that entangled states of these two
mechanical resonators can be generated.


title:
C++QED: An object-oriented framework for wave-function simulations of
  cavity QED systems

abstract:
  We present a framework for efficiently performing Monte Carlo wave-function
simulations in cavity QED with moving particles. It relies heavily on the
object-oriented programming paradigm as realised in C++, and is extensible and
applicable for simulating open interacting quantum dynamics in general. The
user is provided with a number of ``elements'', eg pumped moving particles,
pumped lossy cavity modes, and various interactions to compose complex
interacting systems, which contain several particles moving in electromagnetic
fields of various configurations, and perform wave-function simulations on such
systems. A number of tools are provided to facilitate the implementation of new
elements.


title: On the Pauli graphs of N-qudits

abstract:
  A comprehensive graph theoretical and finite geometrical study of the
commutation relations between the generalized Pauli operators of N-qudits is
performed in which vertices/points correspond to the operators and edges/lines
join commuting pairs of them. As per two-qubits, all basic properties and
partitionings of the corresponding Pauli graph are embodied in the geometry of
the generalized quadrangle of order two. Here, one identifies the operators
with the points of the quadrangle and groups of maximally commuting subsets of
the operators with the lines of the quadrangle. The three basic partitionings
are (a) a pencil of lines and a cube, (b) a Mermin's array and a bipartite-part
and (c) a maximum independent set and the Petersen graph. These factorizations
stem naturally from the existence of three distinct geometric hyperplanes of
the quadrangle, namely a set of points collinear with a given point, a grid and
an ovoid, which answer to three distinguished subsets of the Pauli graph,
namely a set of six operators commuting with a given one, a Mermin's square,
and set of five mutually non-commuting operators, respectively. The generalized
Pauli graph for multiple qubits is found to follow from symplectic polar spaces
of order two, where maximal totally isotropic subspaces stand for maximal
subsets of mutually commuting operators. The substructure of the (strongly
regular) N-qubit Pauli graph is shown to be pseudo-geometric, i. e., isomorphic
to a graph of a partial geometry. Finally, the (not strongly regular) Pauli
graph of a two-qutrit system is introduced; here it turns out more convenient
to deal with its dual in order to see all the parallels with the two-qubit case
and its surmised relation with the generalized quadrangle Q(4, 3), the dual
ofW(3).


title: Non-contact rack and pinion powered by the lateral Casimir force

abstract:
  The lateral Casimir force is employed to propose a design for a potentially
wear-proof rack and pinion with no contact, which can be miniaturized to
nano-scale. The robustness of the design is studied by exploring the relation
between the pinion velocity and the rack velocity in the different domains of
the parameter space. The effects of friction and added external load are also
examined. It is shown that the device can hold up extremely high velocities,
unlike what the general perception of the Casimir force as a weak interaction
might suggest.


title: Infinite plane wave evolution in a 1-D square quantum barrier

abstract:
  We analytically compute the time evolution of an initial infinite plane wave
in the presence of a 1-dimensional square quantum barrier. This calculation
generalizes the analysis of the shutter problem and sets the basis for the
calculation of the transmission of general wave packets, aiming to work out the
explicit contribution of the resonant (Gamow) states. The method relies mainly
on the analytical properties of the Green function. The role of separate
boundary conditions on the Green function and on the evolution equation is
highlighted. As in previous works on related problems, only the determination
of the resonant momenta requires numerical methods.


title: Nonclassical characteristic functions for highly sensitive measurements

abstract:
  Characteristic functions are shown to be useful for highly sensitive
measurements. Redistributions of motional Fock states of a trapped atom can be
directly monitored via the most fragile nonclassical part of the characteristic
function. The method can also be used for decoherence measurements in optical
quantum-information systems.


title: 'Designer atoms' for quantum metrology

abstract:
  Entanglement is recognized as a key resource for quantum computation and
quantum cryptography. For quantum metrology, the use of entangled states has
been discussed and demonstrated as a means of improving the signal-to-noise
ratio. In addition, entangled states have been used in experiments for
efficient quantum state detection and for the measurement of scattering
lengths. In quantum information processing, manipulation of individual quantum
bits allows for the tailored design of specific states that are insensitive to
the detrimental influences of an environment. Such 'decoherence-free subspaces'
protect quantum information and yield significantly enhanced coherence times.
Here we use a decoherence-free subspace with specifically designed entangled
states to demonstrate precision spectroscopy of a pair of trapped Ca+ ions; we
obtain the electric quadrupole moment, which is of use for frequency standard
applications. We find that entangled states are not only useful for enhancing
the signal-to-noise ratio in frequency measurements - a suitably designed pair
of atoms also allows clock measurements in the presence of strong technical
noise. Our technique makes explicit use of non-locality as an entanglement
property and provides an approach for 'designed' quantum metrology.


title: Optimal quantum estimation of loss in bosonic channels

abstract:
  We address the estimation of the loss parameter of a bosonic channel probed
by Gaussian signals. We derive the ultimate quantum bound on precision and show
that no improvement may be obtained by having access to the environment degrees
of freedom. We found that, for small losses, the variance of the optimal
estimator is proportional to the loss parameter itself, a result that
represents a qualitative improvement over the shot noise limit. An observable
based on the symmetric logarithmic derivative is derived, which attains the
ultimate bound and may be implemented using Gaussian operations and photon
counting.


title:
No-signaling, dynamical independence, and the local observability
  principle

abstract:
  Within a general operational framework I show that a-causality at a distance
of "local actions" (the so-called "no-signaling") is a direct consequence of
commutativity of local transformations, i.e. of dynamical independence. On the
other hand, the tensor product of Quantum Mechanics is not just a consequence
of such dynamical independence, but needs in addition the Local Observability
Principle.


title:
On the precise connection between the GRW master-equation and
  master-equations for the description of decoherence

abstract:
  We point out that the celebrated GRW master-equation is invariant under
translations, reflecting the homogeneity of space, thus providing a particular
realization of a general class of translation-covariant Markovian
master-equations. Such master-equations are typically used for the description
of decoherence due to momentum transfers between system and environment.
Building on this analogy we show the exact relationship between the GRW
master-equation and decoherence master-equations, further providing a
collisional decoherence model formally equivalent to the GRW master-equation.
This allows for a direct comparison of order of magnitudes of relevant
parameters. This formal analogy should not lead to confusion on the utterly
different spirit of the two research fields, in particular it has to be
stressed that the decoherence approach does not lead to a solution of the
measurement problem. Building on this analogy however the feasibility of the
extension of spontaneous localization models in order to avoid the infinite
energy growth is discussed. Apart from a particular case considered in the
paper, it appears that the amplification mechanism is generally spoiled by such
modifications.


title: Operational axioms for a C*-algebraic formulation of Quantum Mechanics

abstract:
  A C*-algebra formulation of Quantum Mechanics is derived from purely
operational axioms in which the primary role is played by the "transformations"
that the system undergoes in the course of an "experiment". The notion of the
{\em adjoint} of a transformation is based on the postulated existence of
"faithful states" that allows one to calibrate the experimental apparatus.


title:
Concentration and purification of entanglement for qubit systems with
  ancillary cavity fields

abstract:
  We propose schemes for entanglement concentration and purification for qubit
systems encoded in flying atomic pairs. We use a cavity-quantum electrodynamics
setting as the paradigmatic scenario within which our proposals can be
implemented. Maximally entangled pure states of qubits can be produced as a
result of our protocols. In particular, the concentration protocol yields Bell
states with the largest achievable theoretical probability while the
purification scheme produces arbitrarily pure Bell states. The requirements for
the implementation of these protocols are modest, within the state of the art,
and we address all necessary steps in two specific set-ups based on
experimentally mature microwave technology.


title:
Entanglement in continuous variable systems: Recent advances and current
  perspectives

abstract:
  We review the theory of continuous-variable entanglement with special
emphasis on foundational aspects, conceptual structures, and mathematical
methods. Much attention is devoted to the discussion of separability criteria
and entanglement properties of Gaussian states, for their great practical
relevance in applications to quantum optics and quantum information, as well as
for the very clean framework that they allow for the study of the structure of
nonlocal correlations. We give a self-contained introduction to phase-space and
symplectic methods in the study of Gaussian states of infinite-dimensional
bosonic systems. We review the most important results on the separability and
distillability of Gaussian states and discuss the main properties of bipartite
entanglement. These include the extremal entanglement, minimal and maximal, of
two-mode mixed Gaussian states, the ordering of two-mode Gaussian states
according to different measures of entanglement, the unitary (reversible)
localization, and the scaling of bipartite entanglement in multimode Gaussian
states. We then discuss recent advances in the understanding of entanglement
sharing in multimode Gaussian states, including the proof of the monogamy
inequality of distributed entanglement for all Gaussian states, and its
consequences for the characterization of multipartite entanglement. We finally
review recent advances and discuss possible perspectives on the qualification
and quantification of entanglement in non Gaussian states, a field of research
that is to a large extent yet to be explored.

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


title: Rotationally invariant bipartite states and bound entanglement

abstract:
  We consider rotationally invariant states in $\mathbb{C}^{N_{1}}\ot
\mathbb{C}^{N_{2}}$ Hilbert space with even $N_{1}\geq 4$ and arbitrary
$N_{2}\geq N_{1}$, and show that in such case there always exist states which
are inseparable and remain positive after partial transposition, and thus the
PPT criterion does not suffice to prove separability of such systems. We
demonstrate it applying a map developed recently by Breuer [H.-P. Breuer, Phys.
Rev. Lett {\bf 97}, 080501 (2006)] to states that remain invariant after
partial time reversal.


title:
Is PT-symmetric quantum mechanics just quantum mechanics in a
  non-orthogonal basis?

abstract:
  One of the postulates of quantum mechanics is that the Hamiltonian is
Hermitian, as this guarantees that the eigenvalues are real. Recently there has
been an interest in asking if $H^\dagger = H$ is a necessary condition, and has
lead to the development of PT-symmetric quantum mechanics. This note shows that
any finite physically acceptable non-Hermitian Hamiltonian is equivalent to
doing ordinary quantum mechanics in a non-orthogonal basis. In particular, this
means that there is no experimental distinction between PT-symmetric quantum
mechanics and ordinary quantum mechanics for finite systems. In particular, the
claim that PT-symmetric quantum mechanics allows for faster evolution than
Hermitian quantum mechanics is shown to be a problem of physical
interpretation.


title:
Scattering of polarized laser light by an atomic gas in free space: a
  QSDE approach

abstract:
  We propose a model, based on a quantum stochastic differential equation
(QSDE), to describe the scattering of polarized laser light by an atomic gas.
The gauge terms in the QSDE account for the direct scattering of the laser
light into different field channels. Once the model has been set, we can
rigorously derive quantum filtering equations for balanced polarimetry and
homodyne detection experiments, study the statistics of output processes and
investigate a strong driving, weak coupling limit.


title: Probability, Arrow of Time and Decoherence

abstract:
  This paper relates both to the metaphysics of probability and to the physics
of time asymmetry. Using the formalism of decoherent histories, it investigates
whether intuitions about intrinsic time directedness that are often associated
with probability can be justified in the context of no-collapse approaches to
quantum mechanics. The standard (two-vector) approach to time symmetry in the
decoherent histories literature is criticised, and an alternative approach is
proposed, based on two decoherence conditions ('forwards' and 'backwards')
within the one-vector formalism. In turn, considerations of forwards and
backwards decoherence and of decoherence and recoherence suggest that a
time-directed interpretation of probabilities, if adopted, should be both
contingent and perspectival.


title: Complementarity in a macroscopic observation

abstract:
  Complementarity is usually considered as a phenomenon of microscopic systems.
In this paper we report an experimental observation of complementarity in the
correlated double-slit interference with a pseudothermal light source. The
thermal light beam is divided into test and reference beams which are
correlated with each other. The double-slit is set in the test arm, and the
interference pattern can be observed in the intensity correlation between the
two arms. The experimental results show that the disappearance of interference
fringe depends on whether which-path information is gained through the
reference arm. The experiment therefore witnesses the complementarity occurring
in a macroscopic system.


title: Bound state solution of the Schrodinger equation for Mie potential

abstract:
  Exact solution of Schrodinger equation for the Mie potential is obtained for
an arbitrary angular momentum. The energy eigenvalues and the corresponding
wavefunctions are calculated by the use of the Nikiforov-Uvarov method.
Wavefunctions are expressed in terms of Jacobi polynomials. The bound states
are calculated numerically for some values of l and $n$ with n<5. They are
applied to several diatomic molecules.


title:
Canonical formalism and quantization of perturbative sector of
  higher-derivative theories

abstract:
  The theories defined by Lagrangians containing second time derivative are
considered. It is shown that if the second derivatives enter only the terms
multiplied by coupling constant one can consistently define the perturbative
sector via Dirac procedure. The possibility of introducing standard canonical
variables is analysed in detail. The ambiguities in quantization procedure are
pointed out.


title: Ultra-dispersive adaptive prism

abstract:
  We have experimentally demonstrated an ultra-dispersive optical prism made
from coherently driven Rb atomic vapor. The prism possesses spectral angular
dispersion that is six orders of magnitude higher than that of a prism made of
optical glass; it is the highest spectral angular dispersion that has ever been
shown (such angular dispersion allows one to spatially resolve light beams with
different frequencies separated by a few kHz). The prism operates near the
resonant frequency of atomic vapor and its dispersion is optically controlled
by a coherent driving field.


title: SU(2) nonstandard bases: the case of mutually unbiased bases

abstract:
  This paper deals with bases in a finite-dimensional Hilbert space. Such a
space can be realized as a subspace of the representation space of SU(2)
corresponding to an irreducible representation of SU(2). The representation
theory of SU(2) is reconsidered via the use of two truncated deformed
oscillators. This leads to replace the familiar scheme {j^2, j_z} by a scheme
{j^2, v(ra)}, where the two-parameter operator v(ra) is defined in the
enveloping algebra of the Lie algebra su(2). The eigenvectors of the commuting
set of operators {j^2, v(ra)} are adapted to a tower of chains SO(3) > C(2j+1),
2j integer, where C(2j+1) is the cyclic group of order 2j+1. In the case where
2j+1 is prime, the corresponding eigenvectors generate a complete set of
mutually unbiased bases. Some useful relations on generalized quadratic Gauss
sums are exposed in three appendices.


title: Optimal estimation of ensemble averages from a quantum measurement

abstract:
  We consider the general measurement scenario in which the ensemble average of
an operator is determined via suitable data-processing of the outcomes of a
quantum measurement described by a POVM. After reviewing the optimization of
data processing that minimizes the statistical error of the estimation, we
provide a compact formula for the evaluation of the estimation error.


title:
A return to observability near exceptional points in a schematic
  PT-symmetric model

abstract:
  Many indefinite-metric (often called pseudo-Hermitian or PT-symmetric)
quantum models H prove "physical" (i.e., Hermitian with respect to an
innovated, ad hoc scalar product) inside a characteristic domain of parameters
D. This means that the energies get complex (= unobservable) beyond the
boundary (= Kato's "exceptional points", EPs). In a solvable example we detect
an enlargement of D caused by the emergence of a new degree of freedom. We
conjecture that such a beneficial mechanism of a return to the real spectrum
near EPs may be generic and largely model-independent.


title: Quantum Helicity Entropy of Moving Bodies

abstract:
  Lorentz transformation of the reduced helicity density matrix for a massive
spin 1/2 particle is investigated in the framework of relativistic quantum
information theory for the first time. The corresponding helicity entropy is
calculated, which shows no invariant meaning as that of spin. The variation of
the helicity entropy with the relative speed of motion of inertial observers,
however, differs significantly from that of spin due to their distinct
transformation behaviors under the action of Lorentz group. This novel and odd
behavior unique to the helicity may be readily detected by high energy physics
experiments. The underlying physical explanations are also discussed.


title: Improving fidelity in atomic state teleportation via cavity decay

abstract:
  We propose a modified protocol of atomic state teleportation for the scheme
proposed by Bose et al. (Phys. Rev. Lett. 83, 5158 (1999)). The modified
protocol involves an additional stage in which quantum information distorted
during the first stage is fully recovered by a compensation of the damping
factor. The modification makes it possible to obtain a high fidelity of
teleported state for cavities that are much worse than that required in the
original protocol, i.e., their decay rates can be over 25 times larger. The
improvement in the fidelity is possible at the expense of lowering the
probability of success. We show that the modified protocol is robust against
dark counts.


title:
An efficient quantum algorithm for the hidden subgroup problem in
  extraspecial groups

abstract:
  Extraspecial groups form a remarkable subclass of p-groups. They are also
present in quantum information theory, in particular in quantum error
correction. We give here a polynomial time quantum algorithm for finding hidden
subgroups in extraspecial groups. Our approach is quite different from the
recent algorithms presented in [17] and [2] for the Heisenberg group, the
extraspecial p-group of size p3 and exponent p. Exploiting certain nice
automorphisms of the extraspecial groups we define specific group actions which
are used to reduce the problem to hidden subgroup instances in abelian groups
that can be dealt with directly.


title:
Degenerate three-level laser with parametric amplifier and squeezed
  vacuum

abstract:
  Applying stochastic differential equations, we study the squeezing and
statistical properties of the cavity and output modes of a degenerate
three-level laser whose cavity contains a parametric amplifier and coupled to a
squeezed vacuum reservoir. We consider the case in which the top and bottom
levels of the three-level cascade atoms injected into the cavity are coupled by
the pump mode emerging from the parametric amplifier. It turns out that the
presence of the squeezed vacuum reservoir and the parametric amplifier
contribute considerably to the mean photon number and the degree of squeezing
of the cavity and output modes. It appears that almost perfect squeezing can be
achieved at steady state and at threshold for a suitable choice of parameters.


title: Thermodynamic cost of reversible computing

abstract:
  Since reversible computing requires preservation of all information
throughout the entire computational process, this implies that all errors that
appear as a result of the interaction of the information-carrying system with
uncontrolled degrees of freedom must be corrected. But this can only be done at
the expense of an increase in the entropy of the environment corresponding to
the dissipation, in the form of heat, of the ``noisy'' part of the system's
energy.
  This paper gives an expression of that energy in terms of the effective noise
temperature, and analyzes the relationship between the energy dissipation rate
and the rate of computation. Finally, a generalized Clausius principle based on
the concept of effective temperature is presented.


title:
Experimental implementation of non-Gaussian attacks on a
  continuous-variable quantum key distribution system

abstract:
  An intercept-resend attack on a continuous-variable quantum-key-distribution
protocol is investigated experimentally. By varying the interception fraction,
one can implement a family of attacks where the eavesdropper totally controls
the channel parameters. In general, such attacks add excess noise in the
channel, and may also result in non-Gaussian output distributions. We implement
and characterize the measurements needed to detect these attacks, and evaluate
experimentally the information rates available to the legitimate users and the
eavesdropper. The results are consistent with the optimality of Gaussian
attacks resulting from the security proofs.


title: Quantum Repeaters with Photon Pair Sources and Multi-Mode Memories

abstract:
  We propose a quantum repeater protocol which builds on the well-known DLCZ
protocol [L.M. Duan, M.D. Lukin, J.I. Cirac, and P. Zoller, Nature 414, 413
(2001)], but which uses photon pair sources in combination with memories that
allow to store a large number of temporal modes. We suggest to realize such
multi-mode memories based on the principle of photon echo, using solids doped
with rare-earth ions. The use of multi-mode memories promises a speedup in
entanglement generation by several orders of magnitude and a significant
reduction in stability requirements compared to the DLCZ protocol.


title:
Geometric phase gates based on stimulated Raman adiabatic passage in
  tripod systems

abstract:
  We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod
systems and show how to generate purely geometric phase changes of the quantum
states involved. The geometric phases are controlled by three laser fields
where pulse shapes, relative field strength and phases can be controlled. We
present a robust set of universal gates for quantum computing based on these
geometric phases: a one-qubit phase gate, a Hadamard gate and a two-qubit phase
gate.


title: Spontaneous Breaking of the Quantum Superposition

abstract:
  In this work spontaneous (non-dynamical) breaking (effective hiding) of the
unitary quantum mechanical dynamical symmetry (superposition) is considered. It
represents an especial but very interesting case of the general formalism of
the spontaneous symmetry breaking (effective hiding). Conceptual analogies with
spontaneous breaking of the gauge symmetry in Weinberg-Sallam's electro-weak
interaction are pointed out. Also, consequences of the spontaneous
superposition breaking in the measurement process are discussed. Measurement
can be considered as a typical Landau's continuous phase transition with
spontaneous superposition breaking (effective hiding) effectively corresponding
to collapse. Here critical values of the order parameters are determined by
Heisenberg's uncertainty relations.


title:
Deterministic constant-temperature dynamics for dissipative quantum
  systems

abstract:
  A novel method is introduced in order to treat the dissipative dynamics of
quantum systems interacting with a bath of classical degrees of freedom. The
method is based upon an extension of the Nos\`e-Hoover chain (constant
temperature) dynamics to quantum-classical systems. Both adiabatic and
nonadiabatic numerical calculations on the relaxation dynamics of the
spin-boson model show that the quantum-classical Nos\`e-Hoover chain dynamics
represents the thermal noise of the bath in an accurate and simple way.
Numerical comparisons, both with the constant energy calculation and with the
quantum-classical Brownian motion treatment of the bath, show that the
quantum-classical Nos\`e-Hoover Chain dynamics can be used to introduce
dissipation in the evolution of a quantum subsystem even with just one degree
of freedom for the bath. The algorithm can be computationally advantageous in
modeling, within computer simulation, the dynamics of a quantum subsystem
interacting with complex molecular environments.


title: Phase Sensitivity of a Mach-Zehnder Quantum Sensor

abstract:
  We investigate the dependence of the fidelity of a Mach-Zehnder quantum
interferometer on the prior information about the phase, for Fock state input
and for maximally entangled (N00N) state input. For no prior information, the
fidelity for Fock state input is greater than for N00N state input. In the
limit of a narrow distribution describing the prior information, we find that
both Fock and N00N state inputs lead to nearly equal fidelity.


title: GHZ States, Almost-Complex Structure and Yang--Baxter Equation (I)

abstract:
  Recent study suggests that there are natural connections between quantum
information theory and the Yang--Baxter equation. In this paper, in terms of
the generalized almost-complex structure and with the help of its algebra, we
define the generalized Bell matrix to yield all the GHZ states from the product
base, prove it to form a unitary braid representation and present a new type of
solution of the quantum Yang--Baxter equation. We also study
Yang-Baxterization, Hamiltonian, projectors, diagonalization, noncommutative
geometry, quantum algebra and FRT dual algebra associated with this generalized
Bell matrix.


title: Signal-to-Noise Ratio in Squeezed-Light Laser Radar

abstract:
  The formalism for computing the signal-to-noise ratio (SNR) for laser radar
is reviewed and applied to the tasks of target detection, direction-finding,
and phase change estimation with squeezed light. The SNR for heterodyne
detection of coherent light using a squeezed local oscillator is lower than
that obtained using a coherent local oscillator. This is true for target
detection, for phase estimation, and for direction-finding with a split
detector. Squeezing the local oscillator also lowers SNR in balanced homodyne
and heterodyne detection of coherent light. Loss places an upper bound on the
improvement that squeezing can bring to direct-detection SNR.


title: Genuine tripartite entanglement in the non-interacting Fermi gas

abstract:
  We study genuine tripartite entanglement shared among the spins of three
localized fermions in the non-interacting Fermi gas at zero temperature.
Firstly, we prove analytically with the aid of entanglement witnesses that in a
particular configuration the three fermions are genuinely tripartite entangled.
Then various three-fermion configurations are investigated in order to quantify
and calculate numerically the amount of genuine tripartite entanglement present
in the system. Further we give a lower and an upper limit to the maximum
diameter of the three-fermion configuration below which genuine tripartite
entanglement exists and find that this distance is comparable with the maximum
separation between two entangled fermions. The upper and lower limit turn to be
very close to each other indicating that the applied witness operator is well
suited to reveal genuine tripartite entanglement in the collection of
non-interacting fermions.


title:
Correlation loss and multipartite entanglement across a black hole
  horizon

abstract:
  We investigate the Hawking effect on entangled fields. By considering a
scalar field which is in a two-mode squeezed state from the point of view of
freely falling (Kruskal) observers crossing the horizon of a Schwarzschild
black hole, we study the degradation of quantum and classical correlations in
the state from the perspective of Schwarzschild observers confined outside the
horizon. Due to monogamy constraints on the entanglement distribution, we show
that the lost bipartite entanglement is recovered as multipartite entanglement
among modes inside and outside the horizon. In the limit of a small-mass black
hole, no bipartite entanglement is detected outside the horizon, while the
genuine multipartite entanglement interlinking the inner and outer regions
grows infinitely.

categories: quant-ph astro-ph cond-mat.stat-mech gr-qc hep-th math-ph math.MP


title: Preparation and probing of the ground state coherence in Rubidium

abstract:
  We demonstrate the preparation and probing of the coherence between the
hyperfine ground states |5S_{1/2}, F=1> and |5S_{1/2}, F=2> of the Rubidium 87
isotope. The effect of various coherence control techniques, i.e. fractional
Stimulated Raman Adiabatic Passage and Coherent Population Return on the
coherence are investigated. These techniques are implemented using nearly
degenerate pump and Stokes lasers at 795nm (Rubidium D1 transition) which
couple the two hyperfine ground states via the excited state |5P_{1/2}, F=1>
through a resonant two-photon process, in which a coherent superposition of the
two hyperfine ground states is established. The medium is probed by an
additional weak laser, which generates a four-wave mixing signal proportional
to the ground state coherence, and allows us to monitor its evolution in time.
The experimental data are compared with numerical simulations.


title: Quantum phase transitions with Photons and Polaritons

abstract:
  We show that a system of polaritons - combined atom and photon excitations -
in an array of coupled cavities, under an experimental set-up usually
considered in electromagnetically induced transparency, is described by the
Bose-Hubbard model. This opens up the possibility of using this system as a
quantum simulator, allowing for the observation of quantum phase transitions
and for the measurement of local properties, such as single site observables.
All the basic building blocks of the proposed setting have already been
achieved experimentally, showing the feasibility of its realization in the near
future.


title: Non-negative Wigner functions in prime dimensions

abstract:
  According to a classical result due to Hudson, the Wigner function of a pure,
continuous variable quantum state is non-negative if and only if the state is
Gaussian. We have proven an analogous statement for finite-dimensional quantum
systems. In this context, the role of Gaussian states is taken on by stabilizer
states. The general results have been published in [D. Gross, J. Math. Phys.
47, 122107 (2006)]. For the case of systems of odd prime dimension, a greatly
simplified proof can be employed which still exhibits the main ideas. The
present paper gives a self-contained account of these methods.


title: A decoupling approach to the quantum capacity

abstract:
  We give a short proof that the coherent information is an achievable rate for
the transmission of quantum information through a noisy quantum channel. Our
method is to produce random codes by performing a unitarily covariant
projective measurement on a typical subspace of a tensor power state. We show
that, provided the rank of each measurement operator is sufficiently small, the
transmitted data will with high probability be decoupled from the channel's
environment. We also show that our construction leads to random codes whose
average input is close to a product state and outline a modification yielding
unitarily invariant ensembles of maximally entangled codes.


title: Quantum coding theorem from privacy and distinguishability

abstract:
  We prove direct quantum coding theorem for random quantum codes. The problem
is separated into two parts: proof of distinguishability of codewords by
receiver, and that of indistinguishability of codewords by environment
(privacy). For a large class of codes, only privacy has to be checked.


title: Quantum Mechanical Search and Harmonic Perturbation

abstract:
  Perturbation theory in quantum mechanics studies how quantum systems interact
with their environmental perturbations. Harmonic perturbation is a rare special
case of time-dependent perturbations in which exact analysis exists. Some
important technology advances, such as masers, lasers, nuclear magnetic
resonance, etc., originated from it. Here we add quantum computation to this
list with a theoretical demonstration. Based on harmonic perturbation, a
quantum mechanical algorithm is devised to search the ground state of a given
Hamiltonian. The intrinsic complexity of the algorithm is continuous and
parametric in both time T and energy E. More precisely, the probability of
locating a search target of a Hamiltonian in N-dimensional vector space is
shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is
optimal. As harmonic perturbation provides a different computation mechanism,
the algorithm may suggest new directions in realizing quantum computers.


title:
Polynomial Quantum Algorithms for Additive approximations of the Potts
  model and other Points of the Tutte Plane

abstract:
  In the first 36 pages of this paper, we provide polynomial quantum algorithms
for additive approximations of the Tutte polynomial, at any point in the Tutte
plane, for any planar graph. This includes as special cases the AJL algorithm
for the Jones polynomial, the partition function of the Potts model for any
weighted planer graph at any temperature, and many other combinatorial graph
properties. In the second part of the paper we prove the quantum universality
of many of the problems for which we provide an algorithm, thus providing a
large set of new quantum-complete problems. Unfortunately, we do not know that
this holds for the Potts model case; this is left as an important open problem.
The main progress in this work is in our ability to handle non-unitary
representations of the Temperley Lieb algebra, both when applying them in the
algorithm, and, more importantly, in the proof of universality, when encoding
quantum circuits using non-unitary operators. To this end we develop many new
tools, that allow proving density and applying the Solovay Kitaev theorem in
the case of non-unitary matrices. We hope that these tools will open up new
possibilities of using non-unitary reps in other quantum computation contexts.


title: Unitarity, ergodicity, and quantum thermodynamics

abstract:
  This paper is concerned with the ergodic subspaces of the state spaces of
isolated quantum systems. We prove a new ergodic theorem for closed quantum
systems which shows that the equilibrium state of the system takes the form of
a grand canonical density matrix involving a complete commuting set of
observables including the Hamiltonian. The result obtained, which is derived
for a generic finite-dimensional quantum system, shows that the equilibrium
state arising from unitary evolution is always expressible in the canonical
form, without the consideration of a system-bath decomposition.


title:
Field quantization in inhomogeneous anisotropic dielectrics with
  spatio-temporal dispersion

abstract:
  A quantum damped-polariton model is constructed for an inhomogeneous
anisotropic linear dielectric with arbitrary dispersion in space and time. The
model Hamiltonian is completely diagonalized by determining the creation and
annihilation operators for the fundamental polariton modes as specific linear
combinations of the basic dynamical variables. Explicit expressions are derived
for the time-dependent operators describing the electromagnetic field, the
dielectric polarization and the noise term in the latter. It is shown how to
identify bath variables that generate the dissipative dynamics of the medium.


title: The quantum theory of measurement within dynamical reduction models

abstract:
  We analyze in mathematical detail, within the framework of the QMUPL model of
spontaneous wave function collapse, the von Neumann measurement scheme for the
measurement of a 1/2 spin particle. We prove that, according to the equation of
the model: i) throughout the whole measurement process, the pointer of the
measuring device is always perfectly well localized in space; ii) the
probabilities for the possible outcomes are distributed in agreement with the
Born probability rule; iii) at the end of the measurement the state of the
microscopic system has collapsed to the eigenstate corresponding to the
measured eigenvalue. This analysis shows rigorously how dynamical reduction
models provide a consistent solution to the measurement problem of quantum
mechanics.


title: Attosecond neutron Compton scattering from protons

abstract:
  The effect of "anomalous" scattering of neutrons and electrons from protons
in the electron-volt energy-transfer range is considered, and related
experimental results are mentioned. A recent independent confirmation of this
effect with a new data analysis procedure is presented. Due to the very short
characteristic scattering time, there is no well defined separation of time
scales of electronic and protonic motions. An outline of a proposed theoretical
interpretation is presented, which is based on the fact that scattering protons
represent \textit{open} quantum systems, thus being subject to decoherence.


title: Simultaneous Measurement of Non-Commuting Observables

abstract:
  It is shown that the full unknown state of a spin-1/2 system, S, which,
within Born's statistical interpretation, is meant as the state of an ensamble
of identically prepared systems, can be determined with a simultaneous
measurement with the help of an "assistant" system A whose initial state is
known. The idea is to let S and A interact with each other in a known way
during a proper interaction time, to measure simultaneously two observables,
one of S and one of A and their correlation.
  One thus determines the three unknown components of the polarization vector
of S by means of repeated experiments using a unique setting. In this way one
can measure simultaneously all the non-commutative observables of S, which
might seem prohibited in quantum mechanics.


title:
Generalized entanglement as a framework for complex quantum systems:
  Purity vs delocalization measures

abstract:
  We establish contact between the delocalization properties of pure quantum
states, as quantified by their number of principal components, and the average
generalized entanglement properties, as quantified by purity measures relative
to different observable sets. We find that correlations between products of
state vector components with respect to Hamming distance play an important role
in the structure of subsystem-based purity measures. In particular, we derive
general conditions under which the amount of global multipartite entanglement
relates to the inverse participation ratio averaged over a maximal set of
mutually unbiased product bases. Furthermore, we provide a method for computing
the expected amount of generalized entanglement with respect to an arbitrary
observable set for random pure states. Specific examples and an explicit
application to a disordered quantum spin chain are discussed.


title: Topological quantum gate entangler for a multi-qubit state

abstract:
  We establish a relation between topological and quantum entanglement for a
multi-qubit state by considering the unitary representations of the Artin braid
group. We construct topological operators that can entangle multi-qubit state.
In particular we construct operators that create quantum entanglement for
multi-qubit states based on the Segre ideal of complex multi-projective space.
We also in detail discuss and construct these operators for two-qubit and
three-qubit states.


title:
Perfect state transfer in networks of arbitrary topology and coupling
  configuration

abstract:
  A general formalism of the problem of perfect state transfer is presented. We
show that there are infinitely many Hamiltonians which may provide solution to
this problem. In a first attempt to give a classification of them we
investigate their possible forms and the related dynamics during the transfer.
Finally, we show how the present formalism can be used for the engineering of
perfect quantum wires of various topologies and coupling configurations.


title: Concurrence-based entanglement measure for Werner States

abstract:
  We give explicit expressions for entanglement measures of Werner states in
arbitrary dimensions in terms of concurrence and tangle. We show that an
optimal ensemble decomposition for a joint density matrix of a Werner state can
achieve the minimum average concurrence and tangle simultaneously. Furthermore,
the same decomposition also attains entanglement of formation for Werner
states.


title:
On the Einstein-Podolsky-Rosen Proof of the `Incompleteness' of Quantum
  Mechanics

abstract:
  It is shown that the Einstein-Podolsky-Rosen conclusion concerning the
`incompleteness' of Quantum Mechanics does not follow from the results of their
proposed gedanken experiment, but is rather stated as a premise. If it were
possible to perform the experiment it would, in fact, show that Quantum
  Mechanics is `complete' for the observables discussed.
  Because, however, of the non square-integrable nature of the wave function,
the proposed experiment gives vanishing probabilities for measurements
performed in finite intervals of configuration or momentum space. Hence no
conclusion as to the `completeness', or otherwise, of Quantum Mechanics can be
drawn from the experiment.


title: Robust state transfer and rotation through a spin chain via dark passage

abstract:
  Quantum state transfer through a spin chain via adiabatic dark passage is
proposed. This technique is robust against control field fluctuations and
unwanted environmental coupling of intermediate spins. Our method can be
applied to spin chains with more than three spins. We also propose single qubit
rotation using this technique.


title: How much of one-way computation is just thermodynamics?

abstract:
  In this paper we argue that one-way quantum computation can be seen as a form
of phase transition with the available information about the solution of the
computation being the order parameter. We draw a number of striking analogies
between standard thermodynamical quantities such as energy, temperature, work,
and corresponding computational quantities such as the amount of entanglement,
time, potential capacity for computation, respectively. Aside from being
intuitively pleasing, this picture allows us to make novel conjectures, such as
an estimate of the necessary critical time to finish a computation and a
proposal of suitable architectures for universal one-way computation in 1D.


title: Bell inequalities: many questions, a few answers

abstract:
  What can be more fascinating than {\it experimental metaphysics}, to quote
one of Abner Shimony's enlightening expressions? Bell inequalities are at the
heart of the study of nonlocality. I present a list of open questions,
organised in three categories: fundamental; linked to experiments; and
exploring nonlocality as a resource. New families of inequalities for binary
outcomes are presented.


title:
Optimal unambiguous state discrimination of two density matrices: A
  second class of exact solutions

abstract:
  We consider the Unambiguous State Discrimination (USD) of two mixed quantum
states. We study the rank and the spectrum of the elements of an optimal USD
measurement. This naturally leads to a partial fourth reduction theorem. This
theorem shows that either the failure probability equals its overall lower
bound given in term of the fidelity or a two-dimensional subspace can be split
off from the original Hilbert space. We then use this partial reduction theorem
to derive the optimal solution for any two equally probable Geometrically
Uniform (GU) states $\rho_0$ and $\rho_1=U\rho_0 U^\dagger$, $U^2={\openone}$,
in a four-dimensional Hilbert space. This represents a second class of
analytical solutions for USD problems that cannot be reduced to some pure state
cases. We apply our result to answer two questions that are relevant in
implementations of the Bennett and Brassard 1984 quantum key distribution
protocol using weak coherent states.


title: Contextual logic for quantum systems

abstract:
  In this work we build a quantum logic that allows us to refer to physical
magnitudes pertaining to different contexts from a fixed one without the
contradictions with quantum mechanics expressed in no-go theorems. This logic
arises from considering a sheaf over a topological space associated to the
Boolean sublattices of the ortholattice of closed subspaces of the Hilbert
space of the physical system. Differently to standard quantum logics, the
contextual logic maintains a distributive lattice structure and a good
definition of implication as a residue of the conjunction.


title: Theory of decoherence in Bose-Einstein condensate interferometry

abstract:
  A full treatment of decoherence and dephasing effects in BEC interferometry
has been developed based on using quantum correlation functions for treating
interferometric effects. The BEC is described via a phase space distribution
functional of the Wigner type for the condensate modes and the positive P type
for the non-condensate modes. Ito equations for stochastic condensate and
non-condensate field functions replace the functional Fokker-Planck equation
for the distribution functional and stochastic averages of field function
products determine the quantum correlation functions.


title: An Intrisic Topology for Orthomodular Lattices

abstract:
  We present a general way to define a topology on orthomodular lattices. We
show that in the case of a Hilbert lattice, this topology is equivalent to that
induced by the metrics of the corresponding Hilbert space. Moreover, we show
that in the case of a boolean algebra, the obtained topology is the discrete
one. Thus, our construction provides a general tool for studying orthomodular
lattices but also a way to distinguish classical and quantum logics.

categories: quant-ph math-ph math.GN math.LO math.MP


title:
Quantum Entanglement and Teleportation of Quantum-Dot States in
  Microcavities

abstract:
  Generation and control of quantum entanglement are studied in an
equivalent-neighbor system of spatially-separated semiconductor quantum dots
coupled by a single-mode cavity field. Generation of genuinely multipartite
entanglement of qubit states realized by conduction-band electron-spin states
in quantum dots is discussed. A protocol for quantum teleportation of
electron-spin states via cavity decay is briefly described.


title: Quantum Thermalization With Couplings

abstract:
  We study the role of the system-bath coupling for the generalized canonical
thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein
et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure
states of the "universe" [formed by a system S plus its surrounding heat bath
$B$] to a canonical equilibrium state of S. We present an exactly solvable, but
universal model for this kinematic thermalization with an explicit
consideration about the energy shell deformation due to the interaction between
S and B. By calculating the state numbers of the "universe" and its subsystems
S and B in various deformed energy shells, it is found that, for the
overwhelming majority of the "universe" states (they are entangled at least),
the diagonal canonical typicality remains robust with respect to finite
interactions between S and B. Particularly, the kinematic decoherence is
utilized here to account for the vanishing of the off-diagonal elements of the
reduced density matrix of S. It is pointed out that the non-vanishing
off-diagonal elements due to the finiteness of bath and the stronger
system-bath interaction might offer more novelties of the quantum
thermalization.


title: Entanglement Entropy: Helicity versus Spin

abstract:
  For a massive spin 1/2 field, we present the reduced spin and helicity
density matrix, respectively, for the same pure one particle state. Their
relation has also been developed. Furthermore, we calculate and compare the
corresponding entanglement entropy for spin and helicity within the same
inertial reference frame. Due to the distinct dependence on momentum degree of
freedom between spin and helicity states, the resultant helicity entropy is
different from that of spin in general. In particular, we find that both
helicity entanglement for a spin eigenstate and spin entanglement for a right
handed or left handed helicity state do not vanish and their Von Neumann
entropy has no dependence on the specific form of momentum distribution as long
as it is isotropic.


title: Quantum communication via a continuously monitored dual spin chain

abstract:
  We analyze a recent protocol for the transmission of quantum states via a
dual spin chain [Burgarth and Bose, Phys. Rev. A 71, 052315 (2005)] under the
constraint that the receiver's measurement strength is finite. That is, we
consider the channel where the ideal, instantaneous and complete von Neumann
measurements are replaced with a more realistic continuous measurement. We show
that for optimal performance the measurement strength must be "tuned" to the
channel spin-spin coupling, and once this is done, one is able to achieve a
similar transmission rate to that obtained with ideal measurements. The spin
chain protocol thus remains effective under measurement constraints.


title:
Exact diagonalization for spin-1/2 chains and the first order quantum
  phase transitions of the XXX chain in a uniform transverse field

abstract:
  A simple Mathematica code based on the differential realization of hard-core
boson operators for finding exact solutions of the periodic-N spin-1/2 systems
with or beyond nearest neighbor interactions is proposed, which can easily be
used to study general spin-1/2 interaction systems. As an example, The code is
applied to study XXX spin-1/2 chain with nearest neighbor interaction in a
uniform transverse field. It shows that there are [N/2] level-crossing points
in the ground state, where N is the periodic number of the system and [x]
stands for the integer part of x, when the interaction strength and magnitude
of the magnetic field satisfy certain conditions. The quantum phase
transitional behavior in the ground state of the system in the thermodynamic
limit is also studied.


title:
A scheme for demonstration of fractional statistics of anyons in an
  exactly solvable model

abstract:
  We propose a scheme to demonstrate fractional statistics of anyons in an
exactly solvable lattice model proposed by Kitaev that involves four-body
interactions. The required many-body ground state, as well as the anyon
excitations and their braiding operations, can be conveniently realized through
\textit{dynamic}laser manipulation of cold atoms in an optical lattice. Due to
the perfect localization of anyons in this model, we show that a quantum
circuit with only six qubits is enough for demonstration of the basic braiding
statistics of anyons. This opens up the immediate possibility of
proof-of-principle experiments with trapped ions, photons, or nuclear magnetic
resonance systems.


title: Two-level systems driven by large-amplitude fields

abstract:
  We analyze the dynamics of a two-level system subject to driving by
large-amplitude external fields, focusing on the resonance properties in the
case of driving around the region of avoided level crossing. In particular, we
consider three main questions that characterize resonance dynamics: (1) the
resonance condition, (2) the frequency of the resulting oscillations on
resonance and (3) the width of the resonance. We identify the regions of
validity of different approximations. In a large region of the parameter space,
we use a geometric picture in order to obtain both a simple understanding of
the dynamics and quantitative results. The geometric approach is obtained by
dividing the evolution into discrete time steps, with each time step described
by either a phase shift on the basis states or a coherent mixing process
corresponding to a Landau-Zener crossing. We compare the results of the
geometric picture with those of a rotating-wave approximation. We also comment
briefly on the prospects of employing strong driving as a useful tool to
manipulate two-level systems.


title: Information-disturbance tradeoff in covariant quantum state estimation

abstract:
  We provide a general framework for quantifying the optimal tradeoff between
the information retrieved by a quantum measurement and the disturbance on the
quantum state in covariant quantum state estimation.


title: A Single-Photon Server with Just One Atom

abstract:
  Neutral atoms are ideal objects for the deterministic processing of quantum
information. Entanglement operations have been performed by photon exchange or
controlled collisions. Atom-photon interfaces were realized with single atoms
in free space or strongly coupled to an optical cavity. A long standing
challenge with neutral atoms, however, is to overcome the limited observation
time. Without exception, quantum effects appeared only after ensemble
averaging. Here we report on a single-photon source with one-and-only-one atom
quasi permanently coupled to a high-finesse cavity. Quasi permanent refers to
our ability to keep the atom long enough to, first, quantify the
photon-emission statistics and, second, guarantee the subsequent performance as
a single-photon server delivering up to 300,000 photons for up to 30 seconds.
This is achieved by a unique combination of single-photon generation and atom
cooling. Our scheme brings truly deterministic protocols of quantum information
science with light and matter within reach.


title: Decoherence of two-electron spin states in quantum dots

abstract:
  The time evolution of spin states of two electrons interacting with a nuclear
spin bath in a quantum dot system is studied. The hyperfine interaction between
the electrons and the nuclear spins is modeled by an isotropic Heisenberg
interaction, and the interaction between the electron spins by Heisenberg
exchange. Depending on the extent of the overlap between the spatial wave
functions of the electrons, there are two physically different cases, namely
the two qubits either interact with the same set of nuclear spins or they see
different nuclear spin environment. In the two cases, the decoherence of the
two-qubit state is studied analytically. We have identified a class of
two-qubit states which have a rich dynamics when the exchange interaction
between the qubits becomes large in comparison to the hyperfine interaction
strengths. The decoherence time scale is determined as a function of the
bath-spin distribution and the polarizations of the initial two-qubit state.
States with large decoherence times are identified by performing a minimization
over all the two-qubit pure states.


title:
Entanglement and quantum phase transitions in matrix product spin one
  chains

abstract:
  We consider a one-parameter family of matrix product states of spin one
particles on a periodic chain and study in detail the entanglement properties
of such a state. In particular we calculate exactly the entanglement of one
site with the rest of the chain, and the entanglement of two distant sites with
each other and show that the derivative of both these properties diverge when
the parameter $g$ of the states passes through a critical point. Such a point
can be called a point of quantum phase transition, since at this point, the
character of the matrix product state which is the ground state of a
Hamiltonian, changes discontinuously. We also study the finite size effects and
show how the entanglement depends on the size of the chain. This later part is
relevant to the field of quantum computation where the problem of initial state
preparation in finite arrays of qubits or qutrits is important. It is also
shown that entanglement of two sites have scaling behavior near the critical
point.


title:
Two-particle Wigner functions in a one-dimensional Calogero-Sutherland
  potential

abstract:
  We calculate the Wigner distribution function for the Calogero-Sutherland
system which consists of harmonic and inverse-square interactions. The Wigner
distribution function is separated out into two parts corresponding to the
relative and center-of-mass motions. A general expression for the relative
Wigner function is obtained in terms of the Laguerre polynomials by introducing
a new identity between Hermite and Laguerre polynomials.


title:
On correlation approach to scattering in the decoherence timescale -
  Towards the theoretical interpretation of NCS and ECS experimental findings

abstract:
  We provide a "first principles" description of scattering from open quantum
systems subject to a Lindblad-type dynamics. In particular we consider the case
that the duration of the scattering process is of similar order as the
decoherence time of the scatterer. Under rather general conditions, the
derivations lead to the the following new result: The irreversible
time-evolution may cause a reduction of the system's transition rate being
effectuated by scattering. This is tantamount to a shortfall of scattering
intensity. The possible connection with striking experimental results of
neutron and electron Compton scattering from protons in condensed matter is
mentioned.


title:
Sublattice addressing and spin-dependent motion of atoms in a
  double-well lattice

abstract:
  We load atoms into every site of an optical lattice and selectively spin flip
atoms in a sublattice consisting of every other site. These selected atoms are
separated from their unselected neighbors by less than an optical wavelength.
We also show spin-dependent transport, where atomic wave packets are coherently
separated into adjacent sites according to their internal state. These tools
should be useful for quantum information processing and quantum simulation of
lattice models with neutral atoms.


title: Entangled states close to the maximally mixed state

abstract:
  We give improved upper bounds on the radius of the largest ball of separable
states of an m-qubit system around the maximally mixed state. The ratio between
the upper bound and the best known lower bound (Hildebrand, quant.ph/0601201)
thus shrinks to a constant c = \sqrt{34/27} ~ 1.122, as opposed to a term of
order \sqrt{m\log m} for the best upper bound known previously (Aubrun and
Szarek, quant.ph/0503221). We give concrete examples of separable states on the
boundary to entanglement which realize these upper bounds. As a by-product, we
compute the radii of the largest balls that fit into the projective tensor
product of four unit balls in R^3 and in the projective tensor product of an
arbitrary number of unit balls in R^n for n = 2,4,8.


title: Mapping broadband single-photon wavepackets into an atomic memory

abstract:
  We analyze a quantum optical memory based on the off-resonant Raman
interaction of a single broadband photon, copropagating with a classical
control pulse, with an atomic ensemble. The conditions under which the memory
can perform optimally are found, by means of a `universal' mode decomposition.
This enables the memory efficiency to be specified in terms of a single
parameter, and the control field pulse shape to be determined via a simple
nonlinear scaling. We apply the same decomposition to determine the optimal
configurations for read-out.


title: Tunnelling in quantum superlattices with variable lacunarity

abstract:
  Quantum fractal superlattices are microelectronic devices consisting of a
series of thin layers of two semiconductor materials deposited alternately on
each other over a substrate following the rules of construction of a fractal
set, here, a symmetrical polyadic Cantor fractal. The scattering properties of
electrons in these superlattices may be modeled by using that of quantum
particles in piecewise constant potential wells. The twist plots representing
the reflection coefficient as function of the lacunarity parameter show the
appearance of black curves with perfectly transparent tunnelling which may be
classified as vertical, arc, and striation nulls. Approximate analytical
formulae for these reflection-less curves are derived using the transfer matrix
method. Comparison with the numerical results show their good accuracy.


title: Production of Information and Entropy in measurement of entangled states

abstract:
  Problem of classification of all the set of entangled states is considered.
Invariance of entangled states relative to transformations from a group of
symmetry of qubit space leads to classification of all states of the system
through irreducible representations from that group.
  Excess of entropy of a subsystem over entropy of the whole system indicates
the presence of entaglement in the system.


title:
How good must single photon sources and detectors be for efficient
  linear optical quantum computation?

abstract:
  We present a scheme for linear optical quantum computation (LOQC) which is
highly robust to imperfect single photon sources and inefficient detectors. In
particular we show that if the product of the detector efficiency with the
source efficiency is greater than 2/3, then efficient LOQC is possible. This
threshold is many orders of magnitude more relaxed than those which could be
inferred by application of standard results in fault tolerance. The result is
achieved within the cluster state paradigm for quantum computation.


title:
Experimental quantum "Guess my Number" protocol using multiphoton
  entanglement

abstract:
  We present an experimental demonstration of a modified version of the
entanglement-assisted "Guess my Number" protocol for the reduction of
communication complexity among three separated parties. The results of
experimental measurements imply that the separated parties can compute a
function of distributed inputs by exchanging less classical information than by
using any classical strategy. And the results also demonstrate the advantages
of entanglement-enhanced communication, which is very close to quantum
communication. The advantages are based on the properties of
Greenberger-Horne-Zeilinger states.


title: LU transformation invariant operators and LU transformation invariant

abstract:
  We proposed a concept of LU transformation invariant operators. By using this
operator, arbitrary multi-qubit states LU transformation invariant and SLOCC
invariant could be easily obtained. And we find that presences two kinds of
invariant operators and corresponding invariants. One kind of operators yields
LU invariants and the other operators results in SLOCC invariants. For
three-qubit states, all independence LU transformation invariant are obtained.
Furthermore, by this system method, arbitrary multi-qubit states invariants can
be given.