title:
Stabilizer states and Clifford operations for systems of arbitrary
  dimensions, and modular arithmetic

abstract:
  We describe generalizations of the Pauli group, the Clifford group and
stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We
examine a link with modular arithmetic, which yields an efficient way of
representing the Pauli group and the Clifford group with matrices over the
integers modulo d. We further show how a Clifford operation can be efficiently
decomposed into one and two-qudit operations. We also focus in detail on
standard basis expansions of stabilizer states.


title: What is wrong with von Neumann's theorem on "no hidden variables"

abstract:
  It is shown that, although correct mathematically, the celebrated 1932
theorem of von Neumann which is often interpreted as proving the impossibility
of the existence of "hidden variables" in Quantum Mechanics, is in fact based
on an assumption which is physically not reasonable. Apart from that, the
alleged conclusion of von Neumann proving the impossibility of the existence of
"hidden variables" was already set aside in 1952 by the counterexample of the
possibility of a physical theory, such as given by what is usually called the
"Bohmian Mechanics". Similar arguments apply to other two well known
mathematical theorems, namely, of Gleason, and of Kochen and Specker, which
have often been seen as equally proving the impossibility of the existence of
"hidden variables" in Quantum Mechanics.


title: Differential entropy and time

abstract:
  We give a detailed analysis of the Gibbs-type entropy notion and its
dynamical behavior in case of time-dependent continuous probability
distributions of varied origins: related to classical and quantum systems. The
purpose-dependent usage of conditional Kullback-Leibler and Gibbs (Shannon)
entropies is explained in case of non-equilibrium Smoluchowski processes. A
very different temporal behavior of Gibbs and Kullback entropies is confronted.
A specific conceptual niche is addressed, where quantum von Neumann, classical
Kullback-Leibler and Gibbs entropies can be consistently introduced as
information measures for the same physical system. If the dynamics of
probability densities is driven by the Schr\"{o}dinger picture wave-packet
evolution, Gibbs-type and related Fisher information functionals appear to
quantify nontrivial power transfer processes in the mean. This observation is
found to extend to classical dissipative processes and supports the view that
the Shannon entropy dynamics provides an insight into physically relevant
non-equilibrium phenomena, which are inaccessible in terms of the
Kullback-Leibler entropy and typically ignored in the literature.

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


title:
Distinguishability of non-orthogonal density matrices does not imply
  violations of the second law

abstract:
  The hypothetical possibility of distinguishing preparations described by
non-orthogonal density matrices does not necessarily imply a violation of the
second law of thermodynamics, as was instead stated by von Neumann. On the
other hand, such a possibility would surely mean that the particular
density-matrix space (and related Hilbert space) adopted would not be adequate
to describe the hypothetical new experimental facts. These points are shown by
making clear the distinction between physical preparations and the density
matrices which represent them, and then comparing a "quantum" thermodynamic
analysis given by Peres with a "classical" one given by Jaynes.


title: A Single Photon Source With Linear Optics and Squeezed States

abstract:
  Quantum information processing using photons has recently been stimulated by
the suggestion to use linear optics, single photon sources and detectors. The
recent work by Knill has also shown that errors in photon detectors leads to a
high error rate threshold (around 29%). An important missing element are good
single photon sources. In this paper we show how to make a single photon source
using squeezed states, linear optics and conditional measurement. We use
degenerate squeezed vacuum states, in contrast to the normal non-degenerate
squeezed vacuum states used for single photon production. We show that we can
get a photon with certainty when detectors click appropriately, the last event
happening up to around 25% of the time. We also show the robustness of this
method with respect to a variety of potential imperfections.


title: Finite enumerable but undecidable collections

abstract:
  It is well known that in Zermelo-Fraenkel (ZF) set theory any finite set is
decidable. In this paper we discuss an extension of ZF where this result is no
longer valid. Such an extension is quasi-set theory and it has its origin on
problems motivated by quantum mechanics.


title: An extended class of L2-series solutions of the wave equation

abstract:
  We lift the constraint of a diagonal representation of the Hamiltonian by
searching for square integrable bases that support an infinite tridiagonal
matrix representation of the wave operator. The class of solutions obtained as
such includes the discrete (for bound states) as well as the continuous (for
scattering states) spectrum of the Hamiltonian. The problem translates into
finding solutions of the resulting three-term recursion relation for the
expansion coefficients of the wavefunction. These are written in terms of
orthogonal polynomials, some of which are modified versions of known
polynomials. The examples given, which are not exhaustive, include problems in
one and three dimensions.


title: Causality in Propagation of a Pulse in a Nonlinear Dispersive Medium

abstract:
  We investigate the causal propagation of the pulse through dispersive media
by very precise numerical solution of the coupled Maxwell-Bloch equations
without any approximations about the strength of the input field. We study full
nonlinear behavior of the pulse propagation through solid state media like ruby
and alexandrite. We have demonstrated that the information carried by the
discontinuity, {\it i.e}, front of the pulse, moves inside the media with
velocity $c$ even though the peak of the pulse can travel either with
sub-luminal or with super-luminal velocity. We extend the argument of
Levi-Civita to prove that the discontinuity would travel with velocity $c$ even
in a nonlinear medium.


title:
"Paradoxical" coexistence of continuum of 'bound' waves and discrete set
  of unlimited motion states

abstract:
  We have combined two remarkable phenomena: resonance tunneling and Anderson
localization. It results in unexpected spectrum reverse to usual notions. It is
demonstrated by the quantum system with chaotic distribution of potential
resonance tunneling traps over the whole coordinate axis. The corresponding
spectrum contains continuum of 'bound' states (Anderson's localization) and
discrete tunneling resonances of unlimited wave propagation. It is in contrast
to the usual situation with discrete bound and continuum of scattering states.


title: Experimental demonstration of continuous variable quantum erasing

abstract:
  We experimentally demonstrate the concept of continuous variable quantum
erasing. The amplitude quadrature of the signal state is labelled to another
state via a quantum nondemolition interaction, leading to a large uncertainty
in the determination of the phase quadrature due to the inextricable
complementarity of the two observables. We show that by erasing the amplitude
quadrature information we are able to recover the phase quadrature information
of the signal state.


title:
Time problem in quantum mechanics and its analysis by the concept of
  weak measurement

abstract:
  The model of weak measurements is applied to various problems, related to the
time problem in quantum mechanics. The review and generalization of the
theoretical analysis of the time problem in quantum mechanics based on the
concept of weak measurements are presented. A question of the time interval the
system spends in the specified state, when the final state of the system is
given, is raised. Using the concept of weak measurements the expression for
such time is obtained. The results are applied to the tunneling problem. A
procedure for the calculation of the asymptotic tunneling and reflection times
is proposed. Examples for delta-form and rectangular barrier illustrate the
obtained results. Using the concept of weak measurements the arrival time
probability distribution is defined by analogy with the classical mechanics.
The proposed procedure is suitable to the free particles and to particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time definition.


title: Exact quantum master equation via the calculus on path integrals

abstract:
  An exact quantum master equation formalism is constructed for the efficient
evaluation of quantum non-Markovian dissipation beyond the weak system-bath
interaction regime in the presence of time-dependent external field. A novel
truncation scheme is further proposed and compared with other approaches to
close the resulting hierarchically coupled equations of motion. The interplay
between system-bath interaction strength, non-Markovian property, and required
level of hierarchy is also demonstrated with the aid of simple spin-boson
systems.


title:
Experimental teleportation of quantum entanglement with an optimal
  linear optics Bell-state analyzer

abstract:
  We demonstrate an experiment on entanglement swapping using an optimal
Bell-state measurement capable of identifying two of the four Bell-states for
polarization entangled photons, which is the optimum with linear optical
elements. The two final photons belong to separately created paris. They are
entangled after their original partner photons have been subjected to the Bell
state measurement, whose outcome determines the type of entanglement of the
final photon pair. The resulting violation of Bell's inequality in both cases
confirms the success of the teleportation protocol.


title: Comparison of the relative entropy of entanglement and negativity

abstract:
  It is well known that for two qubits the upper bounds of the relative entropy
of entanglement (REE) for a given concurrence as well as the negativity for a
given concurrence are reached by pure states. We show that, by contrast, there
are two-qubit mixed states for which the REE for some range of a fixed
negativity is higher than that for pure states. Moreover, we demonstrate that a
mixture of a pure entangled state and pure separable state orthogonal to it is
likely to give the maximal REE. By noting that the negativity is a measure of
entanglement cost under operations preserving positivity of partial transpose,
our results provide an explicit example of operations such that, even though
the entanglement cost for an exact preparation is the same, the entanglement of
distillation of a mixed state can exceed that of pure states. This means that
the entanglement manipulation via a pure state can result in a larger
entanglement loss than that via a mixed state.


title:
From Quantum To Classical Dynamics: A Landau Continuous Phase Transition
  With Spontaneous Superposition Breaking

abstract:
  Developing an earlier proposal (Ne'eman, Damnjanovic, etc), we show herein
that there is a Landau continuous phase transition from the exact quantum
dynamics to the effectively classical one, occurring via spontaneous
superposition breaking (effective hiding), as a special case of the
corresponding general formalism (Bernstein). Critical values of the order
parameters for this transition are determined by Heisenberg's indeterminacy
relations, change continuously, and are in excellent agreement with the recent
and remarkable experiments with Bose condensation. It is also shown that such a
phase transition can sucessfully model self-collapse (self-decoherence), as an
effective classical phenomenon, on the measurement device. This then induces a
relative collapse (relative decoherence) as an effective quantum phenomenon on
the measured quantum object by measurement.
  We demonstrate this (including the case of Bose-Einstein condensation) in the
well-known cases of the Stern-Gerlach spin measurement, Bell's inequality and
the recently discussed quantum superposition on a mirror a la Marshall et al.
These results provide for a proof that quantum mechanics, in distinction to all
absolute collapse and hidden-variable theories, is local and objective. There
now appear no insuperable obstacles to solving the open problems in quantum
theory of measurement and foundation of quantum mechanics, and strictly within
the standard quantum-mechanical formalism. Simply put, quantum mechanics is a
field theory over the Hilbert space, the classical mechanics characteristics of
which emerge through spontaneous superposition breaking.


title: Common Space of Spin and Spacetime

abstract:
  Given Lorentz invariance in Minkowski spacetime, we investigate a common
space of spin and spacetime. To obtain a finite spinor representation of the
non-compact homogeneous Lorentz group including Lorentz boosts, we introduce an
indefinite inner product space (IIPS) with a normalized positive probability.
In this IIPS, the common momentum and common variable of a massive fermion turn
out to be ``doubly strict plus-operators''. Due to this nice property, it is
straightforward to show an uncertainty relation between fermion mass and proper
time. Also in IIPS, the newly-defined Lagrangian operators are self-adjoint,
and the fermion field equations are derivable from the Lagrangians. Finally,
the nonlinear QED equations and Lagrangians are presented as an example.


title:
Generalization of Hamilton-Jacobi method and its consequences in
  classical, relativistic, and quantum mechanics

abstract:
  The Hamilton-Jacobi method is generalized, both, in classical and
relativistic mechanics. The implications in quantum mechanics are considered in
the case of Klein-Gordon equation. We find that the wave functions of
Klein-Gordon theory can be considered as describing the motion of an ensemble
of particles that move under the action of the electromagnetic field alone,
without quantum potentials, hidden uninterpreted variables, or zero point
fields. The number of particles is not locally conserved.


title:
On the Harmonic approximation for large Josephson junction coupling
  charge qubits

abstract:
  We revisit the harmonic approximation (HA) for a large Josephson junction
interacting with some charge qubits through the variational approach for the
quantum dynamics of the junction-qubit coupling system. By making use of
numerical calculation and analytical treatment, the conditions under which HA
works well can be precisely presented to control the parameters implementing
the two-qubit quantum logical gate through the couplings to the large junction
with harmonic oscillator (HO) Hamiltonian.


title: Kochen-Specker Vectors

abstract:
  We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.


title:
Bose-Einstein Condensation and strong-correlation behavior of phonons in
  ion traps

abstract:
  We show that the dynamics of phonons in a set of trapped ions interacting
with lasers is described by a Bose-Hubbard model whose parameters can be
externally adjusted. We investigate the possibility of observing several
quantum many-body phenomena, including (quasi) Bose-Einstein condensation as
well as a superfluid-Mott insulator quantum phase transition.


title:
The Spectra of Density Operators and the Kronecker Coefficients of the
  Symmetric Group

abstract:
  Determining the relationship between composite systems and their subsystems
is a fundamental problem in quantum physics. In this paper we consider the
spectra of a bipartite quantum state and its two marginal states. To each
spectrum we can associate a representation of the symmetric group defined by a
Young diagram whose normalised row lengths approximate the spectrum. We show
that, for allowed spectra, the representation of the composite system is
contained in the tensor product of the representations of the two subsystems.
This gives a new physical meaning to representations of the symmetric group. It
also introduces a new way of using the machinery of group theory in quantum
informational problems, which we illustrate by two simple examples.


title: Producing a pure single-photon state from pure superposition states

abstract:
  Two pure states in superpositions of zero and one photons may be processed,
via beam splitters and photodetection, to yield a pure single-photon state.


title:
Schroedinger revisited:How the time-dependent wave equation follows from
  the Hamilton-Jacobi equation

abstract:
  It is shown how using the classical Hamilton-Jacobi equation one can arrive
at the time-dependent wave equation. Although the former equation was
originally used by E.Schroedinger to get the wave equation, we propose a
different approach. In the first place, we do not use the principle of least
action and, in addition, we arrive at the time-dependent equation, while
Schroedinger (in his first seminal paper) used the least action principle and
obtained the stationary wave equation. The proposed approach works for any
classical Hamilton-Jacobi equation. In addition, by introducing information
loss into the Hamilton-Jacobi equation we derive in an elementary fashion the
wave equations (ranging from the Shroedinger to Klein-Gordon, to Dirac
equations). We also apply this technique to a relativistic particle in the
gravitational field and obtain the respective wave equation. All this supports
't Hooft's proposal about a possibility of arriving at quantum description from
a classical continuum in the presence of information loss.


title: Instruments and channels in quantum information theory

abstract:
  While a positive operator valued measure gives the probabilities in a quantum
measurement, an instrument gives both the probabilities and the a posteriori
states. By interpreting the instrument as a quantum channel and by using the
typical inequalities for the quantum and classical relative entropies, many
bounds on the classical information extracted in a quantum measurement, of the
type of Holevo's bound, are obtained in a unified manner.


title: Noise cancellation effect in quantum systems

abstract:
  We consider the time evolution of simple quantum systems under the influence
of random fluctuations of the control parameters. We show that when the
parameters fluctuate sufficiently fast, there is a cancellation effect of the
noise. We propose that such an effect could be experimentally observed by
performing a simple experiment with trapped ions. As a byproduct of our
analysis, we provide an explanation of the robustness against random
perturbations of adiabatic population transfer techniques in atom optics.


title:
Path Integral Approach to 't Hooft's Derivation of Quantum from
  Classical Physics

abstract:
  We present a path-integral formulation of 't Hooft's derivation of quantum
from classical physics. The crucial ingredient of this formulation is Gozzi et
al.'s supersymmetric path integral of classical mechanics. We quantize
explicitly two simple classical systems: the planar mathematical pendulum and
the Roessler dynamical system.


title:
Nonisotropic 3-level Quantum Systems: Complete Solutions for Minimum
  Time and Minimum Energy

abstract:
  We apply techniques of subriemannian geometry on Lie groups and of optimal
synthesis on 2-D manifolds to the population transfer problem in a three-level
quantum system driven by two laser pulses, of arbitrary shape and frequency. In
the rotating wave approximation, we consider a nonisotropic model i.e. a model
in which the two coupling constants of the lasers are different. The aim is to
induce transitions from the first to the third level, minimizing 1) the time of
the transition (with bounded laser amplitudes),
  2) the energy of lasers (with fixed final time). After reducing the problem
to real variables, for the purpose 1) we develop a theory of time optimal
syntheses for distributional problem on 2-D-manifolds, while for the purpose 2)
we use techniques of subriemannian geometry on 3-D Lie groups. The complete
optimal syntheses are computed.


title: Testing a Quantum Computer

abstract:
  The problem of quantum test is formally addressed. The presented method
attempts the quantum role of classical test generation and test set reduction
methods known from standard binary and analog circuits. QuFault, the authors
software package generates test plans for arbitrary quantum circuits using the
very efficient simulator QuIDDPro[1]. The quantum fault table is introduced and
mathematically formalized, and the test generation method explained.


title: From quantum circuits to adiabatic algorithms

abstract:
  This paper explores several aspects of the adiabatic quantum computation
model. We first show a way that directly maps any arbitrary circuit in the
standard quantum computing model to an adiabatic algorithm of the same depth.
Specifically, we look for a smooth time-dependent Hamiltonian whose unique
ground state slowly changes from the initial state of the circuit to its final
state. Since this construction requires in general an n-local Hamiltonian, we
will study whether approximation is possible using previous results on ground
state entanglement and perturbation theory. Finally we will point out how the
adiabatic model can be relaxed in various ways to allow for 2-local partially
adiabatic algorithms as well as 2-local holonomic quantum algorithms.


title: Individuality as an illusion

abstract:
  Elementary particles in quantum mechanics (QM) are indistinguishable when
sharing the same intrinsic properties and the same quantum state. So, we can
consider quantum particles as non-individuals, although non-individuality is
usually considered as a consequence of the formalism of QM, since the
entanglement of states forbids any labelling process. We show how to consider
non-individuality as one of the basic principles of QM, instead of a logical
consequence. The advantages of our framework are discussed as well. We also
show that even in classical particle mechanics it is possible to consider the
existence of non-individual particles. One of our main contributions is to show
how to derive the apparent individuality of classical particles from the
assumption that all physical objects are non-individuals.


title: Correcting quantum channels by measuring the environment

abstract:
  The corrected capacity of a quantum channel is defined as the best one-shot
capacity that can be obtained by measuring the environment and using the result
to correct the output of the channel. It is shown that (i) all qubit channels
have corrected capacity log 2, (ii) a product of N qubit channels has corrected
capacity N log 2, and (iii) all channels have corrected capacity at least log
2. The question is posed of finding the channel with smallest corrected
capacity in any dimension d.


title: Entanglement in XY Spin Chain

abstract:
  We consider the ground state of the XY model on an infinite chain at zero
temperature. Following Bennett, Bernstein, Popescu, and Schumacher we use
entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and
Kitaev conjectured that von Neumann entropy of a large block of neighboring
spins approaches a constant as the size of the block increases. We evaluated
this limiting entropy as a function of anisotropy and transverse magnetic
field. We used the methods based on integrable Fredholm operators and
Riemann-Hilbert problem. The entropy is singular at phase transitions.


title: Quantum Computation of a Complex System : the Kicked Harper Model

abstract:
  The simulation of complex quantum systems on a quantum computer is studied,
taking the kicked Harper model as an example. This well-studied system has a
rich variety of dynamical behavior depending on parameters, displays
interesting phenomena such as fractal spectra, mixed phase space, dynamical
localization, anomalous diffusion, or partial delocalization, and can describe
electrons in a magnetic field. Three different quantum algorithms are presented
and analyzed, enabling to simulate efficiently the evolution operator of this
system with different precision using different resources. Depending on the
parameters chosen, the system is near-integrable, localized, or partially
delocalized. In each case we identify transport or spectral quantities which
can be obtained more efficiently on a quantum computer than on a classical one.
In most cases, a polynomial gain compared to classical algorithms is obtained,
which can be quadratic or less depending on the parameter regime. We also
present the effects of static imperfections on the quantities selected, and
show that depending on the regime of parameters, very different behaviors are
observed. Some quantities can be obtained reliably with moderate levels of
imperfection, whereas others are exponentially sensitive to imperfection
strength. In particular, the imperfection threshold for delocalization becomes
exponentially small in the partially delocalized regime. Our results show that
interesting behavior can be observed with as little as 7-8 qubits, and can be
reliably measured in presence of moderate levels of internal imperfections.


title: Why Classical Certification is Impossible in a Quantum World

abstract:
  We give a simple proof that it is impossible to guarantee the classicality of
inputs into any mistrustful quantum cryptographic protocol. The argument
illuminates the impossibility of unconditionally secure quantum implementations
of essentially classical tasks such as bit commitment with a certified
classical committed bit, classical oblivious transfer, and secure classical
multi-party computations of secret classical data. It applies to both
non-relativistic and relativistic protocols.


title: Geometric origin of Eliott relation

abstract:
  It has been shown that the Elliott relation results from the random
acquisition of geometric phases and represents a special case of a more general
situation - relaxation of the pseudo spin-1/2 induced by stochastic gauge
fields.


title:
Deviations from early--time quasilinear behaviour for the quantum kicked
  rotor near the classical limit

abstract:
  We present experimental measurements of the mean energy for the atom optics
kicked rotor after just two kicks. The energy is found to deviate from the
quasi--linear value for small kicking periods. The observed deviation is
explained by recent theoretical results which include the effect of a
non--uniform initial momentum distribution, previously applied only to systems
using much colder atoms than ours.


title: A completely entangled subspace of maximal dimension

abstract:
  A completely entangled subspace of a tensor product of Hilbert spaces is a
subspace with no non-trivial product vector. K. R. Parthasarathy determined the
maximum dimension possible for such a subspace. Here we present a simple
explicit example of one such space. We determine the set of product vectors in
its orthogonal complement and see that it spans whole of the orthogonal
complement. This way we are able to determine the minimum dimension possible
for an unextendible product basis (UPB) consisting of product vectors which are
linearly independent but not necessarily mutually orthogonal.


title: Quantum Computation Based Probability Density Function Estimation

abstract:
  Signal processing techniques will lean on blind methods in the near future,
where no redundant, resource allocating information will be transmitted through
the channel. To achieve a proper decision, however, it is essential to know at
least the probability density function (pdf), which to estimate is classically
a time consumption and/or less accurate hard task, that may make decisions to
fail. This paper describes the design of a quantum assisted pdf estimation
method also by an example, which promises to achieve the exact pdf by proper
setting of parameters in a very fast way.


title: Photon localization barrier can be overcome

abstract:
  In contradistinction to a widespread belief that the spatial localization of
photons is restricted by a power-law falloff of the photon energy density,
I.Bialynicki-Birula [Phys. Rev. Lett. 80, 5247 (1998)] has proved that any
stronger -- up to an almost exponential -- falloff is allowed. We are showing
that for certain specifically designed cylindrical one-photon states the
localization is even better in lateral directions. If the photon state is built
from the so-called focus wave mode, the falloff in the waist cross-section
plane turns out to be quadratically exponential (Gaussian) and such strong
localization persists in the course of propagation.


title: Quantum Verification of Matrix Products

abstract:
  We present a quantum algorithm that verifies a product of two n*n matrices
over any field with bounded error in worst-case time n^{5/3} and expected time
n^{5/3} / min(w,sqrt(n))^{1/3}, where w is the number of wrong entries. This
improves the previous best algorithm that runs in time n^{7/4}. We also present
a quantum matrix multiplication algorithm that is efficient when the result has
few nonzero entries.


title: Multipartite entanglement detection in bosons

abstract:
  We propose a simple quantum network to detect multipartite entangled states
of bosons, and show how to implement this network for neutral atoms stored in
an optical lattice. We investigate the special properties of cluster states,
multipartite entangled states and superpositions of distinct macroscopic
quantum states that can be identified by the network.


title: A neutral atom quantum register

abstract:
  We demonstrate the realization of a quantum register using a string of single
neutral atoms which are trapped in an optical dipole trap. The atoms are
selectively and coherently manipulated in a magnetic field gradient using
microwave radiation. Our addressing scheme operates with a high spatial
resolution and qubit rotations on individual atoms are performed with 99%
contrast. In a final read-out operation we analyze each individual atomic
state. Finally, we have measured the coherence time and identified the
predominant dephasing mechanism for our register.


title:
Entanglement and spin squeezing in the three-qubit transverse Ising
  model

abstract:
  We study entanglement and spin squeezing in the ground state of three qubits
interacting via the transverse Ising model. We give analytical results for the
entanglement and spin squeezing, and a quantitative relation between the
concurrence, quantifying the entanglement of two spins, and the spin squeezing
parameter, measuring the degree of squeezing. Finally, by appropriately
choosing the exchange interaction and strengths of the transverse field, we
propose a scheme for generating entangled W state from an unentangled initial
state with all spins down.


title:
Multipartite Entanglement in a One-Dimensional Time Dependent Ising
  Model

abstract:
  We study multipartite entanglement measures for a one-dimensional Ising chain
that is capable of showing both integrable and nonintegrable behaviour. This
model includes the kicked transverse Ising model, which we solve exactly using
the Jordan-Wigner transform, as well as nonintegrable and mixing regimes. The
cluster states arise as a special case and we show that while one measure of
entanglement is large, another measure can be exponentially small, while
symmetrizing these states with respect to up and down spins, produces those
with large entanglement content uniformly. We also calculate exactly some
entanglement measures for the nontrivial but integrable case of the kicked
transverse Ising model. In the nonintegrable case we begin on extensive
numerical studies that shows that large multipartite entanglement is
accompanied by diminishing two-body correlations, and that time averaged
multipartite entanglement measures can be enhanced in nonintegrable systems.


title: Relativistic central--field Green's functions for the RATIP package

abstract:
  From perturbation theory, Green's functions are known for providing a simple
and convenient access to the (complete) spectrum of atoms and ions. Having
these functions available, they may help carry out perturbation expansions to
any order beyond the first one. For most realistic potentials, however, the
Green's functions need to be calculated numerically since an analytic form is
known only for free electrons or for their motion in a pure Coulomb field.
Therefore, in order to facilitate the use of Green's functions also for atoms
and ions other than the hydrogen--like ions, here we provide an extension to
the Ratip program which supports the computation of relativistic
(one--electron) Green's functions in an -- arbitrarily given -- central--field
potential $\rV(r)$. Different computational modes have been implemented to
define these effective potentials and to generate the radial Green's functions
for all bound--state energies $E < 0$. In addition, care has been taken to
provide a user--friendly component of the Ratip package by utilizing features
of the Fortran 90/95 standard such as data structures, allocatable arrays, or a
module--oriented design.


title: Curve Crossing Problems: Analytically solvable model

abstract:
  We propose an exactly solvable model for the two state curve crossing
problems. Our model assumes the coupling to be a delta function. It is used to
calculate the effect of curve crossing on electronic absorption spectrum and
resonance Raman excitation profile.


title: Convergence of continuous-time quantum walks on the line

abstract:
  The position density of a "particle" performing a continuous-time quantum
walk on the integer lattice, viewed on length scales inversely proportional to
the time t, converges (as t tends to infinity) to a probability distribution
that depends on the initial state of the particle. This convergence behavior
has recently been demonstrated for the simplest continuous-time random walk
[see quant-ph/0408140]. In this brief report, we use a different technique to
establish the same convergence for a very large class of continuous-time
quantum walks, and we identify the limit distribution in the general case.


title: Equiangular Spherical Codes in Quantum Cryptography

abstract:
  Quantum key distribution protocols based on equiangular spherical codes are
introduced and their behavior under the intercept/resend attack investigated.
Such protocols offer a greater range of secure noise tolerance and speed
options than protocols based on their cousins, the mutually-unbiased bases,
while also enabling the determination of the channel noise rate without the
need to sacrifice key bits. For fixed number of signal states in a given
dimension, the spherical code protocols offer Alice and Bob more noise
tolerance at the price of slower key generation rates.


title: Further Difficulties with the Klein-Gordon Equation

abstract:
  The Dirac equation is compared with the Klein-Gordon one. Unlike the Dirac
case, it is proved that the Klein-Gordon equation has problems with the
Hamiltonian operator of the Schroedinger picture. A special discussion of the
Pauli-Weisskopf article and that of Feshbach-Villars proves that their theories
of a charged Klein-Gordon particle lack a self consistent expression for this
Hamiltonian. Related difficulties are pointed out.


title: Quantum Logic Gates using q-deformed Oscillators

abstract:
  We show that the quantum logic gates, {\it viz.} the single qubit Hadamard
and Phase Shift gates, can also be realised using q-deformed angular momentum
states constructed via the Jordan-Schwinger mechanism with two q-deformed
oscillators.
  {\it Keywords :} quantum logic gates ; q-deformed oscillators ; quantum
computation {\it PACS:} 03.67.Lx ; 02.20.Uw


title: Generalized Quantization Scheme for Two-Person Non-Zero-Sum Games

abstract:
  We have proposed a generalized quantization scheme for non-zero sum games
which can be reduced to two existing quantization schemes under appropriate set
of parameters. Some other important situations are identified which are not
apparent in the exiting two quantizations schemes.


title:
Detecting two-party quantum correlations in quantum key distribution
  protocols

abstract:
  A necessary precondition for secure quantum key distribution (QKD) is that
sender and receiver can prove the presence of entanglement in a quantum state
that is effectively distributed between them. In order to deliver this
entanglement proof one can use the class of entanglement witness (EW) operators
that can be constructed from the available measurements results. This class of
EWs can be used to provide a necessary and sufficient condition for the
existence of quantum correlations even when a quantum state cannot be
completely reconstructed. The set of optimal EWs for two well-known
entanglement based (EB) schemes, the 6-state and the 4-state EB protocols, has
been obtained recently [M. Curty et al., Phys. Rev. Lett. 92, 217903 (2004)].
Here we complete these results, now showing specifically the analysis for the
case of prepare&measure (P&M) schemes. For this, we investigate the signal
states and detection methods of the 4-state and the 2-state P&M schemes. For
each of these protocols we obtain a reduced set of EWs. More importantly, each
set of EWs can be used to derive a necessary and sufficient condition to prove
that quantum correlations are present in these protocols.


title: Transport of Entanglement Through a Heisenberg-XY Spin Chain

abstract:
  The entanglement dynamics of spin chains is investigated using Heisenberg-XY
spin Hamiltonian dynamics. The various measures of two-qubit entanglement are
calculated analytically in the time-evolved state starting from initial states
with no entanglement and exactly one pair of maximally-entangled qubits. The
localizable entanglement between a pair of qubits at the end of chain captures
the essential features of entanglement transport across the chain, and it
displays the difference between an initial state with no entanglement and an
initial state with one pair of maximally-entangled qubits.


title: Universal Leakage Elimination

abstract:
  ``Leakage'' errors are particularly serious errors which couple states within
a code subspace to states outside of that subspace thus destroying the error
protection benefit afforded by an encoded state. We generalize an earlier
method for producing leakage elimination decoupling operations and examine the
effects of the leakage eliminating operations on decoherence-free or noiseless
subsystems which encode one logical, or protected qubit into three or four
qubits. We find that by eliminating the large class of leakage errors, under
some circumstances, we can create the conditions for a decoherence free
evolution. In other cases we identify a combination decoherence-free and
quantum error correcting code which could eliminate errors in solid-state
qubits with anisotropic exchange interaction Hamiltonians and enable universal
quantum computing with only these interactions.


title: All-optical versus electro-optical quantum-limited feedback

abstract:
  All-optical feedback can be effected by putting the output of a source cavity
through a Faraday isolator and into a second cavity which is coupled to the
source cavity by a nonlinear crystal. If the driven cavity is heavily damped,
then it can be adiabatically eliminated and a master equation or quantum
Langevin equation derived for the first cavity alone. This is done for an input
bath in an arbitrary state, and for an arbitrary nonlinear coupling. If the
intercavity coupling involves only the intensity (or one quadrature) of the
driven cavity, then the effect on the source cavity is identical to that which
can be obtained from electro-optical feedback using direct (or homodyne)
detection. If the coupling involves both quadratures, this equivalence no
longer holds, and a coupling linear in the source amplitude can produce a
nonclassical state in the source cavity. The analogous electro-optic scheme
using heterodyne detection introduces extra noise which prevents the production
of nonclassical light. Unlike the electro-optic case, the all-optical feedback
loop has an output beam (reflected from the second cavity). We show that this
may be squeezed, even if the source cavity remains in a classical state.


title:
Violation of a Bell inequality in particle physics experimentally
  verified?

abstract:
  Relevant aspects for testing Bell inequalities with entangled meson-antimeson
systems are analyzed. In particular, we argue that the result of A. Go, J. Mod.
Optics 51, 991 (2004), which nicely illustrate the quantum entanglement of
B-meson pairs, cannot be considered as a Bell-test refuting local realism.


title: Communicating Quantum Processes

abstract:
  We define a language CQP (Communicating Quantum Processes) for modelling
systems which combine quantum and classical communication and computation. CQP
combines the communication primitives of the pi-calculus with primitives for
measurement and transformation of quantum state; in particular, quantum bits
(qubits) can be transmitted from process to process along communication
channels. CQP has a static type system which classifies channels, distinguishes
between quantum and classical data, and controls the use of quantum state. We
formally define the syntax, operational semantics and type system of CQP, prove
that the semantics preserves typing, and prove that typing guarantees that each
qubit is owned by a unique process within a system. We illustrate CQP by
defining models of several quantum communication systems, and outline our plans
for using CQP as the foundation for formal analysis and verification of
combined quantum and classical systems.


title:
A nonlinear mechanism of charge qubit decoherence in a lossy cavity: the
  quasi normal mode approach

abstract:
  In the viewpoint of quasi normal modes, we describe a novel decoherence
mechanism of charge qubit of Josephson Junctions (JJ) in a lossy micro-cavity,
which can appear in the realistic experiment for quantum computation based on
JJ qubit. We show that the nonlinear coupling of a charge qubit to quantum
cavity field can result in an additional dissipation of resonant mode due to
its effective interaction between those non-resonant modes and a resonant mode,
which is induced by the charge qubit itself. We calculate the characterized
time of the novel decoherence by making use of the system plus bath method.


title:
Review of recent experimental progresses in Foundations of Quantum
  Mechanics and Quantum Information obtained in Parametric Down Conversion
  Experiments at IENGF

abstract:
  We review some recent experimental progresses concerning Foundations of
Quantum Mechanics and Quantum Information obtained in Quantum Optics Laboratory
"Carlo Novero" at IENGF.
  More in details, after a short presentation of our polarization entangled
photons source (based on precise superposition of two Type I PDC emission) and
of the results obtained with it, we describe an innovative double slit
experiment where two degenerate photons produced by PDC are sent each to a
specific slit. Beyond representing an interesting example of relation between
visibility of interference and "welcher weg" knowledge, this configuration has
been suggested for testing de Broglie-Bohm theory against Standard Quantum
Mechanics. Our results perfectly fit SQM results, but disagree with dBB
predictions.
  Then, we discuss a recent experiment addressed to clarify the issue of which
wave-particle observables are really to be considered when discussing wave
particle duality. This experiments realises the Agarwal et al. theoretical
proposal, overcoming limitations of a former experiment.
  Finally, we hint to the realization of a high-intensity
high-spectral-selected PDC source to be used for quantum information studies.


title:
Experimental realization of a measurement conditional unitary operation
  at single photon level and application to detector characterization

abstract:
  Our last experimental results on the realization of a measurement-conditional
unitary operation at single photon level are presented. This gate operates by
rotating by $90^o$ the polarization of a photon produced by means of Type-II
Parametric Down Conversion conditional to a polarization measurement on the
correlated photon. We then propose a new scheme for measuring the quantum
efficiency of a single photon detection apparatus by using this set-up. We
present experimental results obtained with this scheme compared with {\it
traditional} biphoton calibration. Our results show the interesting
potentiality of the suggested scheme.


title: On the Interpretation of Energy as the Rate of Quantum Computation

abstract:
  Over the last few decades, developments in the physical limits of computing
and quantum computing have increasingly taught us that it can be helpful to
think about physics itself in computational terms. For example, work over the
last decade has shown that the energy of a quantum system limits the rate at
which it can perform significant computational operations, and suggests that we
might validly interpret energy as in fact being the speed at which a physical
system is "computing," in some appropriate sense of the word. In this paper, we
explore the precise nature of this connection. Elementary results in quantum
theory show that the Hamiltonian energy of any quantum system corresponds
exactly to the angular velocity of state-vector rotation (defined in a certain
natural way) in Hilbert space, and also to the rate at which the state-vector's
components (in any basis) sweep out area in the complex plane. The total angle
traversed (or area swept out) corresponds to the action of the Hamiltonian
operator along the trajectory, and we can also consider it to be a measure of
the "amount of computational effort exerted" by the system, or effort for
short. For any specific quantum or classical computational operation, we can
(at least in principle) calculate its difficulty, defined as the minimum effort
required to perform that operation on a worst-case input state, and this in
turn determines the minimum time required for quantum systems to carry out that
operation on worst-case input states of a given energy. As examples, we
calculate the difficulty of some basic 1-bit and n-bit quantum and classical
operations in an simple unconstrained scenario.


title:
Quantum key distribution without reference frame alignment: Exploiting
  photon orbital angular momentum

abstract:
  We present a new implementation of the BB84 quantum key distribution protocol
that employs a $d$-dimensional Hilbert space spanned by spatial modes of the
propagating beam that have a definite value of orbital angular momentum. Each
photon carries $\log d$ bits of information, increasing the key generation rate
of the protocol. The states used in the transmission part of the protocol are
invariant under rotations about the propagation direction, making this
implementation independent of the alignment between the reference frames of the
sender and receiver. The protocol still works when these reference frames
rotate with respect to each other.


title: Bell's Theorem: a new Derivation that Preserves Heisenberg and Locality

abstract:
  By implicitly assuming that all measurements occur simultaneously, Bell's
Theorem only applied to local theories that violated Heisenberg's Uncertainty
Principle. By explicitly introducing time into our derivation of Bell's
theorem, an extra term related to the time-ordering of actual measurements is
found to augment (i.e. weaken) the upper bound of the inequality. Since the
same locality assumptions hold for this rederivation as for the original, we
conclude that only {\em classical} measurement-order independent local hidden
variable theories are constrained by Bell's inequality; time dependent,
non-classical local theories (i.e. theories respecting Heisenberg's Uncertainty
Principle) can satisfy this new bound while exceeding Bell's limit.
Unconditional nonlocality is only expected to occur with Bell parameters
between $2\sqrt{2}$ and 4. This weakening of Bell's inequality is seen for the
quantum Bell operator (squared) as an extra term involving the commutators of
{\em local} measurement operators. We note that a factorizable second-quantized
wavefunction can reproduce experimental measurements; because such
wavefunctions allow local de Broglie-Bohm hidden variable modelling, we have
another indication that violation of {\em Bell's} inequality does not require
an acceptance of non-locality.


title:
Proposal of Signaling by Interference Control of Delayed-Choice
  Experimental Setup

abstract:
  We propose a new signaling system using the experimental setup of Wheeler's
delayed-choice experiment previously carried out. In the delayed-choice
experiment, the experimental setup shows a wave property or a particle property
at the time when the experimental conditions of the wave-particle duality of
photons are chosen. Choice signals can be used as transmitting signals and the
wave-particle duality of photons is used as receiving signals. For example, if
we choose the wave property of a photon as a transmitting signal, we detect the
interference of the wave at the detector that can be used as a receiving
signal. Therefore, the experimental setup of the delayed-choice experiment can
transmit information through interference.


title: Quantum shutter approach to tunneling time scales with wave packets

abstract:
  The quantum shutter approach to tunneling time scales (G. Garc\'{\i
}a-Calder\'{o}n and A. Rubio, Phys. Rev. A \textbf{55}, 3361 (1997)), which
uses a cutoff plane wave as the initial condition, is extended in such a way
that a certain type of wave packet can be used as the initial condition. An
analytical expression for the time evolved wave function is derived. The
time-domain resonance, the peaked structure of the probability density (as the
function of time) at the exit of the barrier, originally found with the cutoff
plane wave initial condition, is studied with the wave packet initial
conditions. It is found that the time-domain resonance is not very sensitive to
the width of the packet when the transmission process is in the tunneling
regime.


title:
Timescales for decoherence and dissipation: reasons for the success of
  master equations

abstract:
  A perturbative treatment of reduced density operators of quantum subsystems
is implemented in the same spirit as Fermi Golden Rule for scattering. Analytic
expressions for linear entropy (a measure of purity loss, and in some cases of
coherence loss) and for subsystem's energy variations (dissipation) are given.
Application to electromagnetic field superposition states in a dissipative
cavity is performed. Evaluation of typical field and reservoir time scales
($\tau_{F}$ and $\tau_{R}$) show that even for small temperatures they are very
different. We also indicate the condition on the cutoff temperature above which
the decoupling assumption is quantitatively justified.


title:
General Security Definition and Composability for Quantum & Classical
  Protocols

abstract:
  We generalize the universally composable definition of Canetti to the Quantum
World. The basic idea is the same as in the classical world. The main
contribution is that we unfold the result in a new model which is well adapted
to quantum protocols. We also simplify some aspects of the classical case. In
particular, the case of protocols with an arbitrary number of layers of
sub-protocols is naturally covered in the proposed model.


title: Fidelity of Gaussian channels

abstract:
  A noisy Gaussian channel is defined as a channel in which an input field mode
is subjected to random Gaussian displacements in phase space. We introduce the
quantum fidelity of a Gaussian channel for pure and mixed input states, and we
derive a universal scaling law of the fidelity for pure initial states. We also
find the maximum fidelity of a Gaussian channel over all input states. Quantum
cloning and continuous-variable teleportation are presented as physical
examples of Gaussian channels to which the fidelity results can be applied.


title: Theoretical Value of the Electromagnetic Coupling Constant

abstract:
  An insight into bispinor analysis makes it possible to describe the electron
in selfaction as a fundamental steady state. The electromagnetic theory, and
the Dirac equation for the study of an electron in presence of external
potentials, follow as natural extensions of the equations that rule the
electron in selfaction. The electromagnetic coupling constant ($\alpha$) and
the coupling constant ($\beta$) of a gauge invariant matrix vector potential
are interrelated by the equation that defines the electron structure. Here, two
bispinor components carry 1/3 and 2/3 of the physical properties of the
electron: electric charge, mass, spin and magnetic moment. These fractions of
the electron charge seem to be a feature common to both leptons and hadrons. An
eigenvalue equation involving the invariants of the selfpotentials ultimately
determines $\alpha$ and $\beta$.


title: A functional quantum programming language

abstract:
  We introduce the language QML, a functional language for quantum computations
on finite types. Its design is guided by its categorical semantics: QML
programs are interpreted by morphisms in the category FQC of finite quantum
computations, which provides a constructive semantics of irreversible quantum
computations realisable as quantum gates. QML integrates reversible and
irreversible quantum computations in one language, using first order strict
linear logic to make weakenings explicit. Strict programs are free from
decoherence and hence preserve superpositions and entanglement - which is
essential for quantum parallelism.


title: Causality and Cirel'son bounds

abstract:
  An EPR-Bell type experiment carried out on an entangled quantum system can
produce correlations stronger than allowed by local realistic theories. However
there are correlations that are no-signaling and are more non local than the
quantum correlations. Here we show that any correlations more non local than
those achievable in an EPR-Bell type experiment necessarily allow -in the
context of the quantum formalism- both for signaling and for generation of
entanglement. We use our approach to rederive Cirel'son bound for the CHSH
expression, and we derive a new Cirel'son type bound for qutrits. We discuss in
detail the interpretation of our approach.


title:
Energy levels and decoherence properties of single electron and nuclear
  spins in a defect center in diamond

abstract:
  The coherent behavior of the single electron and single nuclear spins of a
defect center in diamond and a 13C nucleus in its vicinity, respectively, are
investigated. The energy levels associated with the hyperfine coupling of the
electron spin of the defect center to the 13C nuclear spin are analyzed.
Methods of magnetic resonance together with optical readout of single defect
centers have been applied in order to observe the coherent dynamics of the
electron and nuclear spins. Long coherence times, in the order of microseconds
for electron spins and tens of microseconds for nuclear spins, recommend the
studied system as a good experimental approach for implementing a 2-qubit gate.


title:
Explicit Form of the Evolution Operator of Tavis-Cummings Model : Three
  and Four Atoms Cases

abstract:
  In this letter the explicit form of evolution operator of the Tavis-Cummings
model with three and four atoms is given. This is an important progress in
quantum optics or mathematical physics.


title:
A Discrete Version of the Inverse Scattering Problem and the J-matrix
  Method

abstract:
  The problem of the Hamiltonian matrix in the oscillator and Laguerre basis
construction from the S-matrix is treated in the context of the algebraic
analogue of the Marchenko method.


title: Harmonic oscillator in a rotating trap: Complete solution in 3D

abstract:
  Complete description of the classical and quantum dynamics of a particle in
an anisotropic, rotating, harmonic trap is given. The problem is studied in
three dimensions and no restrictions on the geometry are imposed. In the
generic case, for an arbitrary orientation of the rotation axis, there are two
regions of instability with different characteristics. The analysis of the
quantum-mechanical problem is made simple due to a direct connection between
the classical mode vectors and the quantum-mechanical wave functions. This
connection is obtained via the matrix Riccati equation that governs the time
evolution of squeezed states of the harmonic oscillator. It is also shown that
the inclusion of gravity leads to a resonant behavior -- the particles are
expelled from the trap.


title:
Quantum spin model fitting the Yule distribution of oligonucleotides in
  DNA

abstract:
  A quantum spin chain is identified by the labels of a vector state of a
Kashiwara crystal basis. The intensity of the one-spin flip is assumed to
depend from the variation of the labels. The rank ordered plot of the
numerically computed, averaged in time, transition probabilities is nicely
fitted by a Yule distribution, which is the observed distribution of the ranked
short oligonucleotides frequency in DNA.


title: Efficient generation of distant atom entanglement

abstract:
  We show how the entanglement of two atoms, trapped in distant separate
cavities, can be generated with arbitrarily high probability of success. The
scheme proposed employs sudden excitation of the atoms proving that the weakly
driven condition is not necessary to obtain the success rate close to unity.
The modified scheme works properly even if each cavity contains many atoms
interacting with the cavity modes. We also show that our method is robust
against the spontaneous atomic decay.


title: Bipartite entanglement and entropic boundary law in lattice spin systems

abstract:
  We investigate bipartite entanglement in spin-1/2 systems on a generic
lattice. For states that are an equal superposition of elements of a group $G$
of spin flips acting on the fully polarized state $\ket{0}^{\otimes n}$, we
find that the von Neumann entropy depends only on the boundary between the two
subsystems $A$ and $B$. These states are stabilized by the group $G$. A
physical realization of such states is given by the ground state manifold of
the Kitaev's model on a Riemann surface of genus $\mathfrak{g}$. For a square
lattice, we find that the entropy of entanglement is bounded from above and
below by functions linear in the perimeter of the subsystem $A$ and is equal to
the perimeter (up to an additive constant) when $A$ is convex. The entropy of
entanglement is shown to be related to the topological order of this model.
Finally, we find that some of the ground states are absolutely entangled, i.e.,
no partition has zero entanglement. We also provide several examples for the
square lattice.


title:
A Remark on the Aharonov-Bohm Potential and a Discussion on the Electric
  Charge Quantization

abstract:
  The purpose of this work is to stress on a mathematical requirement of the
Stokes' theorem that, naturally, yields a reassessment of the electric charge
quantization condition, which is, here, explicitly carried out in the context
of the Aharonov-Bohm set-up. We argue that, by virtue of an ambiguity in the
definition of the circulation of the vector potential, a modified quantization
condition comes out for the electric charge that opens the way for
understanding fundamental fractional charges. One does not, any longer, need to
rely on the existence of a magnetic monopole to justify electric charge
quantization.


title:
Construction of Elementary Gates in Quantum Computation by Joint
  Measurement

abstract:
  In this paper, elementary quantum gate operations, such as the phase gate,
the controlled-NOT gate, the swap and the Fredkin gate are constructed using
joint measurement and pairs of entangled qubit pairs. The relation between the
state of the entangled pair and the joint measurement basis is discussed. Some
other generalization is also discussed.


title:
NMR line shapes of a gas of nuclear spin-1/2 molecules in fluctuating
  nano-containers

abstract:
  Reported in this paper is the impact of the fluctuations of the geometry of
the nano-meter gas containers in the medium on the NMR line shape of the gas
inside of the nano-containers. We calculate exactly the NMR line shape of the
gas of spin-1/2 carrying molecules for two typical dynamics of the
nano-container volume and the orientation with respect to the external magnetic
field: (i) for a Gaussian stochastic dynamics, and (ii) for the regular
harmonic vibrations. For the Gaussian ensemble of static disordered containers
having an infinite correlation time, $\tau_{\sf c} \to \infty $, the overall
line shape is shown to obey a logarithmic low frequency asymptotics, $
I(\omega) = {const} \times \ln (\frac{1}{\omega})$, at $\omega \to 0$, and
exponentially decaying asymptotics in a high frequency domain. For the Gaussian
ensemble of the rapidly fluctuating containers of a finite $\tau_{\sf c}$, the
overall line shape has a bell-shaped profile with $\sim \omega^{-4}$ far wing
behaviour. In addition, we calculate exactly a satellite structure of the NMR
line shape when the nano-bubbles in a liquid are affected by the harmonic
deformations due to the acoustic waves.


title: Modeling Single Electron Transfer in Si:P Double Quantum Dots

abstract:
  Solid-state systems such as P donors in Si have considerable potential for
realization of scalable quantum computation. Recent experimental work in this
area has focused on implanted Si:P double quantum dots (DQDs) that represent a
preliminary step towards the realization of single donor charge-based qubits.
This paper focuses on the techniques involved in analyzing the charge transfer
within such DQD devices and understanding the impact of fabrication parameters
on this process. We show that misalignment between the buried dots and surface
gates affects the charge transfer behavior and identify some of the challenges
posed by reducing the size of the metallic dot to the few donor regime.


title: The Universal Composable Security of Quantum Key Distribution

abstract:
  The existing unconditional security definitions of quantum key distribution
(QKD) do not apply to joint attacks over QKD and the subsequent use of the
resulting key. In this paper, we close this potential security gap by using a
universal composability theorem for the quantum setting. We first derive a
composable security definition for QKD. We then prove that the usual security
definition of QKD still implies the composable security definition. Thus, a key
produced in any QKD protocol that is unconditionally secure in the usual
definition can indeed be safely used, a property of QKD that is hitherto
unproven. We propose two other useful sufficient conditions for composability.
As a simple application of our result, we show that keys generated by repeated
runs of QKD degrade slowly.


title: Visualizing the kinematics of relativistic wave packets

abstract:
  This article investigates some solutions of the time-dependent free Dirac
equation. Visualizations of these solutions immediately reveal strange
phenomena that are caused by the interference of positive- and negative-energy
waves. The effects discussed here include the Zitterbewegung, the opposite
direction of momentum and velocity in negative-energy wave packets, and the
superluminal propagation of the wave packet's local maxima.


title: Exact entanglement bases and general bound entanglement

abstract:
  In this paper has been withrawn by the author due the error in the proof of
theoem 1.


title:
A Survey of Finite Algebraic Geometrical Structures Underlying Mutually
  Unbiased Quantum Measurements

abstract:
  The basic methods of constructing the sets of mutually unbiased bases in the
Hilbert space of an arbitrary finite dimension are discussed and an emerging
link between them is outlined. It is shown that these methods employ a wide
range of important mathematical concepts like, e.g., Fourier transforms, Galois
fields and rings, finite and related projective geometries, and entanglement,
to mention a few. Some applications of the theory to quantum information tasks
are also mentioned.


title: Partition functions and graphs: A combinatorial approach

abstract:
  Although symmetry methods and analysis are a necessary ingredient in every
physicist's toolkit, rather less use has been made of combinatorial methods.
One exception is in the realm of Statistical Physics, where the calculation of
the partition function, for example, is essentially a combinatorial problem. In
this talk we shall show that one approach is via the normal ordering of the
second quantized operators appearing in the partition function. This in turn
leads to a combinatorial graphical description, giving essentially Feynman-type
graphs associated with the theory. We illustrate this methodology by the
explicit calculation of two model examples, the free boson gas and a superfluid
boson model. We show how the calculation of partition functions can be
facilitated by knowledge of the combinatorics of the boson normal ordering
problem; this naturally gives rise to the Bell numbers of combinatorics. The
associated graphical representation of these numbers gives a perturbation
expansion in terms of a sequence of graphs analogous to zero - dimensional
Feynman diagrams.


title:
Complementary classical fidelities as an efficient criterion for the
  evaluation of experimentally realized quantum operations

abstract:
  It is shown that a good estimate of the fidelity of an experimentally
realized quantum process can be obtained by measuring the outputs for only two
complementary sets of input states. The number of measurements required to test
a quantum network operation is therefore only twice as high as the number of
measurements required to test a corresponding classical system.


title:
Generalized Performance of Concatenated Quantum Codes -- A Dynamical
  Systems Approach

abstract:
  We apply a dynamical systems approach to concatenation of quantum error
correcting codes, extending and generalizing the results of Rahn et al. [1] to
both diagonal and nondiagonal channels. Our point of view is global: instead of
focusing on particular types of noise channels, we study the geometry of the
coding map as a discrete-time dynamical system on the entire space of noise
channels. In the case of diagonal channels, we show that any code with distance
at least three corrects (in the infinite concatenation limit) an open set of
errors. For Calderbank-Shor-Steane (CSS) codes, we give a more precise
characterization of that set. We show how to incorporate noise in the gates,
thus completing the framework. We derive some general bounds for noise
channels, which allows us to analyze several codes in detail.


title: Systematic Search of Exactly Solvable Non-Central Potentials

abstract:
  Recently developed supersymmetric perturbation theory has been successfully
employed to make a complete mathematical analysis the reason behind exact
solvability of some non-central potentials. This investigation clarifies once
more the effectiveness of the present formalism.


title: A geometric approach to the canonical reformulation of quantum mechanics

abstract:
  The measure of distinguishability between two neighboring preparations of a
physical system by a measurement apparatus naturally defines the line element
of the preparation space of the system. We point out that quantum mechanics can
be derived from the invariance of this line element in the canonical
formulation. The canonical formulation of quantum statistical mechanics is also
discussed.


title:
Bell inequalities and linear entropy. Comment on the paper of E. Santos
  "Entropy inequalities and Bell inequalities fro two-qubit systems"

abstract:
  It is shown that even if the linear entropy of mixed two-qubit state is not
smaller then 0.457, Bell - CHSH inequalities can be violated. This contradicts
the result obtained in the paper of E. Santos [1].


title: A Random Matrix Model of Adiabatic Quantum Computing

abstract:
  We present an analysis of the quantum adiabatic algorithm for solving hard
instances of 3-SAT (an NP-complete problem) in terms of Random Matrix Theory
(RMT). We determine the global regularity of the spectral fluctuations of the
instantaneous Hamiltonians encountered during the interpolation between the
starting Hamiltonians and the ones whose ground states encode the solutions to
the computational problems of interest. At each interpolation point, we
quantify the degree of regularity of the average spectral distribution via its
Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from
chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor
spacings. We find that for hard problem instances, i.e., those having a
critical ratio of clauses to variables, the spectral fluctuations typically
become irregular across a contiguous region of the interpolation parameter,
while the spectrum is regular for easy instances. Within the hard region, RMT
may be applied to obtain a mathematical model of the probability of avoided
level crossings and concomitant failure rate of the adiabatic algorithm due to
non-adiabatic Landau-Zener type transitions. Our model predicts that if the
interpolation is performed at a uniform rate, the average failure rate of the
quantum adiabatic algorithm, when averaged over hard problem instances, scales
exponentially with increasing problem size.


title: Radiative Decay Engineering by Triaxial Nanoellipsoids

abstract:
  Radiative decay rates of an atom placed near triaxial nanoellipsoid are
investigated in long wavelength approximation. Analytical results are obtained
in general case. It is shown that triaxial ellipsoid can be used for efficient
control of decay rate of an atom, molecule or quantum dot. For example decay
rate near silver ellipsoid can be enhanced by 5 orders of magnitude. It is also
shown, that triaxial nanoellipsoid can be used for simultaneous efficient
control of absorption and emission rates of fluorophores.


title: A new expression for mutually unbiased bases in prime power dimensions

abstract:
  Mutually unbiased bases generalize the X, Y and Z qubit bases. They possess
numerous applications in quantum information science. It is well-known that in
prime power dimensions N=p^m (with p prime and m a positive integer) there
exists a maximal set of N+1 mutually unbiased bases.
  In the present paper, we derive an explicit expression for those bases, in
terms of the (operations of the) associated finite field (Galois division ring)
of N elements. This expression is shown to be equivalent to the expressions
previously obtained by Ivanovic in odd prime dimensions (J. Phys. A, 14, 3241
(1981)), and Wootters and Fields (Ann. Phys. 191, 363 (1989)) in odd prime
power dimensions. In even prime power dimensions, we derive a new explicit
expression for the mutually unbiased bases. The new ingredients of our approach
are, basically, the following: we provide a simple expression of the
generalised Pauli group in terms of the additive characters of the field and we
derive an exact groupal composition law inside the elements of the commuting
subsets of the generalised Pauli group, renormalised by a well-chosen
phase-factor.


title: Coordination Games with Quantum Information

abstract:
  The paper discusses coordination games with remote players that have access
to an entangled quantum state. It shows that the entangled state cannot be used
by players for communicating information, but that in certain games it can be
used for improving coordination of actions. A necessary condition is provided
that helps to determine when an entangled quantum state can be useful for
improving coordination.


title: Detection of incompatible properties without erasure

abstract:
  In this work we show that in double-slit experiment properties incompatible
with Which Slit property can be detected without erasing the knowledge of which
slit each particle passes through and without affecting the point of impact on
the final screen. A systematic procedure to find these particular properties is
provided. A thought experiment which realizes this detection is proposed.


title: Long distance entanglement swapping with photons from separated sources

abstract:
  We report the first experimental realization of entanglement swapping over
large distances in optical fibers. Two photons separated by more than two km of
optical fibers are entangled, although they never directly interacted. We use
two pairs of time-bin entangled qubits created in spatially separated sources
and carried by photons at telecommunication wavelengths. A partial Bell state
measurement is performed with one photon from each pair which projects the two
remaining photons, formerly independent onto an entangled state. A visibility
high enough to violate a Bell inequality is reported, after both photons have
each travelled through 1.1 km of optical fiber.


title: Quantum Register Physics

abstract:
  Motivated by Feynman's 1983 paper on the simulation of physics by computers,
we present a general approach to the description of quantum experiments which
uses quantum bit registers to represent the spatio-temporal changes occurring
in apparatus-systems during the course of such experiments. To illustrate our
ideas, we discuss the Stern-Gerlach experiment, Wollaston prisms, beam
splitters, Mach-Zender interferometers, von Neumann (PVM) tests, the more
general POVM formalism, and a variety of modern quantum experiments, such as
two-particle interferometry and the EPR scenario.


title:
Better bound on the exponent of the radius of the multipartite separable
  ball

abstract:
  We show that for an m-qubit quantum system, there is a ball of radius
asymptotically approaching kappa 2^{-gamma m} in Frobenius norm, centered at
the identity matrix, of separable (unentangled) positive semidefinite matrices,
for an exponent gamma = (1/2)((ln 3/ln 2) - 1), roughly .29248125. This is much
smaller in magnitude than the best previously known exponent, from our earlier
work, of 1/2. For normalized m-qubit states, we get a separable ball of radius
sqrt(3^(m+1)/(3^m+3)) * 2^{-(1 + \gamma)m}, i.e. sqrt{3^{m+1}/(3^m+3)}\times
6^{-m/2} (note that \kappa = \sqrt{3}), compared to the previous 2 * 2^{-3m/2}.
This implies that with parameters realistic for current experiments, NMR with
standard pseudopure-state preparation techniques can access only unentangled
states if 36 qubits or fewer are used (compared to 23 qubits via our earlier
results). We also obtain an improved exponent for m-partite systems of fixed
local dimension d_0, although approaching our earlier exponent as d_0
approaches infinity.


title: MUBs: From finite projective geometry to quantum phase enciphering

abstract:
  This short note highlights the most prominent mathematical problems and
physical questions associated with the existence of the maximum sets of
mutually unbiased bases (MUBs) in the Hilbert space of a given dimension


title: The hidden phase of Fock states; quantum non-local effects

abstract:
  We revisit the question of how a definite phase between Bose-Einstein
condensates can spontaneously appear under the effect of measurements. We first
consider a system that is the juxtaposition of two subsystems in Fock states
with high populations, and assume that successive individual position
measurements are performed. Initially, the relative phase is totally undefined,
and no interference effect takes place in the first position measurement. But,
while successive measurements are accumulated, the relative phase becomes
better and better known, and a clear interference pattern emerges. It turns out
that all observed results can be interpreted in terms of a pre-existing, but
totally unknown, relative phase, which remains exactly constant during the
experiment. We then generalize the results to more condensates. We also
consider other initial quantum states than pure Fock states, and distinguish
between intrinsic phase of a quantum state and phase induced by measurements.
Finally, we examine the case of multiple condensates of spin states. We discuss
a curious quantum effect, where the measurement of the spin angular momentum of
a small number of particles can induce a big angular momentum in a much larger
assembly of particles, even at an arbitrary distance. This spin observable can
be macroscopic, assimilable to the pointer of a measurement apparatus, which
illustrates the non-locality of quantum mechanics with particular clarity.


title:
Multiple-time correlation functions for non-Markovian interaction:
  Beyond the Quantum Regression Theorem

abstract:
  Multiple time correlation functions are found in the dynamical description of
different phenomena. They encode and describe the fluctuations of the dynamical
variables of a system. In this paper we formulate a theory of non-Markovian
multiple-time correlation functions (MTCF) for a wide class of systems. We
derive the dynamical equation of the {\it reduced propagator}, an object that
evolve state vectors of the system conditioned to the dynamics of its
environment, which is not necessarily at the vacuum state at the initial time.
Such reduced propagator is the essential piece to obtain multiple-time
correlation functions. An average over the different environmental histories of
the reduced propagator permits us to obtain the evolution equations of the
multiple-time correlation functions. We also study the evolution of MTCF within
the weak coupling limit and it is shown that the multiple-time correlation
function of some observables satisfy the Quantum Regression Theorem (QRT),
whereas other correlations do not. We set the conditions under which the
correlations satisfy the QRT. We illustrate the theory in two different cases;
first, solving an exact model for which the MTCF are explicitly given, and
second, presenting the results of a numerical integration for a system coupled
with a dissipative environment through a non-diagonal interaction.


title:
BDSW protocol revisited: an efficient method for the key distillation
  without classical computational complexity

abstract:
  In quantum key distribution(QKD), one can use a classical CSS code to distill
the final key. However, there is a constraint for the two codes in CSS code and
so far it is unknown how to construct a large CSS code efficiently. Here we
show that the BDSW method given by Bennett et al can be modified and the error
correction and privacy amplification can be done separately with two
INDEPENDENT parity matrices. With such a modification, BDSW method can be used
to distill the final key without any classical computational complexity. We
also apply the method to the case of imperfect source where a small fraction of
signals are tagged by Eve.


title: Creating single time-bin entangled photon pairs

abstract:
  When a single emitter is excited by two phase-coherent pulses with a time
delay, each of the pulses can lead to the emission of a photon pair, thus
creating a ``time-bin entangled'' state. Double pair emission can be avoided by
initially preparing the emitter in a metastable state. We show how photons from
separate emissions can be made indistinguishable, permitting their use for
multi-photon interference. Possible realizations are discussed. The method
might also allow the direct creation of n-photon entangled states (n>2).


title: Quantum and classical fidelities for Gaussian states

abstract:
  We examine the physical significance of fidelity as a measure of similarity
for Gaussian states, by drawing a comparison with its classical counterpart. We
find that the relationship between these classical and quantum fidelities is
not straightforward, and in general does not seem to provide insight into the
physical significance of quantum fidelity. To avoid this ambiguity we propose
that the efficacy of quantum information protocols be characterized by
determining their transfer function and then calculating the fidelity
achievable for a hypothetical pure reference input state.


title:
Short-time decoherence of Josephson charge qubit nonlinearly coupling
  with its environment

abstract:
  At first, we generally investigate the short-time decoherence of a qubit
nonlinearly coupling with a bath. The measure of the decoherence is chosen as
the maximum norm of the deviation density operator. Then we concretely
investigate the Josephson charge qubit (JCQ) model. It is shown that at the
temperature T=30mK, the loss of fidelity (due to decoherence) of the JCQ is
bigger than the DiVincenzo low decoherence criterion. The decoherence will
decrease with the decrease of the experimental temperature. When the
temperature decreases to T=0.3mK the DiVincenzo low decoherence criterion can
be satisfied.


title: Multi-dimensional trio coherent states

abstract:
  We introduce a novel class of higher-order, three-mode states called
K-dimensional trio coherent states. We study their mathematical properties and
prove that they form a complete set in a truncated Fock space. We also study
their physical content by explicitly showing that they exhibit nonclassical
features such as oscillatory number distribution, sub-poissonian statistics,
Cauchy-Schwarz inequality violation and phase-space quantum interferences.
Finally, we propose an experimental scheme to realize the state with K=2 in the
quantized vibronic motion of a trapped ion.


title:
A robust one-step catalytic machine for high fidelity anti-cloning and
  W-state generation in a multi-qubit system

abstract:
  We propose a physically realizable machine which can either generate
multiparticle W-like states, or implement high fidelity $1 \to M$ ($M=1,2,...
\infty$) anti-cloning of an arbitrary qubit state, in a single step. Moreover
this universal machine acts as a catalyst in that it is unchanged after either
procedure, effectively resetting itself for its next operation. It also
possesses an inherent {\em immunity} to decoherence. Most importantly in terms
of practical multi-party quantum communication, the machine's robustness in the
presence of decoherence actually {\em increases} as the number of qubits $M$
increases.


title: Cavity broadcasting via Raman scattering

abstract:
  The notion of broadcasting is extended to include the case where an arbitrary
input density state of a two-mode radiation field gives rise to an output state
with identical marginal states for the respective modes, albeit different from
the input state. The initial unknown input density state is unitarily related
to the output state but is not equal to the two identical output marginal
states. This extended notion of broadcasting suggests a possible way of
discriminating between two noncommuting quantum states.


title: Channel kets, entangled states, and the location of quantum information

abstract:
  The well-known duality relating entangled states and noisy quantum channels
is expressed in terms of a channel ket, a pure state on a suitable tripartite
system, which functions as a pre-probability allowing the calculation of
statistical correlations between, for example, the entrance and exit of a
channel, once a framework has been chosen so as to allow a consistent set of
probabilities. In each framework the standard notions of ordinary (classical)
information theory apply, and it makes sense to ask whether information of a
particular sort about one system is or is not present in another system.
Quantum effects arise when a single pre-probability is used to compute
statistical correlations in different incompatible frameworks, and various
constraints on the presence and absence of different kinds of information are
expressed in a set of all-or-nothing theorems which generalize or give a
precise meaning to the concept of ``no-cloning.'' These theorems are used to
discuss: the location of information in quantum channels modeled using a
mixed-state environment; the $CQ$ (classical-quantum) channels introduced by
Holevo; and the location of information in the physical carriers of a quantum
code. It is proposed that both channel and entanglement problems be classified
in terms of pure states (functioning as pre-probabilities) on systems of $p\geq
2$ parts, with mixed bipartite entanglement and simple noisy channels belonging
to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by
the dimensions of the Hilbert spaces of the component parts, along with other
criteria yet to be determined.


title:
Experimental Hamiltonian Identification for Qubits subject to Multiple
  Independent Control Mechanisms

abstract:
  We consider a qubit subject to various independent control mechanisms and
present a general strategy to identify both the internal Hamiltonian and the
interaction Hamiltonian for each control mechanism, relying only on a single,
fixed readout process such as $\sigma_z$ measurements.


title:
Synchronization of internal and external degrees of freedom of atoms in
  a standing laser wave

abstract:
  We consider dissipative dynamics of atoms in a strong standing laser wave and
find a nonlinear dynamical effect of synchronization between center-of-mass
motion and internal Rabi oscillations. The synchronization manifests itself in
the phase space as limit cycles which may have different periods and riddled
basins of attraction. The effect can be detected in the fluorescence spectra of
atoms as equidistant sideband frequencies with the space between adjacent peaks
to be inversely proportional to the value of the period of the respective limit
cycle. With increasing the intensity of the laser field, we observe numerically
cascades of bifurcations that eventually end up in settling a strange chaotic
attractor. A broadband noise is shown to destroy a fine structure of the
bifurcation scenario, but prominent features of period-1 and period-3 limit
cycles survive under a weak noise. The character of the atomic motion is
analyzed with the help of the friction force whose zeroes are attractor or
repellor points in the velocity space. We find ranges of the laser parameters
where the atomic motion resembles a random but deterministic walking of atoms
erratically jumping between different wells of the optical potential. Such a
random walking is shown to be fractal in the sense that the measured
characteristic of the motion, time of exit of atoms from a given space of the
standing wave, is a complicated function that has a self-similar structure with
singularities on a Cantor set of values of one of the control parameters.


title: Quantum benchmark for storage and transmission of coherent states

abstract:
  We consider the storage and transmission of a Gaussian distributed set of
coherent states of continuous variable systems. We prove a limit on the average
fidelity achievable when the states are transmitted or stored by a classical
channel, i.e., a measure and repreparation scheme which sends or stores
classical information only. The obtained bound is tight and serves as a
benchmark which has to be surpassed by quantum channels in order to outperform
any classical strategy. The success in experimental demonstrations of quantum
memories as well as quantum teleportation has to be judged on this footing.


title:
Continuous variable noise-free states in correlated quantum noisy
  channels

abstract:
  We explicitly compute the evolution of the density operator of a two-mode
electromagnetic field when the influence of the thermal fluctuation of the
vacuum is common for both modes. From this result, we give an example in which
the bundle of quantum noisy channels turns out to be noiseless for the special
type of signal states due to the correlation.


title: Energy-time entangled qutrits: Bell tests and quantum communication

abstract:
  We have developed a scheme to generate, control, transmit and measure
entangled photonic qutrits (two photons each of dimension d = 3). A Bell test
of this source has previously been reported elsewhere [1], therefore, here we
focus on how the control of the system is realized. Motivated by these results,
we outline how the scheme can be used for two specific quantum protocols,
namely key distribution and coin tossing and discuss some of their advantages
and disadvantages.


title: Persistent Entanglement in the Classical Limit

abstract:
  The apparent difficulty in recovering classical nonlinear dynamics and chaos
from standard quantum mechanics has been the subject of a great deal of
interest over the last twenty years. For open quantum systems - those coupled
to a dissipative environment and/or a measurement device - it has been
demonstrated that chaotic-like behaviour can be recovered in the appropriate
classical limit. In this paper, we investigate the entanglement generated
between two nonlinear oscillators, coupled to each other and to their
environment. Entanglement - the inability to factorise coupled quantum systems
into their constituent parts - is one of the defining features of quantum
mechanics. Indeed, it underpins many of the recent developments in quantum
technologies. Here we show that the entanglement characteristics of two
`classical' states (chaotic and periodic solutions) differ significantly in the
classical limit. In particular, we show that significant levels of entanglement
are preserved only in the chaotic-like solutions.


title: Quantum marginal problem and representations of the symmetric group

abstract:
  We discuss existence of mixed state of multicomponent system with given
spectrum and given reduced density matrices. We give a complete solution of the
problem in terms of linear inequalities on the spectra, accompanied with
extensive tables of marginal inequalities, including arrays up to 4 qubits. In
the second part of the paper we pursue another approach based on reduction of
the problem to representation theory of the symmetric group.


title: Two-dimensional Bloch oscillations: A Lie-algebraic approach

abstract:
  A Lie-algebraic approach successfully used to describe one-dimensional Bloch
oscillations in a tight-binding approximation is extended to two dimensions.
This extension has the same algebraic structure as the one-dimensional case
while the dynamics shows a much richer behaviour. The Bloch oscillations are
discussed using analytical expressions for expectation values and widths of the
operators of the algebra. It is shown under which conditions the oscillations
survive in two dimensions and the centre of mass of a wave packet shows a
Lissajous like motion. In contrast to the one-dimensional case, a wavepacket
shows systematic dispersion that depends on the direction of the field and the
dispersion relation of the field free system.


title:
A multiple-scattering approach to interatomic interactions and
  superradiance in inhomogeneous dielectrics

abstract:
  The dynamics of a collection of resonant atoms embedded inside an
inhomogeneous nondispersive and lossless dielectric is described with a dipole
Hamiltonian that is based on a canonical quantization theory. The dielectric is
described macroscopically by a position-dependent dielectric function and the
atoms as microscopic harmonic oscillators. We identify and discuss the role of
several types of Green tensors that describe the spatio-temporal propagation of
field operators. After integrating out the atomic degrees of freedom, a
multiple-scattering formalism emerges in which an exact Lippmann-Schwinger
equation for the electric field operator plays a central role. The equation
describes atoms as point sources and point scatterers for light. First,
single-atom properties are calculated such as position-dependent
spontaneous-emission rates as well as differential cross sections for elastic
scattering and for resonance fluorescence. Secondly, multi-atom processes are
studied. It is shown that the medium modifies both the resonant and the static
parts of the dipole-dipole interactions. These interatomic interactions may
cause the atoms to scatter and emit light cooperatively. Unlike in free space,
differences in position-dependent emission rates and radiative line shifts
influence cooperative decay in the dielectric. As a generic example, it is
shown that near a partially reflecting plane there is a sharp transition from
two-atom superradiance to single-atom emission as the atomic positions are
varied.


title: All Quantum Adversary Methods are Equivalent

abstract:
  The quantum adversary method is one of the most versatile lower-bound methods
for quantum algorithms. We show that all known variants of this method are
equivalent: spectral adversary (Barnum, Saks, and Szegedy, 2003), weighted
adversary (Ambainis, 2003), strong weighted adversary (Zhang, 2005), and the
Kolmogorov complexity adversary (Laplante and Magniez, 2004). We also pa few
new equivalent formulations of the method. This shows that there is essentially
_one_ quantum adversary method. From our approach, all known limitations of
these versions of the quantum adversary method easily follow.


title: The Schrodinger picture and the zero-point radiation

abstract:
  Dalibard, Dupont-Roc and Cohen-Tannoudji (J. Physique 43 (1982) 1617; 45
(1984) 637) used the Heisenberg picture to show that the atomic transitions,
and the stability of the ground state, can only be explained by introducing
radiation reaction and vacuum fluctuation forces. Here we consider the simple
case of nonrelativistic charged harmonic oscillator, in one dimension, to
investigate how to take into account the radiation reaction and vacuum
fluctuation forces within the Schrodinger picture. We consider classical vacuum
fields and large mass oscillator.


title:
The Segal-Bargmann transform for noncompact symmetric spaces of the
  complex type

abstract:
  We consider the generalized Segal-Bargmann transform, defined in terms of the
heat operator, for a noncompact symmetric space of the complex type. For radial
functions, we show that the Segal-Bargmann transform is a unitary map onto a
certain L^2 space of meromorphic functions. For general functions, we give an
inversion formula for the Segal-Bargmann transform, involving integration
against an "unwrapped" version of the heat kernel for the dual compact
symmetric space. Both results involve delicate cancellations of singularities.


title:
Tunneling as a classical escape rate induced by the vacuum zero-point
  radiation

abstract:
  We make a brief review of the Kramers escape rate theory for the
probabilistic motion of a particle in a potential well U(x), and under the
influence of classical fluctuation forces. The Kramers theory is extended in
order to take into account the action of the thermal and zero-point random
electromagnetic fields on a charged particle. The result is physically relevant
because we get a non null escape rate over the potential barrier at low
temperatures (T -> 0). It is found that, even if the mean energy is much
smaller than the barrier height, the classical particle can escape from the
potential well due to the action of the zero-point fluctuating fields. These
stochastic effects can be used to give a classical interpretation to some
quantum tunneling phenomena. Relevant experimental data are used to illustrate
the theoretical results.


title:
Spin wave based quantum storage of electronic spin with a ring array of
  nuclear spins

abstract:
  We propose a solid state based protocol to implement the universal quantum
storage for electronic spin qubit. The quantum memory in this scheme is the
spin wave excitation in the ring array of nuclei in a quantum dot. We show that
the quantum information carried by an arbitrary state of the electronic spin
can be coherently mapped onto the spin wave excitations or the magnon states.
With an appropriate external control, the stored quantum state in quantum
memory can be read out reversibly. We also explore in detail the quantum
decoherence mechanism due to the inhomogeneous couplings between the electronic
spin and the nuclear spins.


title: Controllability of Scattering States of Quantum Mechanical Systems

abstract:
  This paper provides a framework for the control of quantum mechanical systems
with scattering states, i.e., systems with continuous spectra. We present the
concept and prove a criterion of the approximate strong smooth controllability.
Our results make non-trivial extensions from quantum systems with finite
dimensional control Lie algebras to those with infinite dimensions. It also
opens up many interesting problems for future studies.


title: Quantum Fourier Transform in a Decoherence-Free Subspace

abstract:
  Quantum Fourier transform is of primary importance in many quantum
algorithms. In order to eliminate the destructive effects of decoherence
induced by couplings between the quantum system and its environment, we propose
a robust scheme for quantum Fourier transform over the intrinsic
decoherence-free subspaces. The scheme is then applied to the circuit design of
quantum Fourier transform over quantum networks under collective decoherence.
The encoding efficiency and possible improvements are also discussed.


title:
The time evolution of coherent atomic system and probe light in an EIT
  medium

abstract:
  The adiabatic solutions of Maxwell-Bloch equation governing the three-level
EIT medium is presented. The time evolution of the density matrix elements of
the EIT system and the probe light is thus investigated by using the adiabatic
approximation formulation and the slowly varying envelope condition.