title: Entanglement in phase space

abstract:
  Classical surfaces in phase space correspond to quantum states in Hilbert
space. Subsystems specify factor spaces of the Hilbert space. An entangled
state corresponds semiclassically to a surface that cannot be decomposed into a
product of lower dimensional surfaces. Such a classical factorization never
exists for ergodic eigenstates of a chaotic Hamiltonian. The space of quantum
operators corresponds to a double phase space. The various representations of
the density operator then result from alternative choices of allowed coordinate
planes. In the case of the Wigner function and its Fourier transform, the chord
function, or the quantum characteristic function, this is a phase space on its
own. The reduced Wigner function, representing the partial trace of a density
operator over a subsystem is the projection of the original Wigner function;
the reduced chord function is obtained as a section. The purity of the reduced
density operator, the square of its trace, is a measure of entanglement,
obtained by integrating either the square of the reduced Wigner function, or
the square-modulus of the reduced chord function. Bell inequalities for general
parity measurements can be violated even for classical looking states with
positive Wigner functions that have evolved classically from product states.
These include the original EPR state. Entanglement with an unknown environment
results in decoherence. An example is that of the centre of mass of a large
number of independent particles, entangled with internal variables. In this
case, the Central Limit Theorem for Wigner functions leads to some aspects of
Markovian evolution for the reduced system.


title: Coupled oscillators and Feynman's three papers

abstract:
  According to Richard Feynman, the adventure of our science of physics is a
perpetual attempt to recognize that the different aspects of nature are really
different aspects of the same thing. It is therefore interesting to combine
some, if not all, of Feynman's papers into one. The first of his three papers
is on the ``rest of the universe'' contained in his 1972 book on statistical
mechanics. The second idea is Feynman's parton picture which he presented in
1969 at the Stony Brook conference on high-energy physics. The third idea is
contained in the 1971 paper he published with his students, where they show
that the hadronic spectra on Regge trajectories are manifestations of
harmonic-oscillator degeneracies. In this report, we formulate these three
ideas using the mathematics of two coupled oscillators. It is shown that the
idea of entanglement is contained in his rest of the universe, and can be
extended to a space-time entanglement. It is shown also that his parton model
and the static quark model can be combined into one Lorentz-covariant entity.
Furthermore, Einstein's special relativity, based on the Lorentz group, can
also be formulated within the mathematical framework of two coupled
oscillators.


title:
Quantum jumps of light recording the birth and death of a photon in a
  cavity

abstract:
  A microscopic system under continuous observation exhibits at random times
sudden jumps between its states. The detection of this essential quantum
feature requires a quantum non-demolition (QND) measurement repeated many times
during the system evolution. Quantum jumps of trapped massive particles
(electrons, ions or molecules) have been observed, which is not the case of the
jumps of light quanta. Usual photodetectors absorb light and are thus unable to
detect the same photon twice. They must be replaced by a transparent counter
'seeing' photons without destroying them3. Moreover, the light has to be stored
over a duration much longer than the QND detection time. We have fulfilled
these challenging conditions and observed photon number quantum jumps.
Microwave photons are stored in a superconducting cavity for times in the
second range. They are repeatedly probed by a stream of non-absorbing atoms. An
atom interferometer measures the atomic dipole phase shift induced by the
non-resonant cavity field, so that the final atom state reveals directly the
presence of a single photon in the cavity. Sequences of hundreds of atoms
highly correlated in the same state, are interrupted by sudden
state-switchings. These telegraphic signals record, for the first time, the
birth, life and death of individual photons. Applying a similar QND procedure
to mesoscopic fields with tens of photons opens new perspectives for the
exploration of the quantum to classical boundary.


title: A New Look at the Quantum Mechanics of the Harmonic Oscillator

abstract:
  Classically the Harmonic Oscillator (HO) is the generic example for the use
of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic
transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally
{(q,p)} has the structure of the plane R^2, but {(phi,I)} that of the punctured
plane R^2 -(0,0). This implies qualitative differences for the QM of the two
phase spaces: The quantizing group for the plane R^2 consists of the (centrally
extended) translations generated by {q,p,1}, but the corresponding group for
{(phi,I)} is SO(1,2) = Sp(2,R)/Z_2, (Sp(2,R): symplectic group of the plane),
with Lie algebra basis {h_0 = I, h_1 = I cos phi, h_2 = - I sin phi}. In the QM
for the (phi,I)-model the three h_j correspond to self-adjoint generators K_j,
j=0,1,2, of irreducible unitary representations (positive discrete series) for
SO(1,2) or one of its infinitely many covering groups, the Bargmann index k > 0
of which determines the ground state energy E (k, n=0) = hbar omega k of the
(phi,I)-Hamiltonian H(K). For an m-fold covering the lowest possible value is
k=1/m, which can be made arbitrarily small! The operators Q and P, now
expressed as functions of the K_j, keep their usual properties, but the richer
structure of the K_j quantum model of the HO is ``erased'' when passing to the
simpler Q,P model! The (phi,I)-variant of the HO implies many experimental
tests: Mulliken-type experiments for isotopic diatomic molecules, experiments
with harmonic traps for atoms, ions and BE-condensates, with the (Landau)
levels of charged particles in magnetic fields, with the propagation of light
in vacuum, passing through electric or magnetic fields. Finally it leads to a
new theoretical estimate for the quantum vacuum energy of fields and its
relation to the cosmological constant.

categories: quant-ph astro-ph hep-th math-ph math.MP physics.atom-ph


title:
Approche intrins\`{e}que des fluctuations quantiques en m\'{e}canique
  stochastique (An intrinsic approach of the quantum fluctuations in stochastic
  mechanics)

abstract:
  This note is answering an old questioning about the F\'{e}nyes-Nelson
stochastic mechanics. The Brownian nature of the quantum fluctuations, which
are associated to this mechanics, is deduced from Feynman's interpretation of
the Heisenberg uncertainty principle via infinitesimal random walks stemming
from nonstandard analysis. It is therefore no more necessary to combine those
fluctuations with a background field, which has never been well understood.
Most of the technical details are contained in an extended english abstract.


title:
Distinguishing Arbitrary Multipartite Basis Unambiguously Using Local
  Operations and Classical Communication

abstract:
  We show that an arbitrary basis of a multipartite quantum state space
consisting of $K$ distant parties such that the $k$th party has local dimension
$d_k$ always contains at least $N=\sum_{k=1}^K (d_k-1)+1$ members that are
unambiguously distinguishable using local operations and classical
communication (LOCC). We further show this lower bound is optimal by
analytically constructing a special product basis having only $N$ members
unambiguously distinguishable by LOCC. Interestingly, such a special product
basis not only gives a stronger form of the weird phenomenon ``nonlocality
without entanglement", but also implies the existence of locally
distinguishable entangled basis.


title: A Meaner King uses Biased Bases

abstract:
  The mean king problem is a quantum mechanical retrodiction problem, in which
Alice has to name the outcome of an ideal measurement on a d-dimensional
quantum system, made in one of (d+1) orthonormal bases, unknown to Alice at the
time of the measurement. Alice has to make this retrodiction on the basis of
the classical outcomes of a suitable control measurement including an entangled
copy. We show that the existence of a strategy for Alice is equivalent to the
existence of an overall joint probability distribution for (d+1) random
variables, whose marginal pair distributions are fixed as the transition
probability matrices of the given bases. In particular, for d=2 the problem is
decided by John Bell's classic inequality for three dichotomic variables. For
mutually unbiased bases in any dimension Alice has a strategy, but for randomly
chosen bases the probability for that goes rapidly to zero with increasing d.


title:
"Physical quantity" and " Physical reality" in Quantum Mechanics: an
  epistemological path

abstract:
  We reconsider briefly the relation between "physical quantity" and "physical
reality in the light of recent interpretations of Quantum Mechanics. We argue,
that these interpretations are conditioned from the epistemological relation
between these two fundamental concepts. In detail, the choice as ontic level of
the concept affect, the relative interpretation. We note, for instance, that
the informational view of quantum mechanics (primacy of the subjectivity) is
due mainly to the evidence of the "random" physical quantities as ontic
element. We will analyze four positions: Einstein, Rovelli, d'Espagnat and
Zeilinger.


title: Generalized Phase Space Representation of Operators

abstract:
  Introducing asymmetry into the Weyl representation of operators leads to a
variety of phase space representations and new symbols. Specific
generalizations of the Husimi and the Glauber-Sudarshan symbols are explicitly
derived


title: Quantum Brownian motion and the second law of thermodynamics

abstract:
  We consider a single harmonic oscillator coupled to a bath at zero
temperature. As is well known, the oscillator then has a higher average energy
than that given by its ground state. Here we show analytically that for a
damping model with arbitrarily discrete distribution of bath modes and damping
models with continuous distributions of bath modes with cut-off frequencies,
this excess energy is less than the work needed to couple the system to the
bath, therefore, the quantum second law is not violated. On the other hand, the
second law may be violated for bath modes without cut-off frequencies, which
are, however, physically unrealistic models.


title: Oscillation dynamics of multi-well condensates

abstract:
  We propose a new approach to the macroscopic dynamics of three-well
Bose-Einstein condensates, giving particular emphasis to self-trapping and
Josephson oscillations. Although these effects have been studied quite
thoroughly in the mean-field approximation, a full quantum description is
desirable, since it avoids pathologies due to the nonlinear character of the
mean-field equations. Using superpositions of quantum eigenstates, we construct
various oscillation and trapping scenarios.


title: Quasiprobability methods for multimode conditional optical gates

abstract:
  We present a method for computing the action of conditional linear optical
transformations, conditioned on photon counting, for arbitrary signal states.
The method is based on the Q-function, a quasi probability distribution for
anti normally ordered moments. We treat an arbitrary number of signal and
ancilla modes. The ancilla modes are prepared in an arbitrary product number
state. We construct the conditional, non unitary, signal transformations for an
arbitrary photon number count on each of the ancilla modes.


title: Entanglement in the interaction between two quantum oscillator systems

abstract:
  The fundamental quantum dynamics of two interacting oscillator systems are
studied in two different scenarios. In one case, both oscillators are assumed
to be linear, whereas in the second case, one oscillator is linear and the
other is a non-linear, angular-momentum oscillator; the second case is, of
course, more complex in terms of energy transfer and dynamics. These two
scenarios have been the subject of much interest over the years, especially in
developing an understanding of modern concepts in quantum optics and quantum
electronics. In this work, however, these two scenarios are utilized to
consider and discuss the salient features of quantum behaviors resulting from
the interactive nature of the two oscillators, i.e., coherence, entanglement,
spontaneous emission, etc., and to apply a measure of entanglement in analyzing
the nature of the interacting systems. ... For the coupled linear and
angular-momentum oscillator system in the fully quantum-mechanical description,
we consider special examples of two, three, four-level angular momentum
systems, demonstrating the explicit appearances of entanglement. We also show
that this entanglement persists even as the coupled angular momentum oscillator
is taken to the limit of a large number of levels, a limit which would go over
to the classical picture for an uncoupled angular momentum oscillator.


title:
Quantum dynamics of the dissipative two-state system coupled with a
  sub-Ohmic bath

abstract:
  The decoherence of a two-state system coupled with a sub-Ohmic bath is
investigated theoretically by means of the perturbation approach based on a
unitary transformation. It is shown that the decoherence depends strongly and
sensitively on the structure of environment. Nonadiabatic effect is treated
through the introduction of a function $\xi_k$ which depends on the boson
frequency and renormalized tunneling. The results are as follows:(1) the
non-equilibrium correlation function $P(t)$, the dynamical susceptibility
$\chi''(\omega)$ and the equilibrium correlation function $C(t)$ are
analytically obtained for $s\leq 1$; (2) the phase diagram of thermodynamic
transition shows the delocalized-localized transition point $\alpha_l$ which
agrees with exact results and numerical data from the Numerical Renormalization
Group; (3) the dynamical transition point $\alpha_c$ between coherent and
incoherent phase is explicitly given for the first time. A crossover from the
coherent oscillation to incoherent relaxation appears with increasing coupling
(for $\alpha > \alpha_c $, the coherent dynamics disappear); (4) the Shiba's
relation and sum rule are exactly satisfied when $\alpha \leq \alpha_c $; (5)
an underdamping-overdamping transition point $\alpha_c^{*}$ exists in the
function $S(\omega)$. Consequently, the dynamical phase diagrams in both ohmic
and sub-Ohmic case are mapped out. For $\Delta \ll \omega_c$, the critical
couplings ($\alpha_l, \alpha_c$ and $\alpha_c^{*}$) are proportional to
$\Delta^{1-s}$.


title:
On quantum corrections to classical solutions via generalized
  zeta-function

abstract:
  A general algebraic method of quantum corrections evaluations is presented.
Quantum corrections to a few classical solutions of Landau-Ginzburg model
(phi-in-quadro) are calculated in arbitrary dimensions. The Green function for
heat equation with soliton potential is constructed by Darboux transformation.
The generalized zeta-function is used to evaluate the functional integral and
corrections to mass in quasiclassical approximation. Some natural
generalizations for matrix equations are discussed in conclusion.


title: Bell-type inequalities for cold heteronuclear molecules

abstract:
  We introduce Bell-type inequalities allowing for non-locality and
entanglement tests with two cold heteronuclear molecules. The proposed
inequalities are based on correlations between each molecule spatial
orientation, an observable which can be experimentally measured with present
day technology. Orientation measurements are performed on each subsystem at
diferent times. These times play the role of the polarizer angles in Bell tests
realized with photons. We discuss the experimental implementations of the
proposed tests, which could also be adapted to other high dimensional quantum
angular momenta systems.


title: Accumulation of entanglement in a continuous variable memory

abstract:
  We study the accumulation of entanglement in a memory device built out of two
continuous variable (CV) systems. We address the case of a qubit mediating an
indirect joint interaction between the CV systems. We show that, in striking
contrast with respect to registers built out of bidimensional Hilbert spaces,
entanglement superior to a single ebit can be efficiently accumulated in the
memory, even though no entangled resource is used. We study the protocol in an
immediately implementable setup, assessing the effects of the main
imperfections.


title: Electrically addressing a single self-assembled quantum dot

abstract:
  We report on the use of an aperture in an aluminum oxide layer to restrict
current injection into a single self-assembled InAs quantum dot, from an
ensemble of such dots within a large mesa. The insulating aperture is formed
through the wet-oxidation of a layer of AlAs. Under photoluminescence we
observe that only one quantum dot in the ensemble exhibits a Stark shift, and
that the same single dot is visible under electroluminescence. Autocorrelation
measurements performed on the electroluminescence confirm that we are observing
emission from a single quantum dot.


title:
Control of fine-structure splitting of individual InAs quantum dots by
  rapid thermal annealing

abstract:
  Degeneracy of the bright single exciton spin state is a prerequisite for the
production of triggered polarization-entangled photon pairs from the biexciton
decay of a quantum dot. Normally, however, the exciton spin states are split
due to in-plane asymmetries. Here we demonstrate that the exciton splitting of
an individual dot can be tuned through zero by thermal annealing. Repeated
annealing blueshifts the exciton emission line of the dot, accompanied by a
reduction and inversion in polarization splitting. Annealing is also
demonstrated to control the detuning between the exciton and biexciton
transitions in any selected dot.


title: Nilpotent polynomials approach to four-qubit entanglement

abstract:
  We apply the general formalism of nilpotent polynomials [Mandilara et al,
Phys. Rev. A 74, 022331 (2006)] to the problem of pure-state multipartite
entanglement classification in four qubits. In addition to establishing contact
with existing results, we explicitly show how the nilpotent formalism naturally
suggests constructions of entanglement measures invariant under the required
unitary or invertible class of local operations. A candidate measure of
fourpartite entanglement is also suggested, and its behavior numerically tested
on random pure states.


title: Constrained bounds on measures of entanglement

abstract:
  Entanglement measures constructed from two positive, but not completely
positive maps on density operators are used as constraints in placing bounds on
the entanglement of formation, the tangle, and the concurrence of 4 x N mixed
states. The maps are the partial transpose map and the $\Phi$-map introduced by
Breuer [H.-P. Breuer, Phys. Rev. Lett. 97, 080501 (2006)]. The norm-based
entanglement measures constructed from these two maps, called negativity and
$\Phi$-negativity, respectively, lead to two sets of bounds on the entanglement
of formation, the tangle, and the concurrence. We compare these bounds and
identify the sets of 4 x N density operators for which the bounds from one
constraint are better than the bounds from the other. In the process, we
present a new derivation of the already known bound on the concurrence based on
the negativity. We compute new bounds on the three measures of entanglement
using both the constraints simultaneously. We demonstrate how such doubly
constrained bounds can be constructed. We discuss extensions of our results to
bipartite states of higher dimensions and with more than two constraints.


title: The exact cost of redistributing multipartite quantum states

abstract:
  How correlated are two quantum systems from the perspective of a third? We
answer this by providing an optimal quantum state redistribution protocol for
multipartite product sources. Specifically, given an arbitrary quantum state of
three systems, where Alice holds two and Bob holds one, we identify the cost,
in terms of quantum communication and entanglement, for Alice to give one of
her parts to Bob. The communication cost gives the first known operational
interpretation to quantum conditional mutual information. The optimal procedure
is self-dual under time reversal and is perfectly composable. This generalizes
known protocols such as the state merging and fully quantum Slepian-Wolf
protocols, from which almost every known protocol in quantum Shannon theory can
be derived.


title: A Quantum Logic of Down Below

abstract:
  This chapter is offered as a contribution to the logic of down below. We
attempt to demonstrate that the nature of human agency necessitates that there
actually be such a logic. The ensuing sections develop the suggestion that
cognition down below has a structure strikingly similar to the physical
structure of quantum states. In its general form, this is not an idea that
originates with the present authors. It is known that there exist mathematical
models from the cognitive science of cognition down below that have certain
formal similarities to quantum mechanics. We want to take this idea seriously.
We will propose that the subspaces of von Neumann-Birkhoff lattices are too
crisp for modelling requisite cognitive aspects in relation to subsymbolic
logic. Instead, we adopt an approach which relies on projections into
nonorthogonal density states. The projection operator is motivated from cues
which probe human memory.


title:
Deciding whether a quantum state has secret correlations is an
  NP-complete problem

abstract:
  From the NP-hardness of the quantum separability problem and the relation
between bipartite entanglement and the secret key correlations, it is shown
that the problem deciding whether a given quantum state has secret correlations
in it or not is in NP-complete.


title: Comments on "Best conventional solutions to the King's problem"

abstract:
  Conventional solutions to the (Mean) King's problem without using
entanglement have been investigated by Aravind [P. K. Aravind, ``Best
conventional solutions to the King's problem'', Z. Naturforsch. 58a, 682
(2003)]. We report that the upper bound for the success probability claimed
there is not valid in general, and give a condition for the claim to be
justified.


title: Quantization and noiseless measurements

abstract:
  In accordance with the fact that quantum measurements are described in terms
of positive operator measures (POMs), we consider certain aspects of a
quantization scheme in which a classical variable $f:\R^2\to \R$ is associated
with a unique positive operator measure (POM) $E^f$, which is not necessarily
projection valued. The motivation for such a scheme comes from the well-known
fact that due to the noise in a quantum measurement, the resulting outcome
distribution is given by a POM and cannot, in general, be described in terms of
a traditional observable, a selfadjoint operator. Accordingly, we notice that
the noiseless measurements are the ones which are determined by a selfadjoint
operator. The POM $E^f$ in our quantization is defined through its moment
operators, which are required to be of the form $\Gamma(f^k)$, $k\in \N$, with
$\Gamma$ a fixed map from classical variables to Hilbert space operators. In
particular, we consider the quantization of classical \emph{questions}, that
is, functions $f:\R^2\to\R$ taking only values 0 and 1. We compare two concrete
realizations of the map $\Gamma$ in view of their ability to produce noiseless
measurements: one being the Weyl map, and the other defined by using phase
space probability distributions.


title: An atom-photon pair laser

abstract:
  We study the quantum dynamics of an ultracold atomic gas in a deep optical
lattice within an optical high-$Q$ resonator. The atoms are coherently
illuminated with the cavity resonance tuned to a blue vibrational sideband, so
that photon scattering to the resonator mode is accompanied by vibrational
cooling of the atoms. This system exhibits a threshold above which pairwise
stimulated generation of a cavity photon and an atom in the lowest vibrational
band dominates spontaneous scattering and we find a combination of optical
lasing with a buildup of a macroscopic population in the lowest lattice band.
Including output coupling of ground-state atoms and replenishing of hot atoms
into the cavity volume leads to a coherent, quantum correlated atom-photon pair
source very analogous to twin light beam generation in a nondegenerate optical
parametric oscillator.


title: Hopf Algebra Structure of a Model Quantum Field Theory

abstract:
  Recent elegant work on the structure of Perturbative Quantum Field Theory
(PQFT) has revealed an astonishing interplay between analysis(Riemann Zeta
functions), topology (Knot theory), combinatorial graph theory (Feynman
Diagrams) and algebra (Hopf structure). The difficulty inherent in the
complexities of a fully-fledged field theory such as PQFT means that the
essential beauty of the relationships between these areas can be somewhat
obscured. Our intention is to display some, although not all, of these
structures in the context of a simple zero-dimensional field theory; i.e. a
quantum theory of non-commuting operators which do not depend on spacetime. The
combinatorial properties of these boson creation and annihilation operators,
which is our chosen example, may be described by graphs, analogous to the
Feynman diagrams of PQFT, which we show possess a Hopf algebra structure. Our
approach is based on the partition function for a boson gas. In a subsequent
note in these Proceedings we sketch the relationship between the Hopf algebra
of our simple model and that of the PQFT algebra.


title:
Mesoscopic entanglement of atomic ensembles through non-resonant
  stimulated Raman scattering

abstract:
  We propose a scheme of generating and verifying mesoscopic-level entanglement
between two atomic ensembles using non-resonant stimulated Raman scattering.
Entanglement can be generated by direct detection or balanced homodyne
detection of the Stokes fields from the two cells, after they interfere on a
beam splitter. The entanglement of the collective atomic fields can be
transferred to the anti-Stokes fields in a readout process. By measuring the
operator moments of the anti-Stokes fields, we can verify the presence of
entanglement. We model the effects of practical factors such as Stokes field
detector quantum efficiency and additive thermal noise in the entanglement
generating process, and anti-Stokes field losses in the entanglement
verification process, and find achievable regimes in which entanglement can be
verified at the levels of tens to hundreds of atomic excitations in the
ensembles.


title: Exposed-key weakness of $\alpha \eta$

abstract:
  The $\alpha \eta$ protocol given by Barbosa \emph{et al.}, PRL 90, 227901
(2003) claims to be a secure way of encrypting messages using mesoscopic
coherent states. We show that transmission under $\alpha \eta$ exposes
information about the secret key to an eavesdropper, and we estimate the rate
at which an eavesdropper can learn about the key. We also consider the
consequences of using further randomization to protect the key and how our
analysis applies to this case. We conclude that $\alpha \eta$ is not
informationally secure.


title:
Some thoughts on an information-theoretic motivated nonlinear
  Schrodinger equation

abstract:
  I begin by reviewing the arguments leading to a nonlinear generalisation of
Schrodinger's equation within the context of the maximum uncertainty principle.
Some exact and perturbative properties of that equation are then summarised:
those results depend on a free regulating/interpolation parameter $\eta$. I
discuss here how one may fix that parameter using energetics. Other issues
discussed are, a linear theory with an external potential that reproduces some
unusual exact solutions of the nonlinear equation, and possible symmetry
enhancements in the nonlinear theory.


title:
Sub-wavelength Coherent Imaging of a Pure-Phase Object with Thermal
  Light

abstract:
  We report, for the first time, the observation of sub-wavelength coherent
image of a pure phase object with thermal light,which represents an accurate
Fourier transform. We demonstrate that ghost-imaging scheme (GI) retrieves
amplitude transmittance knowledge of objects rather than the transmitted
intensities as the HBT-type imaging scheme does.


title:
Loading N-Dimensional Vector into Quantum Registers from Classical
  Memory with O(logN) Steps

abstract:
  Vector is the general format of input data of most algorithms. Designing
unitary operation to load all information of vector into quantum registers of
quantum CPU from classical memory is called quantum loading scheme (QLS). QLS
assembles classical memory and quantum CPU as a whole computer, which will be
important for further quantum computation. We present a QLS based on path
interference with time complexity O(logN), while classical loading scheme has
time complexity O(N), that is the efficiency bottleneck of classical computer.


title:
Finite quantum environments as thermostats: an analysis based on the
  Hilbert space average method

abstract:
  We consider discrete quantum systems coupled to finite environments which may
possibly consist of only one particle in contrast to the standard baths which
usually consist of continua of oscillators, spins, etc. We find that such
finite environments may, nevertheless, act as thermostats, i.e., equilibrate
the system though not necessarily in the way predicted by standard open system
techniques. Thus, we apply a novel technique called the Hilbert space Average
Method (HAM) and verify its results numerically.


title: On the Power of Entangled Quantum Provers

abstract:
  We show that the value of a general two-prover quantum game cannot be
computed by a semi-definite program ofvpolynomial size (unless P=NP), a method
that has been successful in more restricted quantum games. More precisely, we
show that proof of membership in the NP-complete problem GAP-3D-Matching can be
obtained by a 2-prover, 1-round quantum interactive proof system where the
provers share entanglement, with perfect completeness and soundness
s=1-2^(-O(n)), and such that the space of the verifier and the size of the
messages are O(log n). This implies that QMIP^*_{log n,1,1-2^(-O(n))}
\nsubseteq P unless P = NP and provides the first non-trivial lower bound on
the power of entangled quantum provers, albeit with an exponentially small gap.
The gap achievable by our proof system might in fact be larger, provided a
certain conjecture on almost commuting versus nearly commuting projector
matrices is true.


title: Concurrence of Lorentz-positive maps

abstract:
  Let L_n be the n-dimensional Lorentz cone. A linear map M from R^m to R^n is
called Lorentz-positive if M[L_m] is contained in L_n. We extend the notion of
concurrence, which was initially introduced to quantify the entanglement of
bipartite density matrices, to Lorentz-positive maps and provide an explicite
formula for it. This allows us to obtain formulae for the concurrence of
arbitrary positive operators taking 2 x 2 complex hermitian matrices as input
and consequently of arbitrary bipartite density matrices of rank 2. Namely, let
P: H(2) \to H(d) be a positive operator, and let \lambda_1,...,\lambda_4 be the
generalized eigenvalues of the pencil \sigma_2(P(X)) - \lambda det X, in
decreasing order, where \sigma_2 is the second symmetric function of the
spectrum. Then the concurrence is given by the expression C(P;X) =
2\sqrt{\sigma_2(P(X)) - \lambda_2 det X}. As an application, we compute the
concurrences of the density matrices of all graphs with 2 edges. Similar
results apply for a function which we call I-fidelity, with the second largest
generalized eigenvalue \lambda_2 replaced by the smallest eigenvalue \lambda_4.


title: Quantum mechanics without measurements

abstract:
  Many of the conceptual problems students have in understanding quantum
mechanics arise from the way probabilities are introduced in standard
(textbook) quantum theory through the use of measurements. Introducing
consistent microscopic probabilities in quantum theory requires setting up
appropriate sample spaces taking proper account of quantum incompatibility.
When this is done the Schrodinger equation can be used to calculate
probabilities independent of whether a system is or is not being measured, and
the results usually ascribed to wave function collapse are obtained in a less
misleading way through conditional probabilities. Toy models that include
measurement apparatus as part of the total quantum system make this approach
accessible to students. Some comments are made about teaching this material.


title:
Improving the security of multiparty quantum secret sharing based on
  entanglement swapping against participant attack

abstract:
  In a recent paper [Z. J. Zhang and Z. X. Man, Phys. Rev. A 72, 022303(2005)],
a multiparty quantum secret sharing protocol based on entanglement swapping was
presented. However, as we show, this protocol is insecure in the sense that an
unauthorized agent group can recover the secret from the dealer. Hence, we
propose an improved version of this protocol which can stand against this kind
of attack.


title:
Continuous photodetection model: quantum jump engineering and hints for
  experimental verification

abstract:
  We examine some aspects of the continuous photodetection model for
photocounting processes in cavities. First, we work out a microscopic model
that describes the field-detector interaction and deduce a general expression
for the Quantum Jump Superoperator (QJS), that shapes the detector's
post-action on the field upon a detection. We show that in particular cases our
model recovers the QJSs previously proposed ad hoc in the literature and point
out that by adjusting the detector parameters one can engineer QJSs. Then we
set up schemes for experimental verification of the model. By taking into
account the ubiquitous non-idealities, we show that by measuring the lower
photocounts moments and the mean waiting time one can check which QJS better
describes the photocounting phenomenon.


title:
Quantum mechanics in general quantum systems (IV): Green operator and
  path integral

abstract:
  We first rewrite the perturbation expansion of the time evolution operator
[An Min Wang, quant-ph/0611216] in a form as concise as possible. Then we
derive out the perturbation expansion of the time-dependent complete Green
operator and prove that it is just the Fourier transformation of the Dyson
equation. Moreover, we obtain the perturbation expansion of the complete
transition amplitude in the Feynman path integral formulism, and give an
integral expression that relates the complete transition amplitude with the
unperturbed transition amplitude. Further applications of these results can be
expected and will be investigated in the near future.


title: Alternative perspective on photonic tunneling

abstract:
  A relativistic quantum-mechanical description of guided waves is given, based
on which we present an alternative way to describe and interpret the
propagation of electromagnetic wave packets through an undersized waveguide. In
particular, we show that the superluminal phenomenon of evanescent modes is
actually a known conclusion in quantum field theory, and it preserves a
quantum-mechanical causality.


title: Ghost Imaging: What is quantum, what is not

abstract:
  We provide a unified treatment of classical and quantum Gaussian-state
sources that unambiguously identifies which features of ghost imaging are
strictly quantum mechanical. We show that ghost-image formation is
fundamentally classical, with the image being expressible in terms of the
phase-insensitive and phase-sensitive cross correlations between the detected
fields. We then consider ghost-imaging scenarios with either phase-insensitive
or phase-sensitive sources, where the former are always classical but the
latter may be classical or quantum mechanical. We show that if their
auto-correlations are identical, then a quantum source provides resolution
improvement in its near-field and field-of-view improvement in its far field
when compared to a classical source.


title: Comment on "Quantum string seal is insecure"

abstract:
  Recently an attack strategy was proposed by Chau [H. F. Chau,
quant-ph/0602099 v3], which was claimed to be able to break all quantum string
seal protocols, including the one proposed by He [G. P. He, Int. J. Quant.
Inform. 4, 677 (2006)]. Here it will be shown that the information obtained in
He's protocol by the attack is trivial. Thus Chau's conclusion that all quantum
string seals are insecure is wrong. It will also be shown that some other
claims in Chau's paper are inaccurate either.


title:
Entanglement Distillation; A Discourse on Bound Entanglement in Quantum
  Information Theory

abstract:
  PhD thesis (University of York). The thesis covers in a unified way the
material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160,
quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large
review chapters on entanglement and distillation.


title:
Fault-tolerant linear optics quantum computation by error-detecting
  quantum state transfer

abstract:
  A scheme for linear optical implementation of fault-tolerant quantum
computation is proposed, which is based on an error-detecting code. Each
computational step is mediated by transfer of quantum information into an
ancilla system embedding error-detection capability. Photons are assumed to be
subjected to both photon loss and depolarization, and the threshold region of
their strengths for scalable quantum computation is obtained, together with the
amount of physical resources consumed. Compared to currently known results, the
present scheme reduces the resource requirement, while yielding a comparable
threshold region.


title: Quantum chaos with spin-chains in pulsed magnetic fields

abstract:
  Recently it was found that the dynamics in a Heisenberg spin-chain subjected
to a sequence of periodic pulses from an external, parabolic, magnetic field
can have a close correspondence with the quantum kicked rotor (QKR). The QKR is
a key paradigm of quantum chaos; it has as its classical limit the well-known
Standard Map. It was found that a single spin excitation could be converted
into a pair of non-dispersive, counter-propagating spin coherent states
equivalent to the accelerator modes of the Standard Map. Here we consider how
other types of quantum chaotic systems such as a double-kicked quantum rotor or
a quantum rotor with a double-well potential might be realized with spin
chains; we discuss the possibilities regarding manipulation of the one-magnon
spin waves.


title:
Experimental tests of hidden variable theories from dBB to Stochastic
  Electrodynamics

abstract:
  In this paper we present some of our experimental results on testing hidden
variable theories, which range from Bell inequalities measurements to a
conclusive test of stochastic electrodynamics.


title: A Variant and Explanation of the Delayed Choice Experiment

abstract:
  In this work we suggest a variant of the remarkable Wheeler's delayed choice
gedanken experiment. In our experiment, single photon described by a
superposition state with two terms dynamically interacts with an atom.
Preparation of the atom in any of two excited states can be realized
practically in the last moment before interaction. For atom in the first
excited state there is practically none dynamical interaction between atom and
photon so that the interference effects on the photon can be detected later by
a photo plate. For atom in the second excited state dynamical interaction
between photon and atom causes certainly the stimulated emission of a new
photon that moves coherently with the first photon. Both photons do a
super-system described by an entangled quantum state. But in this case photo
plate, that realizes simultaneously sub-systemic measurement at any photon,
does not detect interference effects. We suggest a simple explanation of given
as well as original variant of the delayed choice experiment in full agreement
with standard quantum mechanical formalism.


title: A Re-evaluation of Shor's Algorithm

abstract:
  Shor's algorithm is examined critically from the standpoint of it's eventual
use to obtain the factors of large integers.


title: Monitoring approach to open quantum dynamics using scattering theory

abstract:
  It is shown how S-matrix theory and the concept of continuous quantum
measurements can be combined to yield Markovian master equations which describe
the environmental interaction non-perturbatively. The method is then applied to
obtain the master equation for the effects of a gas on the internal dynamics of
an immobile complex quantum system, such as a trapped molecule, in terms of the
exact multi-channel scattering amplitudes.


title: Narrow entanglement beats

abstract:
  We study how the entanglement between two atoms can be created or modified
even when they do not interact but when each of them interacts dispersively,
i.e., weak and far from the resonance with a single mode of the field.
Considering that regime we apply a method which makes use of a small nonlinear
deformation of the usual SU(2) algebra in order to obtain the effective
Hamiltonian describing correctly the dynamics for any initial states. In
particular we study two cases: In the first one we consider each atom initially
in a pure state and in the second case we assume that they start in a Werner
state. We find that both atoms can reach, periodically, maximum entanglement if
each of them starts in any eigenstate of the x-componet of the Pauli oprator,
independent of the initial Fock state of the mode. Thus we find that a
dispersive vacuum can generate entanglement between two two-level atoms. In the
second case and when the field mode is initially in a coherent or thermal
state, we find that in the high energy limit, in general, there is no
entanglement between the two atoms however at well defined moments the initial
entanglement is as suddenly recovered as removed. This time behavior looks like
narrow beats separated by the so called entanglement dead valleys.


title:
Loss-Induced Limits to Phase Measurement Precision with Maximally
  Entangled States

abstract:
  The presence of loss limits the precision of an approach to phase measurement
using maximally entangled states, also referred to as NOON states. A
calculation using a simple beam-splitter model of loss shows that, for all
nonzero values L of the loss, phase measurement precision degrades with
increasing number N of entangled photons for N sufficiently large. For L above
a critical value of approximately 0.785, phase measurement precision degrades
with increasing N for all values of N. For L near zero, phase measurement
precision improves with increasing N down to a limiting precision of
approximately 1.018 L radians, attained at N approximately equal to 2.218/L,
and degrades as N increases beyond this value. Phase measurement precision with
multiple measurements and a fixed total number of photons N_T is also examined.
For L above a critical value of approximately 0.586, the ratio of phase
measurement precision attainable with NOON states to that attainable by
conventional methods using unentangled coherent states degrades with increasing
N, the number of entangled photons employed in a single measurement, for all
values of N. For L near zero this ratio is optimized by using approximately
N=1.279/L entangled photons in each measurement, yielding a precision of
approximately 1.340 sqrt(L/N_T) radians.


title: Detecting Hidden Differences via Permutation Symmetries

abstract:
  We present a method for describing and characterizing the state of N
particles that may be distinguishable in principle but not in practice due to
experimental limitations. The technique relies upon a careful treatment of the
exchange symmetry of the state among experimentally accessible and
experimentally inaccessible degrees of freedom. The approach we present allows
a new formalisation of the notion of indistinguishability and can be
implemented easily using currently available experimental techniques. Our work
is of direct relevance to current experiments in quantum optics, for which we
provide a specific implementation.


title:
Photon storage in Lambda-type optically dense atomic media. I. Cavity
  model

abstract:
  In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we
used a universal physical picture to optimize and demonstrate equivalence
between a wide range of techniques for storage and retrieval of photon wave
packets in Lambda-type atomic media in free space, including the adiabatic
reduction of the photon group velocity, pulse-propagation control via
off-resonant Raman techniques, and photon-echo-based techniques. In the present
paper, we perform the same analysis for the cavity model. In particular, we
show that the retrieval efficiency is equal to C/(1+C) independent of the
retrieval technique, where C is the cooperativity parameter. We also derive the
optimal strategy for storage and, in particular, demonstrate that at any
detuning one can store, with the optimal efficiency of C/(1+C), any smooth
input mode satisfying T C gamma >> 1 and a certain class of resonant input
modes satisfying T C gamma ~ 1, where T is the duration of the input mode and 2
gamma is the transition linewidth. In the two subsequent papers of the series,
we present the full analysis of the free-space model and discuss the effects of
inhomogeneous broadening on photon storage.


title:
Photon storage in Lambda-type optically dense atomic media. II.
  Free-space model

abstract:
  In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)], we
presented a universal physical picture for describing a wide range of
techniques for storage and retrieval of photon wave packets in Lambda-type
atomic media in free space, including the adiabatic reduction of the photon
group velocity, pulse-propagation control via off-resonant Raman techniques,
and photon-echo based techniques. This universal picture produced an optimal
control strategy for photon storage and retrieval applicable to all approaches
and yielded identical maximum efficiencies for all of them. In the present
paper, we present the full details of this analysis as well some of its
extensions, including the discussion of the effects of non-degeneracy of the
two lower levels of the Lambda system. The analysis in the present paper is
based on the intuition obtained from the study of photon storage in the cavity
model in the preceding paper [Gorshkov et al., Phys. Rev. A 76, 033804 (2007)].


title:
Photon storage in Lambda-type optically dense atomic media. III. Effects
  of inhomogeneous broadening

abstract:
  In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and
in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007);
76, 033805 (2007)], we used a universal physical picture to optimize and
demonstrate equivalence between a wide range of techniques for storage and
retrieval of photon wave packets in homogeneously broadened Lambda-type atomic
media, including the adiabatic reduction of the photon group velocity,
pulse-propagation control via off-resonant Raman techniques, and
photon-echo-based techniques. In the present paper, we generalize this
treatment to include inhomogeneous broadening. In particular, we consider the
case of Doppler-broadened atoms and assume that there is a negligible
difference between the Doppler shifts of the two optical transitions. In this
situation, we show that, at high enough optical depth, all atoms contribute
coherently to the storage process as if the medium were homogeneously
broadened. We also discuss the effects of inhomogeneous broadening in solid
state samples. In this context, we discuss the advantages and limitations of
reversing the inhomogeneous broadening during the storage time, as well as
suggest a way for achieving high efficiencies with a nonreversible
inhomogeneous profile.


title:
Randomized and Quantum Solution of Initial-Value Problems for Ordinary
  Differential Equations of Order k

abstract:
  We study possible advantages of randomized and quantum computing over
deterministic computing for scalar initial-value problems for ordinary
differential equations of order k. For systems of equations of the first order
this question has been settled modulo some details in \cite{Kacewicz05}. A
speed-up over deterministic computing shown in \cite{Kacewicz05} is related to
the increased regularity of the solution with respect to that of the right-hand
side function. For a scalar equation of order k (which can be transformed into
a special system of the first order), the regularity of the solution is
increased by k orders of magnitude. This leads to improved complexity bounds
depending on k for linear information in the deterministic setting, see
\cite{Szczesny05}. This may suggest that in the randomized and quantum settings
a speed-up can also be achieved depending on k.
  We show in this paper that a speed-up dependent on k is not possible in the
randomized and quantum settings. We establish lower complexity bounds, showing
that the randomized and quantum complexities remain at the some level as for
systems of the first order, no matter how large k is. Thus, the algorithms from
\cite{Kacewicz05} remain (almost) optimal, even if we restrict ourselves to a
subclass of systems arising from scalar equations of order k.


title: Continuous-time cross-phase modulation and quantum computation

abstract:
  The weak nonlinear Kerr interaction between single photons and intense laser
fields has been recently proposed as a basis for distributed optics-based
solutions to few-qubit applications in quantum communication and computation.
Here, we analyze the above Kerr interaction by employing a continuous-time
multi-mode model for the input/output fields to/from the nonlinear medium. In
contrast to previous single-mode treatments of this problem, our analysis takes
into account the full temporal content of the free-field input beams as well as
the non-instantaneous response of the medium. The main implication of this
model, in which the cross-Kerr phase shift on one input is proportional to the
photon flux of the other input, is the existence of phase noise terms at the
output. We show that these phase noise terms will preclude satisfactory
performance of the parity gate proposed by Munro, Nemoto, and Spiller [New J.
Phys. 7, 137 (2005)].


title:
Dense-coding quantum key distribution based on continuous-variable
  entanglement

abstract:
  We proposed a scheme of continuous-variable quantum key distribution, in
which the bright Einstein-Podolsky-Rosen entangled optical beams are utilized.
The source of the entangled beams is placed inside the receiving station, where
half of the entangled beams are transmitted with round trip and the other half
are retained by the receiver. The amplitude and phase signals modulated on the
signal beam by the sender are simultaneously extracted by the authorized
receiver with the scheme of the dense-coding correlation measurement for
continuous quantum variables, thus the channel capacity is significantly
improved. Two kinds of possible eavesdropping are discussed. The mutual
information and the secret key rates are calculated and compared with those of
unidirectional transmission schemes.


title:
Singularity of Berry Connections Inhibits the Accuracy of Adiabatic
  Approximation

abstract:
  Adiabatic approximation for quantum evolution is investigated quantitatively
with addressing its dependence on the Berry connections. We find that, in the
adiabatic limit, the adiabatic fidelity may uniformly converge to unit or
diverge manifesting the breakdown of adiabatic approximation, depending on the
type of the singularity of the Berry connections as the functions of
slowly-varying parameter $R$. When the Berry connections have a singularity of
$1/R^\sigma$ type with $\sigma < 1$, the adiabatic fidelity converges to unit
in a power-law; whereas when the singularity index $\sigma$ is larger than one,
adiabatic approximation breaks down. Two-level models are used to substantiate
our theory.


title:
On the impossibility of a quantum sieve algorithm for graph isomorphism:
  unconditional results

abstract:
  It is known that any quantum algorithm for Graph Isomorphism that works
within the framework of the hidden subgroup problem (HSP) must perform highly
entangled measurements across \Omega(n \log n) coset states. One of the only
known models for how such a measurement could be carried out efficiently is
Kuperberg's algorithm for the HSP in the dihedral group, in which quantum
states are adaptively combined and measured according to the decomposition of
tensor products into irreducible representations. This ``quantum sieve'' starts
with coset states, and works its way down towards representations whose
probabilities differ depending on, for example, whether the hidden subgroup is
trivial or nontrivial.
  In this paper we show that no such approach can produce a polynomial-time
quantum algorithm for Graph Isomorphism. Specifically, we consider the natural
reduction of Graph Isomorphism to the HSP over the the wreath product S_n\wr
Z_2. Using a recently proved bound on the irreducible characters of S_n, we
show that no algorithm in this family can solve Graph Isomorphism in less than
e^{\Omega(\sqrt{n})} time, no matter what adaptive rule it uses to select and
combine quantum states. In particular, algorithms of this type can offer
essentially no improvement over the best known classical algorithms, which run
in time e^{O(\sqrt{n \log n})}.


title: Zitterbewegung at the level of quantum field theory

abstract:
  Traditionally, the zitterbewegung (ZB) of the Dirac electron has just been
studied at the level of quantum mechanics. Seeing that the fact that an old
interest in ZB has recently been rekindled by the investigations on spintronic,
graphene, and superconducting systems, etc., in this paper we present a
quantum-field-theory investigation on ZB and obtain the conclusion that, the ZB
of an electron arises from the influence of virtual electron-positron pairs (or
vacuum fluctuations) on the electron.


title: On the unitarity of higher-dervative and nonlocal theories

abstract:
  We consider two simple models of higher-derivative and nonlocal quantu
systems.It is shown that, contrary to some claims found in literature, they can
be made unitary.


title:
Information/disturbance trade-off in single and sequential measurements
  on a qudit signal

abstract:
  We address the trade-off between information gain and state disturbance in
measurement performed on qudit systems and devise a class of optimal
measurement schemes that saturate the ultimate bound imposed by quantum
mechanics to estimation and transmission fidelities. The schemes are minimal,
i.e. they involve a single additional probe qudit, and optimal, i.e. they
provide the maximum amount of information compatible with a given level of
disturbance. The performances of optimal single-user schemes in extracting
information by sequential measurements in a N -user transmission line are also
investigated, and the optimality is analyzed by explicit evaluation of
fidelities. We found that the estimation fidelity does not depend on the number
of users, neither for single-measure inference nor for collective one, whereas
the transmission fidelity decreases with N . The resulting trade-off is no
longer optimal and degrades with increasing N . We found that optimality can be
restored by an effective preparation of the probe states and present explicitly
calculations for the 2-user case.


title: Lorentz-covariant deformed algebra with minimal length

abstract:
  The $D$-dimensional two-parameter deformed algebra with minimal length
introduced by Kempf is generalized to a Lorentz-covariant algebra describing a
($D+1$)-dimensional quantized space-time. For D=3, it includes Snyder algebra
as a special case. The deformed Poincar\'e transformations leaving the algebra
invariant are identified. Uncertainty relations are studied. In the case of D=1
and one nonvanishing parameter, the bound-state energy spectrum and
wavefunctions of the Dirac oscillator are exactly obtained.


title:
More on an exactly solvable position-dependent mass Schroedinger
  equation in two dimensions: Algebraic approach and extensions to three
  dimensions

abstract:
  An exactly solvable position-dependent mass Schr\"odinger equation in two
dimensions, depicting a particle moving in a semi-infinite layer, is
re-examined in the light of recent theories describing superintegrable
two-dimensional systems with integrals of motion that are quadratic functions
of the momenta. To get the energy spectrum a quadratic algebra approach is used
together with a realization in terms of deformed parafermionic oscillator
operators. In this process, the importance of supplementing algebraic
considerations with a proper treatment of boundary conditions for selecting
physical wavefunctions is stressed. Some new results for matrix elements are
derived. Finally, the two-dimensional model is extended to two integrable and
exactly solvable (but not superintegrable) models in three dimensions,
depicting a particle in a semi-infinite parallelepipedal or cylindrical
channel, respectively.


title: Dynamics of the Jayne-Cummings and Rabi models: old wine in new bottles

abstract:
  By using a wave packet approach, this paper reviews the Jaynes-Cummings model
with and without the rotating wave approximation in a non-standard way. This
gives new insight, not only of the two models themselves, but of the rotating
wave approximation as well. Expressing the models by field quadrature
operators, instead of the typically used boson ladder operators, wave packet
simulations are presented. Several known phenomena of these systems, such as
collapse-revivals, Rabi oscillation, squeezing and entanglement, are reviewed
and explained in this new picture, either in an adiabatic or diabatic frame.
The harmonic shape of the potential curves that the wave packets evolve on and
the existence of a level crossing make these results interesting in a broader
sense than only for models in quantum optics, especially in atomic and
molecular physics.


title: Compatibility of representations of quantum systems

abstract:
  There is a natural equivalence relation on representations of the states of a
given quantum system in a Hilbert space, two representations being equivalent
iff they are related by a unitary transformation. There are two equivalence
classes, with members of opposite classes being related by a conjugate-unitary
(anti-unitary) transformation. These two conjugacy classes are related in much
the same way as are the two imaginary units of a complex field, and there is a
priori no basis on which to prefer one over the other in any individual case.
This is potentially problematic in that the choice of conjugacy class of a
representation determines the sign of energy and other quantities defined as
generators of continuous symmetries of the system in question, so that it would
appear that principles like conservation of energy for a compound system may
hold or fail depending on relative choices of conjugacy class of
representations of its subsystems. We show that for any finite set of quantum
systems there are exactly two ways of choosing conjugacy classes of
representations consistent with the usual tensor-product construction for
representing the compound system composed of these. Each is obtained from the
other by reversing the conjugacy of all the representations at once. The
relation of unitary equivalence for representations of a single system is
therefore uniquely extendible to representations of all systems that can
interact with it.


title: Stabilizer Quantum Error Correction with Qubus Computation

abstract:
  In this paper we investigate stabilizer quantum error correction codes using
controlled phase rotations of strong coherent probe states. We explicitly
describe two methods to measure the Pauli operators which generate the
stabilizer group of a quantum code. First, we show how to measure a Pauli
operator acting on physical qubits using a single coherent state with large
average photon number, displacement operations, and photon detection. Second,
we show how to measure the stabilizer operators fault-tolerantly by the
deterministic preparation of coherent cat states along with one-bit
teleportations between a qubit-like encoding of coherent states and physical
qubits.


title: Multipartite entanglement characterization of a quantum phase transition

abstract:
  A probability density characterization of multipartite entanglement is tested
on the one-dimensional quantum Ising model in a transverse field. The average
and second moment of the probability distribution are numerically shown to be
good indicators of the quantum phase transition. We comment on multipartite
entanglement generation at a quantum phase transition.


title: Entanglement quantification with Fisher information

abstract:
  We show that the Fisher information associated with entanglement-assisted
coding has a monotonic relationship with the logarithmic negativity, an
important entanglement measure, for certain classes of continuous variable (CV)
quantum states of practical significance. These are the two-mode squeezed
states and the non-Gaussian states obtained from them by photon subtraction.
This monotonic correspondence can be expressed analytically in the case of pure
states. Numerical analysis shows that this relationship holds to a very good
approximation even in the mixed state case of the photon-subtracted squeezed
states. The Fisher information is evaluated by the CV Bell measurement in the
limit of weak signal modulation. Our results suggest that the logarithmic
negativity of certain sets of non-Gaussian mixed states can be experimentally
accessed without homodyne tomography, leading to significant simplification of
the experimental procedure.


title:
Preamplified photodetectors for high-fidelity postselecting optical
  devices

abstract:
  The fidelity of postselecting devices based on direct photon number detection
can be significantly improved by insertion of a phase-insensitive optical
amplifier in front of the detector. The scheme is simple, and the cost to the
probability of obtaining the appropriate detector outcome is low.


title: Sequential Generation of Matrix-Product States in Cavity QED

abstract:
  We study the sequential generation of entangled photonic and atomic
multi-qubit states in the realm of cavity QED. We extend the work of C. Schoen
et al. [Phys. Rev. Lett. 95, 110503 (2005)], where it was shown that all states
generated in a sequential manner can be classified efficiently in terms of
matrix-product states. In particular, we consider two scenarios: photonic
multi-qubit states sequentially generated at the cavity output of a
single-photon source and atomic multi-qubit states generated by their
sequential interaction with the same cavity mode.


title: Theoretical evidence for the superluminality of evanescent modes

abstract:
  Though both theoretical and experimental investigations have revealed the
superluminal behavior of evanescent electromagnetic waves, there are many
disputes about the physical meaning and validity of such superluminal
phenomenon, which is due to the fact that the traditional investigations are
based on the theory of tunneling time, and concerned with the problem of what
the group velocity of evanescent waves means. In this paper, by studying the
quantum probability amplitude for photons to propagate over a spacelike
interval along an undersized waveguide, we present theoretical evidence for
such superluminality.


title: Some remarks on the theorems of Gleason and Kochen-Specker

abstract:
  A Gleason-type theorem is proved for two restricted classes of
informationally complete POVMs in the qubit case. A particular (incomplete)
Kochen-Specker colouring, suggested by Appleby in dimension three, is
generalized to arbitrary dimension. We investigate its effectivity as a
function of dimension, using two different measures of this. In particular, we
will derive a limit for the fraction of the sphere that can be satisfactorily
coloured using the generalized Appleby construction as the number of dimensions
approaches infinity. The second, and physically more relevant measure of
effectivity, is to look at the fraction of possible ON-bases properly coloured.
Using this measure, we will derive a 'lower bound for the upper bound' in three
and four real dimensions.


title:
Anisotropically high entanglement of biphotons generated in spontaneous
  parametric down conversion

abstract:
  We show that the wave packet of a biphoton generated via spontaneous
parametric down conversion is strongly anisotropic. Its anisotropic features
manifest themselves very clearly in comparison of measurements performed in two
different schemes: when the detector scanning plane is perpendicular or
parallel to the plane containing the crystal optical axis and the laser axis.
The first of these two schemes is traditional whereas the second one gives rise
to such unexpected new results as anomalously strong narrowing of the biphoton
wave packet measured in the coincidence scheme and very high degree of
entanglement. The results are predicted theoretically and confirmed
experimentally.


title:
Numerical Bayesian state assignment for a three-level quantum system. I.
  Absolute-frequency data; constant and Gaussian-like priors

abstract:
  This paper offers examples of concrete numerical applications of Bayesian
quantum-state-assignment methods to a three-level quantum system. The
statistical operator assigned on the evidence of various measurement data and
kinds of prior knowledge is computed partly analytically, partly through
numerical integration (in eight dimensions) on a computer. The measurement data
consist in absolute frequencies of the outcomes of N identical von Neumann
projective measurements performed on N identically prepared three-level
systems. Various small values of N as well as the large-N limit are considered.
Two kinds of prior knowledge are used: one represented by a plausibility
distribution constant in respect of the convex structure of the set of
statistical operators; the other represented by a Gaussian-like distribution
centred on a pure statistical operator, and thus reflecting a situation in
which one has useful prior knowledge about the likely preparation of the
system.
  In a companion paper the case of measurement data consisting in average
values, and an additional prior studied by Slater, are considered.


title: Error-resistant Single Qubit Gates with Trapped Ions

abstract:
  Coherent operations constitutive for the implementation of single and
multi-qubit quantum gates with trapped ions are demonstrated that are robust
against variations in experimental parameters and intrinsically indeterministic
system parameters. In particular, pulses developed using optimal control theory
are demonstrated for the first time with trapped ions. Their performance as a
function of error parameters is systematically investigated and compared to
composite pulses.


title:
How a Clebsch-Gordan Transform Helps to Solve the Heisenberg Hidden
  Subgroup Problem

abstract:
  It has recently been shown that quantum computers can efficiently solve the
Heisenberg hidden subgroup problem, a problem whose classical query complexity
is exponential. This quantum algorithm was discovered within the framework of
using pretty-good measurements for obtaining optimal measurements in the hidden
subgroup problem. Here we show how to solve the Heisenberg hidden subgroup
problem using arguments based instead on the symmetry of certain hidden
subgroup states. The symmetry we consider leads naturally to a unitary
transform known as the Clebsch-Gordan transform over the Heisenberg group. This
gives a new representation theoretic explanation for the pretty-good
measurement derived algorithm for efficiently solving the Heisenberg hidden
subgroup problem and provides evidence that Clebsch-Gordan transforms over
finite groups are a new primitive in quantum algorithm design.


title:
Nonlinear entanglement witnesses, covariance matrices and the geometry
  of separable states

abstract:
  Entanglement witnesses provide a standard tool for the analysis of
entanglement in experiments. We investigate possible nonlinear entanglement
witnesses from several perspectives. First, we demonstrate that they can be
used to show that the set of separable states has no facets. Second, we give a
new derivation of nonlinear witnesses based on covariance matrices. Finally, we
investigate extensions to the multipartite case.


title: About the Exact Role of Disturbance in Heisenberg's Uncertainty Relation

abstract:
  It is generally accepted that the disturbance interpretation cannot explain
Heisenberg's uncertainty relation DxDp=h. In this paper a clear distinction
will be made between the notions of state preparation and measurement, noting
that the disturbance that is referred to in Heisenberg's disturbance
interpretation is usually caused by the measurement. The main goal of this
paper is to examine and discuss to what extent disturbance during the state
preparation plays a role in the interpretation of Heisenberg's uncertainty
relation. This examination will be done in the context of a single-slit
experiment. To conclude this paper a novel single-slit experiment will be
proposed and discussed with which a clearer insight could be gained into the
exact role of disturbance when a quantum system passes a single-slit.


title:
Quantum fluctuations of Coulomb Potential as a Source of Flicker Noise.
  The Influence of Heat Bath

abstract:
  The power spectrum of finite-temperature quantum electromagnetic fluctuations
produced by elementary charge carriers under the influence of external electric
field is investigated. It is found that under the combined action of the photon
heat bath and the external field, the low-frequency asymptotic of the power
spectrum is modified both qualitatively and quantitatively. The new term in the
power spectrum is inversely proportional to, but is odd in frequency. It comes
from the connected part of the correlation function, and is related to the
temperature and external field corrections to the photon and charge carrier
propagators. In application to the case of a biased conducting sample, this
term gives rise to a contribution to the voltage power spectrum which is
proportional to the absolute system temperature, the charge carrier mobility,
the bias voltage squared, and a factor describing dependence of the noise
intensity on the sample geometry. It is verified that the derived expression is
in agreement with the experimental data on 1/f-noise measurements in metal
films.


title:
Multi-impurity effects on the entanglement of anisotropic Heisenberg
  ring XXZ under a homogeneous magnetic field

abstract:
  The effects of multi-impurity on the entanglement of anisotropic Heisenberg
ring XXZ under a homogeneous magnetic field have been studied. The impurities
make the equal pairwise entanglement in a ring compete with each other so that
the pairwise entanglement exhibits oscillation. If the impurities are of larger
couplings, both the critical temperature and pairwise entanglement can be
improved


title: Secure self-calibrating quantum random bit generator

abstract:
  Random bit generators (RBGs) are key components of a variety of information
processing applications ranging from simulations to cryptography. In
particular, cryptographic systems require "strong" RBGs that produce
high-entropy bit sequences, but traditional software pseudo-RBGs have very low
entropy content and therefore are relatively weak for cryptography. Hardware
RBGs yield entropy from chaotic or quantum physical systems and therefore are
expected to exhibit high entropy, but in current implementations their exact
entropy content is unknown. Here we report a quantum random bit generator
(QRBG) that harvests entropy by measuring single-photon and entangled
two-photon polarization states. We introduce and implement a quantum
tomographic method to measure a lower bound on the "min-entropy" of the system,
and we employ this value to distill a truly random bit sequence. This approach
is secure: even if an attacker takes control of the source of optical states, a
secure random sequence can be distilled.


title: A new construction for a QMA complete 3-local Hamiltonian

abstract:
  We present a new way of encoding a quantum computation into a 3-local
Hamiltonian. Our construction is novel in that it does not include any terms
that induce legal-illegal clock transitions. Therefore, the weights of the
terms in the Hamiltonian do not scale with the size of the problem as in
previous constructions. This improves the construction by Kempe and Regev, who
were the first to prove that 3-local Hamiltonian is complete for the complexity
class QMA, the quantum analogue of NP.
  Quantum k-SAT, a restricted version of the local Hamiltonian problem using
only projector terms, was introduced by Bravyi as an analogue of the classical
k-SAT problem. Bravyi proved that quantum 4-SAT is complete for the class QMA
with one-sided error (QMA_1) and that quantum 2-SAT is in P. We give an
encoding of a quantum circuit into a quantum 4-SAT Hamiltonian using only
3-local terms. As an intermediate step to this 3-local construction, we show
that quantum 3-SAT for particles with dimensions 3x2x2 (a qutrit and two
qubits) is QMA_1 complete. The complexity of quantum 3-SAT with qubits remains
an open question.


title:
Fake one-time pad cannot be used to improve the efficiency of quantum
  communication

abstract:
  Two misuses of one-time pad in improving the efficiency of quantum
communication are pointed out. One happens when using some message bits to
encrypt others, the other exists because the key bits are not truly random.
Both of them result in the decrease of security. Therefore, one-time pad should
be used carefully in designing quantum communication protocols.


title:
Quantum dynamics of double-qubits in a spin star lattice with an XY
  interaction

abstract:
  The dynamics of two coupled spins-1/2 interacting with a spin-bath via the
quantum Heisenberg XY coupling is studied. The pair of central spins served as
a quantum open subsystem are initially prepared in two types of states: the
product states and the Bell states. The bath, which consists of $N$ (in the
thermodynamic limit $N\to\infty$) mutually coupled spins-1/2, is in a thermal
state at the beginning. By the Holstein-Primakoff transformation, the model can
be treated effectively as two spin qubits embedded in a single mode cavity. The
time-evolution of the purity, z-component summation and the concurrence of the
central spins can be determined by a Laguerre polynomial scheme. It is found
that (i) at a low temperature, the uncoupled subsystem in a product state can
be entangled due to the interaction with bath, which is tested by the
Peres-Horodecki separability; however, at a high temperature, the bath produces
a stronger destroy effect on the purity and entanglement of the subsystem; (ii)
when the coupling strength between the two central spins is large, they are
protected strongly against the bath; (iii) when the interaction between the
subsystem and the bath is strong, the collapse of the two spin qubits from
their initial entangled state is fast.


title:
New experimental limit on Pauli Exclusion Principle violation by
  electrons (the VIP experiment)

abstract:
  The Pauli exclusion principle (PEP) represents one of the basic principles of
modern physics and, even if there are no compelling reasons to doubt its
validity, it still spurs a lively debate, because an intuitive, elementary
explanation is still missing, and because of its unique stand among the basic
symmetries of physics. A new limit on the probability that PEP is violated by
electrons was estabilished by the VIP (VIolation of the Pauli exclusion
principle) Collaboration, using the method of searching for PEP forbidden
atomic transitions in copper. The preliminary value, ${1/2}\beta^{2} \textless
4.5\times 10^{-28}$, represents an improvement of about two orders of magnitude
of the previous limit. The goal of VIP is to push this limit at the level of
$10^{-30}$.


title: Entanglement of three-qubit geometry

abstract:
  Geometric quantum mechanics aims to express the physical properties of
quantum systems in terms of geometrical features preferentially selected in the
space of pure states. Geometric characterisations are given here for systems of
one, two, and three spin-1/2 particles, drawing attention to the classification
of quantum states into entanglement types.


title: Introduction to decoherence theory

abstract:
  This is an introduction to the theory of decoherence with an emphasis on its
microscopic origins and on a dynamic description. The text corresponds to a
chapter soon to be published in: A. Buchleitner, C. Viviescas, and M. Tiersch
(Eds.), Entanglement and Decoherence. Foundations and Modern Trends, Lecture
Notes in Physics, Vol 768, Springer, Berlin (2009)


title: Fibre-optics implementation of asymmetric phase-covariant quantum cloner

abstract:
  We present the experimental realization of optimal symmetric and asymmetric
phase-covariant 1->2 cloning of qubit states using fiber optics. State of each
qubit is encoded into a single photon which can propagate through two optical
fibers. The operation of our device is based on one- and two-photon
interference. We have demonstrated creation of two copies of any state of a
qubit from the equator of the Bloch sphere. The measured fidelities of both
copies are close to the theoretical values and they surpass the theoretical
maximum obtainable with the universal cloner.


title: On quantum microcanonical equilibrium

abstract:
  A quantum microcanonical postulate is proposed as a basis for the equilibrium
properties of small quantum systems. Expressions for the corresponding density
of states are derived, and are used to establish the existence of phase
transitions for finite quantum systems. A grand microcanonical ensemble is
introduced, which can be used to obtain new rigorous results in quantum
statistical mechanics.


title:
Security of decoy-state quantum key distribution with inexactly
  controlled source

abstract:
  We show the unconditional security of decoy-state method quantum cryptography
with whatever intensity error pattern provided that the error is not too large.
Our result immediately applies to the existing experimental data. Our result is
not limitted to coherent states.


title: A q-Oscillator with 'Accidental' Degeneracy of Energy Levels

abstract:
  We study main features of the exotic case of q-deformed oscillators
(so-called Tamm-Dancoff cutoff oscillator) and find some special properties:
(i) degeneracy of the energy levels E_{n_1} = E_{n_1+1}, n_1\ge 1, at the {\em
real value} q=\sqrt{\frac{n_1}{n_1+2}} of deformation parameter, as well as the
occurrence of other degeneracies E_{n_1} = E_{n_1+k}, for k \ge 2, at the
corresponding values of q which depend on both n_1 and k; (ii) the position and
momentum operators X and P {\em commute on the state} |m> if q is fixed as
q=\frac{m}{m+1}, that implies unusual uncertainty relation; (iii) two commuting
copies of the creation, annihilation, and number operators of this q-oscillator
generate the corresponding q-deformation of the {\em non-simple} Lie algebra
su(2)\oplus u(1) whose nontrivial q-deformed commutation relation is: [ J_+,
J_- ] = 2 J_0 q^{2J_3-1} where J_0\equiv \frac12 (N_1-N_2) and J_3\equiv
\frac12 (N_1+N_2).

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


title: Impossibility of partial swapping of Quantum Information

abstract:
  It is a well known fact that a quantum state $|\psi(\theta,\phi)>$ are
represented by a point on the Bloch sphere, characterized by two parameters
$\theta$ and $\phi$. Here in this work, we find out another impossible
operation in quantum information theory . We name this impossibility as
'Impossibility of partial swapping of quantum information '. By this we mean
that if two unknown quantum states are given at the input port, there exists no
physical process, consistent with the principles of quantum mechanics, by which
we can partially swap either of the two parameters $\theta$ and $\phi$ between
these two quantum states. In this work we provided the impossibility proofs for
the qubits(i.e the quantum states taken from two dimensional Hilbert space) and
this impossible operation can be shown to hold in higher dimension also.


title:
High-Rate Entanglement Source via Two-Photon Emission from Semiconductor
  Quantum Wells

abstract:
  We propose a compact high-intensity room-temperature source of entangled
photons based on the efficient second-order process of two-photon spontaneous
emission from electrically-pumped semiconductor quantum wells in a photonic
microcavity. Two-photon emission rate in room-temperature semiconductor devices
is determined solely by the carrier density, regardless of the residual
one-photon emission. The microcavity selects two-photon emission for a specific
signal and idler wavelengths and at a preferred direction without modifying the
overall rate. Pair-generation rate in GaAs/AlGaAs quantum well structure is
estimated using a 14-band model to be 3 orders of magnitude higher than for
traditional broadband parametric down-conversion sources.


title:
Intrinsic Regularization in a Lorentz invariant non-orthogonal Euclidean
  Space

abstract:
  It is shown that the Lorentz transformations can be derived for a
non-orthogonal Euclidean space. In this geometry one finds the same relations
of special relativity as the ones known from the orthogonal Minkowski space. In
order to illustrate the advantage of a non-orthogonal Euclidean metric the
two-point Green's function at x = 0 for a self-interacting scalar field is
calculated. In contrast to the Minkowski space the one loop mass correction
derived from this function gives a convergent result due to an intrinsic
regularization parameter called effective dimension. This parameter is an
entropy related measure for the information loss caused by quantum fluctuations
of the metric at energies higher than the Planckian limit.


title: Dynamics of a Quantum Reference Frame

abstract:
  We analyze a quantum mechanical gyroscope which is modeled as a large spin
and used as a reference against which to measure the angular momenta of
spin-1/2 particles. These measurements induce a back-action on the reference
which is the central focus of our study. We begin by deriving explicit
expressions for the quantum channel representing the back-action. Then, we
analyze the dynamics incurred by the reference when it is used to sequentially
measure particles drawn from a fixed ensemble. We prove that the reference
thermalizes with the measured particles and find that generically, the thermal
state is reached in time which scales linearly with the size of the reference.
This contrasts a recent conclusion of Bartlett et al. that this takes a
quadratic amount of time when the particles are completely unpolarized. We now
understand their result in terms of a simple physical principle based on
symmetries and conservation laws. Finally, we initiate the study of the
non-equilibrium dynamics of the reference. Here we find that a reference in a
coherent state will essentially remain in one when measuring polarized
particles, while rotating itself to ultimately align with the polarization of
the particles.


title: Violation of monogamy inequality for higher-dimensional objects

abstract:
  Bipartite quantum entanglement for qutrits and higher-dimensional objects is
considered. We analyze the possibility of violation of monogamy inequality,
introduced by Coffman, Kundu, and Wootters, for some systems composed of such
objects. An explicit counterexample with a three-qutrit totally antisymmetric
state is presented. Since three-tangle has been confirmed to be a natural
measure of entanglement for qubit systems, our result shows that the
three-tangle is no longer a legitimate measure of entanglement for states with
three qutrits or higher dimensional objects.


title:
Entangling two atoms in spatially separated cavities through both photon
  emission and absorption processes

abstract:
  We consider a system consisting of a $\Lambda$-type atom and a V-type atom,
which are individually trapped in two spatially separated cavities that are
connected by an optical fibre. We show that an extremely entangled state of the
two atoms can be deterministically generated through both photon emission of
the $\Lambda$-type atom and photon absorption of the V-type atom in an ideal
situation. The influence of various decoherence processes such as spontaneous
emission and photon loss on the fidelity of the entangled state is also
investigated. We find that the effect of photon leakage out of the fibre on the
fidelity can be greatly diminished in some special cases. As regards the effect
of spontaneous emission and photon loss from the cavities, we find that the
present scheme with a fidelity higher than 0.98 may be realized under current
experiment conditions.


title: Photon number states generated from a continuous-wave light source

abstract:
  Conditional preparation of photon number states from a continuous-wave
nondegenerate optical parametric oscillator is investigated. We derive the
phase space Wigner function for the output state conditioned on photo detection
events that are not necessarily simultaneous, and we maximize its overlap with
the desired photon number state by choosing the optimal temporal output state
mode function. We present a detailed numerical analysis for the case of
two-photon state generation from a parametric oscillator driven with an
arbitrary intensity below threshold, and in the low intensity limit, we present
a formalism that yields the optimal output state mode function and fidelity for
higher photon number states.


title:
Passive Optical Network Approach to GigaHertz-Clocked Multiuser Quantum
  Key Distribution

abstract:
  We present the application of quantum key distribution technologies to
fiber-based broadband passive optical access networks. This application is
based on our 850 nm wavelength gigahertz clock-rate single-receiver system, is
compatible with existing telecommunications fiber and exploits a wavelength
band not currently utilized in access networks. The developed quantum key
distribution networks are capable of transmitting over distances consistent
with the span of access links for metropolitan networks (10 km), at clock
frequencies ranging up to 3 GHz.


title:
Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field
  theory approach

abstract:
  We calculate correlation function in the Einstein--Podolsky--Rosen type of
experiment with massive relativistic Dirac particles in the framework of the
quantum field theory formalism. We perform our calculations for states which
are physically interesting and transforms covariantly under the full Lorentz
group action, i.e. for pseudoscalar and vector state.


title:
Experimental Realization of $1 \to 2$ Asymmetric Phase-Covariant Quantum
  Cloning

abstract:
  While exact cloning of an unknown quantum state is prohibited by the
linearity of quantum mechanics, approximate cloning is possible and has been
used, e.g., to derive limits on the security of quantum communication
protocols. In the case of asymmetric cloning, the information from the input
state is distributed asymmetrically between the different output states. Here,
we consider asymmetric phase-covariant cloning, where the goal is to optimally
transfer the phase information from a single input qubit to different output
qubits. We construct an optimal quantum cloning machine for two qubits that
does not require ancilla qubits and implement it on an NMR quantum information
processor.


title:
Entanglement and its applications in systems with many degrees of
  freedom

abstract:
  Entanglement are the non-local correlations permitted by quantum theory,
believed to play a fundamental role in a quantum computer. We have investigated
these correlations in a number of theoretical models for condensed matter
systems. Such systems are likely candidates for quantum computing, and
experimentally feasible for instance as superconducting qubits. At quantum
critical points the ground state of these systems is very complicated, and the
entanglement is usually larger than at non-critical points. This entanglement
can be used to identify the critical points through what we denote the
entanglement signature, even for very small systems. From another perspective,
it seems that the entanglement is an essential tool to find an unknown ground
state, since this gives rise to a simple decomposition of the state.


title: Slow-light solitons: influence of relaxation

abstract:
  We have applied the transformation of the slow light equations to Liouville
theory that we developed in our previous work, to study the influence of
relaxation on the soliton dynamics. We solved the problem of the soliton
dynamics in the presence of relaxation and found that the spontaneous emission
from the upper atomic level is strongly suppressed. Our solution proves that
the spatial shape of the soliton is well preserved even if the relaxation time
is much shorter than the soliton time length. This fact is of great importance
for applications of the slow-light soliton concept in optical information
processing. We also demonstrate that the relaxation plays a role of resistance
to the soliton motion and slows the soliton down even if the controlling field
is constant.


title:
Tunable control of the bandwidth and frequency correlations of entangled
  photons

abstract:
  We demonstrate experimentally a new technique to control the bandwidth and
the type of frequency correlations (correlation, anticorrelation, and even
uncorrelation) of entangled photons generated by spontaneous parametric
downconversion. The method is based on the control of the group velocities of
the interacting waves. This technique can be applied in any nonlinear medium
and frequency band of interest. It is also demonstrated that this technique
helps enhance the quality of polarization entanglement even when femtosecond
pulses are used as a pump.


title: Unified approach to QED in arbitrary linear media

abstract:
  We give a unified approach to macroscopic QED in arbitrary linearly
responding media, based on the quite general, nonlocal form of the conductivity
tensor as it can be introduced within the framework of linear response theory,
and appropriately chosen sets of bosonic variables. The formalism generalizes
the quantization schemes that have been developed previously for diverse
classes of linear media. In particular, it turns out that the scheme developed
for locally responding linear magnetodielectric media can be recovered from the
general scheme as a limiting case for weakly spatially dispersive media. With
regard to practical applications, we furthermore address the dielectric
approximation for the conductivity tensor and the surface impedance method for
the calculation of the Green tensor of the macroscopic Maxwell equations, the
two central quantities of the theory.


title: Macroscopic tunneling, decoherence and noise-induced activation

abstract:
  We study the effects of the environment at zero temperature on tunneling in
an open system described by a static double-well potential. We show that the
evolution of the system in an initial Schrodinger cat state, can be summarized
in terms of three main physical phenomena, namely decoherence, quantum
tunneling and noise-induced activation. Using large-scale numerical
simulations, we obtain a detailed picture of the main stages of the evolution
and of the relevant dynamical processes


title: Ultrahigh finesse Fabry-Perot superconducting resonator

abstract:
  We have built a microwave Fabry-Perot resonator made of diamond-machined
copper mirrors coated with superconducting niobium. Its damping time (Tc = 130
ms at 51 GHz and 0.8 K) corresponds to a ﬁnesse of 4.6 x 109, the
highest ever reached for a Fabry-Perot in any frequency range. This result
opens novel perspectives for quantum information, decoherence and non-locality
studies.


title: Topological Photon

abstract:
  We associate intrinsic energy equal to $h\nu/2$ with the spin angular
momentum of photon and propose a topological model based on orbifold in space
and tifold in time as topological obstructions. The model is substantiated
using vector wavefield disclinations. The physical photon is suggested to be a
particle like topological photon and a propagating wave such that the energy
$h\nu$ of photon is equally divided between spin energy and translational
energy corresponding to linear momentum of $h\nu/c$. The enigma of
wave-particle duality finds natural resolution and the proposed model gives new
insights into the phenomena of interference and emission of radiation.


title:
Quantum statistical properties of the Jaynes-Cummings model in the
  presence of a classical homogeneous gravitational field

abstract:
  The temporal evolution of quantum statistical properties of an interacting
atom-radiation field system in the presence of a classical homogeneous
gravitational field is investigated within the framework of the Jaynes-Cummings
model. To analyse the dynamical evolution of the atom-radiation system a
quantum treatment of the internal and external dynamics of the atom is
presented based on an alternative su(2) dynamical algebraic structure. By
solving the Schr\"{o}dinger equation in the interaction picture, the evolving
state of the system is found by which the influence of the gravitational field
on the dynamical behavior of the atom-radiation system is explored. Assuming
that initially the radiation field is prepared in a coherent state and the
two-level atom is in a coherent superposition of the excited and ground states,
the influence of gravity on the collapses and revivals of the atomic population
inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting
statistics and quadrature squeezing of the radiation field is studied.


title:
Violation of Bell's Inequality with Continuous Variables and Fractional
  Fourier Transforms

abstract: This paper has been withdrawn due to a crucial theoretical error.


title:
The information theory and the collapse of a wavefunction at the
  measurement of a spin 1/2 projection

abstract:
  From the point of view of the information theory, a model of the collapse
phenomena at the measurement of a spin 1/2 projection is developed. This model
phenomenologically includes an observer. The model allows not only to determine
the state of a system after the measurement but also to compute the state of
the observer. The state of the observer is equivalent to the operator of a spin
projection which the observer will measure at the next measurement.


title:
Influence of a classical homogeneous gravitational field on dissipative
  dynamics of the Jaynes-Cummings model with phase damping

abstract:
  In this paper, we study the dissipative dynamics of the Jaynes-Cummings model
with phase damping in the presence of a classical homogeneous gravitational
field. The model consists of a moving two-level atom simultaneously exposed to
the gravitational field and a single-mode traveling radiation field in the
presence of the phase damping. We present a quantum treatment of the internal
and external dynamics of the atom based on an alternative su(2) dynamical
algebraic structure. By making use of the super-operator technique, we obtain
the solution of the master equation for the density operator of the quantum
system, under the Markovian approximation. Assuming that initially the
radiation field is prepared in a Glauber coherent state and the two-level atom
is in the excited state, we investigate the influence of gravity on the
temporal evolution of collapses and revivals of the atomic population
inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting
statistics and quadrature squeezing of the radiation field in the presence of
phase damping.


title:
Transfer of d-Level quantum states through spin chains by random
  swapping

abstract:
  We generalize an already proposed protocol for quantum state transfer to spin
chains of arbitrary spin. An arbitrary unknown $d-$ level state is transferred
through a chain with rather good fidelity by the natural dynamics of the chain.
We compare the performance of this protocol for various values of $d$. A
by-product of our study is a much simpler method for picking up the state at
the destination as compared with the one proposed previously. We also discuss
entanglement distribution through such chains and show that the quality of
entanglement transition increases with the number of levels $d$.


title: A Study on the Sudden Death of Entanglement

abstract:
  The dynamics of entanglement and the phenomenon of entanglement sudden death
(ESD) \cite{yu} are discussed in bipartite systems, measured by Wootters
Concurrence. Our calculation shows that ESD appears whenever the system is open
or closed and is dependent on the initial condition. The relation of the
evolution of entanglement and energy transfer between the system and its
surroundings is also studied.


title: Quantifying Superposition

abstract:
  Measures are introduced to quantify the degree of superposition in mixed
states with respect to orthogonal decompositions of the Hilbert space of a
quantum system.
  These superposition measures can be regarded as analogues to entanglement
measures, but can also be put in a more direct relation to the latter. By a
second quantization of the system it is possible to induce superposition
measures from entanglement measures. We consider the measures induced from
relative entropy of entanglement and entanglement of formation. We furthermore
introduce a class of measures with an operational interpretation in terms of
interferometry. We consider the superposition measures under the action of
subspace preserving and local subspace preserving channels. The theory is
illustrated with models of an atom undergoing a relaxation process in a
Mach-Zehnder interferometer.