title: Steering, Entanglement, Nonlocality, and the EPR Paradox

abstract:
  The concept of steering was introduced by Schrodinger in 1935 as a
generalization of the EPR paradox for arbitrary pure bipartite entangled states
and arbitrary measurements by one party. Until now, it has never been
rigorously defined, so it has not been known (for example) what mixed states
are steerable (that is, can be used to exhibit steering). We provide an
operational definition, from which we prove (by considering Werner states and
Isotropic states) that steerable states are a strict subset of the entangled
states, and a strict superset of the states that can exhibit Bell-nonlocality.
For arbitrary bipartite Gaussian states we derive a linear matrix inequality
that decides the question of steerability via Gaussian measurements, and we
relate this to the original EPR paradox.


title: Phase vortices from a Young's three-pinhole interferometer

abstract:
  An analysis is presented of the phase vortices generated in the far field, by
an arbitrary arrangement of three monochromatic point sources of complex
spherical waves. In contrast with the case of three interfering plane waves, in
which an infinitely-extended vortex lattice is generated, the spherical sources
generate a finite number of phase vortices. Analytical expressions for the
vortex core locations are developed and shown to have a convenient
representation in a discrete parameter space. Our analysis may be mapped onto
the case of a coherently-illuminated Young's interferometer, in which the
screen is punctured by three rather than two pinholes.


title:
A sufficient and necessary condition for superdense coding of quantum
  states

abstract:
  Recently, Harrow et al. [Phys. Rev. Lett. 92, 187901 (2004)] gave a method
for preparing an arbitrary quantum state with high success probability by
physically transmitting some qubits, and by consuming a maximally entangled
state, together with exhausting some shared random bits. In this paper, we
discover that some states are impossible to be perfectly prepared by Alice and
Bob initially sharing those entangled states that are superposed by the ground
states, as the states to be prepared. In particular, we present a sufficient
and necessary condition for the states being enabled to be exactly prepared
with probability one, in terms of the initial entangled states (maybe
nonmaximally) superposed by the ground states. In contrast, if the initially
shared entanglement is maximal, then the probabilities for preparing these
quantum states are smaller than one. Furthermore, the lower bound on the
probability for preparing some states are derived.


title:
Oscillation structures in the spontaneous emission rate of an atom in a
  medium with refractive index n between mirrors: a solvable model

abstract:
  We study the multi-periodic oscillations in the spontaneous emission rate of
an atom in a medium with refractive index n sandwiched between two parallel
mirrors. The oscillations are not obvious in the analytical formula for the
rate derived based on Fermi's golden rule but can be extracted using Fourier
transforms by varying the system scale while holding the configuration. The
oscillations are interpreted as interferences and correspond to various
closed-orbits of the emitted photon going away from and returning to the atom.
This system provides a rare example that the oscillations can be explicitly
derived by following the emitted wave until it returns to the emitting atom. We
demonstrate the summation over a large number of closed-orbits converges to the
rate formula of golden rule.


title: Information dynamics in quantum theory

abstract:
  Shannon entropy and Fisher information functionals are known to quantify
certain information-theoretic properties of continuous probability
distributions of various origins. We carry out a systematic study of these
functionals, while assuming that the pertinent probability density has a
quantum mechanical appearance $\rho \doteq |\psi |^2$, with $\psi \in L^2(R)$.
Their behavior in time, due to the quantum Schr\"{o}dinger picture
evolution-induced dynamics of $\rho (x,t)$ is investigated as well, with an
emphasis on thermodynamical features of quantum motion.


title: Bound states in the continuum in a single-level Fano-Anderson model

abstract:
  Bound states in the continuum (BIC) are shown to exist in a single-level
Fano-Anderson model with a colored interaction between the discrete state and a
tight-binding continuum, which may describe mesoscopic electron or photon
transport in a semi-infinite one-dimensional lattice. The existence of BIC is
explained in the lattice realization as a boundary effect induced by lattice
truncation.


title:
A Mathematician's Viewpoint to Bell's theorem: In Memory of Walter
  Philipp

abstract:
  In this paper dedicated to the memory of Walter Philipp, we formalize the
rules of classical$\to$ quantum correspondence and perform a rigorous
mathematical analysis of the assumptions in Bell's NO-GO arguments.


title:
General linear-optical quantum state generation scheme: Applications to
  maximally path-entangled states

abstract:
  We introduce schemes for linear-optical quantum state generation. A quantum
state generator is a device that prepares a desired quantum state using product
inputs from photon sources, linear-optical networks, and postselection using
photon counters. We show that this device can be concisely described in terms
of polynomial equations and unitary constraints. We illustrate the power of
this language by applying the Grobner-basis technique along with the notion of
vacuum extensions to solve the problem of how to construct a quantum state
generator analytically for any desired state, and use methods of convex
optimization to identify bounds to success probabilities. In particular, we
disprove a conjecture concerning the preparation of the maximally
path-entangled |n,0)+|0,n) (NOON) state by providing a counterexample using
these methods, and we derive a new upper bound on the resources required for
NOON-state generation.


title: A father protocol for quantum broadcast channels

abstract:
  A new protocol for quantum broadcast channels based on the fully quantum
Slepian-Wolf protocol is presented. The protocol yields an achievable rate
region for entanglement-assisted transmission of quantum information through a
quantum broadcast channel that can be considered the quantum analogue of
Marton's region for classical broadcast channels. The protocol can be adapted
to yield achievable rate regions for unassisted quantum communication and for
entanglement-assisted classical communication; in the case of unassisted
transmission, the region we obtain has no independent constraint on the sum
rate, only on the individual transmission rates. Regularized versions of all
three rate regions are provably optimal.


title: On the use of photonic N00N states for practical quantum interferometry

abstract:
  The performance of photonic $N00N$ states, propagating in an attenuating
medium, is analyzed with respect to phase estimation. It is shown that, for
$N00N$ states propagating through a lossy medium, the Heisenberg limit is never
achieved. It is also shown that, for a given value of $N$, a signal comprised
of an attenuated separable state of $N$ photons will actually produce a better
phase estimate than will a signal comprised of an equally attenuated $N00N$
state, unless the transmittance of the medium is very high. This is a
consequence of the need to utilize measurement operators appropriate to the
different signal states. The result is that, for most practical applications in
realistic scenarios with attenuation, the resolution of $N00N$ state-based
phase estimation not only does not achieve the Heisenberg Limit, but is
actually worse than the Standard Quantum Limit. It is demonstrated that this
performance deficit becomes more pronounced as the number, $N$, of photons in
the signal increases.


title:
Continuous-Variable Quantum Cloning of Coherent states with
  Phase-Conjugate Input Modes Using Linear Optics

abstract:
  We propose a scheme for continuous-variable quantum cloning of coherent
states with phase-conjugate input modes using linear optics. The quantum
cloning machine yields $M$ identical optimal clones from $N$ replicas of a
coherent state and $N$ its replicas of phase conjugate. This scheme can be
straightforwardly implemented with the setup accessible at present since its
optical implementation only employs simple linear optical elements and homodyne
detection. Compared with the original scheme for continuous variables quantum
cloning with phase-conjugate input modes proposed by Cerf and Iblisdir [Phys.
Rev. Lett. 87, 247903 (2001)], which utilized a nondegenerate optical
parametric amplifier, our scheme loses the output of phase-conjugate clones and
is regarded as irreversible quantum cloning.


title:
Attainable entanglement of unitary transformed thermal states in
  liquid-state nuclear magnetic resonance with the chemical shift

abstract:
  Recently, Yu, Brown, and Chuang [Phys. Rev. A {\bf 71}, 032341 (2005)]
investigated the entanglement attainable from unitary transformed thermal
states in liquid-state nuclear magnetic resonance (NMR). Their research gave an
insight into the role of the entanglement in a liquid-state NMR quantum
computer. Moreover, they attempted to reveal the role of mixed-state
entanglement in quantum computing. However, they assumed that the Zeeman energy
of each nuclear spin which corresponds to a qubit takes a common value for all;
there is no chemical shift. In this paper, we research a model with the
chemical shifts and analytically derive the physical parameter region where
unitary transformed thermal states are entangled, by the positive partial
transposition (PPT) criterion with respect to any bipartition. We examine the
effect of the chemical shifts on the boundary between the separability and the
nonseparability, and find it is negligible.


title: Weak Measurements and Counterfactual Computation

abstract:
  Vaidman, in a recent article adopts the method of 'quantum weak measurements
in pre- and postselected ensembles' to ascertain whether or not the
chained-Zeno counterfactual computation scheme proposed by Hosten et al. is
counterfactual; which has been the topic of a debate on the definition of
counterfactuality. We disagree with his conclusion, which brings up some
interesting aspects of quantum weak measurements and some concerns about the
way they are interpreted.


title:
Alternative scheme for two-qubit conditional phase gate by adiabatic
  passage under dissipation

abstract:
  We check a recent proposal [H. Goto and K. Ichimura Phys. Rev. A 70, 012305
(2004)] for controlled phase gate through adiabatic passage under the influence
of spontaneous emission and the cavity decay. We show a modification of above
proposal could be used to generate the necessary conditional phase gates in the
two-qubit Grover search. Conditioned on no photon leakage either from the
atomic excited state or from the cavity mode during the gating period, we
numerically analyze the success probability and the fidelity of the two-qubit
conditional phase gate by adiabatic passage. The comparison made between our
proposed gating scheme and a previous one shows that Goto and Ichimura's scheme
is an alternative and feasible way in the optical cavity regime for two-qubit
gates and could be generalised in principle to multi-qubit gates.


title: Generation of N-qubit W state with rf-SQUID qubits by adiabatic passage

abstract:
  A simple scheme is presented to generate n-qubit W state with
rf-superconducting quantum interference devices (rf-SQUIDs) in cavity QED
through adiabatic passage. Because of the achievable strong coupling for
rf-SQUID qubits embedded in cavity QED, we can get the desired state with high
success probability. Furthermore, the scheme is insensitive to position
inaccuracy of the rf-SQUIDs. The numerical simulation shows that, by using
present experimental techniques, we can achieve our scheme with very high
success probability, and the fidelity could be eventually unity with the help
of dissipation.


title: Where the mathematical structure of Quantum Mechanics coms from

abstract:
  The mathematical formulation of Quantum Mechanics is derived from purely
operational axioms based on a general definition of "experiment" as a set of
transformations. The main ingredient of the mathematical construction is the
postulated existence of "faithful states" that allows one to calibrate the
experimental apparatus. Such notion is at the basis of the operational
definitions of the scalar product and of the "adjoint" of a transformation.


title:
Uncoupling Which-Way Information from Interference: A Novel Interference
  Experiment using a Super-Focused Laser Beam

abstract:
  The generally accepted view in quantum theory is that information about which
way the quantum system traveled and interference visibility are complementary.
In all which-way experiments, however, an intervention takes place in the
interference process in order to determine which way the quantum system took.
This intervention can imply the tagging of a which-way marker to a quantum
system or, for instance, blocking off one of the paths in a Mach-Zehnder
interferometer so that one indirectly knows that the quantum system took the
other (open) path. It is, however, this intervention that destroys the
interference. In this paper a novel two-slit which-way interference experiment
will be discussed and proposed for implementation that provides maximum
which-way information without intervening in the interference process so that
simultaneously maximum interference visibility remains preserved. This, in
fact, implies an uncoupling of which-way information from interference and
consequently also entails violating the duality relation P^2+V^2<1. Basically,
the purpose of the proposed experiment and of this paper is to scrutinize this
duality relation. The experiment makes use of a super-focused laser beam that
is launched into only one of the two slits of the two-slit interference
experiment.


title: Non-Abelian generalization of off-diagonal geometric phases

abstract:
  If a quantum system evolves in a noncyclic fashion the corresponding
geometric phase or holonomy may not be fully defined. Off-diagonal geometric
phases have been developed to deal with such cases. Here, we generalize these
phases to the non-Abelian case, by introducing off-diagonal holonomies that
involve evolution of more than one subspace of the underlying Hilbert space.
Physical realizations of the off-diagonal holonomies in adiabatic evolution and
interferometry are put forward.


title: Optimal control of a qubit coupled to a non-Markovian environment

abstract:
  A central challenge for implementing quantum computing in the solid state is
decoupling the qubits from the intrinsic noise of the material. We investigate
the implementation of quantum gates for a paradigmatic, non-Markovian model: A
single qubit coupled to a two-level system that is exposed to a heat bath. We
systematically search for optimal pulses using a generalization of the novel
open systems Gradient Ascent Pulse Engineering (GRAPE) algorithm. We show and
explain that next to the known optimal bias point of this model, there are
optimal shapes which refocus unwanted terms in the Hamiltonian. We study the
limitations of controls set by the decoherence properties. This can lead to a
significant improvement of quantum operations in hostile environments.


title:
Coherent States for generalized oscillator with finite-dimensional
  Hilbert space

abstract:
  The construction of oscillator-like systems connected with the given set of
orthogonal polynomials and coherent states for such systems developed by
authors is extended to the case of the systems with finite-dimensional state
space. As example we consider the generalized oscillator connected with
Krawtchouk polynomials.


title: Entanglement Percolation in Quantum Networks

abstract:
  Quantum networks are composed of nodes which can send and receive quantum
states by exchanging photons. Their goal is to facilitate quantum communication
between any nodes, something which can be used to send secret messages in a
secure way, and to communicate more efficiently than in classical networks.
These goals can be achieved, for instance, via teleportation. Here we show that
the design of efficient quantum communication protocols in quantum networks
involves intriguing quantum phenomena, depending both on the way the nodes are
displayed, and the entanglement between them. These phenomena can be employed
to design protocols which overcome the exponential decrease of signals with the
number of nodes. We relate the problem of establishing maximally entangled
states between nodes to classical percolation in statistical mechanics, and
demonstrate that quantum phase transitions can be used to optimize the
operation of quantum networks.


title: Distribution of interference in random quantum algorithms

abstract:
  We study the amount of interference in random quantum algorithms using a
recently derived quantitative measure of interference. To this end we introduce
two random circuit ensembles composed of random sequences of quantum gates from
a universal set, mimicking quantum algorithms in the quantum circuit
representation. We show numerically that these ensembles converge to the
well--known circular unitary ensemble (CUE) for general complex quantum
algorithms, and to the Haar orthogonal ensemble (HOE) for real quantum
algorithms. We provide exact analytical formulas for the average and typical
interference in the circular ensembles, and show that for sufficiently large
numbers of qubits a random quantum algorithm uses with probability close to one
an amount of interference approximately equal to the dimension of the Hilbert
space. As a by-product, we offer a new way of efficiently constructing random
operators from the Haar measures of CUE or HOE in a high dimensional Hilbert
space using universal sets of quantum gates.


title: Gradient Echo Quantum Memory for Light using Two-level Atoms

abstract:
  We propose a quantum memory for light that is analogous to the NMR gradient
echo. Our proposal is ideally perfectly efficient and provides simplifications
to current 3-level quantum memory schemes based on controlled inhomogeneous
broadening. Our scheme does not require auxiliary light fields. Instead the
input optical pulse interacts only with two-level atoms that have linearly
increasing Stark shifts. By simply reversing the sign of the atomic Stark
shifts, the pulse is retrieved in the forward direction. We present analytical,
numerical and experimental results of this scheme. We report experimental
efficiencies of up to 15% and suggest simple realizable improvements to
significantly increase the efficiency.


title: Coherent Communication with Continuous Quantum Variables

abstract:
  The coherent bit (cobit) channel is a resource intermediate between classical
and quantum communication. It produces coherent versions of teleportation and
superdense coding. We extend the cobit channel to continuous variables by
providing a definition of the coherent nat (conat) channel. We construct
several coherent protocols that use both a position-quadrature and a
momentum-quadrature conat channel with finite squeezing. Finally, we show that
the quality of squeezing diminishes through successive compositions of coherent
teleportation and superdense coding.


title: On the measurement probability of quantum phases

abstract:
  We consider the probability by which quantum phase measurements of a given
precision can be done successfully. The least upper bound of this probability
is derived and the associated optimal state vectors are determined. The
probability bound represents an unique and continuous transition between
macroscopic and microscopic measurement precisions.


title:
Improving the entanglement transfer from continuous variable systems to
  localized qubits using non Gaussian states

abstract:
  We investigate the entanglement transfer from a bipartite continuous-variable
(CV) system to a pair of localized qubits assuming that each CV mode couples to
one qubit via the off-resonance Jaynes-Cummings interaction with different
interaction times for the two subsystems. First, we consider the case of the CV
system prepared in a Bell-like superposition and investigate the conditions for
maximum entanglement transfer. Then we analyze the general case of two-mode CV
states that can be represented by a Schmidt decomposition in the Fock number
basis. This class includes both Gaussian and non Gaussian CV states, as for
example twin-beam (TWB) and pair-coherent (TMC, also known as two-mode-coher
ent) states respectively. Under resonance conditions, equal interaction times
for both qubits and different initial preparations, we find that the
entanglement transfer is more efficient for TMC than for TWB states. In the
perspective of applications such as in cavity QED or with superconducting
qubits, we analyze in details the effects of off-resonance interactions
(detuning) and different interaction times for the two qubits, and discuss
conditions to preserve the entanglement transfer.


title:
Quantum kinematics on q-deformed quantum spaces I, Mathematical
  Framework

abstract:
  The aim of these two papers (I and II) is to try to give fundamental concepts
of quantum kinematics to q-deformed quantum spaces. Paper I introduces the
relevant mathematical concepts. A short review of the basic ideas of q-deformed
analysis is given. These considerations are continued by introducing q-deformed
analogs of Fourier transformations and delta functions. Their properties are
discussed in detail. Furthermore, q-deformed versions of sesquilinear forms are
defined, their basic properties are derived, and q-analogs of the
Fourier-Plancherel identity are proved. In paper II these reasonings are
applied to wave functions on position and momentum space.


title:
Quantum kinematics on q-deformed quantum spaces II, Wave functions on
  position and momentum space

abstract:
  The aim of Part II of this paper is to try to describe wave functions on
q-deformed versions of position and momentum space. This task is done within
the framework developed in Part I of the paper. In order to make Part II
self-contained the most important results of Part I are reviewed. Then it is
shown that q-deformed exponentials and q-deformed delta functions play the role
of momentum and position eigenfunctions, respectively. Their completeness and
orthonormality relations are derived. For both bases of eigenfunctions matrix
elements of position and momentum operators are calculated. A q-deformed
version of the spectral decomposition of multiplication operators is discussed
and q-analogs of Heaviside functions are proposed. Interpreting the results
from the point of view provided by the concept of quasipoints gives the
formalism a physical meaning. The definition of expectation values and the
calculation of probability densities are explained in detail. Finally, it is
outlined how the considerations so far carry over to antisymmetrized spaces.


title:
Hyperspherical elliptic coordinates treatment of muon transfer from
  muonic hydrogen to atomic oxygen

abstract:
  Quantum-mechanical calculations of muon transfer between muonic hydrogen and
an oxygen nuclei for $s$ waves and collision energies in the range $10^{-3} -
10^3$ eV, are presented. Close-coupling time-independent Schr\"odinger
equations, written in terms of hyperspherical elliptic coordinates were
integrated along the hyper-radius to obtain the partial and total muon-transfer
probabilities. The results show the expected Wigner-Bethe threshold behavior up
to collision energies of the order of $10^{-2}$ eV and pronounced maxima at
$10^2$ eV which can be interpreted in terms of crossings between potential
energy curves corresponding to the entrance channel state $(\mu p)_{1s} + \mO$
and two product channels which asymptotically correlate to $p +
(\mO\mu)_{n=5,6}$.
  The population of the final states with different orbital angular momenta is
found to be essentially independent of energy in the range considered in this
work. This can be attributed to a strong selection rule for the conservation of
the quantum number associated to one of the elliptic hyperangles.


title: A photon loss tolerant Zeno CSIGN gate

abstract:
  We model an optical implementation of a CSIGN gate that makes use of the
Quantum Zeno effect [1,2] in the presence of photon loss. The raw operation of
the gate is severely affected by this type of loss. However, we show that by
using the same photon loss codes that have been proposed for linear optical
quantum computation (LOQC), the performance is greatly enhanced and such gates
can outperform LOQC equivalents. The technique can be applied to other types of
nonlinearities, making the implementation of nonlinear optical gates much more
attractive.


title: Nonlinear Inequalities and Entropy-Concurrence Plane

abstract:
  Nonlinear inequalities based on the quadratic Renyi entropy for mixed
two-qubit states are characterized on the Entropy-Concurrence plane. This class
of inequalities is stronger than Clauser-Horne-Shimony-Holt (CHSH) inequalities
and, in particular, are violated "in toto" by the set of Type I
Maximally-Entangled-Mixture States (MEMS I).


title:
Quantum Logic of Semantic Space: An Exploratory Investigation of Context
  Effects in Practical Reasoning

abstract:
  This article is an exploratory account of the the non-monotonic behaviour of
conceptual associations in the light of context. Computational approximations
of conceptual space are furnished by semantic space models which are emerging
from the fields of cognition and computational linguistics. Semantic space
models not only provide a cognitively motivated basis to underpin human
practical reasoning, but from a mathematical perspective, they are real-valued
Hilbert spaces. This introduces the highly speculative prospect of formalizing
aspects of human practical reasoning via quantum mechanics. This account
focuses on how to formalize context effects in relation to concepts as well as
keeping an eye on operational issues.


title: Multiple Qubits as Symplectic Polar Spaces of Order Two

abstract:
  It is surmised that the algebra of the Pauli operators on the Hilbert space
of N-qubits is embodied in the geometry of the symplectic polar space of rank N
and order two, W_{2N - 1}(2). The operators (discarding the identity) answer to
the points of W_{2N - 1}(2), their partitionings into maximally commuting
subsets correspond to spreads of the space, a maximally commuting subset has
its representative in a maximal totally isotropic subspace of W_{2N - 1}(2)
and, finally, "commuting" translates into "collinear" (or "perpendicular").


title: Designing spin-1 lattice models using polar molecules

abstract:
  We describe how to design a large class of always on spin-1 interactions
between polar molecules trapped in an optical lattice. The spin degrees of
freedom correspond to the hyperfine levels of a ro-vibrational ground state
molecule. Interactions are induced using a microwave field to mix ground states
in one hyperfine manifold with the spin entangled dipole-dipole coupled excited
states. Using multiple fields anistropic models in one, two, or three
dimensions, can be built with tunable spatial range. An illustrative example in
one dimension is the generalized Haldane model, which at a specific parameter
has a gapped valence bond solid ground state. The interaction strengths are
large compared to decoherence rates and should allow for probing the rich phase
structure of strongly correlated systems, including dimerized and gapped
phases.


title:
Scheme for the implementation of optimal cloning of arbitrary single
  particle atomic state into two photonic states

abstract:
  We present a feasible scheme to implement the $1 \to 2$ optimal cloning of
arbitrary single particle atomic state into two photonic states, which is
important for applications in long distance quantum communication. Our scheme
also realizes the tele-NOT gate of one atom to the other distant atom trapped
in another cavity. The scheme is based on the adiabatic passage and the
polarization measurement. It is robust against a number of practical noises
such as the violation of the Lamb-Dicke condition, spontaneous emission and
detection inefficiency.


title: Local-field correction to one- and two-atom van der Waals interactions

abstract:
  Based on macroscopic quantum electrodynamics in linearly and causally
responding media, we study the local-field corrected van der Waals potentials
and forces for unpolarized ground-state atoms placed within a magnetoelectric
medium of arbitrary size and shape. We start from general expressions for the
van der Waals potentials in terms of the (classical) Green tensor of the
electromagnetic field and the atomic polarizability and incorporate the
local-field correction by means of the real-cavity model. In this context,
special emphasis is given to the decomposition of the Green tensor into a
medium part multiplied by a global local-field correction factor and, in the
single-atom case, a part that only depends on the cavity characteristics. The
result is used to derive general formulas for the local-field corrected van der
Waals potentials and forces. As an application, we calculate the van der Waals
potential between two ground-state atoms placed within magnetoelectric bulk
material.


title:
Interference induced preparation of spinpolarized electrons in a
  three-terminal quantum ring

abstract:
  We present an exact, analytic solution of the spin dependent quantum
transport problem with spin-orbit interaction in a one-dimensional mesoscopic
ring with one input and two output leads. We demonstrate that for appropriate
parameters spatial interference in the ring leads to a behavior analogous to
that of the Stern-Gerlach apparatus: different spin polarizations can be
achieved in the two output channels from an originally totally unpolarized
incoming spin state. It is shown that this requires an appropriate interference
of states that carry oppositely directed currents. We find that spin
polarization is possible for several geometries, including the case when the
device is not symmetric with respect to the incoming lead. A clear connection
is established between the Stern-Gerlach like property of the device and the
relevant Aharonov-Casher phases in the loop geometry.


title: Normal Forms and Tensor Ranks of Pure States of Four Qubits

abstract:
  We examine the SLOCC classification of the (non-normalized) pure states of
four qubits obtained by F. Verstraete et al. The rigorous proofs of their basic
results are provided and necessary corrections implemented. We use Invariant
Theory to solve the problem of equivalence of pure states under SLOCC
transformations of determinant 1 and qubit permutations. As a byproduct, we
produce a new set of generators for the invariants of the Weyl group of type
F_4. We complete the determination of the tensor ranks of 4-qubit pure states
initiated by J.-L. Brylinski. As a result we obtain a simple algorithm for
computing these ranks. We obtain also a very simple classification of pure
states of rank at most 3.


title: Approaches to Quantum Error Correction

abstract:
  The purpose of this little survey is to give a simple description of the main
approaches to quantum error correction and quantum fault-tolerance. Our goal is
to convey the necessary intuitions both for the problems and their solutions in
this area. After characterising quantum errors we present several
error-correction schemes and outline the elements of a full fledged
fault-tolerant computation, which works error-free even though all of its
components can be faulty. We also mention alternative approaches to
error-correction, so called error-avoiding or decoherence-free schemes.
Technical details and generalisations are kept to a minimum.


title: Graph states as ground states of many-body spin-1/2 Hamiltonians

abstract:
  We consider the problem whether graph states can be ground states of local
interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at
most two-body interactions, we show that no n-qubit graph state can be the
exact, non-degenerate ground state. We determine for any graph state the
minimal d such that it is the non-degenerate ground state of a d-body
interaction Hamiltonian, while we show for d'-body Hamiltonians H with d'<d
that the resulting ground state can only be close to the graph state at the
cost of H having a small energy gap relative to the total energy. When allowing
for ancilla particles, we show how to utilize a gadget construction introduced
in the context of the k-local Hamiltonian problem, to obtain n-qubit graph
states as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting
on n'>n spins.


title: Perspectives on the quantum Zeno paradox

abstract:
  As of October 2006, there were approximately 535 citations to the seminal
1977 paper of Misra and Sudarshan that pointed out the quantum Zeno paradox
(more often called the quantum Zeno effect). In simple terms, the quantum Zeno
effect refers to a slowing down of the evolution of a quantum state in the
limit that the state is observed continuously. There has been much disagreement
as to how the quantum Zeno effect should be defined and as to whether it is
really a paradox, requiring new physics, or merely a consequence of "ordinary"
quantum mechanics. The experiment of Itano, Heinzen, Bollinger, and Wineland,
published in 1990, has been cited around 347 times and seems to be the one most
often called a demonstration of the quantum Zeno effect. Given that there is
disagreement as to what the quantum Zeno effect is, there naturally is
disagreement as to whether that experiment demonstrated the quantum Zeno
effect. Some differing perspectives regarding the quantum Zeno effect and what
would constitute an experimental demonstration are discussed.


title: An all-optical trap for a gram-scale mirror

abstract:
  We report on a stable optical trap suitable for a macroscopic mirror, wherein
the dynamics of the mirror are fully dominated by radiation pressure. The
technique employs two frequency-offset laser fields to simultaneously create a
stiff optical restoring force and a viscous optical damping force. We show how
these forces may be used to optically trap a free mass without introducing
thermal noise; and we demonstrate the technique experimentally with a 1 gram
mirror. The observed optical spring has an inferred Young's modulus of 1.2 TPa,
20% stiffer than diamond. The trap is intrinsically cold and reaches an
effective temperature of 0.8 K, limited by technical noise in our apparatus.


title: Semiclassical limits to the linewidth of an atom laser

abstract:
  We investigate the linewidth of a quasi-continuous atom laser within a
semiclassical framework. In the high flux regime, the lasing mode can exhibit a
number of undesirable features such as density fluctuations. We show that the
output therefore has a complicated structure that can be somewhat simplified
using Raman outcoupling methods and energy-momentum selection rules. In the
weak outcoupling limit, we find that the linewidth of an atom laser is
instantaneously Fourier limited, but, due to the energy `chirp' associated with
the draining of a condensate, the long-term linewidth of an atom laser is
equivalent to the chemical potential of the condensate source. We show that
correctly sweeping the outcoupling frequency can recover the Fourier-limited
linewidth.


title: Pooling quantum states obtained by indirect measurements

abstract:
  We consider the pooling of quantum states when Alice and Bob both have one
part of a tripartite system and, on the basis of measurements on their
respective parts, each infers a quantum state for the third part S. We denote
the conditioned states which Alice and Bob assign to S by alpha and beta
respectively, while the unconditioned state of S is rho. The state assigned by
an overseer, who has all the data available to Alice and Bob, is omega. The
pooler is told only alpha, beta, and rho. We show that for certain classes of
tripartite states, this information is enough for her to reconstruct omega by
the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two
classes of states for which this pooling formula works: (i) all pure states for
which the rank of rho is equal to the product of the ranks of the states of
Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states
that are mutually orthogonal on S.


title: Multimode quantum limits to the linewidth of an atom laser

abstract:
  The linewidth of an atom laser can be limited by excitation of higher energy
modes in the source Bose-Einstein condensate, energy shifts in that condensate
due to the atomic interactions, or phase diffusion of the lasing mode due to
those interactions. The first two are effects that can be described with a
semiclassical model, and have been studied in detail for both pumped and
unpumped atom lasers. The third is a purely quantum statistical effect, and has
been studied only in zero dimensional models. We examine an unpumped atom laser
in one dimension using a quantum field theory using stochastic methods based on
the truncated Wigner approach. This allows spatial and statistical effects to
be examined simultaneously, and the linewidth limit for unpumped atom lasers is
quantified in various limits.


title: Loss of coherence and dressing in QED

abstract:
  The dynamics of a free charged particle, initially described by a coherent
wave packet, interacting with an environment, i.e. the electromagnetic field
characterized by a temperature $T$, is studied. Using the dipole approximation
the exact expressions for the evolution of the reduced density matrix both in
momentum and configuration space and the vacuum and the thermal contribution to
decoherence, are obtained. The time behaviour of the coherence lengths in the
two representations are given. Through the analysis of the dynamic of the field
structure associated to the particle the vacuum contribution is shown to be
linked to the birth of correlations between the single momentum components of
the particle wave packet and the virtual photons of the dressing cloud.


title:
Realization of quantum mechanical weak values of observables using
  entangled photons

abstract:
  We present a scheme for realization of quantum mechanical weak values of
observables using entangled photons produced in parametric down conversion. We
consider the case when the signal and idler modes are respectively in a
coherent state and vacuum. We use a low efficiency detector to detect the
photons in the idler mode.This weak detection leads to a large displacement and
fluctuations in the signal field's quantum state which can be studied by
monitoring the photon number and quadrature distributions.


title: Geometric Phases and Critical Phenomena in a Chain of Interacting Spins

abstract:
  The geometric phase can act as a signature for critical regions of
interacting spin chains in the limit where the corresponding circuit in
parameter space is shrunk to a point and the number of spins is extended to
infinity; for finite circuit radii or finite spin chain lengths, the geometric
phase is always trivial (a multiple of 2pi). In this work, by contrast, two
related signatures of criticality are proposed which obey finite-size scaling
and which circumvent the need for assuming any unphysical limits. They are
based on the notion of the Bargmann invariant whose phase may be regarded as a
discretized version of Berry's phase. As circuits are considered which are
composed of a discrete, finite set of vertices in parameter space, they are
able to pass directly through a critical point, rather than having to
circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool
for criticality in the case of a given non-solvable one-dimensional spin chain
with nearest-neighbour interactions in the presence of an external magnetic
field.


title:
Dynamics of Josephson-junction qubits with exactly solvable
  time-dependent bias pulses

abstract:
  The quantum dynamics of a two-state system (qubit) can be governed by means
of external control parameters present in time-dependent bias pulses of special
forms. We consider the class of biases for which the time evolution equation
without a dissipation can be solved exactly. Concentrating for definiteness on
the flux qubit we calculate the probability of the definite direction of the
current in the loop and its time-averaged values as functions of the qubit's
control parameters both analytically and solving numerically the equation of
motion for the density matrix in the presence of relaxation and decoherence. It
is shown that there exist such time-dependent biases that the definite current
direction probability with no dissipation taken into account becomes a
monotonously growing function of time tending to a value which may exceed 1/2.
We also calculate the probability to find the system in the excited state and
show the possibility of the inverse population in a properly driven two-state
system provided the relaxation and dephasing rates are small enough.


title:
A Bootstrapping Approach for Generating Maximally Path-Entangled Photon
  States

abstract:
  We propose a bootstrapping approach to generation of maximally path-entangled
states of photons, so called ``NOON states''. Strong atom-light interaction of
cavity QED can be employed to generate NOON states with about 100 photons;
which can then be used to boost the existing experimental Kerr nonlinearities
based on quantum coherence effects to facilitate NOON generation with
arbitrarily large number of photons all within the current experimental state
of the art technology. We also offer an alternative scheme that uses an
atom-cavity dispersive interaction to obtain sufficiently high
Kerr-nonlinearity necessary for arbitrary NOON generation.


title:
Experimental Demonstration of Continuous Variable Cloning with
  Phase-Conjugate Inputs

abstract:
  We report the experimental demonstration of continuous variable cloning of
phase conjugate coherent states as proposed by Cerf and Iblisdir (Phys. Rev.
Lett. 87, 247903 (2001)). In contrast to the proposal of Cerf and Iblisdir, the
cloning transformation is accomplished using only linear optical components,
homodyne detection and feedforward. Three clones are succesfully produced with
fidelities about 89%.


title:
Sub-shot-noise photon-number correlation in mesoscopic twin-beam of
  light

abstract:
  We demonstrate sub-shot-noise photon-number correlations in a (temporal)
multimode mesoscopic ($\sim 10^3$ detected photons) twin-beam produced by
ps-pulsed spontaneous non-degenerate parametric downconversion. We have
separately detected the signal and idler distributions of photons collected in
twin coherence areas and found that the variance of the photon-count difference
goes below the shot-noise limit by 3.25 dB. The number of temporal modes
contained in the twin-beam, as well as the size of the twin coherence areas,
depends on the pump intensity. Our scheme is based on spontaneous
downconversion and thus does not suffer from limitations due to the finite gain
of the parametric process. Twin-beams are also used to demonstrate the
conditional preparation of a nonclassical (sub-Poissonian) state.


title: Lineal: A linear-algebraic Lambda-calculus

abstract:
  We provide a computational definition of the notions of vector space and
bilinear functions. We use this result to introduce a minimal language
combining higher-order computation and linear algebra. This language extends
the Lambda-calculus with the possibility to make arbitrary linear combinations
of terms alpha.t + beta.u. We describe how to "execute" this language in terms
of a few rewrite rules, and justify them through the two fundamental
requirements that the language be a language of linear operators, and that it
be higher-order. We mention the perspectives of this work in the field of
quantum computation, whose circuits we show can be easily encoded in the
calculus. Finally, we prove the confluence of the entire calculus.


title:
Coherent optical detection of highly excited Rydberg states using
  electromagnetically induced transparency

abstract:
  We observe electromagnetically induced transparency (EIT) on the 5s to 5p
transition in a room temperature rubidium vapour cell by coupling the 5p state
to a Rydberg state (ns or nd with n=26 to 124). We demonstrate that the narrow
line-width of the EIT resonance (2 MHz) allows precise measurement of the d
state fine structure splitting, and together with the sensitivity of the
Rydberg state to electric fields, we are able to detect transient electric
fields produced by the dynamics of charges within the cell. Coherent coupling
of Rydberg states via EIT could also be used for cross-phase modulation and
photon entanglement.


title: Decoherence-induced geometric phase in a multilevel atomic system

abstract:
  We consider the STIRAP process in a three-level atom. Viewed as a closed
system, no geometric phase is acquired. But in the presence of spontaneous
emission and/or collisional relaxation we show numerically that a
non-vanishing, purely real, geometric phase is acquired during STIRAP, whose
magnitude grows with the decay rates. Rather than viewing this
decoherence-induced geometric phase as a nuisance, it can be considered an
example of "beneficial decoherence": the environment provides a mechanism for
the generation of geometric phases which would otherwise require an extra
experimental control knob.


title:
On convergence to equilibrium in strongly coupled Bogoliubov's
  oscillator model

abstract:
  We examine classical Bogoliubov's model of a particle coupled to a heat bath
which consists of infinitely many stochastic oscillators. Bogoliubov's result
suggests that, in the stochastic limit, the model exhibits convergence to
thermodynamical equilibrium. It has recently been shown that the system does
attain the equilibrium if the coupling constant is small enough. We show that
in the case of the large coupling constant the distribution function
$\rho_{S}(q,p,t)\to 0$ pointwise as $t\to\infty$. This implies that if there is
convergence to equilibrium, then the limit measure has no finite momenta.
Besides, the probability to find the particle in any finite domain of phase
space tends to zero. This is also true for domains in the coordinate space and
in the momentum space.


title:
Superseded version of the WKB approximation and explanation of emergence
  of classicality

abstract:
  Regarding the limit hbar-->0 as the classical limit of quantum mechanics
seems to be silly because hbar is a definite constant of physics, but it was
successfully used in the derivation of the WKB approximation. A superseded
version of the WKB approximation is proposed in the classical limit alpha-->0
where alpha=m/M is the screening parameter of an object in which m is the mass
of the effective screening layer and M the total mass. This version is
applicable to not only approximate solution of Schrodinger equation of a
quantum particle but also that of a nanoparticle. Moreover, the version shows
that the quantization rules for nanoparticles can be achieved by substituting
alpha times hbar for hbar in the Bohr-Sommerfeld quantization rules of the old
quantum theory. Most importantly, the version helps clarify the essential
difference between classical and quantum realities and understand the
transition from quantum to classical mechanics as well as quantum mechanics
itself.


title:
Sequential Attack with Intensity Modulation on the
  Differential-Phase-Shift Quantum Key Distribution Protocol

abstract:
  In this paper, we discuss the security of the differential-phase-shift
quantum key distribution (DPSQKD) protocol by introducing an improved version
of the so-called sequential attack, which was originally discussed by Waks et
al. Our attack differs from the original form of the sequential attack in that
the attacker Eve modulates not only the phases but also the amplitude in the
superposition of the single-photon states which she sends to the receiver.
Concentrating especially on the "discretized gaussian" intensity modulation, we
show that our attack is more effective than the individual attack, which had
been the best attack up to present. As a result of this, the recent experiment
with communication distance of 100km reported by Diamanti et al. turns out to
be insecure. Moreover it can be shown that in a practical experimental setup
which is commonly used today, the communication distance achievable by the
DPSQKD protocol is less than 95km.


title: Mixed Qubit Cannot Be Universally Broadcast

abstract:
  We show that there does not exist any universal quantum cloning machine that
can broadcast an arbitrary mixed qubit with a constant fidelity. Based on this
result, we investigate the dependent quantum cloner in the sense that some
parameter of the input qubit $\rho_s(\theta,\omega,\lambda)$ is regarded as
constant in the fidelity. For the case of constant $\omega$, we establish the
$1\to2$ optimal symmetric dependent cloner with a fidelity 1/2. It is also
shown that the $1\to M$ optimal quantum cloning machine for pure qubits is also
optimal for mixed qubits, when $\lambda$ is the unique parameter in the
fidelity. For general $N\to M$ broadcasting of mixed qubits, the situation is
very different.


title:
Revisiting controlled quantum secure direct communication using a
  non-symmetric quantum channel with quantum superdense coding

abstract:
  Recently Xia and Song [Phys. Lett. A (In press)] have proposed a controlled
quantum secure direct communication (CQSDC) protocol. They claimed that in
their protocol only with the help of the controller Charlie, the receiver Alice
can successfully extract the secret message from the sender Bob. In this
letter, first we will show that within their protocol the controller Charlie's
role can be excluded due to their unreasonable design. We then revise the
Xia-Song CQSDC protocol such that its original advantages are retained and the
CQSDC can be really realized.


title: Quantum Phase Transitions and Matrix Product States in Spin Ladders

abstract:
  We investigate quantum phase transitions in ladders of spin 1/2 particles by
engineering suitable matrix product states for these ladders. We take into
account both discrete and continuous symmetries and provide general classes of
such models. We also study the behavior of entanglement of different
neighboring sites near the transition point and show that quantum phase
transitions in these systems are accompanied by divergences in derivatives of
entanglement.


title: Quantum Key Distribution Using Quantum Faraday Rotators

abstract:
  We propose a new quantum key distribution (QKD) protocol based on the fully
quantum mechanical states of the Faraday rotators. The protocol is
unconditionally secure against collective attacks for multi-photon source up to
two photons on a noisy environment. It is also robust against impersonation
attacks. The protocol may be implemented experimentally with the current
spintronics technology on semiconductors.


title: On Arguments for Linear Quantum Dynamics

abstract:
  Two recent arguments for linear dynamics in quantum theory are critically
re-examined. Neither argument is found to be satisfactory as it stands,
although an improved version of one of the arguments can in fact be given. This
improved version turns out to be still not completely unproblematic, but it is
argued that it contains only a single actual loophole, which is identical to a
loophole that remains in experimental proofs of nonlocality of Bell-type. It is
concluded that - within the context of the standard quantum kinematical
framework and in agreement with what has been concluded by earlier authors - a
nonlinear dynamics of density operators is inconsistent with relativistic
causality. However, it is also stressed that this conclusion in itself has
little implication for the nature of dynamics at the Hilbert space level - in
particular, it does not force dynamics to be linear at this level - nor does it
continue to be valid in contexts that go beyond the standard quantum
kinematical framework. Despite their seeming triviality, these last two points
have not always been appreciated in the literature. Finally, it is also pointed
out that the argument for complete positivity, as given in conjunction with one
of the two recent arguments for linear dynamics, in fact only establishes a
condition that is weaker than complete positivity.


title:
Collective multipole-like signatures of entanglement in symmetric
  N-qubit systems

abstract:
  A cogent theory of collective multipole-like quantum correlations in
symmetric multiqubit states is presented by employing SO(3) irreducible
spherical tensor representation. An arbitrary bipartite division of this system
leads to a family of inequalities to detect entanglement involving averages of
these tensors expressed in terms of the total system angular momentum operator.
Implications of this theory to the quantum nature of multipole-like
correlations of all orders in the Dicke states are deduced. A selected set of
examples illustrate these collective tests. Such tests detect entanglement in
macroscopic atomic ensembles, where individual atoms are not accessible.


title: Fuzzy Propositional Logic Associated with Quantum Computational Gates

abstract:
  We apply residuated structures associated with fuzzy logic to develop certain
aspects of information processing in quantum computing from a logical
perspective. For this purpose, we introduce an axiomatic system whose natural
interpretation is the irreversible quantum Poincare structure.


title:
Bell inequalities for two-photon experiments testable at low detection
  efficiency without assuming fair sampling

abstract:
  A family of local models containing two angles as hidden variables is defined
for experiments measuring polarization correlation of optical photons.
Searching for the best model of the family, that is giving predictions most
close to quantum mechanics, allows deriving Bell-type inequalities which may be
tested with relatively low detection efficiency.


title:
Control of the geometric phase and pseudo-spin dynamics on coupled
  Bose-Einstein condensates

abstract:
  We describe the behavior of two coupled Bose-Einstein condensates in
time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using
the two-mode approach. Starting from Bloch states, we succeed to get analytical
solutions for the TD Schroedinger equation and present a detailed analysis of
the relative and geometric phases acquired by the wave function of the
condensates, as well as their population imbalance. We also establish a
connection between the geometric phases and constants of motion which
characterize the dynamic of the system. Besides analyzing the affects of
temporality on condensates that differs by hyperfine degrees of freedom
  (internal Josephson effect), we also do present a brief discussion of a one
specie condensate in a double-well potential
  (external Josephson effect).


title:
Manipulation of the quantum state by Majorana transition in spinor
  Bose-Einstein condensates

abstract:
  Manipulation of the quantum state by the Majorana transition in spinor BEC
system has been realized by altering the rotation frequency of the magnetic
field's direction. This kind of manipulation method has no limitation on the
transition speed in principle and the system is well closed, which provides a
new and superior tool to manipulate quantum states. Using this methord on
pulsed atom laser, multicomponent spinor atom laser is generated. We
demonstrate that the experiment results are agreed with the theoretical
predication.


title:
Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and
  Thermodynamics

abstract:
  We discuss and motivate the form of the generator of a nonlinear quantum
dynamical group 'designed' so as to accomplish a unification of quantum
mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum
Thermodynamics (QT). Its conceptual foundations differ from those of (von
Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information
theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the
same mathematics, and for zero entropy states it reduces to standard unitary
QM. The nonlinear dynamical group of QT is construed so that the second law
emerges as a theorem of existence and uniqueness of a stable equilibrium state
for each set of mean values of the energy and the number of constituents. It
implements two fundamental ansatzs. The first is that in addition to the
standard QM states described by idempotent density operators (zero entropy), a
strictly isolated system admits also states that must be described by
non-idempotent density operators (nonzero entropy). The second is that for such
additional states the law of causal evolution is determined by the simultaneous
action of a Schroedinger-von Neumann-type Hamiltonian generator and a nonlinear
dissipative generator which conserves the mean values of the energy and the
number of constituents, and (in forward time) drives any density operator, no
matter how far from TE, in the 'direction' of steepest entropy ascent (maximal
entropy increase). The equation of motion can be solved not only in forward
time, to describe relaxation towards TE, but also backwards in time, to
reconstruct the 'ancestral' or primordial lowest entropy state or limit cycle
from which the system originates.


title: In praise of measurement

abstract:
  The role of measurement in quantum computation is examined in the light of
John Bell's critique of the how the term ``measurement'' is used in quantum
mechanics. I argue that within the field of quantum computer science the
concept of measurement is precisely defined, unproblematic, amd forms the
foundation of the entire subject.


title: Quantum Mechanics from the Hamilton-Jacobi Point of View

abstract:
  In this article, we develop quantum mechanics upon the framework of the
quantum mechanical Hamilton-Jacobi theory. We will show, that the Schroedinger
point of view and the Hamilton-Jacobi point of view are fully equivalent in
their description of physical systems, but differ in their descriptive manner.
As a main result, a wave function in Hamilton-Jacobi theory can be decomposed
into travelling waves in any point in space, not only asymptotically. The well
known WKB-theory will be a special result of the more general theory, we will
develop below. By the example of the linear potential and the harmonic
oscillator, we will discuss quantum mechanics from the Hamilton-Jacobi point of
view. Soft boundary value problems as the connection problem can be solved
exactely. Quantizised energies and Maslov-indices can be calculated directely
without orthonormalizing wave-functions. Also, we will focus on trajectory
themes, which, in contrast to the Schroedinger point of view, follow naturally
from the quantum mechanical action function.


title: Universality and optimality of programmable quantum processors

abstract:
  We analyze and compare the optimality of approximate and probabilistic
universal programmable quantum processors. We define several characteristics
how to quantify the optimality and we study in detail performance of three
types of programmable quantum processors based on (1) the C-NOT gate, (2) the
SWAP operation, and (3) the model of the quantum information distributor - the
QID processor. We show under which conditions the measurement assisted QID
processor is optimal. We also investigate optimality of the so-called
U-processors and we also compare the optimal approximative implementation of
U(1) qubit rotations with the known probabilistic implementation as introduced
by Vidal, Masanes and Cirac [ {\em Phys. Rev. Lett.} {\bf 88}, 047905 (2002)].


title: Entanglement may enhance the channel capacity in arbitrary dimensions

abstract:
  We consider explicitly two examples of d-dimensional quantum channels with
correlated noise and show that, in agreement with previous results on Pauli
qubit channels, there are situations where maximally entangled input states
achieve higher values of the output mutual information than product states. We
obtain a strong dependence of this effect on the nature of the noise
correlations as well as on the parity of the space dimension, and conjecture
that when entanglement gives an advantage in terms of mutual information,
maximally entangled states achieve the channel capacity.


title: Semi-classical Scar functions in phase space

abstract:
  We develop a semi-classical approximation for the scar function in the
  Weyl-Wigner representation in the neighborhood of a classically unstable
periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic
fringes, asymptotic to the stable and unstable manifolds, is verified
computationally for a (linear) cat map, after the theory is adapted to a
discrete phase space appropriate to a quantized torus. Characteristic fringe
patterns can be distinguished even for quasi-energies where the fixed point is
not Bohr-quantized. Also the patterns are highly localized in the neighborhood
of the periodic orbit and along its stable and unstable manifolds without any
long distance patterns that appears for the case of the spectral Wigner
function.


title: Two Party Non-Local Games

abstract:
  In this work we have introduced two party games with respective winning
conditions. One cannot win these games deterministically in the classical world
if they are not allowed to communicate at any stage of the game. Interestingly
we find out that in quantum world, these winning conditions can be achieved if
the players share an entangled state. We also introduced a game which is
impossible to win if the players are not allowed to communicate in classical
world (both probabilistically and deterministically), yet there exists a
perfect quantum strategy by following which, one can attain the winning
condition of the game.


title:
Entanglement in the dispersive interaction of trapped ions with a
  quantized field

abstract:
  The mode-mode entanglement between trapped ions and cavity fields is
investigated in the dispersive regime. We show how a simple initial preparation
of Gaussian coherent states and a postselection may be used to generate
motional non-local mesoscopic states (NLMS) involving ions in different traps.
We also present a study of the entanglement induced by dynamical Stark-shifts
considering a cluster of N-trapped ions. In this case, all entanglement is due
to the dependence of the Stark-shifts on the ions' state of motion manifested
as a cross-Kerr interaction between each ion and the field.


title:
Effects of environmental parameters to total, quantum and classical
  correlations

abstract:
  We quantify the total, quantum, and classical correlations with entropic
measures, and quantitatively compare these correlations in a quantum system, as
exemplified by a Heisenberg dimer which is subjected to the change of
environmental parameters: temperature and nonuniform external field. Our
results show that the quantum correlation may exceed the classical correlation
at some nonzero temperatures, though the former is rather fragile than the
later under thermal fluctuation. The effect of the external field to the
classical correlation is quite different from the quantum correlation.


title:
Consistent Quantum-Classical Interaction and Solution of the Measurement
  Problem in Quantum Mechanics

abstract:
  Supmech, an algebraic scheme of mechanics integrating noncommutative
symplectic geometry and noncommutative probability, subsumes quantum and
classical mechanics and permits consistent treatment of interaction of quantum
and classical systems. Quantum measurements are treated in this framework; the
von Neumann reduction rule (generally postulated) is derived and interpreted in
physical terms.


title: Bound entangled states with nonzero distillable key rate

abstract:
  In this paper, we present sufficient conditions for states to have positive
distillable key rate. Exploiting the conditions, we show that the bound
entangled states given by Horodecki et al. [Phys. Rev. Lett. 94, 160502 (2005),
quant-ph/0506203] have nonzero distillable key rate, and finally exhibit a new
class of bound entangled states with positive distillable key rate, but with
negative Devetak-Winter lower bound of distillable key rate for the ccq states
of their privacy squeezed versions.


title: Scopes and Limits of Modality in Quantum Mechanics

abstract:
  We develop an algebraic frame for the simultaneous treatment of actual and
possible properties of quantum systems. We show that, in spite of the fact that
the language is enriched with the addition of a modal operator to the
orthomodular structure, contextuality remains a central feature of quantum
systems.


title: A Topological Study of Contextuality and Modality in Quantum Mechanics

abstract:
  Kochen-Specker theorem rules out the non-contextual assignment of values to
physical magnitudes. Here we enrich the usual orthomodular structure of quantum
mechanical propositions with modal operators. This enlargement allows to refer
consistently to actual and possible properties of the system. By means of a
topological argument, more precisely in terms of the existence of sections of
sheaves, we give an extended version of Kochen-Specker theorem over this new
structure. This allows us to prove that contextuality remains a central feature
even in the enriched propositional system.


title: Nuclear Spins in a Nanoscale Device for Quantum Information Processing

abstract:
  Coherent oscillations between any two levels from four nuclear spin states of
I=3/2 have been demonstrated in a nanometre-scale NMR semiconductor device,
where nuclear spins are all-electrically controlled. Using this device, we
discuss quantum logic operations on two fictitious qubits of the I=3/2 system,
and propose a quantum state tomography scheme based on the measurement of
longitudinal magnetization, $M_z$.


title: Decoherence vs entanglement in coined quantum walks

abstract:
  Quantum versions of random walks on the line and cycle show a quadratic
improvement in their spreading rate and mixing times respectively. The addition
of decoherence to the quantum walk produces a more uniform distribution on the
line, and even faster mixing on the cycle by removing the need for
time-averaging to obtain a uniform distribution. We calculate numerically the
entanglement between the coin and the position of the quantum walker and show
that the optimal decoherence rates are such that all the entanglement is just
removed by the time the final measurement is made.


title:
Can quantum-mechanical description of physical reality be considered
  incomplete?

abstract:
  In loving memory of Asher Peres, we discuss a most important and influential
paper written in 1935 by his thesis supervisor and mentor Nathan Rosen,
together with Albert Einstein and Boris Podolsky. In that paper, the trio known
as EPR questioned the completeness of quantum mechanics. The authors argued
that the then-new theory should not be considered final because they believed
it incapable of describing physical reality. The epic battle between Einstein
and Bohr intensified following the latter's response later the same year. Three
decades elapsed before John S. Bell gave a devastating proof that the EPR
argument was fatally flawed. The modest purpose of our paper is to give a
critical analysis of the original EPR paper and point out its logical
shortcomings in a way that could have been done 70 years ago, with no need to
wait for Bell's theorem. We also present an overview of Bohr's response in the
interest of showing how it failed to address the gist of the EPR argument.


title: Can EPR correlations be driven by an effective wormhole?

abstract:
  We consider the two-particle wave function of an EPR system given by a two
dimensional relativistic scalar field model. The Bohm-de Broglie interpretation
is applied and the quantum potential is viewed as modifying the Minkowski
geometry. In such a way singularities appear in the metric, opening the
possibility, following Holland, of interpreting the EPR correlations as
originated by a wormhole effective geometry, through which physical signals can
propagate.


title:
Separable quantum states do not have stronger correlations than local
  realism. A comment on quant-ph/0611126 of Z. Chen

abstract:
  Chen (quant-ph/0611126) has recently claimed ``exponential violation of local
realism by separable states", in the sense that multi-partite separable quantum
states are supposed to give rise to correlations and fluctuations that violate
a Bell-type inequality that Chen takes to be satisfied by local realism.
However, this can not be true since all predictions (including all correlations
and fluctuations) that separable quantum states give rise to have a local
realistic description and thus satisfy all Bell-type inequalities, and this
holds for all number of parties. Since Chen claims otherwise by presenting a
new inequality, claimed to be a Bell-type one, which separable states
supposedly can violate, there must be a flaw in the argumentation. I will
expose this flaw, not merely for clarification of this issue, but perhaps even
more importantly since it re-teaches us an old lesson John Bell taught us over
40 years ago. I will argue that this lesson provides us with a new morale
especially relevant to modern research in Bell-type inequalities.


title: The geometry of quantum computation

abstract:
  Determining the quantum circuit complexity of a unitary operation is closely
related to the problem of finding minimal length paths in a particular curved
geometry [Nielsen et al, Science 311, 1133-1135 (2006)]. This paper
investigates many of the basic geometric objects associated to this space,
including the Levi-Civita connection, the geodesic equation, the curvature, and
the Jacobi equation. We show that the optimal Hamiltonian evolution for
synthesis of a desired unitary necessarily obeys a simple universal geodesic
equation. As a consequence, once the initial value of the Hamiltonian is set,
subsequent changes to the Hamiltonian are completely determined by the geodesic
equation. We develop many analytic solutions to the geodesic equation, and a
set of invariants that completely determine the geodesics. We investigate the
problem of finding minimal geodesics through a desired unitary, U, and develop
a procedure which allows us to deform the (known) geodesics of a simple and
well understood metric to the geodesics of the metric of interest in quantum
computation. This deformation procedure is illustrated using some three-qubit
numerical examples. We study the computational complexity of evaluating
distances on Riemmanian manifolds, and show that no efficient classical
algorithm for this problem exists, subject to the assumption that good
pseudorandom generators exist. Finally, we develop a canonical extension
procedure for unitary operations which allows ancilla qubits to be incorporated
into the geometric approach to quantum computing.


title: Negativity as a distance from a separable state

abstract:
  The computable measure of the mixed-state entanglement, the negativity, is
shown to admit a clear geometrical interpretation, when applied to
Schmidt-correlated (SC) states: the negativity of a SC state equals a distance
of the state from a pertinent separable state. As a consequence, a SC state is
separable if and only if its negativity vanishes. Another remarkable
consequence is that the negativity of a SC can be estimated "at a glance" on
the density matrix. These results are generalized to mixtures of SC states,
which emerge in certain quantum-dynamical settings.


title: Quasi-hermitian Quantum Mechanics in Phase Space

abstract:
  We investigate quasi-hermitian quantum mechanics in phase space using
standard deformation quantization methods: Groenewold star products and Wigner
transforms. We focus on imaginary Liouville theory as a representative example
where exact results are easily obtained. We emphasize spatially periodic
solutions, compute various distribution functions and phase-space metrics, and
explore the relationships between them.


title:
Deterministic generation of large cluster states using non-deterministic
  collective measurements based on quantum Zeno effect

abstract:
  We propose a method to generate large cluster states without using
conditional (e.g., CNOT, C-phase) gates. Indeed, an arbitrarily large cluster
state can be generated and expanded almost deterministically by single-qubit
rotations and a special non-deterministic collective detection. If the rotation
of each step is sufficiently small, the quantum Zeno effect will guarantee that
the state is projected into the intended subspace after each measurement, and
an almost-perfect cluster state can be produced. We also propose a possible
implementation of this approach using superconducting flux qubits.


title: Theory of Dicke narrowing in coherent population trapping

abstract:
  The Doppler effect is one of the dominant broadening mechanisms in thermal
vapor spectroscopy. For two-photon transitions one would naively expect the
Doppler effect to cause a residual broadening, proportional to the wave-vector
difference. In coherent population trapping (CPT), which is a narrow-band
phenomenon, such broadening was not observed experimentally. This has been
commonly attributed to frequent velocity-changing collisions, known to narrow
Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show
theoretically that such a narrowing mechanism indeed exists for CPT resonances.
The narrowing factor is the ratio between the atom's mean free path and the
wavelength associated with the wave-vector difference of the two radiation
fields. A possible experiment to verify the theory is suggested.


title: Monogamy and ground-state entanglement in highly connected systems

abstract:
  We consider the ground-state entanglement in highly connected many-body
systems, consisting of harmonic oscillators and spin-1/2 systems. Varying their
degree of connectivity, we investigate the interplay between the enhancement of
entanglement, due to connections, and its frustration, due to monogamy
constraints. Remarkably, we see that in many situations the degree of
entanglement in a highly connected system is essentially of the same order as
in a low connected one. We also identify instances in which the entanglement
decreases as the degree of connectivity increases.


title:
Limitations on the principle of stationary phase when it is applied to
  tunneling analysis

abstract:
  Using a recently developed procedure - multiple wave packet decomposition -
here we study the phase time formulation for tunneling/reflecting particles
colliding with a potential barrier. To partially overcome the analytical
difficulties which frequently arise when the stationary phase method is
employed for deriving phase (tunneling) time expressions, we present a
theoretical exercise involving a symmetrical collision between two identical
wave packets and an one-dimensional rectangular potential barrier. Summing the
amplitudes of the reflected and transmitted waves - using a method we call
multiple peak decomposition - is shown to allow reconstruction of the scattered
wave packets in a way which allows the stationary phase principle to be
recovered.


title: Negative Differential Resistance of Electrons in Graphene Barrier

abstract:
  The graphene is a native two-dimensional crystal material consisting of a
single sheet of carbon atoms. In this unique one-atom-thick material, the
electron transport is ballistic and is described by a quantum relativistic-like
Dirac equation rather than by the Schrodinger equation. As a result, a graphene
barrier behaves very differently compared to a common semiconductor barrier. We
show that a single graphene barrier acts as a switch with a very high on-off
ratio and displays a significant differential negative resistance, which
promotes graphene as a key material in nanoelectronics.


title: Metamaterials for Ballistic Electrons

abstract:
  The paper presents a metamaterial for ballistic electrons, which consists of
a quantum barrier formed in a semiconductor with negative effective electron
mass. This barrier is the analogue of a metamaterial for electromagnetic waves
in media with negative electrical permittivity and magnetic permeability.
Besides applications similar to those of optical metamaterials, a nanosized
slab of a metamaterial for ballistic electrons, sandwiched between quantum
wells of positive effective mass materials, reveals unexpected conduction
properties, e.g. single or multiple room temperature negative differential
conductance regions at very low voltages and with considerable peak-to-valley
ratios, while the traversal time of ballistic electrons can be tuned to larger
or smaller values than in the absence of the metamaterial slab. Thus, slow and
fast electrons, analogous to slow and fast light, occur in metamaterials for
ballistic electrons.


title: Witnessing Macroscopic Entanglement in a Staggered Magnetic Field

abstract:
  We investigate macroscopic entanglement in an infinite XX spin-1/2 chain with
staggered magnetic field, B_l=B+e^{-i\pi l}b. Using single-site entropy and by
constructing an entanglement witness, we search for the existence of
entanglement when the system is at absolute zero, as well as in thermal
equilibrium. Although the role of the alternating magnetic field b is, in
general, to suppress entanglement as do B and T, we find that when T=0,
introducing b allows the existence of entanglement even when the uniform
magnetic field B is arbitrarily large. We find that the region and the amount
of entanglement in the spin chain can be enhanced by a staggered magnetic
field.


title: Dynamical Reduction Models: present status and future developments

abstract:
  We review the major achievements of the dynamical reduction program, showing
why and how it provides a unified, consistent description of physical
phenomena, from the microscopic quantum domain to the macroscopic classical
one. We discuss the difficulties in generalizing the existing models in order
to comprise also relativistic quantum field theories. We point out possible
future lines of research, ranging from mathematical physics to phenomenology.


title: Classical States and Their Quantum Correspondence

abstract:
  We point out a correspondence between classical and quantum states, by
showing that for every classical distribution over phase--space, one can
construct a corresponding quantum state, such that in the classical limit of
$\hbar\to 0$ the latter converges to the former with respect to all measurable
quantities.


title:
Reply to Comments of Bassi, Ghirardi, and Tumulka on the Free Will
  Theorem

abstract:
  We show that the authors in the title have erred in claiming that our axiom
FIN is false by conflating it with Bell locality. We also argue that the
predictions of quantum mechanics, and in particular EPR, are fully Lorentz
invariant, whereas the Free Will Theorem shows that theories with a mechanism
of reduction, such as GRW, cannot be made fully invariant.


title: High-speed linear optics quantum computing using active feed-forward

abstract:
  As information carriers in quantum computing, photonic qubits have the
advantage of undergoing negligible decoherence. However, the absence of any
significant photon-photon interaction is problematic for the realization of
non-trivial two-qubit gates. One solution is to introduce an effective
nonlinearity by measurements resulting in probabilistic gate operations. In
one-way quantum computation, the random quantum measurement error can be
overcome by applying a feed-forward technique, such that the future measurement
basis depends on earlier measurement results. This technique is crucial for
achieving deterministic quantum computation once a cluster state (the highly
entangled multiparticle state on which one-way quantum computation is based) is
prepared. Here we realize a concatenated scheme of measurement and active
feed-forward in a one-way quantum computing experiment. We demonstrate that,
for a perfect cluster state and no photon loss, our quantum computation scheme
would operate with good fidelity and that our feed-forward components function
with very high speed and low error for detected photons. With present
technology, the individual computational step (in our case the individual
feed-forward cycle) can be operated in less than 150 ns using electro-optical
modulators. This is an important result for the future development of one-way
quantum computers, whose large-scale implementation will depend on advances in
the production and detection of the required highly entangled cluster states.


title:
Control momentum entanglement with atomic spontaneously generated
  coherence

abstract:
  With atomic spontaneously generated coherence (SGC), we propose a novel
scheme to coherently control the atom--photon momentum entanglement through
atomic internal coherence. A novel phenomena of ``phase entanglement in
momentum'' is proposed, and we found, under certain conditions, that
super--high degree of momentum entanglement can be produced with this scheme.


title:
Quantum gravity computers: On the theory of computation with indefinite
  causal structure

abstract:
  A quantum gravity computer is one for which the particular effects of quantum
gravity are relevant. In general relativity, causal structure is non-fixed. In
quantum theory non-fixed quantities are subject to quantum uncertainty. It is
therefore likely that, in a theory of quantum gravity, we will have indefinite
causal structure. This means that there will be no matter of fact as to whether
a particular interval is timelike or not. We study the implications of this for
the theory of computation. Classical and quantum computations consist in
ivolving the state of the computer through a sequence of time steps. This will,
most likely, not be possible for a quantum gravity computer because the notion
of a time step makes no sense if we have indefinite causal structure. We show
that it is possible to set up a model for computation even in the absence of
definite causal structure by using a certain framework (the causaloid
formalism) that was developed for the purpose of correlating data taken in this
type of situation. Corresponding to a physical theory is a causaloid, Lambda
(this is a mathematical object containing information about the causal
connections between different spacetime regions). A computer is given by the
pair {Lambda, S} where S is a set of gates. Working within the causaloid
formalism, we explore the question of whether universal quantum gravity
computers are possible. We also examine whether a quantum gravity computer
might be more powerful than a quantum (or classical) computer. In particular,
we ask whether indefinite causal structure can be used as a computational
resource.


title: Quantum Quasi-Cyclic LDPC Codes

abstract:
  In this paper, a construction of a pair of "regular" quasi-cyclic LDPC codes
as ingredient codes for a quantum error-correcting code is proposed. That is,
we find quantum regular LDPC codes with various weight distributions.
Furthermore our proposed codes have lots of variations for length, code rate.
These codes are obtained by a descrete mathematical characterization for model
matrices of quasi-cyclic LDPC codes.
  Our proposed codes achieve a bounded distance decoding (BDD) bound, or known
as VG bound, and achieve a lower bound of the code length.

categories: quant-ph cs.IT math-ph math.CO math.IT math.MP


title:
Nonclassicality of quantum excitation of classical coherent field in
  photon loss channel

abstract:
  We investigate the nonclassicality of photon-added coherent states in the
photon loss channel by exploring the entanglement potential and negative Wigner
distribution. The total negative probability defined by the absolute value of
the integral of the Wigner function over the negative distribution region
reduces with the increase of decay time. The total negative probability and the
entanglement potential of pure photon-added coherent states exhibit the similar
dependence on the beam intensity. The reduce of the total negative probability
is consistent with the behavior of entanglement potential for the dissipative
single-photon-added coherent state at short decay times.


title: Some new results concerning the QFT vacuum in the Heisenberg picture

abstract:
  In has been recently shown [1] that in Dirac's hole theory the vacuum state
is not the minimum energy state but that there exist quantum states with less
energy than that of the vacuum state. In this paper we extend this discussion
to quantum field theory (QFT) and consider the question of whether or not the
vacuum in QFT is the state of minimum energy. It will be shown that for a
"simple" field theory, consisting of a quantized fermion field interacting with
a classical electric field in 1-1D space-time, there exist quauntum states with
less energy than that of the vacuum state.


title:
Quantum jumps of saturation level rigidity and anomalous oscillations of
  level number variance in the semiclassical spectrum of a modified Kepler
  problem

abstract:
  We discover quantum Hall like jumps in the saturation spectral rigidity in
the semiclassical spectrum of a modified Kepler problem as a function of the
interval center. These jumps correspond to integer decreases of the radial
winding numbers in classical periodic motion. We also discover and explain
single harmonic dominated oscillations of the level number variance with the
width of the energy interval. The level number variance becomes effectively
zero for the interval widths defined by the frequency of the shortest periodic
orbit. This signifies that there are virtually no variations from sample to
sample in the number of levels on such intervals.


title: Quantum Imaging with Incoherent Photons

abstract:
  We propose a technique to obtain sub-wavelength resolution in quantum imaging
with potentially 100% contrast using incoherent light. Our method requires
neither path-entangled number states nor multi-photon absorption. The scheme
makes use of N photons spontaneously emitted by N atoms and registered by N
detectors. It is shown that for coincident detection at particular detector
positions a resolution of \lambda / N can be achieved.


title:
Probabilistic reversing operation with fidelity and purity gain for
  macroscopic quantum superposition

abstract:
  It is shown that a large class of weak disturbances on macroscopic quantum
superpositions can be canceled by a probabilistic reversing operation on the
system. We illustrate this for spin systems undergoing an Ising-type
interaction with the environment and demonstrate that both the fidelity to the
original state and the purity of the amended state can simultaneously be
increased by the reversing operation. A possible experimental scheme to
implement our scheme is discussed.


title: Truncated states obtained by iteration

abstract:
  Quantum states of the electromagnetic field are of considerable importance,
finding potential application in various areas of physics, as diverse as solid
state physics, quantum communication and cosmology. In this paper we introduce
the concept of truncated states obtained via iterative processes (TSI) and
study its statistical features, making an analogy with dynamical systems theory
(DST). As a specific example, we have studied TSI for the doubling and the
logistic functions, which are standard functions in studying chaos. TSI for
both the doubling and logistic functions exhibit certain similar patterns when
their statistical features are compared from the point of view of DST. A
general method to engineer TSI in the running-wave domain is employed, which
includes the errors due to the nonidealities of detectors and photocounts.


title: Violation of the principle of Complementarity, and its implications

abstract:
  Bohr's principle of complementarity predicts that in a welcher weg
("which-way") experiment, obtaining fully visible interference pattern should
lead to the destruction of the path knowledge. Here I report a failure for this
prediction in an optical interferometry experiment. Coherent laser light is
passed through a dual pinhole and allowed to go through a converging lens,
which forms well-resolved images of the respective pinholes, providing complete
path knowledge. A series of thin wires are then placed at previously measured
positions corresponding to the dark fringes of the interference pattern
upstream of the lens. No reduction in the resolution and total radiant flux of
either image is found in direct disagreement with the predictions of the
principle of complementarity. In this paper, a critique of the current
measurement theory is offered, and a novel nonperturbative technique for
ensemble properties is introduced. Also, another version of this experiment
without an imaging lens is suggested, and some of the implications of the
violation of complementarity for another suggested experiment to investigate
the nature of the photon and its "empty wave" is briefly discussed.


title: First order quantum phase transitions in the XX spin chain

abstract:
  Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain
with nearest neighbor interaction in a uniform transverse field is studied
based on the simple exact solutions. It is found that there are [N/2]
level-crossing points in the ground state, where N is the periodic number of
the system and [x] stands for the integer part of x, when the interaction
strength and magnitude of the magnetic field satisfy certain conditions. The
quantum phase transitions are of the first order due to the level-crossing. The
ground state in the thermodynamic limit will be divided into three
distinguishable quantum phases.


title:
Characterizing the complete hierarchy of correlations in an $n$-party
  system

abstract:
  A characterization of the complete correlation structure in an $n$-party
system is proposed in terms of a series of $(k,n)$ threshold classical secret
sharing protocols ($2\le k\le n$). The total correlation is shown to be the sum
of independent correlations of 2-, 3-,$...$, $n$-parties. Our result unifies
several earlier scattered works, and shines new light at the important topic of
multi-party quantum entanglement. As an application, we explicitly construct
the hierarchy of correlations in an $n$-qubit graph state.


title:
The states of W-class as shared resources for perfect teleportation and
  superdense coding

abstract:
  As we know, the states of triqubit systems have two important classes:
GHZ-class and W-class.
  In this paper, the states of W-class are considered for teleportation and
superdense coding, and are generalized to multi-particle systems. First we
describe two transformations of the shared resources for teleportation and
superdense coding, which allow many new protocols from some known ones for
that. As an application of these transformations, we obtain a sufficient and
necessary condition for a state of W-class being suitable for perfect
teleportation and superdense coding. As another application, we find that state
  $|W>_{123}={1/2}(|100>_{123}+|010>_{123}+\sqrt{2}|001>_{123})$ can be used to
transmit three classical bits by sending two qubits, which was considered to be
impossible by P. Agrawal and A. Pati [Phys. Rev. A to be published]. We
generalize the states of W-class to multi-qubit systems and multi-particle
systems with higher dimension. We propose two protocols for teleportation and
superdense coding by using W-states of multi-qubit systems that generalize the
protocols by using $|W>_{123}$ proposed by P. Agrawal and A. Pati. We obtain an
optimal way to partition some W-states of multi-qubit systems into two
subsystems, such that the entanglement between them achieves maximum value.


title: Variation on a theme by GHZM

abstract:
  In the Greenberger-Horne-Zeilinger-Mermin (GHZM) proof of Bell's theorem, a
source periodically emits an entangled state of three particles whose
properties are analyzed by three distant observers and used to prove Bell's
nonlocality theorem. This paper analyzes a somewhat different gedanken
experiment involving only two observers that nevertheless makes indirect use of
the GHZ states to prove Bell's theorem. The relationship of the GHZM proof to
the present one is discussed, and it is pointed out that the latter provides an
interesting new view of the connection between the "two theorems of John Bell".


title:
SLOCC invariant and semi-invariants for SLOCC classification of
  four-qubits

abstract:
  We show there are at least 28 distinct true SLOCC entanglement classes for
four-qubits by means of SLOCC invariant and semi-invariants and derive the
number of the degenerated SLOCC classes for n-qubits.


title: Graph identification by quantum walks

abstract:
  This paper has been withdrawn by the authors; replaced by arXiv:0705.2531v2
[quant-ph].


title: Localization of coherent exciton transport in phase space

abstract:
  We study numerically the dynamics of excitons on discrete rings in the
presence of static disorder. Based on continuous-time quantum walks we compute
the time evolution of the Wigner function (WF) both for pure diagonal (site)
disorder, as well as for diagonal and off-diagonal (site and transfer)
disorder. In both cases, large disorder leads to localization and destroys the
characteristic phase space patterns of the WF found in the absence of disorder.


title: Comments on quant-ph/0609176

abstract:
  In this note, we show the mistake which has been made in quant-ph/0609176.
Further more, we provide a sketch of proof to show the impossibility of the
effort of such kind toward improving the efficiency of Grover's Algorithm.


title: Feedback Control of Non-linear Quantum Systems: a Rule of Thumb

abstract:
  We show that in the regime in which feedback control is most effective --
when measurements are relatively efficient, and feedback is relatively strong
-- then, in the absence of any sharp inhomogeneity in the noise, it is always
best to measure in a basis that does not commute with the system density matrix
than one that does. That is, it is optimal to make measurements that disturb
the state one is attempting to stabilize.


title:
Quantum Convolutional Codes Derived From Reed-Solomon and Reed-Muller
  Codes

abstract:
  Convolutional stabilizer codes promise to make quantum communication more
reliable with attractive online encoding and decoding algorithms. This paper
introduces a new approach to convolutional stabilizer codes based on direct
limit constructions. Two families of quantum convolutional codes are derived
from generalized Reed-Solomon codes and from Reed- Muller codes. A Singleton
bound for pure convolutional stabilizer codes is given.


title: Theory of chaotic atomic transport in an optical lattice

abstract:
  A semiclassical theory of chaotic atomic transport in a one-dimensional
nondissipative optical lattice is developed. Using the basic equations of
motion for the Bloch and translational atomic variables, we derive a stochastic
map for the synchronized component of the atomic dipole moment that determines
the center-of-mass motion. We find the analytical relations between the atomic
and lattice parameters under which atoms typically alternate between flying
through the lattice and being trapped in the wells of the optical potential. We
use the stochastic map to derive formulas for the probability density functions
(PDFs) for the flight and trapping events. Statistical properties of chaotic
atomic transport strongly depend on the relations between the atomic and
lattice parameters. We show that there is a good quantitative agreement between
the analytical PDFs and those computed with the stochastic map and the basic
equations of motion for different ranges of the parameters. Typical flight and
trapping PDFs are shown to be broad distributions with power law ``heads'' with
the slope -1.5 and exponential ``tails''. The lengths of the power law and
exponential parts of the PDFs depend on the values of the parameters and can be
varied continuously. We find analytical conditions, under which deterministic
atomic transport has fractal properties, and explain a hierarchical structure
of the dynamical fractals.


title: Violation of Bohr's Complementarity: One Slit or Both?

abstract:
  We have implemented a novel double-slit "which-way" experiment which raises
interesting questions of interpretation. Coherent laser light is passed through
a converging lens and then through a dual pinhole producing two beams crossing
over at the focal point of the lens, and fully separating further downstream
providing which-way information. A thin wire is then placed at a minimum of the
interference pattern formed at the cross-over region. No significant reduction
in the total flux or resolution of the separated beams is found, providing
evidence for coexistence of perfect interference and which-way information in
the same experiment, contrary to the common readings of Bohr's principle of
complementarity. This result further supports the conclusions of the original
experiment by the author in which an imaging lens was employed to obtain
which-way information. Finally, a short discussion of the novel
non-perturbative measurement technique for ensemble properties is offered.