title: The Localized Quantum Vacuum Field

abstract:
  A model for the localized quantum vacuum is proposed in which the zero-point
energy of the quantum electromagnetic field originates in energy- and
momentum-conserving transitions of material systems from their ground state to
an unstable state with negative energy. These transitions are accompanied by
emissions and re-absorptions of real photons, which generate a localized
quantum vacuum in the neighborhood of material systems. The model could help
resolve the cosmological paradox associated to the zero-point energy of
electromagnetic fields, while reclaiming quantum effects associated with
quantum vacuum such as the Casimir effect and the Lamb shift; it also offers a
new insight into the Zitterbewegung of material particles.


title: Frequency Conversion of Entangled State

abstract:
  The quantum characteristics of sum-frequency process in an optical cavity
with an input signal optical beam, which is a half of entangled optical beams,
are analyzed. The calculated results show that the quantum properties of the
signal beam can be maintained after its frequency is conversed during the
intracavity nonlinear optical interaction. The frequency-conversed output
signal beam is still in an entangled state with the retained other half of
initial entangled beams. The resultant quantum correlation spectra and the
parametric dependences of the correlations on the initial squeezing factor, the
optical losses and the pump power of the sum-frequency cavity are calculated.
The proposed system for the frequency conversion of entangled state can be used
in quantum communication network and the calculated results can provide direct
references for the design of experimental systems.


title: Representation Systems and Quantum Structures

abstract:
  Two important classes of quantum structures, namely orthomodular posets and
orthomodular lattices, can be characterized in a classical context, using
notions like partial information and points of view. Using the formalism of
representation systems, we show that these quantum structures can be obtained
by expressing conditions on the existence of particular points of view, of
particular ways to observe a system.


title: On positive decomposable maps

abstract: The new paper will be submitted.


title: Deciding universality of quantum gates

abstract:
  We say that collection of $n$-qudit gates is universal if there exists
$N_0\geq n$ such that for every $N\geq N_0$ every $N$-qudit unitary operation
can be approximated with arbitrary precision by a circuit built from gates of
the collection. Our main result is an upper bound on the smallest $N_0$ with
the above property. The bound is roughly $d^8 n$, where $d$ is the number of
levels of the base system (the '$d$' in the term qu$d$it.) The proof is based
on a recent result on invariants of (finite) linear groups.


title:
Beamsplitting attack to the revised KKKP protocol and a possible
  solution

abstract:
  We show that the revised KKKP protocol proposed by Kye and Kim [Phys. Rev.
Lett. 95,040501(2005)] is still insecure with coherent states by a type of
beamsplitting attack. We then further revise the KKKP protocol so that it is
secure under such type of beamsplitting attack. The revised scheme can be used
for not-so-weak coherent state quantum key distribution.


title:
How to Derive the Hilbert-Space Formulation of Quantum Mechanics From
  Purely Operational Axioms

abstract:
  In the present paper I show how it is possible to derive the Hilbert space
formulation of Quantum Mechanics from a comprehensive definition of "physical
experiment" and assuming "experimental accessibility and simplicity" as
specified by five simple Postulates. This accomplishes the program presented in
form of conjectures in the previous paper quant-ph/0506034. Pivotal roles are
played by the "local observability principle", which reconciles the holism of
nonlocality with the reductionism of local observation, and by the postulated
existence of "informationally complete observables" and of a "symmetric
faithful state". This last notion allows one to introduce an operational
definition for the real version of the "adjoint"--i. e. the transposition--from
which one can derive a real Hilbert-space structure via either the
Mackey-Kakutani or the Gelfand-Naimark-Segal constructions. Here I analyze in
detail only the Gelfand-Naimark-Segal construction, which leads to a real
Hilbert space structure analogous to that of (classes of generally unbounded)
selfadjoint operators in Quantum Mechanics. For finite dimensions, general
dimensionality theorems that can be derived from a local observability
principle, allow us to represent the elements of the real Hilbert space as
operators over an underlying complex Hilbert space (see, however, a still open
problem at the end of the paper). The route for the present operational
axiomatization was suggested by novel ideas originated from Quantum Tomography.


title: Gibbs States and the Consistency of Local Density Matrices

abstract:
  Suppose we have an n-qubit system, and we are given a collection of local
density matrices rho_1,...,rho_m, where each rho_i describes some subset of the
qubits. We say that rho_1,...,rho_m are "consistent" if there exists a global
state sigma (on all n qubits) whose reduced density matrices match
rho_1,...,rho_m.
  We prove the following result: if rho_1,...,rho_m are consistent with some
state sigma > 0, then they are also consistent with a state sigma' of the form
sigma' = (1/Z) exp(M_1+...+M_m), where each M_i is a Hermitian matrix acting on
the same qubits as rho_i, and Z is a normalizing factor. (This is known as a
Gibbs state.) Actually, we show a more general result, on the consistency of a
set of expectation values <T_1>,...,<T_r>, where the observables T_1,...,T_r
need not commute. This result was previously proved by Jaynes (1957) in the
context of the maximum-entropy principle; here we provide a somewhat different
proof, using properties of the partition function.


title:
Eavesdropping Attack with Hong-Ou-Mandel Interferometer and Random Basis
  Shuffling in Quantum Key Distribution

abstract:
  We introduce new sophisticated attacks with a Hong-Ou-Mandel interferometer
against quantum key distribution (QKD) and propose a new QKD protocol grafted
with random basis shuffling to block up those attacks. When the polarization
basis is randomly and independently shuffled by sender and receiver, the new
protocol can overcome the attacks even for not-so-weak coherent pulses. We
estimate the number of photons to guarantee the security of the protocol.


title:
Probing Quantum Phase Transition in Macroscopic Qubit Array via circuit
  QED architecture

abstract:
  We demonstrate a universal physical mechanism to probe the macroscopic
quantum phase transition based on circuit QED architecture. We found that, with
certain parameters, the Josephson junction qubit array behaves as an
antiferromagnetic Ising model in transverse field and the coupled transmission
line resonator serves as a bosonic quantum probe. Our investigation shows that,
at the critical point, the drastic broadening of the spectrum of the probe
indicates the quantum phase transition.


title:
General construction of noiseless networks detecting entanglement with
  help of linear maps

abstract:
  We present the general scheme for construction of noiseless networks
detecting entanglement with the help of linear, hermiticity-preserving maps. We
show how to apply the method to detect entanglement of unknown state without
its prior reconstruction. In particular, we prove there always exists noiseless
network detecting entanglement with the help of positive, but not completely
positive maps. Then the generalization of the method to the case of
entanglement detection with arbitrary, not necessarily hermiticity-preserving,
linear contractions on product states is presented.


title:
Quantum correlations of two optical fields close to electromagnetically
  induced transparency

abstract:
  We show that three-level atoms excited by two cavity modes in a $\Lambda$
configuration close to electromagnetically induced transparency can produce
strongly squeezed bright beams or correlated beams which can be used for
quantum non demolition measurements. The input intensity is the experimental
"knob" for tuning the system into a squeezer or a quantum non demolition
device. The quantum correlations become ideal at a critical point characterized
by the appearance of a switching behavior in the mean fields intensities. Our
predictions, based on a realistic fully quantum 3-level model including cavity
losses and spontaneous emission, allow direct comparison with future
experiments.


title: Feats, Features and Failures of the PR-box

abstract:
  One of the most intriguing features of quantum physics is the non-locality of
correlations that can be obtained by measuring entangled particles. Recently,
it has been noticed that non-locality can be studied without reference to the
Hilbert space formalism. I review here the properties of the basic mathematical
tool used for such studies, the so called Popescu-Rohrlich-box, in short
PR-box. Among its feats, are the simulation of the correlations of the singlet
and of other non-local probability distributions. Among its features, the
"anomaly of non-locality" and a great power for information-theoretical tasks.
Among its failures, the impossibility of reproducing all multi-partite
distributions and the triviality of the allowed dynamics.


title:
Causal Loops and Collapse in the Transactional Interpretation of Quantum
  Mechanics

abstract:
  Cramer's transactional interpretation of quantum mechanics is reviewed, and a
number of issues related to advanced interactions and state vector collapse are
analyzed. Where some have suggested that Cramer's predictions may not be
correct or definite, I argue that they are, but I point out that the
classical-quantum distinction problem in the Copenhagen interpretation has its
parallel in the transactional interpretation.


title: `Lazy' quantum ensembles

abstract:
  We compare different strategies aimed to prepare an ensemble with a given
density matrix $\rho$. Preparing the ensemble of eigenstates of $\rho$ with
appropriate probabilities can be treated as `generous' strategy: it provides
maximal accessible information about the state. Another extremity is the
so-called `Scrooge' ensemble, which is mostly stingy to share the information.
We introduce `lazy' ensembles which require minimal efforts to prepare the
density matrix by selecting pure states with respect to completely random
choice.
  We consider two parties, Alice and Bob, playing a kind of game. Bob wishes to
guess which pure state is prepared by Alice. His null hypothesis, based on the
lack of any information about Alice's intention, is that Alice prepares any
pure state with equal probability. Then, the average quantum state measured by
Bob turns out to be $\rho$, and he has to make a new hypothesis about Alice's
intention solely based on the information that the observed density matrix is
$\rho$. The arising `lazy' ensemble is shown to be the alternative hypothesis
which minimizes the Type I error.


title: Wave packet dynamics of entangled two-mode states

abstract:
  We consider a model Hamiltonian describing the interaction of a single-mode
radiation field with the atoms of a nonlinear medium, and study the dynamics of
entanglement for specific non-entangled initial states of interest: namely,
those in which the field mode is initially in a Fock state, a coherent state,
or a photon-added coherent state. The counterparts of near-revivals and
fractional revivals are shown to be clearly identifiable in the entropy of
entanglement. The ``overlap fidelity'' of the system is another such indicator,
and its behaviour corroborates that of the entropy of entanglement in the
vicinity of near-revivals. The expectation values and higher moments of
suitable quadrature variables are also examined, with reference to possible
squeezing and higher-order squeezing.


title: Decoherence control: A feedback mechanism based on hamiltonian tracking

abstract:
  Enviroment - caused dissipation disrupts the hamiltonian evolution of all
quantum systems not fully isolated from any bath. We propose and examine a
feedback-control scheme to eliminate such dissipation, by tracking the free
hamiltonian evolution. We determine a driving-field that maximizes the
projection of the actual molecular system onto the freely propagated one. The
evolution of a model two level system in a dephasing bath is followed, and the
driving field that overcomes the decoherence is calculated. An implementation
of the scheme in the laboratory using feedback control is suggested.


title: Spatial mode properties of plasmon assisted transmission

abstract:
  Orbital angular momentum of photons is explored to study the spatial mode
properties of plasmon assisted transmission process. We found that photons
carrying different orbital angular momentums have different transmission
efficiencies, while the coherence between these spatial modes can be preserved.


title:
Differential Realization of Pseudo-Hermiticity: A quantum mechanical
  analog of Einstein's field equation

abstract:
  For a given pseudo-Hermitian Hamiltonian of the standard form: H=p^2/2m+v(x),
we reduce the problem of finding the most general (pseudo-)metric operator \eta
satisfying H^\dagger=\eta H \eta^{-1} to the solution of a differential
equation. If the configuration space is the real line, this is a Klein-Gordon
equation with a nonconstant mass term. We obtain a general series solution of
this equation that involves a pair of arbitrary functions. These characterize
the arbitrariness in the choice of \eta. We apply our general results to
calculate \eta for the PT-symmetric square well, an imaginary scattering
potential, and a class of imaginary delta-function potentials. For the first
two systems, our method reproduces the known results in a straightforward and
extremely efficient manner. For all these systems we obtain the most general
\eta up to second order terms in the coupling constants.


title: Privacy of a lossy bosonic memory channel

abstract:
  We study the security of the information transmission between two honest
parties realized through a lossy bosonic memory channel when losses are
captured by a dishonest party. We then show that entangled inputs can enhance
the private information of such a channel, which however does never overcome
that of unentangled inputs in absence of memory.


title:
Intensity correlation and anticorrelations in coherently prepared atomic
  vapor

abstract:
  Motivated by the recent experiment [V.A. Sautenkov, Yu.V. Rostovtsev, and
M.O. Scully, Phys. Rev. A 72, 065801 (2005)], we develop a theoretical model in
which the field intensity fluctuations resulted from resonant interaction of a
dense atomic medium with laser field having finite bandwidth. The
intensity-intensity cross correlation between two circular polarized beams can
be controlled by the applied external magnetic field. A smooth transition from
perfect correlations to anti-correlations (at zero delay time) of the outgoing
beams as a function of the magnetic field strength is observed. It provides us
with the desired information about decoherence rate in, for example, $^{87}$Rb
atomic vapor.


title: Dark Energy: Casimir Effect, Generalized Homogeneity and Axions

abstract:
  This paper has been withdrawn because a much better version, G. Gazzola, M.
C. Nemes and W. F. Wreszinski - On the Casimir Energy for a massive quantum
scalar field and the cosmological constant- Annals of Physics (N.Y.) vol. 324,
2095-2107 (2009) has appeared, which corrects several conceptual errors in the
present one.


title:
On the Common Structure of Bohmian Mechanics and the
  Ghirardi-Rimini-Weber Theory

abstract:
  Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite
resolutions of the quantum measurement problem: the former postulates
additional variables (the particle positions) besides the wave function,
whereas the latter implements spontaneous collapses of the wave function by a
nonlinear and stochastic modification of Schr\"odinger's equation. Still, both
theories, when understood appropriately, share the following structure: They
are ultimately not about wave functions but about ``matter'' moving in space,
represented by either particle trajectories, fields on space-time, or a
discrete set of space-time points. The role of the wave function then is to
govern the motion of the matter.


title:
Simultaneous Magneto-Optical Trapping of Bosonic and Fermionic Chromium
  Atoms

abstract:
  We report on magneto-optical trapping of fermionic 53Cr atoms. A
Zeeman-slowed atomic beam provides loading rates up to 3 10^6 /s. We present
systematic characterization of the magneto-optical trap (MOT). We obtain up to
5 10^5 atoms in the steady state MOT. The atoms radiatively decay from the
excited P state into metastable D states, and, due to the large dipolar
magnetic moment of chromium atoms in these states, they can remain magnetically
trapped in the quadrupole field gradient of the MOT. We study the accumulation
of metastable 53Cr atoms into this magnetic trap. We also report on the first
simultaneous magneto-optical trapping of bosonic 52Cr and fermionic 53Cr atoms.
Finally, we characterize the light assisted collision losses in this Bose-Fermi
cold mixture.


title: On the damping of the angular momentum of three harmonic oscillators

abstract:
  In the frame of the Lindblad theory of open quantum systems, the system of
three uncoupled harmonic oscillators with opening operators linear in the
coordinates and momenta of the considered system is analyzed. The damping of
the angular momentum and of its projection is obtained.


title:
Defense of "Impossibility of distant indirect measurement of the quantum
  Zeno effect"

abstract:
  Recently, Wallentowitz and Toschek [Phys. Rev. A 69, 046101 (2005)]
criticized the assertion made by Hotta and Morikawa [Phys. Rev. A 69, 052114
(2004)] that distant indirect measurements do not cause the quantum Zeno
effect, and claimed that their proof is faulty and that their claim is
unfounded. Here, it is shown that the argument given by Wallentowitz and
Toschek includes a mathematical flaw and that their criticism is unfounded.


title: Channel capacities of classical and quantum list decoding

abstract:
  We focus on classical and quantum list decoding. The capacity of list
decoding was obtained by Nishimura in the case when the number of list does not
increase exponentially. However, the capacity of the exponential-list case is
open even in the classical case while its converse part was obtained by
Nishimura. We derive the channel capacities in the classical and quantum case
with an exponentially increasing list. The converse part of the quantum case is
obtained by modifying Nagaoka's simple proof for strong converse theorem for
channel capacity. The direct part is derived by a quite simple argument.


title:
Modeling Pauli measurements on graph states with nearest-neighbor
  classical communication

abstract:
  We propose a communication-assisted local-hidden-variable model that yields
the correct outcome for the measurement of any product of Pauli operators on an
arbitrary graph state, i.e., that yields the correct global correlation among
the individual measurements in the Pauli product. Within this model,
communication is restricted to a single round of message passing between
adjacent nodes of the graph. We show that any model sharing some general
properties with our own is incapable, for at least some graph states, of
reproducing the expected correlations among all subsets of the individual
measurements. The ability to reproduce all such correlations is found to depend
on both the communication distance and the symmetries of the communication
protocol.


title: Fractional revivals of quantum state in tight-binding chain

abstract:
  We investigate the time evolution of Gaussian wave packet (GWP) in the
tight-binding chain with uniform nearest neighbor (NN) hopping integral.
Analytical analysis and numerical simulations show that the fractional revival
of the quantum state occurs in such system, i.e., at appropriate time, a GWP
can evolve into many copies of the initial state at different positions. The
application of this quantum phenomenon to the scheme of quantum information
transfer in solid-state system is discussed.


title: New upper and lower bounds for randomized and quantum Local Search

abstract:
  Local Search problem, which finds a local minimum of a black-box function on
a given graph, is of both practical and theoretical importance to combinatorial
optimization, complexity theory and many other areas in theoretical computer
science. In this paper, we study the problem in the randomized and quantum
query models and give new lower and upper bound techniques in both models.
  The lower bound technique works for any graph that contains a product graph
as a subgraph. Applying it to the Boolean hypercube {0,1}^n and the constant
dimensional grids [n]^d, two particular product graphs that recently drew much
attention, we get the following tight results:
  RLS({0,1}^n) = \Theta(2^{n/2}n^{1/2}), QLS({0,1}^n) = \Theta(2^{n/3}n^{1/6}),
  RLS([n]^d) = \Theta(n^{d/2}) for d \geq 4, QLS([n]^d) = \Theta(n^{d/3}) for d
\geq 6.
  Here RLS(G) and QLS(G) are the randomized and quantum query complexities of
Local Search on G, respectively. These improve the previous results by Aaronson
[STOC'04], Ambainis (unpublished) and Santha and Szegedy [STOC'04].
  Our new algorithms work well when the underlying graph expands slowly. As an
application to [n]^2, a new quantum algorithm using O(\sqrt{n}(\log\log
n)^{1.5}) queries is given. This improves the previous best known upper bound
of O(n^{2/3}) (Aaronson, [STOC'04]), and implies that Local Search on grids
exhibits different properties in low dimensions.


title: Existence Criterion of Genuine Tripartite Entanglement

abstract:
  In this paper, an intuitive mathematical formulation is provided to
generalize the residual entanglement for tripartite systems of qubits (Phys.
Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher
dimension. The spirit lies in the tensor treatment of tripartite pure states
(Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the
present generalization is that the formulation for higher dimensional systems
is invariant under permutation of the subsystems, hence is employed as a
criterion to test the existence of genuine tripartite entanglement.
Furthermore, the formulation for pure states can be conveniently extended to
the case of mixed states by utilizing the kronecker product approximate
technique. As applications, we give the analytic approximation of the criterion
for weakly mixed tripartite quantum states and consider the existence of
genuine tripartite entanglement of some weakly mixed states.


title: Remote Preparation of a Qudit Using Maximally Entangled States of Qubits

abstract:
  Known quantum pure states of a qudit can be remotely prepared onto a group of
particles of qubits exactly or probabilistically with the aid of two-level
Einstein-Podolsky-Rosen states. We present a protocol for such kind of remote
state preparation. We are mainly focused on the remote preparation of the
ensembles of equatorial states and those of states in real Hilbert space. In
particular, a kind of states of qudits in real Hilbert space have been shown to
be remotely prepared in faith without the limitation of the input space
dimension.


title: Bright entanglement in the intracavity nonlinear coupler

abstract:
  We show that the intracavity Kerr nonlinear coupler is a potential source of
bright continuous variable entangled light beams which are tunable and
spatially separated. This system may be realised with integrated optics and
thus provides a potentially rugged and stable source of bright entangled beams.


title: Global Entanglement for Multipartite Quantum States

abstract:
  Based on the residual entanglement [9] (Phys. Rev. A \textbf{71}, 044301
(2005)), we present the global entanglement for a multipartite quantum state.
The measure is shown to be also obtained by the bipartite partitions of the
multipartite state. The distinct characteristic of the global entanglement is
that it consists of the sum of different entanglement contributions. The
measure can provide sufficient and necessary condition of fully separability
for pure states and be conveniently extended to mixed states by minimizing the
convex hull. To test the sufficiency of the measure for mixed states, we
evaluate the global entanglement of bound entangled states. The properties of
the measure discussed finally show the global entanglement is an entanglement
monotone.


title:
Effects of cavity-field statistics on atomic entanglement in the
  Jaynes-Cummings model

abstract:
  We study the entanglement properties of a pair of two-level atoms going
through a cavity one after another. The initial joint state of two successive
atoms that enter the cavity is unentangled. Interactions mediated by the cavity
photon field result in the final two-atom state being of a mixed entangled
type. We consider the field statistics of the Fock state field, and the thermal
field, respectively, inside the cavity. The entanglement of formation of the
joint two-atom state is calculated for both these cases as a function of the
Rabi-angle $gt$. We present a comparitive study of two-atom entanglement for
low and high mean photon number cases corresponding to the different fields
statistics.


title:
Parametrization of the feedback Hamiltonian realizing a pure steady
  state

abstract:
  Feedback control is expected to considerably protect quantum states against
decoherence caused by interaction between the system and environment.
Especially, Markovian feedback scheme developed by Wiseman can modify the
properties of decoherence and eventually recover the purity of the steadystate
of the corresponding master equation. This paper provides a condition for which
the modified master equation has a pure steady state. By applying this
condition to a two-qubit system, we obtain a complete parametrization of the
feedback Hamiltonian such that the steady state becomes a maximally entangled
state.


title:
One-way Quantum Key Distribution System based on Planar Lightwave
  Circuits

abstract:
  We developed a one-way quantum key distribution (QKD) system based upon a
planar lightwave circuit (PLC) interferometer. This interferometer is expected
to be free from the backscattering inherent in commercially available two-way
QKD systems and phase drift without active compensation. A key distribution
experiment with spools of standard telecom fiber showed that the bit error rate
was as low as 6% for a 100-km key distribution using an attenuated laser pulse
with a mean photon number of 0.1 and was determined solely by the detector
noise. This clearly demonstrates the advantages of our PLC-based one-way QKD
system over two-way QKD systems for long distance key distribution.


title:
Perturbation hydrogen-atom spectrum in deformed space with minimal
  length

abstract:
  We study energy spectrum for hydrogen atom with deformed Heisenberg algebra
leading to minimal length. We develop correct perturbation theory free of
divergences. It gives a possibility to calculate analytically in the 3D case
the corrections to $s$-levels of hydrogen atom caused by the minimal length.
Comparing our result with experimental data from precision hydrogen
spectroscopy an upper bound for the minimal length is obtained.


title: Leaky cavities with unwanted noise

abstract:
  A phenomenological approach is developed that allows one to completely
describe the effects of unwanted noise, such as the noise associated with
absorption and scattering, in high-Q cavities. This noise is modeled by a block
of beam splitters and an additional input-output port. The replacement schemes
enable us to formulate appropriate quantum Langevin equations and input-output
relations. It is demonstrated that unwanted noise renders it possible to
combine a cavity input mode and the intracavity mode in a nonmonochromatic
output mode. Possible applications to unbalanced and cascaded homodyning of the
intracavity mode are discussed and the advantages of the latter method are
shown.


title: Optical Transparency Using Interference Between Two Modes of a Cavity

abstract:
  In electromagnetically-induced transparency (EIT), the absorption of a probe
beam is greatly reduced due to destructive interference between two dressed
atomic states produced by a strong laser beam. Here we show that a similar
reduction in the single-photon absorption rate can be achieved by tuning a
probe beam to be halfway between the resonant frequencies of two modes of a
cavity. This technique is expected to be useful in enhancing two-photon
absorption while reducing losses due to single-photon scattering.


title: The Question of Simultaneity in Relativity and Quantum Mechanics

abstract:
  In relativity, two simultaneous events at two different places are not
simultaneous for observers in different Lorentz frames. In the
Einstein-Podolsky-Rosen experiment, two simultaneous measurements are taken at
two different places. Would they still be simultaneous to observers in moving
frames? It is a difficult question, but it is still possible to study this
problem in the microscopic world. In the hydrogen atom, the uncertainty can be
considered to be entirely associated with the ground-state. However, is there
an uncertainty associated with the time-separation variable between the proton
and electron? This time-separation variable is a forgotten, if not hidden,
variable in the present form of quantum mechanics. The first step toward the
simultaneity problem is to study the role of this time-separation variable in
the Lorentz-covariant world. It is shown possible to study this problem using
harmonic oscillators applicable to hadrons which are bound states of quarks. It
is also possible to derive consequences that can be tested experimentally.


title:
Some Comments on the Formal Structure of Spontaneous Localization
  Theories

abstract:
  We propose a mathematical and a conceptual framework (called the `E-model'
and the `event ontology' resp.) that encompasses and generalizes the `flash'
ontology discussed in a recent paper by R. Tumulka (arXiv:quant-ph/0602208)


title:
Real time approach to tunneling in open quantum systems: decoherence and
  anomalous diffusion

abstract:
  Macroscopic quantum tunneling is described using the master equation for the
reduced Wigner function of an open quantum system at zero temperature. Our
model consists of a particle trapped in a cubic potential interacting with an
environment characterized by dissipative and normal and anomalous diffusion
coefficients. A representation based on the energy eigenfunctions of the
isolated system, i.e. the system uncoupled to the environment, is used to write
the reduced Wigner function, and the master equation becomes simpler in that
representation. The energy eigenfunctions computed in a WKB approximation
incorporate the tunneling effect of the isolated system and the effect of the
environment is described by an equation that it is in many ways similar to a
Fokker-Planck equation. Decoherence is easily identified from the master
equation and we find that when the decoherence time is much shorter than the
tunneling time the master equation can be approximated by a Kramers like
equation describing thermal activation due to the zero point fluctuations of
the quantum environment. The effect of anomalous diffusion can be dealt with
perturbatively and its overall effect is to inhibit tunneling.


title: Experimental interference of independent photons

abstract:
  Interference of photons emerging from independent sources is essential for
modern quantum information processing schemes, above all quantum repeaters and
linear-optics quantum computers. We report an observation of non-classical
interference of two single photons originating from two independent, separated
sources, which were actively synchronized with an r.m.s. timing jitter of 260
fs. The resulting (two-photon) interference visibility was 83(+/-)4 %.


title: Stimulated wave of polarization in spin chains

abstract:
  Stimulated wave of polarization, triggered by a flip of a single spin,
presents a simple model of quantum amplification. Previously, it has been found
that such wave can be excited in a 1D Ising chain with nearest-neighbor
interactions, irradiated by a weak resonant transverse field. Here we explore
models with more realistic Hamiltonians, in particular, with natural
dipole-dipole interactions. Results of simulations for 1D spin chains and rings
with up to nine spins are presented.


title: Quantum Violation: Beyond Clauser-Horne-Shimony-Holt Inequality

abstract:
  The best upper bound for the violation of the Clauser-Horne-Shimony-Holt
(CHSH) inequality was first derived by Tsirelson. For increasing number of $\pm
1$ valued observables on both sites of the correlation experiment, Tsirelson
obtained the Grothendieck's constant ($\mathcal{K}_{G}\approx 1.73\pm0.06$) as
a limit for the maximal violation. In this paper, we construct a generalization
of the CHSH inequality with four $\pm 1$ valued observables on both sites of a
correlation experiment and show that the quantum violation approaching 1.58.
Moreover, we estimate the maximal quantum violation of a correlation experiment
for large and equal number of $\pm 1$ valued observables on both sites. In this
case, the maximal quantum violation converges to $\sqrt{3}\approx1.73$ for very
large $n$, which coincides with the approximate value of Grothendieck's
constant.


title:
The Projective Line Over the Finite Quotient Ring GF(2)[$x$]/$< x^{3} -
  x>$ and Quantum Entanglement I. Theoretical Background

abstract:
  The paper deals with the projective line over the finite factor ring
$R\_{\clubsuit} \equiv$ GF(2)[$x$]/$<x^{3} - x>$. The line is endowed with 18
points, spanning the neighbourhoods of three pairwise distant points. As
$R\_{\clubsuit}$ is not a local ring, the neighbour (or parallel) relation is
not an equivalence relation so that the sets of neighbour points to two distant
points overlap. There are nine neighbour points to any point of the line,
forming three disjoint families under the reduction modulo either of two
maximal ideals of the ring. Two of the families contain four points each and
they swap their roles when switching from one ideal to the other; the points of
the one family merge with (the image of) the point in question, while the
points of the other family go in pairs into the remaining two points of the
associated ordinary projective line of order two. The single point of the
remaining family is sent to the reference point under both the mappings and its
existence stems from a non-trivial character of the Jacobson radical, ${\cal
J}\_{\clubsuit}$, of the ring. The factor ring $\widetilde{R}\_{\clubsuit}
\equiv R\_{\clubsuit}/ {\cal J}\_{\clubsuit}$ is isomorphic to GF(2) $\otimes$
GF(2). The projective line over $\widetilde{R}\_{\clubsuit}$ features nine
points, each of them being surrounded by four neighbour and the same number of
distant points, and any two distant points share two neighbours. These
remarkable ring geometries are surmised to be of relevance for modelling
entangled qubit states, to be discussed in detail in Part II of the paper.


title: Quantum Games with Correlated Noise

abstract:
  We analyze quantum game with correlated noise through generalized
quantization scheme. Four different combinations on the basis of entanglement
of initial quantum state and the measurement basis are analyzed. It is shown
that the advantage that a quantum player can get by exploiting quantum
strategies is only valid when both the initial quantum state and the
measurement basis are in entangled form. Furthermore, it is shown that for
maximum correlation the effects of decoherence diminish and it behaves as a
noiseless game.


title:
Classical simulation of two spin-$S$ singlet state correlations
  involving spin measurements

abstract:
  We give a classical protocol to exactly simulate quantum correlations implied
by a spin-$s$ singlet state for the infinite sequence of spins satisfying $(2s
+ 1) = 2^{n}$, in the worst-case scenario, where $n$ is a positive integer. The
class of measurements we consider here are only those corresponding to spin
observables. The required amount of communication is found to be $log_{2}d$
where $d = 2s + 1$ is the dimension of the spin-$s$ Hilbert space.


title:
Elastic vs. inelastic coherent backscattering of laser light by cold
  atoms: a master equation treatment

abstract:
  We give a detailed derivation of the master equation description of the
coherent backscattering of laser light by cold atoms. In particular, our
formalism accounts for the nonperturbative nonlinear response of the atoms when
the injected intensity saturates the atomic transition. Explicit expressions
are given for total and elastic backscattering intensities in the different
polarization channels, for the simplest nontrivial multiple scattering scenario
of intense laser light multiply scattering from two randomly placed atoms.


title: Werner states and the two-spinors Heisenberg anti-ferromagnet

abstract:
  We ascertain, following ideas of Arnesen, Bose, and Vedral concerning thermal
entanglement [Phys. Rev. Lett. {\bf 87} (2001) 017901] and using the
statistical tool called {\it entropic non-triviality} [Lamberti, Martin,
Plastino, and Rosso, Physica A {\bf 334} (2004) 119], that there is a one to
one correspondence between (i) the mixing coefficient $x$ of a Werner state, on
the one hand, and (ii) the temperature $T$ of the one-dimensional Heisenberg
two-spin chain with a magnetic field $B$ along the $z-$axis, on the other one.
This is true for each value of $B$ below a certain critical value $B_c$. The
pertinent mapping depends on the particular $B-$value one selects within such a
range.


title: Maximally Entangled Mixed States and Conditional Entropies

abstract:
  The maximally entangled mixed states of Munro, James, White, and Kwiat [Phys.
Rev. A {\bf 64} (2001) 030302] are shown to exhibit interesting features vis a
vis conditional entropic measures. The same happens with the Ishizaka and
Hiroshima states [Phys. Rev. A {\bf 62} 022310 (2000)], whose
entanglement-degree can not be increased by acting on them with logic gates.
Special types of entangled states that do not violate classical entropic
inequalities are seen to exist in the space of two qubits. Special meaning can
be assigned to the Munro {\it et al.} special participation ratio of 1.8.


title:
On the distribution of entanglement changes produced by unitary
  operations

abstract:
  We consider the change of entanglement of formation $\Delta E$ produced by a
unitary transformation acting on a general (pure or mixed) state $\rho$
describing a system of two qubits. We study numerically the probabilities of
obtaining different values of $\Delta E$, assuming that the initial state is
randomly distributed in the space of all states according to the product
measure introduced by Zyczkowski {\it et al.} [Phys. Rev. A {\bf 58} (1998)
883].


title:
A general approach to physical realization of unambiguous quantum-state
  discrimination

abstract:
  We present a general scheme to realize the POVMs for the unambiguous
discrimination of quantum states. For any set of pure states it enables us to
set up a feasible linear optical circuit to perform their optimal
discrimination, if they are prepared as single-photon states. An example of
unknown states discrimination is discussed as the illustration of the general
scheme.


title: Entanglement Distribution and Entangling Power of Quantum Gates

abstract:
  Quantum gates, that play a fundamental role in quantum computation and other
quantum information processes, are unitary evolution operators $\hat U$ that
act on a composite system changing its entanglement. In the present
contribution we study some aspects of these entanglement changes. By recourse
of a Monte Carlo procedure, we compute the so called "entangling power" for
several paradigmatic quantum gates and discuss results concerning the action of
the CNOT gate. We pay special attention to the distribution of entanglement
among the several parties involved.


title:
Understanding Quantum Entanglement: Qubits, Rebits and the Quaternionic
  Approach

abstract:
  It has been recently pointed out by Caves, Fuchs, and Rungta that real
quantum mechanics (that is, quantum mechanics defined over real vector spaces
provides an interesting foil theory whose study may shed some light on just
which particular aspects of quantum entanglement are unique to standard quantum
theory, and which ones are more generic over other physical theories endowed
with this phenomenon. Following this work, we discuss some entanglement
properties of two-rebits systems, making a comparison with the basic properties
of two-qubits systems, i.e., the ones described by standard complex quantum
mechanics. We also discuss the use of quaternionic quantum mechanics as applied
to the phenomenon of entanglement.


title:
Decompositions of unitary evolutions and entanglement dynamics of
  bipartite quantum systems

abstract:
  We describe a decomposition of the Lie group of unitary evolutions for a
bipartite quantum system of arbitrary dimensions. The decomposition is based on
a recursive procedure which systematically uses the Cartan classification of
the symmetric spaces of the Lie group SO(n). The resulting factorization of
unitary evolutions clearly displays the local and entangling character of each
factor.


title: Reconsidering Rapid Qubit Purification by Feedback

abstract:
  This paper reconsiders the claimed rapidity of a scheme for the purification
of the quantum state of a qubit, proposed recently in Jacobs 2003 Phys. Rev.
A67 030301(R). The qubit starts in a completely mixed state, and information is
obtained by a continuous measurement. Jacobs' rapid purification protocol uses
Hamiltonian feedback control to maximise the average purity of the qubit for a
given time, with a factor of two increase in the purification rate over the
no-feedback protocol. However, by re-examining the latter approach, we show
that it mininises the average time taken for a qubit to reach a given purity.
In fact, the average time taken for the no-feedback protocol beats that for
Jacobs' protocol by a factor of two. We discuss how this is compatible with
Jacobs' result, and the usefulness of the different approaches.


title: Matter-wave diffraction in time with a linear potential

abstract:
  Diffraction in time of matter waves incident on a shutter which is removed at
time $t=0$ is studied in the presence of a linear potential. The solution is
also discussed in phase space in terms of the Wigner function. An alternative
configuration relevant to current experiments where particles are released from
a hard wall trap is also analyzed for single-particle states and for a
Tonks-Girardeau gas.


title:
Quantum diffraction and interference of spatially correlated photon
  pairs and its Fourier-optical analysis

abstract:
  We present one- and two-photon diffraction and interference experiments
involving parametric down-converted photon pairs. By controlling the divergence
of the pump beam in parametric down-conversion, the diffraction-interference
pattern produced by an object changes from a quantum (perfectly correlated)
case to a classical (uncorrelated) one. The observed diffraction and
interference patterns are accurately reproduced by Fourier-optical analysis
taking into account the quantum spatial correlation. We show that the relation
between the spatial correlation and the object size plays a crucial role in the
formation of both one- and two-photon diffraction-interference patterns.


title: A Bayesian Analogue of Gleason's Theorem

abstract:
  We introduce a novel notion of probability within quantum history theories
and give a Gleasonesque proof for these assignments. This involves introducing
a tentative novel axiom of probability. We also discuss how we are to interpret
these generalised probabilities as partially ordered notions of preference and
we introduce a tentative generalised notion of Shannon entropy. A Bayesian
approach to probability theory is adopted throughout, thus the axioms we use
will be minimal criteria of rationality rather than ad hoc mathematical axioms.


title:
A Quantum Key Distribution Protocol with Selecting Announced States,
  Robust against Photon Number Splitting Attacks

abstract:
  We propose a new class of quantum key distribution protocol, that ended up to
be robust against photon number splitting attacks in the weak laser pulse
implementations. This protocol comprises of BB84 protocol and SARG protocol,
especially in aspects of controlling classical sifting procedures of two
protocols. The protocol is more secure than both of BB84 protocol and SARG
protocol, and the ultimate limit of robustness in the proposed protocol expands
as well than both of them.


title: The decay law can have an irregular character

abstract:
  Within a well-known decay model describing a particle confined initially
within a spherical $\delta$ potential shell, we consider the situation when the
undecayed state has an unusual energy distribution decaying slowly as
$k\to\infty$; the simplest example corresponds to a wave function constant
within the shell. We show that the non-decay probability as a function of time
behaves then in a highly irregular, most likely fractal way.


title:
High Efficient Secret Key Distillation for Long Distance Continuous
  Variable Quantum Key Distribution

abstract:
  The continuous variable quantum key distribution is expected to provide high
secret key rate without single photon source and detector, but the lack of the
secure and effective key distillation method makes it unpractical. Here, we
present a secure single-bit-reverse-reconciliation protocol combined with
secret information concentration and post-selection, which can distill the
secret key with high efficiency and low computational complexity. The
simulation results show that this protocol can provide high secret key rate
even when the transmission fiber is longer than 150km, which may make the
continuous variable scheme to outvie the single photon one.


title:
The Jones polynomial: quantum algorithms and applications in quantum
  complexity theory

abstract:
  We analyze relationships between quantum computation and a family of
generalizations of the Jones polynomial. Extending recent work by Aharonov et
al., we give efficient quantum circuits for implementing the unitary
Jones-Wenzl representations of the braid group. We use these to provide new
quantum algorithms for approximately evaluating a family of specializations of
the HOMFLYPT two-variable polynomial of trace closures of braids. We also give
algorithms for approximating the Jones polynomial of a general class of
closures of braids at roots of unity. Next we provide a self-contained proof of
a result of Freedman et al. that any quantum computation can be replaced by an
additive approximation of the Jones polynomial, evaluated at almost any
primitive root of unity. Our proof encodes two-qubit unitaries into the
rectangular representation of the eight-strand braid group. We then give
QCMA-complete and PSPACE-complete problems which are based on braids. We
conclude with direct proofs that evaluating the Jones polynomial of the plat
closure at most primitive roots of unity is a #P-hard problem, while learning
its most significant bit is PP-hard, circumventing the usual route through the
Tutte polynomial and graph coloring.


title: Wave-Particle Duality and the Coherent Quantum Domain Picture

abstract:
  It is proposed that the paradox of wave-particle duality in quantum mechanics
may be resolved using a physical picture analogous to magnetic domains. Within
this picture, a quantum particle represents a coherent region of a quantum wave
with characteristic total energy, momentum, and spin. The dynamics of such a
state are described by the usual linear quantum wave equations. But the
coherence is maintained by a nonlinear self-interaction term that is evident
only during transitions from one quantum state to another. This is analogous to
the self-organizing property of domains in a ferromagnetic material, in which a
single domain may appear as a stable macro-particle, but with rapid transitions
between different domain configurations also possible. For the quantum case,
this implies that the "collapse of the wave function" is a real dynamical
physical process that occurs continuously in spacetime. This picture may also
permit the resolution of apparent paradoxes associated with quantum measurement
and entangled states.


title:
Generalized Entanglement as a Natural Framework for Exploring Quantum
  Chaos

abstract:
  We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev.
A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum
chaotic behavior. Since generalized entanglement depends directly on a choice
of preferred observables, exploring how generalized entanglement increases
under dynamical evolution is possible without invoking an auxiliary coupled
system or decomposing the system into arbitrary subsystems. We find that, in
the chaotic regime, the long-time saturation value of generalized entanglement
agrees with random matrix theory predictions. For our system, we provide
physical intuition into generalized entanglement within a single system by
invoking the notion of extent of a state. The latter, in turn, is related to
other signatures of quantum chaos.


title: A complete algorithm to find flows in the one-way measurement model

abstract:
  This article is the complement to [quant-ph/0611284], which proves that flows
(as introduced by [quant-ph/0506062]) can be found efficiently for patterns in
the one-way measurement model which have non-empty input and output subsystems
of the same size. This article presents a complete algorithm for finding flows,
and a proof of its' correctness, without assuming any knowledge of
graph-theoretic algorithms on the part of the reader. This article is a revised
version of [quant-ph/0603072v2], where the results of [quant-ph/0611284] also
first appeared.


title: Vector Potential and Berry phase-induced Force

abstract:
  We present a general theoretical framework for the exact treatment of a
hybrid system that is composed of a quantum subsystem and a classical
subsystem. When the quantum subsystem is dynamically fast and the classical
subsystem is slow, a vector potential is generated with a simple canonical
transformation. This vector potential, on one hand, gives rise to the familiar
Berry phase in the fast quantum dynamics; on the other hand, it yields a
Lorentz-like force in the slow classical dynamics. In this way, the pure phase
(Berry phase) of a wavefunction is linked to a physical force.


title: Binary projective measurement via linear optics and photon counting

abstract:
  We investigate the implementation of binary projective measurements with
linear optics. This problem can be viewed as a single-shot discrimination of
two orthogonal pure quantum states. We show that any two orthogonal states can
be perfectly discriminated using only linear optics, photon counting, coherent
ancillary states, and feedforward. The statement holds in the asymptotic limit
of large number of these physical resources.


title:
On Existence of a Biorthonormal Basis Composed of Eigenvectors of
  Non-Hermitian Operators

abstract:
  We present a set of necessary conditions for the existence of a biorthonormal
basis composed of eigenvectors of non-Hermitian operators. As an illustration,
we examine these conditions in the case of normal operators. We also provide a
generalization of the conditions which is applicable to non-diagonalizable
operators by considering not only eigenvectors but also all root vectors.


title: A generalization of Margolus-Levitin bound

abstract:
  The Margolus-Levitin lower bound on minimal time required for a state to be
transformed into an orthogonal state is generalized. It is shown that for some
initial states new bound is stronger than the Margolus-Levitin one.


title:
Generalized Deformed Commutation Relations with Nonzero Minimal
  Uncertainties in Position and/or Momentum and Applications to Quantum
  Mechanics

abstract:
  Two generalizations of Kempf's quadratic canonical commutation relation in
one dimension are considered. The first one is the most general quadratic
commutation relation. The corresponding nonzero minimal uncertainties in
position and momentum are determined and the effect on the energy spectrum and
eigenfunctions of the harmonic oscillator in an electric field is studied. The
second extension is a function-dependent generalization of the simplest
quadratic commutation relation with only a nonzero minimal uncertainty in
position. Such an uncertainty now becomes dependent on the average position.
With each function-dependent commutation relation we associate a family of
potentials whose spectrum can be exactly determined through supersymmetric
quantum mechanical and shape invariance techniques. Some representations of the
generalized Heisenberg algebras are proposed in terms of conventional position
and momentum operators $x$, $p$. The resulting Hamiltonians contain a
contribution proportional to $p^4$ and their $p$-dependent terms may also be
functions of $x$. The theory is illustrated by considering P\"oschl-Teller and
Morse potentials.


title: Asymptotic quantum cloning is state estimation

abstract:
  The impossibility of perfect cloning and state estimation are two fundamental
results in Quantum Mechanics. It has been conjectured that quantum cloning
becomes equivalent to state estimation in the asymptotic regime where the
number of clones tends to infinity. We prove this conjecture using two known
results of Quantum Information Theory: the monogamy of quantum correlations and
the properties of entanglement breaking channels.


title:
Intensity correlations and entanglement by frequency doubling in a dual
  ported resonator

abstract:
  We show that non-classical intensity correlations and quadrature entanglement
can be generated by frequency doubling in a resonator with two output ports. We
predict twin-beam intensity correlations 6 dB below the coherent state limit,
and that the product of the inference variances of the quadrature fluctuations
gives an Einstein-Podolsky-Rosen (EPR) correlation coefficient of V_EPR = 0.6 <
1. Comparison with an entanglement source based on combining two frequency
doublers with a beam splitter shows that the dual ported resonator provides
stronger entanglement at lower levels of individual beam squeezing.
Calculations are performed using a self-consistent propagation method that does
not invoke a mean field approximation. Results are given for physically
realistic parameters that account for the Gaussian shape of the intracavity
beams, as well as intracavity losses.


title:
Interference in the resonance fluorescence of two incoherently coupled
  transitions

abstract:
  The fluorescence light emitted by a 4-level system in $J=1/2$ to $J=1/2$
configuration driven by a monochromatic laser field and in an external magnetic
field is studied. We show that the spectrum of resonance fluorescence emitted
on the $\pi$ transitions shows a signature of spontaneously generated
interference effects. The degree of interference in the fluorescence spectrum
can be controlled by means of the external magnetic field, provided that the
Land\'e g-factors of the excited and the ground state doublet are different.
For a suitably chosen magnetic field strength, the relative weight of the
Rayleigh line can be completely suppressed, even for low intensities of the
coherent driving field. The incoherent fluorescence spectrum emitted on the
$\pi$ transitions exhibits a very narrow peak whose width and weight depends on
the magnetic field strength. We demonstrate that the spectrum of resonance
fluorescence emitted on the $\sigma$ transitions show an indirect signature of
interference. A measurement of the relative peak heights in the spectrum from
the $\sigma$ transitions allows to determine the branching ratio of the
spontaneous decay of each excited state into the $\sigma$ channel.


title: Parallelism for Quantum Computation with Qudits

abstract:
  Robust quantum computation with d-level quantum systems (qudits) poses two
requirements: fast, parallel quantum gates and high fidelity two-qudit gates.
We first describe how to implement parallel single qudit operations. It is by
now well known that any single-qudit unitary can be decomposed into a sequence
of Givens rotations on two-dimensional subspaces of the qudit state space.
Using a coupling graph to represent physically allowed couplings between pairs
of qudit states, we then show that the logical depth of the parallel gate
sequence is equal to the height of an associated tree. The implementation of a
given unitary can then optimize the tradeoff between gate time and resources
used. These ideas are illustrated for qudits encoded in the ground hyperfine
states of the atomic alkalies $^{87}$Rb and $^{133}$Cs. Second, we provide a
protocol for implementing parallelized non-local two-qudit gates using the
assistance of entangled qubit pairs. Because the entangled qubits can be
prepared non-deterministically, this offers the possibility of high fidelity
two-qudit gates.


title:
Remark on a Group-Theoretical Formalism for Quantum Mechanics and the
  Quantum-to-Classical Transition

abstract:
  We sketch a group-theoretical framework, based on the Heisenberg-Weyl group,
encompassing both quantum and classical statistical descriptions of mechanical
systems. We re-define in group-theoretical terms the kinematical arena and the
state-space of the system, achieving a unified quantum-classical language and a
novel version of the correspondence principle. We briefly discuss the structure
of observables and dynamics within our framework.


title:
Scheme for generating a sequence of single photons of alternating
  polarisation

abstract:
  Single-photons of well-defined polarisation that are deterministically
generated in a single spatio-temporal field mode are the key to the creation of
multi-partite entangled states in photonic networks. Here, we present a novel
scheme to produce such photons from a single atom in an optical cavity, by
means of vacuum-stimulated Raman transitions between the Zeeman substates of a
single hyperfine state. Upon each transition, a photon is emitted into the
cavity, with a polarisation that depends on the direction of the Raman process.


title: Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

abstract:
  We discuss the questions: How to compare quantitatively classical chaos with
quantum chaos? Which one is stronger? What are the underlying physical reasons?


title:
General entanglement-assisted transformation for bipartite pure quantum
  states

abstract:
  We introduce the general catalysts for pure entanglement transformations
under local operations and classical communications in such a way that we
disregard the profit and loss of entanglement of the catalysts per se. As such,
the possibilities of pure entanglement transformations are greatly expanded.
Remarkably, we find an interesting phenomenon that, in some situations,
incomparable pairs ${| \psi> ,| \phi> \} $ and ${| \chi> ,| \chi^{\prime}> \} $
can assist each other mutually so as to realize the transformation $| \psi> |
\chi> \to| \phi> | \chi^{\prime}>$. We also design an efficient algorithm to
detect whether a $k\times k$ general catalyst exists for a given entanglement
transformation. This algorithm can as well be exploited to witness the
existence of standard catalysts.


title:
Computation of topological charges of optical vortices via
  non-degenerate four-wave-mixing

abstract:
  In this paper, we report an experiment, which demonstrates computation of
topological charges of two optical vortices via non-degenerate four-wave-mixing
process. We show that the output signal beam carries orbital angular momentum
which equals to the subtraction of the orbital angular momenta of the probe
light and the backward pump light. The ⁸⁵Rb atoms are used as the
nonlinear medium, which transfer the orbital angular momenta of lights.


title:
Creation of Entanglement and Implementation of Quantum Logic Gate
  Operations Using a Three-Dimensional Photonic Crystal Single-Mode Cavity

abstract:
  We solve the Jaynes-Cummings Hamiltonian with time-dependent coupling
parameters under dipole and rotating-wave approximation for a three-dimensional
(3D) photonic crystal (PC) single mode cavity with a sufficiently high quality
(Q) factor. We then exploit the results to show how to create a maximally
entangled state of two atoms, and how to implement several quantum logic gates:
a dual-rail Hadamard gate, a dual-rail NOT gate, and a SWAP gate. The atoms in
all of these operations are syncronized, which is not the case in previous
studies [1,2] in PCs. Our method has the potential for extension to N-atom
entanglement, universal quantum logic operations, and the implementation of
other useful, cavity QED based quantum information processing tasks.


title:
Quantum temporal correlations and entanglement via adiabatic control of
  vector solitons

abstract:
  It is shown that optical pulses with a mean position accuracy beyond the
standard quantum limit can be produced by adiabatically expanding an optical
vector soliton followed by classical dispersion management. The proposed scheme
is also capable of entangling positions of optical pulses and can potentially
be used for general continuous-variable quantum information processing.


title: Propagation of temporal entanglement

abstract:
  The equations that govern the temporal evolution of two photons in the
Schr{\"o}dinger picture are derived, taking into account the effects of loss,
group-velocity dispersion, temporal phase modulation, linear coupling among
different optical modes, and four-wave mixing. Inspired by the formalism, we
propose the concept of quantum temporal imaging, which uses dispersive elements
and temporal phase modulators to manipulate the temporal correlation of two
entangled photons. We also present the exact solution of a two-photon vector
soliton, in order to demonstrate the ease of use and intuitiveness of the
proposed formulation.


title:
Finite-dimensional states and entanglement generation for a nonlinear
  coupler

abstract:
  We discuss a system comprising two nonlinear (Kerr-like) oscillators coupled
mutually by a nonlinear interaction. The system is excited by an external
coherent field that is resonant to the frequency of one of the oscillators. We
show that the coupler evolution can be closed within a finite set of $n$-photon
states, analogously as in the \textit{nonlinear quantum scissors} model.
Moreover, for this type of evolution our system can be treated as a
\textit{Bell-like states} generator. Thanks to the nonlinear nature of both:
oscillators and their internal coupling, these states can be generated even if
the system exhibits its energy dissipating nature, contrary to systems with
linear couplings.


title:
Real Description of Classical Hamiltonian Dynamics Generated by a
  Complex Potential

abstract:
  Analytic continuation of the classical dynamics generated by a standard
Hamiltonian, H = p^2/2m + v(x), into the complex plane yields a particular
complex classical dynamical system. For an analytic potential v, we show that
the resulting complex system admits a description in terms of the phase space
R^4 equipped with an unconventional symplectic structure. This in turn allows
for the construction of an equivalent real description that is based on the
conventional symplectic structure on R^4, and establishes the equivalence of
the complex extension of classical mechanics that is based on the
above-mentioned analytic continuation with the conventional classical
mechanics. The equivalent real Hamiltonian turns out to be twice the real part
of H, while the imaginary part of H plays the role of an independent integral
of motion ensuring the integrability of the system. The equivalent real
description proposed here is the classical analog of the equivalent Hermitian
description of unitary quantum systems defined by complex, typically
PT-symmetric, potentials.

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


title: Is Quantum Reduction the Ultimate Outcome of Decoherence ?

abstract:
  This model was crazy (or not crazy enough for this topic) and it would lead
to a reduction time much longer than the age of the universe.


title: Bloch-Zener oscillations

abstract:
  It is well known that a particle in a periodic potential with an additional
constant force performs Bloch oscillations. Modulating every second period of
the potential, the original Bloch band splits into two subbands. The dynamics
of quantum particles shows a coherent superposition of Bloch oscillations and
Zener tunneling between the subbands, a Bloch-Zener oscillation. Such a system
is modelled by a tight-binding Hamiltonian, a system of two minibands with an
easily controllable gap. The dynamics of the system is investigated by using an
algebraic ansatz leading to a differential equation of Whittaker-Hill type. It
is shown that the parameters of the system can be tuned to generate a periodic
reconstruction of the wave packet and thus of the occupation probability. As an
application, the construction of a matter wave beam splitter and a Mach-Zehnder
interferometer is briefly discussed.


title: Bell-type inequalities for non-local resources

abstract:
  We present bipartite Bell-type inequalities which allow the two partners to
use some non-local resource. Such inequality can only be violated if the
parties use a resource which is more non-local than the one permitted by the
inequality. We introduce a family of N-inputs non-local machines, which are
generalizations of the well-known PR-box. Then we construct Bell-type
inequalities that cannot be violated by strategies that use one these new
machines. Finally we discuss implications for the simulation of quantum states.


title: Saturation of fidelity in the atom-optics kicked rotor

abstract:
  We show that the quantum fidelity is accessible to cold atom experiments for
a large class of evolutions in periodical potentials, properly taking into
account the experimental initial conditions of the atomic ensemble. We prove
analytically that, at the fundamental quantum resonances of the atom-optics
kicked rotor, the fidelity saturates at a constant, time-independent value
after a small number of kicks. The latter saturation arises from the bulk of
the atomic ensemble, whilst for the resonantly accelerated atoms the fidelity
is predicted to decay slowly according to a power law.


title:
Comment on ``On Existence of a Biorthonormal Basis Composed of
  Eigenvectors of Non-Hermitian Operators [quant-ph/0603075]''

abstract:
  We point out that T. Tanaka's recent criticism [quant-ph/0603075] of the
results of J. Math. Phys. 43, 3944 (2002) [math-ph/0203005] is based on an
assumption which was never made in the latter paper, namely that the
diagonalizability of an operator implies that it is normal. Therefore, Tanaka's
objections regarding this paper are not valid.


title: Numerical approach to the dynamical Casimir effect

abstract:
  The dynamical Casimir effect for a massless scalar field in 1+1-dimensions is
studied numerically by solving a system of coupled first-order differential
equations. The number of scalar particles created from vacuum is given by the
solutions to this system which can be found by means of standard numerics. The
formalism already used in a former work is derived in detail and is applied to
resonant as well as off-resonant cavity oscillations.


title: Quantum broadcast channels

abstract:
  We consider quantum channels with one sender and two receivers, used in
several different ways for the simultaneous transmission of independent
messages. We begin by extending the technique of superposition coding to
quantum channels with a classical input to give a general achievable region. We
also give outer bounds to the capacity regions for various special cases from
the classical literature and prove that superposition coding is optimal for a
class of channels. We then consider extensions of superposition coding for
channels with a quantum input, where some of the messages transmitted are
quantum instead of classical, in the sense that the parties establish bipartite
or tripartite GHZ entanglement. We conclude by using state merging to give
achievable rates for establishing bipartite entanglement between different
pairs of parties with the assistance of free classical communication.


title: Quantum Recurrences in Periodically Driven Systems

abstract:
  We investigate the quantum recurrence phenomena in periodically driven
systems.
  We calculate the classical period and the quantum recurrence time and develop
their interdependence. We further predict the behavior of the recurrence
phenomena for the power law potentials.


title:
Quantum secure direct communication based on order rearrangement of
  single photons

abstract:
  Based on the ideal of order rearrangement and block transmission of photons,
we present a quantum secure direct communication scheme using single photons.
The security of the present scheme is ensured by quantum no-cloning theory and
the secret transmitting order of photons. The present scheme is efficient in
that all of the polarized photons are used to transmit the sender's secret
message except those chosen for eavesdropping check. We also generalize this
scheme to a multiparty controlled quantum secret direct communication scheme
which the sender's secret message can only be recovered by the receiver under
the permission of all the controllers.


title: QKD Quantum Channel Authentication

abstract:
  Several simple yet secure protocols to authenticate the quantum channel of
various QKD schemes, by coupling the photon sender's knowledge of a shared
secret and the QBER Bob observes, are presented. It is shown that Alice can
encrypt certain portions of the information needed for the QKD protocols, using
a sequence whose security is based on computational-complexity, without
compromising all of the sequence's entropy. It is then shown that after a
Man-in-the-Middle attack on the quantum and classical channels, there is still
enough entropy left in the sequence for Bob to detect the presence of Eve by
monitoring the QBER. Finally, it is shown that the principles presented can be
implemented to authenticate the quantum channel associated with any type of QKD
scheme, and they can also be used for Alice to authenticate Bob.


title: Geometric multipartite entanglement measures

abstract:
  Within the framework of constructions for quantifying entanglement, we build
a natural scenario for the assembly of multipartite entanglement measures based
on Hopf bundle-like mappings obtained through Clifford algebra representations.
Then, given the non-factorizability of an arbitrary two-qubit density matrix,
we give an alternate quantity that allows the construction of two types of
entanglement measures based on their arithmetical and geometrical averages over
all pairs of qubits in a register of size N, and thus fully characterize its
degree and type of entanglement. We find that such an arithmetical average is
both additive and strongly super additive.


title:
Hermitian Tensor Product Approximation of Complex Matrices and
  Separability

abstract:
  The approximation of matrices to the sum of tensor products of Hermitian
matrices is studied. A minimum decomposition of matrices on tensor space
$H_1\otimes H_2$ in terms of the sum of tensor products of Hermitian matrices
on $H_1$ and $H_2$ is presented. From this construction the separability of
quantum states is discussed.


title:
A Note on Equivalence of Bipartite States under Local Unitary
  Transformations

abstract:
  The equivalence of arbitrary dimensional bipartite states under local unitary
transformations (LUT) is studied. A set of invariants and ancillary invariants
under LUT is presented. We show that two states are equivalent under LUT if and
only if they have the same values for all of these invariants.


title: A Class of Bound Entangled States

abstract:
  We construct a set of PPT (positive partial transpose) states and show that
these PPT states are not separable, thus present a class of bound entangled
quantum states.


title: Quantum channel capacities - multiparty communication

abstract:
  We analyze different aspects of multiparty communication over quantum
memoryless channels and generalize some of key results known from bipartite
channels to that of multiparty scenario. In particular, we introduce multiparty
versions of minimal subspace transmission fidelity and entanglement
transmission fidelity. We also provide alternative, local, versions of
fidelities and show their equivalence to the global ones in context of capacity
regions defined. The equivalence of two different capacity notions with respect
to two types of the fidelities is proven. In analogy to bipartite case it is
shown, via sufficiency of isometric encoding theorem, that additional classical
forward side channel does not increase capacity region of any quantum channel
with $k$ senders and $m$ receivers which represents a compact unit of general
quantum networks theory. The result proves that recently provided capacity
region of multiple access channel ([M. Horodecki et al, Nature {\bf 436} 673
(2005)], [J.Yard et al, quant-ph/0501045]) is optimal also in the scenario of
additional support of forward classical communication.


title:
Spontaneously generated coherence induced second-order susceptibility in
  atomic gases

abstract:
  The second-order susceptibility which vanishes in the electric-dipole
approximation for an atom is induced by the spontaneously generated coherence.
The spontaneously generated coherence considered in a lambda-type atomic system
causes an indirect coupling between the lower two levels which acts
equivalently as a DC-field and therefore makes possible the existence of
second-order susceptibility.


title: Concurrence in collective models

abstract:
  We review the entanglement properties in collective models and their
relationship with quantum phase transitions. Focusing on the concurrence which
characterizes the two-spin entanglement, we show that for first-order
transition, this quantity is singular but continuous at the transition point,
contrary to the common belief. We also propose a conjecture for the concurrence
of arbitrary symmetric states which connects it with a recently proposed
criterion for bipartite entanglement.


title: Decoherence induced by a phase-damping reservoir

abstract:
  A phase damping reservoir composed by $N$-bosons coupled to a system of
interest through a cross-Kerr interaction is proposed and its effects on
quantum superpo sitions are investigated. By means of analytical calculations
we show that: i-) the reservoir induces a Gaussian decay of quantum coherences,
and ii-) the inher ent incommensurate character of the spectral distribution
yields irreversibility . A state-independent decoherence time and a master
equation are both derived an alytically. These results, which have been
extended for the thermodynamic limit, show that nondissipative decoherence can
be suitably contemplated within the EI D approach. Finally, it is shown that
the same mechanism yielding decoherence ar e also responsible for inducing
dynamical disentanglement.


title: Still more on norms of completely positive maps

abstract:
  King and Ruskai asked whether the norm of a completely positive map acting
between Schatten classes of operators is equal to that of its restriction to
the real subspace of self-adjoint operators. Proofs have been promptly supplied
by Watrous and Audenaert. Here we provide one more proof, in fact of a slightly
more general fact, under the (slightly weaker) assumption of 2-positivity. The
argument is elementary and self-contained.


title:
Experimental test for the conductivity properties from the Casimir force
  between metal and semiconductor

abstract:
  The experimental investigation of the Casimir force between a large
metallized sphere and semiconductor plate is performed using an atomic force
microscope. Improved calibration and measurement procedures permitted reduction
in the role of different uncertainties. Rigorous statistical procedures are
applied for the analysis of random, systematic and total experimental errors at
95% confidence. The theoretical Casimir force is computed for semiconductor
plates with different conductivity properties taking into account all
theoretical uncertainties discussed in literature. The comparison between
experiment and theory is done at both 95 and 70% confidence. It is demonstrated
that the theoretical results computed for the semiconductor plate used in
experiment are consistent with data. At the same time, theory describing a
dielectric plate is excluded by experiment at 70% confidence. Thus, the Casimir
force is proved to be sensitive to the conductivity properties of
semiconductors.


title: Aspects of multistation quantum information broadcasting

abstract:
  We study quantum information transmission over multiparty quantum channel. In
particular, we show an equivalence of different capacity notions and provide a
multiletter characterization of a capacity region for a general quantum channel
with $k$ senders and $m$ receivers. We point out natural generalizations to the
case of two-way classical communication capacity.


title:
New Bardeen-Cooper-Schrieffer-type theory at finite temperature with
  particle-number conservation

abstract:
  We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite
temperature, by deriving a set of variational equations of the free energy
after the particle-number projection. With its broad applicability, this theory
can be a useful tool for investigating the pairing phase transition in finite
systems with the particle-number conservation. This theory provides effects of
the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite
fermionic systems, distinctively from those of additional quantum fluctuations.
It is shown by numerical calculations that the phase transition is compatible
with the conservation in this theory, and that the SRF shifts up the critical
temperature ($T^\mathrm{cr}$). This shift of $T^\mathrm{cr}$ occurs due to
reduction of degrees-of-freedom in canonical ensembles, and decreases only
slowly as the particle-number increases (or as the level spacing narrows), in
contrast to the conventional BCS theory.


title: General entanglement scaling laws from time evolution

abstract:
  We establish a general scaling law for the entanglement of a large class of
ground states and dynamically evolving states of quantum spin chains: we show
that the geometric entropy of a distinguished block saturates, and hence
follows an entanglement-boundary law. These results apply to any ground state
of a gapped model resulting from dynamics generated by a local hamiltonian, as
well as, dually, to states that are generated via a sudden quench of an
interaction as recently studied in the case of dynamics of quantum phase
transitions. We achieve these results by exploiting ideas from quantum
information theory and making use of the powerful tools provided by
Lieb-Robinson bounds. We also show that there exist noncritical fermionic
systems and equivalent spin chains with rapidly decaying interactions whose
geometric entropy scales logarithmically with block length. Implications for
the classical simulatability are outlined.

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


title: Fast rate estimation of an unitary operation in SU(d)

abstract:
  We give an explicit procedure based on entangled input states for estimating
a $SU(d)$ operation $U$ with rate of convergence $1/N^2$ when sending $N$
particles through the device. We prove that this rate is optimal. We also
evaluate the constant $C$ such that the asymptotic risk is $C/N^2$. However
other strategies might yield a better const ant $C$.


title:
Accurate quantum state estimation via "Keeping the experimentalist
  honest"

abstract:
  In this article, we derive a unique procedure for quantum state estimation
from a simple, self-evident principle: an experimentalist's estimate of the
quantum state generated by an apparatus should be constrained by honesty. A
skeptical observer should subject the estimate to a test that guarantees that a
self-interested experimentalist will report the true state as accurately as
possible. We also find a non-asymptotic, operational interpretation of the
quantum relative entropy function.


title: Clean positive operator valued measures for qubits and similar cases

abstract:
  In a recent paper, Buscemi and al. defined a notion of clean positive
operator valued measures (POVMs). We here characterize which POVMs are clean in
some class that we call quasi-qubit POVMs, namely POVMs whose elements are all
rank-one or full-rank. We give an algorithm to check whether a given
quasi-qubit POVM satisfies to this condition. We describe explicitely all the
POVMs that are clean for the qubit. On the way we give a sufficient condition
for a general POVM to be clean.


title: Methods for scalable optical quantum computation

abstract:
  We propose a scalable method for implementing linear optics quantum
computation using the ``linked-state'' approach. Our method avoids the
two-dimensional spread of errors occurring in the preparation of the
linked-state. Consequently, a proof is given for the scalability of this
modified linked-state model, and an exact expression for the efficiency of the
method is obtained. Moreover, a considerable improvement in the efficiency,
relative to the original linked-state method, is achieved. The proposed method
is applicable to Nielsen's optical ``cluster-state'' approach as well.


title: Universal optical amplification without nonlinearity

abstract:
  We propose and experimentally realize a new scheme for universal
phase-insensitive optical amplification. The presented scheme relies only on
linear optics and homodyne detection, thus circumventing the need for nonlinear
interaction between a pump field and the signal field. The amplifier
demonstrates near optimal quantum noise limited performance for a wide range of
amplification factors.


title: Lateral Casimir force beyond the Proximity Force Approximation

abstract:
  We argue that the appropriate variable to study a non trivial geometry
dependence of the Casimir force is the lateral component of the Casimir force,
which we evaluate between two corrugated metallic plates outside the validity
of the Proximity Force Approximation (PFA). The metallic plates are described
by the plasma model, with arbitrary values for the plasma wavelength, the plate
separation and the corrugation period, the corrugation amplitude remaining the
smallest length scale. Our analysis shows that in realistic experimental
situations the Proximity Force Approximation overestimates the force by up to
30%.


title:
Lieb-Robinson bounds and the generation of correlations and topological
  quantum order

abstract:
  The Lieb-Robinson bound states that local Hamiltonian evolution in
nonrelativistic quantum mechanical theories gives rise to the notion of an
effective light-cone with exponentially decaying tails. We discuss several
consequences of this result in the context of quantum information theory.
First, we show that the information that leaks out to space-like separated
regions is negligable, and that there is a finite speed at which correlations
and entanglement can be distributed. Second, we discuss how these ideas can be
used to prove lower bounds on the time it takes to convert states without
topological quantum order to states with that property. Finally, we show that
the rate at which entropy can be created in a block of spins scales like the
boundary of that block.


title: The Real Exact Solutions to the Hyperbolic Scarf Potential

abstract:
  The exact solutions of the Schrodinger equation with the hyperbolic Scarf
potential reported in the literature so far rely upon Jacobi polynomials with
imaginary arguments and parameters. We here show that upon a suitable
factorization these solutions can be expressed alternatively by means of real
orthogonal polynomials distinct but the classical ones as they satisfy a new
self-adjoint differential equation of the hypergeometric type.


title: Levinson theorem for Aharonov-Bohm scattering in two dimensions

abstract:
  We apply the recently generalized Levinson theorem for potentials with
inverse square singularities [Sheka et al, Phys.Rev.A, v.68, 012707 (2003)] to
Aharonov-Bohm systems in two-dimensions. By this theorem, the number of bound
states in a given m-th partial wave is related to the phase shift and the
magnetic flux. The results are applied to 2D soliton-magnon scattering.


title: Characterization of Quantum Entangled States and Information Measures

abstract:
  The present Thesis covers the subject of the characterization of entangled
states by recourse to entropic measures, as well as the description of
entanglement related to several issues in quantum mechanics, such as the speed
of a quantum evolution or the connections existing between quantum entanglement
and quantum phase transitions.


title:
On decoherence of electromagnetically-induced transparency in atomic
  vapor

abstract:
  We report characterization of electromagnetically induced transparency (EIT)
resonances in the D1 line of Rb-87 under various experimental conditions. The
dependence of the EIT linewidth on the power of the pump field was
investigated, at various temperatures, for the ground states of the
lambda-system associated with different hyperfine levels of the atomic 5S_1/2
state as well as magnetic sublevels of the same hyperfine level. Strictly
linear behavior was observed in all cases. A theoretical analysis of our
results shows that dephasing in the ground state is the main source of
decoherence, with population exchange playing a minor role.


title: Experimental Polarization State Tomography using Optimal Polarimeters

abstract:
  We report on the experimental implementation of a polarimeter based on a
scheme known to be optimal for obtaining the polarization vector of ensembles
of spin-1/2 quantum systems, and the alignment procedure for this polarimeter
is discussed. We also show how to use this polarimeter to estimate the
polarization state for identically prepared ensembles of single photons and
photon pairs and extend the method to obtain the density matrix for generic
multi-photon states. State reconstruction and performance of the polarimeter is
illustrated by actual measurements on identically prepared ensembles of single
photons and polarization entangled photon pairs.


title: General pure multipartite entangled states and the Segre variety

abstract:
  In this paper, we construct a measure of entanglement by generalizing the
quadric polynomial of the Segre variety for general multipartite states. We
give explicit expressions for general pure three-partite and four-partite
states. Moreover, we will discuss and compare this measure of entanglement with
the generalized concurrence.


title:
Comment on "Effects of spatial dispersion on electromagnetic surface
  modes and on modes associated with a gap between two half spaces"

abstract:
  Recently Bo E. Sernelius [Phys. Rev. B {\bf 71}, 235114 (2005)] investigated
the effects of spatial dispersion on the thermal Casimir force between two
metal half spaces. He claims that incorporating spatial dispersion results in a
negligible contribution from the transverse electric mode at zero frequency as
compared to the transverse magnetic mode. We demonstrate that this conclusion
is not reliable because, when applied to the Casimir effect, the approximate
description of spatial dispersion used is unjustified.


title:
Adiabatic Mach-Zehnder Interferometry on A Quantized Bose-Josephson
  Junction

abstract:
  We propose a scheme to achieve a Mach-Zehnder interferometry using a
quantized Bose-Josephson junction with negative charging energy. The quantum
adiabatic evolution through a dynamical bifurcation is used to accomplish the
beam splitting and recombination. The negative charging energy ensures the
existence of a path-entangled state which enhances the phase measurement
precision to the Heisenberg limit. A feasible detection procedure is also
presented. The scheme should be realizable with current technology.


title:
Error tolerance and tradeoffs in loss- and failure-tolerant quantum
  computing schemes

abstract:
  Qubit loss and gate failure are significant problems for the development of
scalable quantum computing. Recently various schemes have been proposed for
tolerating qubit loss and gate failure. These include schemes based on cluster
and parity states. We show that by designing such schemes specifically to
tolerate these error types we cause an exponential blow-out in depolarizing
noise. We discuss several examples and propose techniques for minimizing this
problem. In general this introduces a tradeoff with other undesirable effects.
In some cases this is physical resource requirements, while in others it is
noise rates.


title: Spin Networks and Anyonic Topological Computing

abstract:
  We review the q-deformed spin network approact to Topological Quantum Field
Theory and apply these methods to produce unitary representations of the braid
groups that are dense in the unitary groups. These methods produce a concise
proof that quantum computation can be performed within a single representation
of the Artin Braid Group.


title: Quantum Algorithms with Fixed Points: The Case of Database Search

abstract:
  The standard quantum search algorithm lacks a feature, enjoyed by many
classical algorithms, of having a fixed-point, i.e. a monotonic convergence
towards the solution. Here we present two variations of the quantum search
algorithm, which get around this limitation. The first replaces selective
inversions in the algorithm by selective phase shifts of $\frac{\pi}{3}$. The
second controls the selective inversion operations using two ancilla qubits,
and irreversible measurement operations on the ancilla qubits drive the
starting state towards the target state. Using $q$ oracle queries, these
variations reduce the probability of finding a non-target state from $\epsilon$
to $\epsilon^{2q+1}$, which is asymptotically optimal. Similar ideas can lead
to robust quantum algorithms, and provide conceptually new schemes for error
correction.


title: One-dimensional models of disordered quantum wires: general formalism

abstract:
  In this work we describe, compile and generalize a set of tools that can be
used to analyse the electronic properties (distribution of states, nature of
states, ...) of one-dimensional disordered compositions of potentials. In
particular, we derive an ensemble of universal functional equations which
characterize the thermodynamic limit of all one-dimensional models and which
only depend formally on the distributions that define the disorder. The
equations are useful to obtain relevant quantities of the system such as
density of states or localization length in the thermodynamic limit.


title:
Quantum particles trapped in a position-dependent mass barrier; a
  d-dimensional recipe

abstract:
  We consider a free particle,V(r)=0, with position-dependent mass
m(r)=1/(1+zeta^2*r^2)^2 in the d-dimensional schrodinger equation. The
effective potential turns out to be a generalized Poschl-Teller potential that
admits exact solution.


title: Interaction in Quantum Communication

abstract:
  In some scenarios there are ways of conveying information with many fewer,
even exponentially fewer, qubits than possible classically. Moreover, some of
these methods have a very simple structure--they involve only few message
exchanges between the communicating parties. It is therefore natural to ask
whether every classical protocol may be transformed to a ``simpler'' quantum
protocol--one that has similar efficiency, but uses fewer message exchanges.
  We show that for any constant k, there is a problem such that its k+1 message
classical communication complexity is exponentially smaller than its k message
quantum communication complexity. This, in particular, proves a round hierarchy
theorem for quantum communication complexity, and implies, via a simple
reduction, an Omega(N^{1/k}) lower bound for k message quantum protocols for
Set Disjointness for constant k.
  Enroute, we prove information-theoretic lemmas, and define a related measure
of correlation, the informational distance, that we believe may be of
significance in other contexts as well.


title: Sure success partial search

abstract:
  Partial search has been proposed recently for finding the target block
containing a target element with fewer queries than the full Grover search
algorithm which can locate the target precisely. Since such partial searches
will likely be used as subroutines for larger algorithms their success rate is
important. We propose a partial search algorithm which achieves success with
unit probability.


title:
The ground state of a class of noncritical 1D quantum spin systems can
  be approximated efficiently

abstract:
  We study families H_n of 1D quantum spin systems, where n is the number of
spins, which have a spectral gap \Delta E between the ground-state and
first-excited state energy that scales, asymptotically, as a constant in n. We
show that if the ground state |\Omega_m> of the hamiltonian H_m on m spins,
where m is an O(1) constant, is locally the same as the ground state
|\Omega_n>, for arbitrarily large n, then an arbitrarily good approximation to
the ground state of H_n can be stored efficiently for all n. We formulate a
conjecture that, if true, would imply our result applies to all noncritical 1D
spin systems. We also include an appendix on quasi-adiabatic evolutions.


title:
Theoretical analysis of the implementation of a quantum phase gate with
  neutral atoms on atom chips

abstract:
  We present a detailed, realistic analysis of the implementation of a proposal
for a quantum phase gate based on atomic vibrational states, specializing it to
neutral rubidium atoms on atom chips. We show how to create a double--well
potential with static currents on the atom chips, using for all relevant
parameters values that are achieved with present technology. The potential
barrier between the two wells can be modified by varying the currents in order
to realize a quantum phase gate for qubit states encoded in the atomic external
degree of freedom. The gate performance is analyzed through numerical
simulations; the operation time is ~10 ms with a performance fidelity above
99.9%. For storage of the state between the operations the qubit state can be
transferred efficiently via Raman transitions to two hyperfine states, where
its decoherence is strongly inhibited. In addition we discuss the limits
imposed by the proximity of the surface to the gate fidelity.


title:
Investigation of Continuous-Time Quantum Walk Via Modules of Bose-Mesner
  and Terwilliger Algebras

abstract:
  The continuous-time quantum walk on the underlying graphs of association
schemes have been studied, via the algebraic combinatorics structures of
association schemes, namely semi-simple modules of their Bose-Mesner and
(reference state dependent) Terwilliger algebras. By choosing the (walk)
starting site as a reference state, the Terwilliger algebra connected with this
choice turns the graph into the metric space, hence stratifies the graph into a
(d+1) disjoint union of strata, where the amplitudes of observing the
continuous-time quantum walk on all sites belonging to a given stratum are the
same. In graphs of association schemes with known spectrum, the transition
amplitudes and average probabilities are given in terms of dual eigenvalues of
association schemes. As most of association schemes arise from finite groups,
hence the continuous-time walk on generic group association schemes have been
studied in great details, where the transition amplitudes are given in terms of
characters of groups. Further investigated examples are the walk on graphs of
association schemes of symmetric $S_n$, Dihedral $D_{2m}$ and cyclic groups.
Also, following Ref.\cite{js}, the spectral distributions connected to the
highest irreducible representations of Terwilliger algebras of some rather
important graphs, namely distance regular graphs, have been presented. Then
using spectral distribution, the amplitudes of continuous-time quantum walk on
graphs such as cycle graph $C_n$, Johnson and normal subgroup graphs have been
evaluated. {\bf Keywords: Continuous-time quantum walk, Association scheme,
Bose-Mesner algebra, Terwilliger algebra, Spectral distribution, Distance
regular graph.} {\bf PACs Index: 03.65.Ud}


title: Is Grover's Algorithm a Quantum Hidden Subgroup Algorithm ?

abstract:
  The arguments given in this paper suggest that Grover's and Shor's algorithms
are more closely related than one might at first expect. Specifically, we show
that Grover's algorithm can be viewed as a quantum algorithm which solves a
non-abelian hidden subgroup problem (HSP). But we then go on to show that the
standard non-abelian quantum hidden subgroup (QHS) algorithm can not find a
solution to this particular HSP.
  This leaves open the question as to whether or not there is some modification
of the standard non-abelian QHS algorithm which is equivalent to Grover's
algorithm.


title: Single Photon Source Using Laser Pulses and Two-Photon Absorption

abstract:
  We have previously shown that two-photon absorption (TPA) and the quantum
Zeno effect can be used to make deterministic quantum logic devices from an
otherwise linear optical system. Here we show that this type of quantum Zeno
gate can be used with additional two-photon absorbing media and weak laser
pulses to make a heralded single photon source. A source of this kind is
expected to have a number of practical advantages that make it well suited for
large scale quantum information processing applications.