title: Quantum mechanics as a theory of probability

abstract:
  We develop and defend the thesis that the Hilbert space formalism of quantum
mechanics is a new theory of probability. The theory, like its classical
counterpart, consists of an algebra of events, and the probability measures
defined on it. The construction proceeds in the following steps: (a) Axioms for
the algebra of events are introduced following Birkhoff and von Neumann. All
axioms, except the one that expresses the uncertainty principle, are shared
with the classical event space. The only models for the set of axioms are
lattices of subspaces of inner product spaces over a field K. (b) Another axiom
due to Soler forces K to be the field of real, or complex numbers, or the
quaternions. We suggest a probabilistic reading of Soler's axiom. (c) Gleason's
theorem fully characterizes the probability measures on the algebra of events,
so that Born's rule is derived. (d) Gleason's theorem is equivalent to the
existence of a certain finite set of rays, with a particular orthogonality
graph (Wondergraph). Consequently, all aspects of quantum probability can be
derived from rational probability assignments to finite "quantum gambles". We
apply the approach to the analysis of entanglement, Bell inequalities, and the
quantum theory of macroscopic objects. We also discuss the relation of the
present approach to quantum logic, realism and truth, and the measurement
problem.


title: Hashing protocol for distilling multipartite CSS states

abstract:
  We present a hashing protocol for distilling multipartite CSS states by means
of local Clifford operations, Pauli measurements and classical communication.
It is shown that this hashing protocol outperforms previous versions by
exploiting information theory to a full extent an not only applying CNOTs as
local Clifford operations. Using the information-theoretical notion of a
strongly typical set, we calculate the asymptotic yield of the protocol as the
solution of a linear programming problem.


title: Experimental realization of a minimal disturbance quantum measurement

abstract:
  We report the first experimental realization of an ''optimal'' quantum device
able to perform a Minimal Disturbance Measurement (MDM) on polarization encoded
qubits saturating the theoretical boundary established between the classical
knowledge acquired of any input state, i.e. the classical "guess", and the
fidelity of the same state after disturbance due to measurement . The device
has been physically realized by means of a linear optical qubit manipulation,
post-selection measurement and a classical feed-forward process.


title:
Quantization and Asymptotic Behaviour of $\epsilon_{V^{k}}$ Quantum
  Random Walk on Integers

abstract:
  Quantization and asymptotic behaviour of a variant of discrete random walk on
integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the
novel feature that it uses many identical quantum coins keeping at the same
time characteristic quantum features like the quadratically faster than the
classical spreading rate, and unexpected distribution cutoffs. A weak limit of
the position probability distribution (pd) is obtained, and universal
properties of this arch sine asymptotic distribution function are examined.
Questions of driving the walk are investigated by means of a quantum optical
interaction model that reveals robustness of quantum features of walker's
asymptotic pd, against stimulated and spontaneous quantum noise on the coin
system.


title: Single-passage read-out of atomic quantum memory

abstract:
  A scheme for retrieving quantum information stored in collective atomic spin
systems onto optical pulses is presented. Two off-resonant light pulses cross
the atomic medium in two orthogonal directions and are interferometrically
recombined in such a way that one of the outputs carries most of the
information stored in the medium. In contrast to previous schemes our approach
requires neither multiple passes through the medium nor feedback on the light
after passing the sample which makes the scheme very efficient. The price for
that is some added noise which is however small enough for the method to beat
the classical limits.


title: Electron dynamics in parallel electric and magnetic fields

abstract:
  We examine the spatial distribution of electrons generated by a fixed energy
point source in uniform, parallel electric and magnetic fields. This problem is
simple enough to permit analytic quantum and semiclassical solution, and it
harbors a rich set of features which find their interpretation in the unusual
and interesting properties of the classical motion of the electrons: For
instance, the number of interfering trajectories can be adjusted in this
system, and the turning surfaces of classical motion contain a complex array of
singularities. We perform a comprehensive analysis of both the semiclassical
approximation and the quantum solution, and we make predictions that should
serve as a guide for future photodetachment experiments.


title: Bell's Theorem Reexamined

abstract:
  An Einstein-Podolsky-Rosen (EPR)-like argument using events separated by a
time-like interval strongly suggestes that measuring the polarization state of
a photon of an entangled pair changes the polarization state of the other
distant photon. Trough a very simple demonstration, the Wigner-D'Espagnat
inequality is used to show that in order to prove Bell's theorem neither the
assumption that there is a well-defined space of complete states $\lambda $ of
the particle pair and well-defined probability distribution $\rho (\lambda)$
over this space nor the use of counterfactuals is necessary. These results
reinforce the viewpoint that quantum mechanics implicitly presupposes some sort
of nonlocal connection between the particles of an entangled pair. As will
become evident from our discussion, relinquishing realism and/or free will
cannot solve this apparent puzzle.


title: Observables as functions: Antonymous functions

abstract:
  Antonymous functions are real-valued functions on the Stone spectrum of a von
Neumann algebra R. They correspond to the self-adjoint operators in R, which
are interpreted as observables in quantum physics. Antonymous functions turn
out to be generalized Gelfand transforms, related to de Groote's observable
functions.


title:
Coupling curvature to a uniform magnetic field; an analytic and
  numerical study

abstract:
  The Schrodinger equation for an electron near an azimuthally symmetric curved
surface $\Sigma$ in the presence of an arbitrary uniform magnetic field
$\mathbf B$ is developed. A thin layer quantization procedure is implemented to
bring the electron onto $\Sigma$, leading to the well known geometric potential
$V_C \propto h^2-k$ and a second potential that couples $A_N$, the component of
$\mathbf A$ normal to $\Sigma$ to mean surface curvature, as well as a term
dependent on the normal derivative of
  $A_N$ evaluated on $\Sigma$. Numerical results in the form of ground state
energies as a function of the applied field in several orientations are
presented for a toroidal model.


title: Information-disturbance tradeoff in quantum measurements

abstract:
  We present a simple information-disturbance tradeoff relation valid for any
general measurement apparatus: The disturbance between input and output states
is lower bounded by the information the apparatus provides in distinguishing
these two states.


title: Manipulating quantum information by propagation

abstract:
  We study creation of bi- and multipartite continuous variable entanglement in
structures of coupled quantum harmonic oscillators. By adjusting the
interaction strengths between nearest neighbors we show how to maximize the
entanglement production between the arms in a Y-shaped structure where an
initial single mode squeezed state is created in the first oscillator of the
input arm. We also consider the action of the same structure as an approximate
quantum cloner. For a specific time in the system dynamics the last oscillators
in the output arms can be considered as imperfect copies of the initial state.
By increasing the number of arms in the structure, multipartite entanglement is
obtained, as well as 1 to M cloning. Finally, we are considering configurations
that implement the symmetric splitting of an initial entangled state. All
calculations are carried out within the framework of the rotating wave
approximation in quantum optics, and our predictions could be tested with
current available experimental techniques.


title:
Fine grading of $sl(p^2,\mathbb{C})$ generated by tensor product of
  generalized Pauli matrices and its symmetries

abstract:
  Study of the normalizer of the MAD-group corresponding to a finegrading
offers the most important tool for describing symmetries in the system of
non-linear equations connected with contraction of a Lie algebra. One fine
grading that is always present in any Lie algebra $sl(n,\mathbb{C})$ is the
Pauli grading. The MAD-group corresponding to it is generated by generalized
Pauli matrices. For such MAD-group, we already know its normalizer; its
quotient group is isomorphic to the Lie group $Sl(2,\mathbb{Z}_n)\times
v\mathbb{Z}_2$.
  In this paper, we deal with a more complicated situation, namely that the
fine grading of $sl(p^2, \mathbb{C})$ is given by a tensor product of the Pauli
matrices of the same order $p$, $p$ being a prime. We describe the normalizer
of the corresponding MAD-group and we show that its quotient group is
isomorphic to $Sp(4,\mathbb{Z}_p)\times\mathbb{Z}_2$.


title: Error Analysis For Encoding A Qubit In An Oscillator

abstract:
  In the paper titled "Encoding A Qubit In An Oscillator" Gottesman, Kitaev,
and Preskill [quant-ph/0008040] described a method to encode a qubit in the
continuous Hilbert space of an oscillator's position and momentum variables.
This encoding provides a natural error correction scheme that can correct
errors due to small shifts of the position or momentum wave functions (i.e.,
use of the displacement operator). We present bounds on the size of correctable
shift errors when both qubit and ancilla states may contain errors. We then use
these bounds to constrain the quality of input qubit and ancilla states.


title: Multiplayer quantum Minority game with decoherence

abstract:
  A quantum version of the Minority game for an arbitrary number of agents is
considered. It is known that when the number of agents is odd, quantizing the
game produces no advantage to the players, but for an even number of agents new
Nash equilibria appear that have no classical analogue and have improved
payoffs. We study the effect on the Nash equilibrium payoff of various forms of
decoherence. As the number of players increases the multipartite GHZ state
becomes increasingly fragile, as indicated by the smaller error probability
required to reduce the Nash equilibrium payoff to the classical level.


title: Quantum state swapping via qubit network with Hubbard interaction

abstract:
  We study the quantum state transfer (QST) in a class of qubit network with
on-site interaction, which is described by the generalized Hubbard model with
engineered couplings. It is proved that the system of two electrons with
opposite spins in this quantum network of $N$ sites can be rigorously reduced
into $N$ one dimensional engineered single Bloch electron models with central
potential barrier. With this observation we find that such system can perform a
perfect QST, the quantum swapping between two distant electrons with opposite
spins. Numerical results show such QST and the resonant-tunnelling for the
optimal on-site interaction strengths.


title: Quantum Cat's Dilemma

abstract:
  We study a quantum version of the sequential game illustrating problems
connected with making rational decisions. We compare the results that the two
models (quantum and classical) yield. In the quantum model intransitivity gains
importance significantly. We argue that the quantum model describes our
spontaneously shown preferences more precisely than the classical model, as
these preferences are often intransitive.


title:
Optical Dipole Trapping beyond Rotating Wave Approximation: The case of
  Large Detuning

abstract:
  We show that the inclusion of counter-rotating terms, usually dropped in
evaluations of interaction of an electric dipole of a two level atom with the
electromagnetic field, leads to significant modifications of trapping potential
in the case of large detuning. The results are shown to be in excellent
numerical agreement with recent experimental findings, for the case of modes of
Laguerre-Gauss spatial profile.


title: Asymptotics of Quantum Random Walk Driven by Optical Cavity

abstract:
  We investigate a novel quantum random walk (QRW) model, possibly useful in
quantum algorithm implementation, that achieves a quadratically faster
diffusion rate compared to its classical counterpart.
  We evaluate its asymptotic behavior expressed in the form of a limit
probability distribution of a double horn shape. Questions of robustness and
control of that limit distribution are addressed by introducing a quantum
optical cavity in which a resonant Jaynes-Cummings type of interaction between
the quantum walk coin system realized in the form of a two-level atom and a
laser field is taking place. Driving the optical cavity by means of the
coin-field interaction time and the initial quantum coin state, we determine
two types of modification of the asymptotic behavior of the QRW. In the first
one the limit distribution is robustly reproduced up to a scaling, while in the
second one the quantum features of the walk, exemplified by enhanced diffusion
rate, are washed out and Gaussian asymptotics prevail. Verification of these
findings in an experimental setup that involves two quantum optical cavities
that implement the driven QRW and its quantum to classical transition is
discussed.


title:
Heralded single-photon generation using imperfect single-photon sources
  and a two-photon-absorbing medium

abstract:
  We propose a setup for a heralded, i.e. announced generation of a pure
single-photon state given two imperfect sources whose outputs are represented
by mixtures of the single-photon Fock state $\ket{1}$ with the vacuum
$\ket{0}$. Our purification scheme uses beam splitters, photodetection and a
two-photon-absorbing medium. The admixture of the vacuum is fully eliminated.
We discuss two potential realizations of the scheme.


title: Control of mixed-state quantum systems by a train of short pulses

abstract:
  A density matrix approach is developped for the control of a mixed-state
quantum system using a time-dependent external field such as a train of pulses.
This leads to the definition of a target density matrix constructed in a
reduced Hilbert space as a specific combination of the eigenvectors of a given
observable through weighting factors related with the initial statistics of the
system. A train of pulses is considered as a possible strategy to reach this
target. An illustration is given by considering the laser control of molecular
alignment / orientation in thermal equilibrium.


title:
A solid-state NMR three-qubit homonuclear system for quantum information
  processing: control and characterization

abstract:
  A three-qubit 13C solid-state nuclear magnetic resonance (NMR) system for
quantum information processing, based on the malonic acid molecule, is used to
demonstrate high-fidelity universal quantum control via strongly-modulating
radio-frequency pulses. This control is achieved in the strong-coupling regime,
in which the timescales of selective qubit addressing and of two-qubit
interactions are comparable.


title: Comment on "Operator Quantum Error Correction"

abstract:
  The attempt to equate operator quantum error correction (quant-ph/0504189v1)
with the quantum computer condition (quant-ph/0507141) in version two of
quant-ph/0504189 is shown to be invalid.


title:
On de Broglie's soliton wave function of many particles with finite
  masses, energies and momenta

abstract:
  We consider a mass-less manifestly covariant {\it linear} Schr\"odinger
equation. First, we show that it possesses a class of non-dispersive soliton
solution with finite-size spatio-temporal support inside which the quantum
amplitude satisfies the Klein-Gordon equation with finite {\it emergent} mass.
We then proceed to interpret the soliton wave function as describing a particle
with finite mass, energy and momentum. Inside the spatio-temporal support, the
wave function shows spatio-temporal internal vibration with angular frequency
and wave number that are determined by the energy-momentum of the particle as
firstly conjectured by de Broglie. Imposing resonance of the internal vibration
inside the spatio-temporal support leads to Planck-Einstein quantization of
energy-momentum. The first resonance mode is shown to recover the classical
energy-momentum relation developed in special relativity. We further show that
the linearity of the Schr\"odinger equation allows one to construct many
solitons solution through superposition, each describing a particle with
various masses, energies and momenta.


title:
Unifying the Construction of Various Types of Generalized Coherent
  States

abstract:
  In this tutorial I intend to present some of the results I obtained through
my PhD work in the "quantum optics group of the University of Isfahan" under
consideration Dr. R. Roknizadeh and Prof. S. Twareque Ali as my supervisor and
advisor, respectively. I will revisit some of the pioneering proposals recently
developed the concept of generalized CSs. As it can be observed the customary
three generalization methods {\it (symmetry, algebraic and dynamical)} have
never been considered in neither of them. Our intention in this work is at
first to investigate the lost ring between the customary three methods and the
recently developed ones, as possible. For this purpose it has been devised
general analytic descriptions, which successfully demonstrate how different
varieties of CSs (which are nonlinear in nature) can be obtained by two
processes, first the {\it "nonlinear CSs"} method and second by {\it "basis
transformations on an underlying Hilbert spaces"}. As a result, I will
systematize the recently introduced generalized CSs in a clear and concise way.
It will be clear also, that how our results can be considered as a first step
in the generation process of the mathematical physics CSs in the context of
quantum optics. Besides this, some new results emerge from our studies. I
introduce a large classes of generalized CSs, namely the {\it "dual family"}
associated with each set of early known CSs. But, in this relation, the
previous processes for constructing the dual pair of Gazeau-Klauder CSs fail to
work well, so I outlined a rather different method based on the {\it "temporal
stability"} requirement of generalized nonlinear CSs.


title: Upper Bound Imposed upon Responsivity of Optical Modulators

abstract:
  We study theoretically the responsivity of optical modulators. For the case
of linear response we find using perturbation theory an upper bound imposed
upon the responsivity. For the case of two mode modulator we find a lower bound
imposed upon the optical path required for achieving full modulation when the
maximum birefringence strength is given.


title: The epistemic view of quantum states and the ether

abstract:
  The idea that the wave function represents information, or knowledge, rather
than the state of a microscopic object has been held to solve foundational
problems of quantum mechanics. Realist interpretation schemes, like Bohmian
trajectories, have been compared to the ether in pre-relativistic theories. I
argue that the comparison is inadequate, and that the epistemic view of quantum
states begs the question of interpretation.


title:
Quantum extension of European option pricing based on the
  Ornstein-Uhlenbeck process

abstract:
  In this work we propose a option pricing model based on the
Ornstein-Uhlenbeck process. It is a new look at the Black-Scholes formula which
is based on the quantum game theory. We show the differences between a
classical look which is price changing by a Wiener process and the pricing is
supported by a quantum model.


title: On the vortex interpretation of Schroedinger's wave equation

abstract:
  There has been a recent tendency to apply Schroedinger's wave equation to
macroscopic domains, from Bose-Einstein condensates in neutron stars to
planetary orbits. In these applications a hydrodynamical interpretation,
involving vortices in some 'fluid' medium is often given. The vortex picture
appears surprising in light of more traditional interpretations of
Schroedinger's equation, and indeed often appears to rely on ad hoc analogies.
The purpose of this letter is to examine the vortex hypothesis in light of a
simple, transparent mathematical framework. We find that Schroedinger's
equation implies waves can be vortices also for a class of wave functions.
Vortices occur in pairs that perform a sort of quantum computation by
collapsing into either 0 or 1. Vortices collapsing to 0 ('0-vortices') are
longer-lived, and their ratio to 1-vortices is discussed.


title:
Uncertainty relations describing the short-term violations of Lorentz
  invariance: superluminal phenomena, particles transformations

abstract:
  The refinement and specifications of time-energy uncertainty relations have
shown that the experimentally observed phenomena of superluminal signaling are
describable by such their form: $\Delta E\Delta\tau\geq\pi\hbar$, where both
standard deviations are negative. When $\Delta\tau<0$, these evanescent photons
would be instantly tunneling from one light cone into another on the distance
$c| \Delta\tau| $. (This assertion, previously proved via dispersion relations,
is described here by the temporal parameters of process.) Special forms of
these relations describe the transmutation of particles into their partners of
bigger mass, in $K^{0}$ and $B^{0}$ cases and at the $\nu$'s transmutations.
Thus, the violations of relativistic causality by evanescent particles can be
considered as the tunneling, as an analog of the short-term violation of
conservation laws at virtual transitions. The absence of Lorentz invariance at
such transitions can, probably, allow violations of some other symmetries.


title: Angular Momentum and Mutually Unbiased Bases

abstract:
  The Lie algebra of the group SU(2) is constructed from two deformed
oscillator algebras for which the deformation parameter is a root of unity.
This leads to an unusual quantization scheme, the {J2,Ur} scheme, an
alternative to the familiar {J2,Jz} quantization scheme corresponding to common
eigenvectors of the Casimir operator J2 and the Cartan operator Jz. A
connection is established between the eigenvectors of the complete set of
commuting operators {J2,Ur} and mutually unbiased bases in spaces of constant
angular momentum.


title: Canonical averaging of the equations of quantum mechanics

abstract:
  The representation of a Schrodinger equations as a classic Hamiltonian system
allows to construct a unified perturbation theory both in classic, and in a
quantum mechanics grounded on the theory of canonical transformations, and also
to receive asymptotic estimations of affinity of the precisian approximated
solutions of Schrodinger equations


title:
Results of the Investigations of the Nature of the Long -Term
  Instability in Quantum Frequency Standards and Magnetometers

abstract:
  The problem analysis results made the author to draw a conclusion that the
nature of the resonance frequency long-term instability and drift at harmonic
excitation is related to the phase dynamics of the "atom + field" system in the
small vicinity of the resonance. The investigation is based on the strictly
substantiated asymptotic Krylov-Bogolyubov perturbation theory. A
time-dependent (drift) first-order correction of the perturbing field amplitude
to the resonance frequency was disclosed. It was found that this correction is
always present and is responsible for the frequency drift and long-term
instability. The necessary and sufficient conditions of accurate resonance, as
well as the conditions of realization of a stable (stationary, steady-state)
drift-free oscillation regime in a quantum system, are obtained.


title: Theory of decoherence due to scattering events and L\'evy processes

abstract:
  A general connection between the characteristic function of a L\'evy process
and loss of coherence of the statistical operator describing the center of mass
degrees of freedom of a quantum system interacting through momentum transfer
events with an environment is established. The relationship with microphysical
models and recent experiments is considered, focusing on the recently observed
transition between a dynamics described by a compound Poisson process and a
Gaussian process.


title: On Algebraic and Quantum Random Walks

abstract:
  Algebraic random walks (ARW) and quantum mechanical random walks (QRW) are
investigated and related. Based on minimal data provided by the underlying
bialgebras of functions defined on e. g the real line R, the abelian finite
group Z_N, and the canonical Heisenberg-Weyl algebra hw, and by introducing
appropriate functionals on those algebras, examples of ARWs are constructed.
These walks involve short and long range transition probabilities as in the
case of R walk, bistochastic matrices as for the case of Z_N walk, or coherent
state vectors as in the case of hw walk. The increase of classical entropy due
to majorization order of those ARWs is shown, and further their corresponding
evolution equations are obtained. Especially for the case of hw ARW, the
diffusion limit of evolution equation leads to a quantum master equation for
the density matrix of a boson system interacting with a bath of quantum
oscillators prepared in squeezed vacuum state. A number of generalizations to
other types of ARWs and some open problems are also stated. Next, QRWs are
briefly presented together with some of their distinctive properties, such as
their enhanced diffusion rates, and their behavior in respect to the relation
of majorization to quantum entropy. Finally, the relation of ARWs to QRWs is
investigated in terms of the theorem of unitary extension of completely
positive trace preserving (CPTP) evolution maps by means of auxiliary vector
spaces. It is applied to extend the CPTP step evolution map of a ARW for a
quantum walker system into a unitary step evolution map for an associated QRW
of a walker+quantum coin system. Examples and extensions are provided.


title:
The effects of nonlinear couplings and external magnetic field on the
  thermal entanglement in a two-spin-qutrit system

abstract:
  We investigate the effects of nonlinear couplings and external magnetic field
on the thermal entanglement in a two-spin-qutrit system by applying the concept
of negativity. It is found that the nonlinear couplings favor the thermal
entanglement creating. Only when the nonlinear couplings $|K|$ are larger than
a certain critical value does the entanglement exist. The dependence of the
thermal entanglement in this system on the magnetic field and temperature is
also presented. The critical magnetic field increases with the increasing
nonlinear couplings constant $|K|$. And for a fixed nonlinear couplings
constant, the critical temperature is independent of the magnetic field $B$.


title: Teleportation from a Projection Operator Point of View

abstract:
  The process of quantum state teleportation is described from the point of
view of the properties of projections onto one-dimensional subspaces. It is
introduced as a generalization of the remote preparation of a known state by
use of an EPR pair. The discrete and continuous cases are treated in a unified
way. The conceptual and calculational simplicity is pedagogically advantageous.


title: Is the Adiabatic Approximation Inconsistent?

abstract:
  Marzlin and Sanders \cite{marzlin} have shown rigorously that the adiabatic
approximation can be very inaccurate when applied to a Hamiltonian $H(t)$ that
generates the evolution $U^{\dagger} (t)$ even if it gives an excellent
approximation to the evolution $U(t)$ generated by a dual Hamiltonian $h(t)$.
We show that this is not inconsistent with the adiabatic theorem and find that
in general even if $h(t)$ satisfies the conditions of the adiabatic theorem,
$H(t)$ will likely violate those conditions.


title: Entanglement quantifiers and phase transitions

abstract:
  By the topological argument that the identity matrix is surrounded by a set
of separable states follows the result that if a system is entangled at thermal
equilibrium for some temperature, then it presents a phase transition (PT)
where entanglement can be viewed as the order parameter. However, analyzing
different entanglement measures in the 2-qubit context, we see that different
entanglement quantifiers can indicate different orders for the same PT.
Examples are given for different Hamiltonians. Moving to the multipartite
context we show necessary and sufficient conditions for a family of
entanglement monotones to attest quantum phase transitions.


title:
Infinitesimal change is a Non-local Operation: Hidden power of Quantum
  Entanglement

abstract:
  We show that the global infinitesimal change in the multi-particle pure
product state gives rise to an entangled state. This suggests that even if
there is no interaction present between the subsystems, i.e., at each time
instant the state is non-entangled, the tangent vector is typically entangled.
Since the tangent space vectors tell the state-space vectors how to change this
implies that quantum entanglement is necessary for motion or change in general.
This is truly a `hidden power' of quantum entanglement. During quantum
computation even though at each time instant the state is not entangled,
quantum entanglement guides the process of computation. This observation
applies to multi-particle pure, pseudo-pure and mixed states as well.


title: The vacuum electromagnetic fields and the Schrodinger picture

abstract:
  Several authors have used the Heisenberg picture to show that the atomic
transitions, the stability of the ground state and the position-momentum
commutation relation [x,p]=ih, can only be explained by introducing radiation
reaction and vacuum electromagnetic fluctuation forces. Here we consider the
simple case of a nonrelativistic charged harmonic oscillator, in one dimension,
to investigate how to take into account the radiation reaction and vacuum
fluctuation forces within the Schrodinger picture. We consider the effects of
both classical zero-point and thermal electromagnetic vacuum fields. We show
that the zero-point electromagnetic fluctuations are dynamically related to the
momentum operator p=-ih d/dx used in the Schrodinger picture. Consequently, the
introduction of the zero-point electromagnetic fields in the vector potential
A_x(t) used in the Schrodinger equation, generates ``double counting'', as was
shown recently by A.J. Faria et al. (Physics Letters A 305 (2002) 322). We
explain, in details, how to avoid the ``double counting'' by introducing only
the radiation reaction and the thermal electromagnetic fields into the
Schrodinger equation.


title: A fault-tolerant one-way quantum computer

abstract:
  We describe a fault-tolerant one-way quantum computer on cluster states in
three dimensions. The presented scheme uses methods of topological error
correction resulting from a link between cluster states and surface codes. The
error threshold is 1.4% for local depolarizing error and 0.11% for each source
in an error model with preparation-, gate-, storage- and measurement errors.


title: Hitting time for quantum walks on the hypercube

abstract:
  Hitting times for discrete quantum walks on graphs give an average time
before the walk reaches an ending condition. To be analogous to the hitting
time for a classical walk, the quantum hitting time must involve repeated
measurements as well as unitary evolution. We derive an expression for hitting
time using superoperators, and numerically evaluate it for the discrete walk on
the hypercube. The values found are compared to other analogues of hitting time
suggested in earlier work. The dependence of hitting times on the type of
unitary ``coin'' is examined, and we give an example of an initial state and
coin which gives an infinite hitting time for a quantum walk. Such infinite
hitting times require destructive interference, and are not observed
classically. Finally, we look at distortions of the hypercube, and observe that
a loss of symmetry in the hypercube increases the hitting time. Symmetry seems
to play an important role in both dramatic speed-ups and slow-downs of quantum
walks.


title: Quantum Separability of Thermal Spin One Boson Systems

abstract:
  Using the temperature Green's function approach we investigate entanglement
between two non-interacting spin 1 bosons in thermal equilibrium. We show that,
contrary to the fermion case, the entanglement is absent in the spin density
matrix. Separability is demonstrated using the Peres-Horodecki criterion for
massless particles such as photons in black body radiation. For massive
particles, we show that the density matrix can be decomposed with separable
states.


title: Deficient Mathematical Models of Quantum Theory

abstract:
  The lack of the Max Born interpretation of the wave function as a probability
density describing the localization of a quantum system in configuration space
is pointed out related to the recent category based model of quantum mechanics
suggested in Abramski & Coecke [1,2] and Coecke.


title: Scheme for implementing the Deutsch-Jozsa algorithm via atomic ensembles

abstract:
  We propose a physical scheme for implementing the Deutsch-Jozsa algorithm
using atomic ensembles and optical devices. The scheme has inherent fault
tolerance to the realistic noise and efficient scaling with the number of
ensembles for some entangled states within the reach of current technology. It
would be an important step toward more complex quantum computation via atomic
ensembles.


title:
Region Operators of Wigner Function: Transformations, Realizations and
  Bounds

abstract:
  An integral of the Wigner function of a wavefunction |psi >, over some region
S in classical phase space is identified as a (quasi) probability measure (QPM)
of S, and it can be expressed by the |psi > average of an operator referred to
as the region operator (RO). Transformation theory is developed which provides
the RO for various phase space regions such as point, line, segment, disk and
rectangle, and where all those ROs are shown to be interconnected by completely
positive trace increasing maps. The latter are realized by means of unitary
operators in Fock space extended by 2D vector spaces, physically identified
with finite dimensional systems. Bounds on QPMs for regions obtained by tiling
with discs and rectangles are obtained by means of majorization theory.


title:
Possibility of Inhomogeneous Coupling Leading to Decoherence in an
  Electromagnetically-Induced-Transparency Quantum-Memory Process

abstract:
  The effect of inhomogeneous coupling between three-level atoms and external
light fields is studied in the electromagnetically induced transparency (EIT)
quantum memory techqnique. By introducing a subensemble-atomic system to deal
with present inhomogeneous coupling case, we find there is a non-symmetric
dark-state subspace (DSS) that allows the EIT quantum memory technique to
function perfectly. This shows that such memory scheme can work ideally even if
the atomic state is very far from being a symmetric one.


title:
Entanglement-assisted local transformations between inequivalent classes
  of three-particle entangled states

abstract:
  We show that bipartite and tripartite entangled states cannot be used as
catalysis states to enable local transformations inbetween inequivalent classes
of three-particle entangled states which are non-interchangeable under local
transformations. We find the optimal protocol for conversion of a certain
family of the W-states and an EPR-pair into the GHZ-state.


title:
Broadcasting of entanglement at a distance using linear optics and
  telecloning of entanglement

abstract:
  We propose a scheme for broadcasting entanglement at a distance based on
linear optics. We show that an initial polarization entangled state can be
simultaneously split and transmitted to a pair of observers situated at
different locations with the help of two conditional Bell-state analyzers based
on two beam splitters characterized by the same reflectivity R. In particular
for R=1/3 the final states coincide with the output states obtained by the
broadcasting protocol proposed by Buzek et al. [Phys. Rev. A 55, 3327 (1997)].
Further we present a different protocol called telecloning of entanglement,
which combines the many-to-many teleportation and nonlocal optimal asymmetric
cloning of an arbitrary entangled state. This scheme allows the optimal
transmission of the two nonlocal optimal clones of an entangled state to two
pairs of spatially separated receivers.


title: Quantum Authentication and Quantum Key Distribution Protocol

abstract:
  We propose a quantum key distribution protocol with quantum based user
authentication. Our protocol is the first one in which users can authenticate
each other without previously shared secret and then securely distribute a key
where the key may not be exposed to even a trusted third party. The security of
our protocol is guaranteed by the properties of the entanglement.


title: Complementarity and additivity for depolarizing channels

abstract:
  In this paper we use the method of a recent paper (quant-ph/0509101) to
compute complementary channels for certain important cases, such as
depolarizing and transpose-depolarizing channels. This method allows us to
easily obtain the minimal Kraus representations from non--minimal ones. We also
study the properties of the output purity of the tensor product of a channel
and its complement.


title:
Quantum Analogical Modeling: A General Quantum Computing Algorithm for
  Predicting Language Behavior

abstract:
  This paper proposes a general quantum algorithm that can be applied to any
classical computer program. Each computational step is written using reversible
operators, but the operators remain classical in that the qubits take on values
of only zero and one. This classical restriction on the quantum states allows
the copying of qubits, a necessary requirement for doing general classical
computation. Parallel processing of the quantum algorithm proceeds because of
the superpositioning of qubits, the only aspect of the algorithm that is
strictly quantum mechanical. Measurement of the system collapses the
superposition, leaving only one state that can be observed. In most instances,
the loss of information as a result of measurement would be unacceptable. But
the linguistically motivated theory of Analogical Modeling (AM) proposes that
the probabilistic nature of language behavior can be accurately modeled in
terms of the simultaneous analysis of all possible contexts (referred to as
supracontexts) providing one selects a single supracontext from those
supracontexts that are homogeneous in behavior (namely, supracontexts that
allow no increase in uncertainty). The amplitude for each homogeneous
supracontext is proportional to its frequency of occurrence, with the result
that the probability of selecting one particular supracontext to predict the
behavior of the system is proportional to the square of its frequency.


title: Optimal quantum cloning via spin networks

abstract:
  In this paper we present an approach to quantum cloning via free dynamical
evolution of spin networks. By properly designing the network and the couplings
between spins, we show that optimal 1->M phase covariant cloning can be
achieved without any external control. Especially, when M is an odd number, the
optimal phase-covariant cloning can be achieved without ancillas. Moreover, we
demonstrate that the same framework is capable for optimal 1->2 universal
cloning.


title: On Weyl-covariant channels

abstract:
  Formalism of discrete noncommutative Fourier transform is developed and
applied to the study of Weyl-covariant channels. We then extend a result in
quant-ph/0509126 concerning a bound of the maximal output 2-norm of a
Weyl-covariant channel. A class of channels which attain the bound is
introduced, for which the multiplicativity of the maximal output 2-norm is
proven. Complementary channels are described which share the multiplicativity
properties with the Weyl-covariant channels.


title:
Correlated Photons from Collective Excitations of Three-Level Atomic
  Ensemble

abstract:
  We systematically study the interaction between two quantized optical fields
and a cyclic atomic ensemble driven by a classic optical field. This so-called
atomic cyclic ensemble consists of three-level atoms with Delta-type
transitions due to the symmetry breaking, which can also be implemented in the
superconducting quantum circuit by Yu-xi Liu et al. [Phys. Rev. Lett. 95,
087001 (2005)]. We explore the dynamic mechanisms to creating the quantum
entanglements among photon states, and between photons and atomic collective
excitations by the coherent manipulation of the atom-photon system. It is shown
that the quantum information can be completely transferred from one quantized
optical mode to another, and the quantum information carried by the two
quantized optical fields can be stored in the collective modes of this atomic
ensemble by adiabatically controlling the classic field Rabi frequencies.


title: The damped harmonic oscillator in deformation quantization

abstract:
  We propose a new approach to the quantization of the damped harmonic
oscillator in the framework of deformation quantization. The quantization is
performed in the Schr\"{o}dinger picture by a star-product induced by a
modified "Poisson bracket". We determine the eigenstates in the damped regime
and compute the transition probability between states of the undamped harmonic
oscillator after the system was submitted to dissipation.


title:
A phase-space study of the quantum Loschmidt Echo in the semiclassical
  limit

abstract:
  The notion of Loschmidt echo (also called "quantum fidelity") has been
introduced in order to study the (in)-stability of the quantum dynamics under
perturbations of the Hamiltonian. It has been extensively studied in the past
few years in the physics literature, in connection with the problems of
"quantum chaos", quantum computation and decoherence. In this paper, we study
this quantity semiclassically (as $\hbar \to 0$), taking as reference quantum
states the usual coherent states. The latter are known to be well adapted to a
semiclassical analysis, in particular with respect to semiclassical estimates
of their time evolution. For times not larger than the so-called "Ehrenfest
time" $C | \log \hbar |$, we are able to estimate semiclassically the Loschmidt
Echo as a function of $t$ (time), $\hbar$ (Planck constant), and $\delta$ (the
size of the perturbation). The way two classical trajectories merging from the
same point in classical phase-space, fly apart or come close together along the
evolutions governed by the perturbed and unperturbed Hamiltonians play a major
role in this estimate. We also give estimates of the "return probability"
(again on reference states being the coherent states) by the same method, as a
function of $t$ and $\hbar$.


title: Quantum information processing in diamond

abstract:
  Quantum computing is an attractive and multidisciplinary field, which became
a focus for experimental and theoretical research during last decade. Among
other systems, like ions in traps or superconducting circuits, solid-states
based qubits are considered to be promising candidates for first experimental
tests of quantum hardware. Here we report recent progress in quantum
information processing with point defect in diamond. Qubits are defined as
single spin states (electron or nuclear). This allows exploring long coherence
time (up to seconds for nuclear spins at cryogenic temperatures). In addition,
the optical transition between ground and excited electronic states allows
coupling of spin degrees of freedom to the state of the electromagnetic field.
Such coupling gives access to the spin state readout via spin-selective
scattering of photon. This also allows using of spin state as robust memory for
flying qubits (photons).


title: Non separable Werner states in spontaneous parametric down-conversion

abstract:
  The multiphoton states generated by high-gain spontaneous parametric
down-conversion (SPDC) in presence of large losses are investigated
theoretically and experimentally. The explicit form for the two-photon output
state has been found to exhibit a Werner structure very resilient to losses for
any value of the gain parameter, g. The theoretical results are found in
agreement with the experimental data. The last ones are obtained by quantum
tomography of the state generated by a high-gain SPDC.


title: Nonlinear response and observable signatures of equilibrium entanglement

abstract:
  We investigate how equilibrium entanglement is manifested in the nonlinear
response of an $N$-qubit system. We show that in the thermodynamic limit the
irreducible part of the $n$th-order nonlinear susceptibility indicates that the
eigenstates of the system contain entangled $(n+1)$-qubit clusters. This opens
the way to a directly observable multiqubit entanglement signature. We show
that the irreducible part of the static cubic susceptibility of a system of
four flux qubits, as a function of external parameters, behaves as a global
4-qubit entanglement measure introduced in Ref.\cite{Love}.
  We discuss the possibility of extracting purely-entanglement-generated
contribution from the general multipoint correlators in a multiqubit system.


title: Optimal superbroadcasting of mixed qubit states

abstract:
  "Broadcasting", namely distributing information over many users, suffers
in-principle limitations when the information is quantum. This poses a critical
issue in quantum information theory, for distributed processing and networked
communications. For pure states ideal broadcasting coincides with the so-called
"quantum cloning", describing an hypothetical ideal device capable of producing
from a finite number N of copies of a state (drawn from a set) a larger number
M>N of output copies of the same state. Since such a transformation is not
isometric, it cannot be achieved by any physical machine for a quantum state
drawn from a non orthogonal set: this is essentially the content of the
"no-cloning" theorem. For mixed states the situation is quite different, since
from the point of view of each single user a local marginal mixed state is
indistinguishable from the partial trace of an entangled state, and there are
infinitely many joint output states that correspond to ideal broadcasting.
Indeed, for sufficiently large number $N$ of input copies, not only ideal
broadcasting of noncommuting mixed states is possible, but one can even purify
the state in the process. Such state purification with an increasing number of
copies has been named "superbroadcasting". In this paper we will review some
recent results on superbroadcasting of qubits, for two different sets of input
states, corresponding to universally covariant broadcasting and to
phase-covariant broadcasting of equatorial states.


title:
On the meaning and interpretation of Tomography in abstract Hilbert
  spaces

abstract:
  The mechanism of describing quantum states by standard probability
(tomographic one) instead of wave function or density matrix is elucidated.
Quantum tomography is formulated in an abstract Hilbert space framework, by
means of the identity decompositions in the Hilbert space of hermitian linear
operators, with trace formula as scalar product of operators. Decompositions of
identity are considered with respect to over-complete families of projectors
labeled by extra parameters and containing a measure, depending on these
parameters. It plays the role of a Gram-Schmidt orthonormalization kernel. When
the measure is equal to one, the decomposition of identity coincides with a
positive operator valued measure (POVM) decomposition. Examples of spin
tomography, photon number tomography and symplectic tomography are reconsidered
in this new framework.


title: Lyapunov Generation of Entanglement and the Correspondence Principle

abstract:
  We show how a classically vanishing interaction generates entanglement
between two initially nonentangled particles, without affecting their classical
dynamics. For chaotic dynamics, the rate of entanglement is shown to saturate
at the Lyapunov exponent of the classical dynamics as the interaction strength
increases. In the saturation regime, the one-particle Wigner function follows
classical dynamics better and better as one goes deeper and deeper in the
semiclassical limit. This demonstrates that quantum-classical correspondence at
the microscopic level requires neither high temperatures, nor coupling to a
large number of external degrees of freedom.


title: Optimal full estimation of qubit mixed states

abstract:
  We obtain the optimal scheme for estimating unknown qubit mixed states when
an arbitrary number N of identically prepared copies is available. We discuss
the case of states in the whole Bloch sphere as well as the restricted
situation where these states are known to lie on the equatorial plane. For the
former case we obtain that the optimal measurement does not depend on the prior
probability distribution provided it is isotropic. Although the
equatorial-plane case does not have this property for arbitrary N, we give a
prior-independent scheme which becomes optimal in the asymptotic limit of large
N. We compute the maximum mean fidelity in this asymptotic regime for the two
cases. We show that within the pointwise estimation approach these limits can
be obtained in a rather easy and rapid way. This derivation is based on
heuristic arguments that are made rigorous by using van Trees inequalities. The
interrelation between the estimation of the purity and the direction of the
state is also discussed. In the general case we show that they correspond to
independent estimations whereas for the equatorial-plane states this is only
true asymptotically.


title: A Quantitative Measure of Interference

abstract:
  We introduce an interference measure which allows to quantify the amount of
interference present in any physical process that maps an initial density
matrix to a final density matrix. In particular, the interference measure
enables one to monitor the amount of interference generated in each step of a
quantum algorithm. We show that a Hadamard gate acting on a single qubit is a
basic building block for interference generation and realizes one bit of
interference, an ``i-bit''. We use the interference measure to quantify
interference for various examples, including Grover's search algorithm and
Shor's factorization algorithm. We distinguish between ``potentially
available'' and ``actually used'' interference, and show that for both
algorithms the potentially available interference is exponentially large.
However, the amount of interference actually used in Grover's algorithm is only
about 3 i-bits and asymptotically independent of the number of qubits, while
Shor's algorithm indeed uses an exponential amount of interference.


title: Channelization architecture for wide-band slow light in atomic vapors

abstract:
  We propose a ``channelization'' architecture to achieve wide-band
electromagnetically induced transparency (EIT) and ultra-slow light propagation
in atomic Rb-87 vapors. EIT and slow light are achieved by shining a strong,
resonant ``pump'' laser on the atomic medium, which allows slow and
unattenuated propagation of a weaker ``signal'' beam, but only when a
two-photon resonance condition is satisfied. Our wideband architecture is
accomplished by dispersing a wideband signal spatially, transverse to the
propagation direction, prior to entering the atomic cell. When particular
Zeeman sub-levels are used in the EIT system, then one can introduce a magnetic
field with a linear gradient such that the two-photon resonance condition is
satisfied for each individual frequency component. Because slow light is a
group velocity effect, utilizing differential phase shifts across the spectrum
of a light pulse, one must then introduce a slight mismatch from perfect
resonance to induce a delay. We present a model which accounts for diffusion of
the atoms in the varying magnetic field as well as interaction with levels
outside the ideal three-level system on which EIT is based. We find the maximum
delay-bandwidth product decreases with bandwidth, and that delay-bandwidth
product ~1 should be achievable with bandwidth ~50 MHz (~5 ns delay). This is a
large improvement over the ~1 MHz bandwidths in conventional slow light systems
and could be of use in signal processing applications.


title: Approximate programmable quantum processors

abstract:
  A quantum processor is a programmable quantum circuit in which both the data
and the program, which specifies the operation that is carried out on the data,
are quantum states. We study the situation in which we want to use such a
processor to approximate a set of unitary operators to a specified level of
precision. We measure how well an operation is performed by the process
fidelity between the desired operation and the operation produced by the
processor. We show how to find the program for a given processor that produces
the best approximation of a particular unitary operation. We also place bounds
on the dimension of the program space that is necessary to approximate a set of
unitary operators to a specified level of precision.


title: Entanglement dynamics for two interacting spins

abstract:
  We study the dynamical generation of entanglement for a very simple system: a
pair of interacting spins, s1 and s2, in a constant magnetic field. Two
different situations are considered:(a) s1 ->\infty, s2 = 1/2 and (b) s1 = s2
->\infty, corresponding, respectively, to a quantum degree of freedom coupled
to a semiclassical one (a qubit in contact with an environment) and a fully
semiclassical system, which in this case displays chaotic behavior. Relations
between quantum entanglement and classical dynamics are investigated.


title:
Implementing Non-Projective Measurements via Linear Optics: an Approach
  Based on Optimal Quantum State Discrimination

abstract:
  We discuss the problem of implementing generalized measurements (POVMs) with
linear optics, either based upon a static linear array or including conditional
dynamics. In our approach, a given POVM shall be identified as a solution to an
optimization problem for a chosen cost function. We formulate a general
principle: the implementation is only possible if a linear-optics circuit
exists for which the quantum mechanical optimum (minimum) is still attainable
after dephasing the corresponding quantum states. The general principle enables
us, for instance, to derive a set of necessary conditions for the linear-optics
implementation of the POVM that realizes the quantum mechanically optimal
unambiguous discrimination of two pure nonorthogonal states. This extends our
previous results on projection measurements and the exact discrimination of
orthogonal states.


title: Overdamping by weakly coupled environments

abstract:
  A quantum system weakly interacting with a fast environment usually undergoes
a relaxation with complex frequencies whose imaginary parts are damping rates
quadratic in the coupling to the environment, in accord with Fermi's ``Golden
Rule''. We show for various models (spin damped by harmonic-oscillator or
random-matrix baths, quantum diffusion, quantum Brownian motion) that upon
increasing the coupling up to a critical value still small enough to allow for
weak-coupling Markovian master equations, a new relaxation regime can occur. In
that regime, complex frequencies lose their real parts such that the process
becomes overdamped. Our results call into question the standard belief that
overdamping is exclusively a strong coupling feature.


title:
Can optical squeezing be generated via polarization self-rotation in a
  thermal vapour cell?

abstract:
  The traversal of an elliptically polarized optical field through a thermal
vapour cell can give rise to a rotation of its polarization axis. This process,
known as polarization self-rotation (PSR), has been suggested as a mechanism
for producing squeezed light at atomic transition wavelengths. In this paper,
we show results of the characterization of PSR in isotopically enhanced
Rubidium-87 cells, performed in two independent laboratories. We observed that,
contrary to earlier work, the presence of atomic noise in the thermal vapour
overwhelms the observation of squeezing. We present a theory that contains
atomic noise terms and show that a null result in squeezing is consistent with
this theory.


title:
Continuous-Variable Quantum Information Distributor: Reversible
  Telecloning

abstract:
  We propose a scheme of continuous-variable reversible telecloning, which
broadcast the information of an unknown state without loss from a sender to
several spatially separated receivers exploiting multipartite entanglement as
quantum channels. In this scheme, quantum information of an unknown state is
distributed into $M$ optimal clones and $M-1$ anticlones using $2M$% -partite
entanglement. For the perfect quantum information distribution that is optimal
cloning, $2M$-partite entanglement is required to be a maximum two-party
entanglement. Comparing with the quantum telecloning proposed by Loock and
Braunstein [Phys. Rev. Lett. 87, 247901 (2001)], this protocol produces the
anticlones (or time-reversed state) of the unknown quantum state, thus, keep
all information of an unknown state.


title: Experimenter's Freedom in Bell's Theorem and Quantum Cryptography

abstract:
  Bell's theorem states that no local realistic explanation of quantum
mechanical predictions is possible, in which the experimenter has a freedom to
choose between different measurement settings. Within a local realistic picture
the violation of Bell's inequalities can only be understood if this freedom is
denied. We determine the minimal degree to which the experimenter's freedom has
to be abandoned, if one wants to keep such a picture and be in agreement with
the experiment. Furthermore, the freedom in choosing experimental arrangements
may be considered as a resource, since its lacking can be used by an
eavesdropper to harm the security of quantum communication. We analyze the
security of quantum key distribution as a function of the (partial) knowledge
the eavesdropper has about the future choices of measurement settings which are
made by the authorized parties (e.g. on the basis of some quasi-random
generator). We show that the equivalence between the violation of Bell's
inequality and the efficient extraction of a secure key - which exists for the
case of complete freedom (no setting knowledge) - is lost unless one adapts the
bound of the inequality according to this lack of freedom.


title:
Quantum trajectory approach to the geometric phase: open bipartite
  systems

abstract:
  Through the quantum trajectory approach, we calculate the geometric phase
acquired by a bipartite system subjected to decoherence. The subsystems that
compose the bipartite system interact with each other, and then are entangled
in the evolution. The geometric phase due to the quantum jump for both the
bipartite system and its subsystems are calculated and analyzed. As an example,
we present two coupled spin-$\frac 1 2 $ particles to detail the calculations.


title:
Generation and control of Greenberger-Horne-Zeilinger entanglement in
  superconducting circuits

abstract:
  Going beyond the entanglement of microscopic objects (such as photons, spins,
and ions), here we propose an efficient approach to produce and control the
quantum entanglement of three macroscopic coupled superconducting qubits. By
conditionally rotating, one by one, selected Josephson charge qubits, we show
that their Greenberger-Horne-Zeilinger (GHZ) entangled states can be
deterministically generated. The existence of GHZ correlations between these
qubits could be experimentally demonstrated by effective single-qubit
operations followed by high-fidelity single-shot readouts. The possibility of
using the prepared GHZ correlations to test the macroscopic conflict between
the noncommutativity of quantum mechanics and the commutativity of classical
physics is also discussed.


title:
Optimum measurement for unambiguously discriminating two mixed states:
  General considerations and special cases

abstract:
  Based on our previous publication [U. Herzog and J. A. Bergou, Phys.Rev. A
71, 050301(R) (2005)] we investigate the optimum measurement for the
unambiguous discrimination of two mixed quantum states that occur with given
prior probabilities. Unambiguous discrimination of nonorthogonal states is
possible in a probabilistic way, at the expense of a nonzero probability of
inconclusive results, where the measurement fails. Along with a discussion of
the general problem, we give an example illustrating our method of solution. We
also provide general inequalities for the minimum achievable failure
probability and discuss in more detail the necessary conditions that must be
fulfilled when its absolute lower bound, proportional to the fidelity of the
states, can be reached.


title: Numerical Implementation of Non-Markovian Quantum State Diffusion

abstract:
  Non-Markovian quantum state diffusion (NMQSD) is a non-relativistic but
otherwise exact theory which expresses the reduced density matrix of an
arbitrary subsystem, interacting linearly with an uncoupled harmonic oscillator
bath, as an average of diadics formed from state vectors which obey stochastic
variational-differential equations. The vacuum radiation field can be
represented as such an oscillator bath, and so this model is in widespread use
in quantum optics. Prior to the development of NMQSD, exact subsystem solutions
could only be obtained in a few special cases (e.g. spin-1/2, harmonic
oscillator). Unfortunately, it has not yet been possible to obtain exact
solutions to new problems using NMQSD due to the difficulty of solving the
variational-differential equations. Here we show that these equations can be
transformed into a pair of coupled nonlinear integrodifferential equations. We
develop exact numerical methods for the integrodifferential equations and show
that solutions can be readily obtained to good accuracy for quite general
subsystems. We exactly solve various examples including tunneling in a double
well representing molecular isomerization or racemization, suppression of
fluorescence from a two-level atom in a band gap, and intermittent fluorescence
from a driven three level system representing electronic states of singly
ionized magnesium.


title:
Scattering in abrupt heterostructures using a position dependent mass
  Hamiltonian

abstract:
  Transmission probabilities of the scattering problem with a position
dependent mass are studied. After sketching the basis of the theory, within the
context of the Schr\"{o}dinger equation for spatially varying effective mass,
the simplest problem, namely, tranmission through a square well potential with
a position dependent mass barrier is studied and its novel properties are
obtained. The solutions presented here may be adventageous in the design of
semiconductor devices.


title: Unconditional two-mode squeezing of separated atomic ensembles

abstract:
  We propose schemes for the unconditional preparation of a two-mode squeezed
state of effective bosonic modes realized in a pair of atomic ensembles
interacting collectively with optical cavity and laser fields. The scheme uses
Raman transitions between stable atomic ground states and under ideal
conditions produces pure entangled states in the steady state. The scheme works
both for ensembles confined within a single cavity and for ensembles confined
in separate, cascaded cavities.


title:
Investigation of Continuous-Time Quantum Walk Via Spectral Distribution
  Associated with Adjacency Matrix

abstract:
  Using the spectral distribution associated with the adjacency matrix of
graphs, we introduce a new method of calculation of amplitudes of
continuous-time quantum walk on some rather important graphs, such as line,
cycle graph $C_n$, complete graph $K_n$, graph $G_n$, finite path and some
other finite and infinite graphs, where all are connected with orthogonal
polynomials such as Hermite, Laguerre, Tchebichef and some other orthogonal
polynomials. It is shown that using the spectral distribution, one can obtain
the infinite time asymptotic behavior of amplitudes simply by using the method
of stationary phase approximation(WKB approximation), where as an example, the
method is applied to star, two-dimensional comb lattices, infinite Hermite and
Laguerre graphs. Also by using the Gauss quadrature formula one can approximate
infinite graphs with finite ones and vice versa, in order to derive large time
asymptotic behavior by WKB method. Likewise, using this method, some new graphs
are introduced, where their amplitude are proportional to product of amplitudes
of some elementary graphs, even though the graphs themselves are not the same
as Cartesian product of their elementary graphs. Finally, via calculating mean
end to end distance of some infinite graphs at large enough times, it is shown
that continuous time quantum walk at different infinite graphs belong to
different universality classes which are also different than those of the
corresponding classical ones.


title: Entangled Photon Holes

abstract:
  Most experimental demonstrations of entanglement require nonclassical states
and correlated measurements of single-photon detection events. It is shown here
that entanglement can produce a large decrease in the rate of two-photon
absorption for a classical input state that can be observed using classical
detectors. These effects can be interpreted as being due to the creation of
entangled photon holes that are somewhat analogous to the holes of
semiconductor theory.


title: Bayesian prediction of the Gaussian states from n sample

abstract:
  Recently quantum prediction problem was proposed in the Bayesian framework.
It is shown that Bayesian predictive density operators are the best predictive
density operators when we evaluate them by using the average relative entropy
based on a prior.As an illustrative example, we treat the Gaussian states
family adopting the Gaussian distribution as a prior and give the Bayesian
predictive density operator with the heterodyne measurement fixed. We show that
it is better than the plug-in predictive density operator based on the maximum
likelihood estimate by calculating each average relative entropy.


title:
Non-Markovian quantum dynamics: Correlated projection superoperators and
  Hilbert space averaging

abstract:
  The time-convolutionless (TCL) projection operator technique allows a
systematic analysis of the non-Markovian quantum dynamics of open systems. We
introduce a class of projection superoperators which project the states of the
total system onto certain correlated system-environment states. It is shown
that the application of the TCL technique to this class of correlated
superoperators enables the non-perturbative treatment of the dynamics of
system-environment models for which the standard approach fails in any finite
order of the coupling strength. We demonstrate further that the correlated
superoperators correspond to the idea of a best guess of conditional quantum
expectations which is determined by a suitable Hilbert space average. The
general approach is illustrated by means of the model of a spin which interacts
through randomly distributed couplings with a finite reservoir consisting of
two energy bands. Extensive numerical simulations of the full Schroedinger
equation of the model reveal the power and efficiency of the method.


title:
Classification and Quantification of Entangled Bipartite Qutrit Pure
  States

abstract:
  A complete analysis of entangled bipartite qutrit pure states is carried out
based on a simple entanglement measure. An analysis of all possible extremally
entangled pure bipartite qutrit states is shown to reduce, with the help of
SLOCC transformations, to three distinct types. The analysis and the results
should be helpful for finding different entanglement types in multipartite pure
state systems.


title: Quest for Fast Partial Search Algorithm

abstract:
  Quantum algorithm can find target item in a database faster than any
classical. One can trade accuracy for speed and find a part of the database (a
block) containing the target item even faster: this is partial search. One can
think of partial search in following terms: an exact address of the target item
is given by a sequence of many bites, but we want to find only several first
bites of the address. We consider different partial search algorithms
consisting of a sequence of global and local searches and suggest the optimal
one. Global search consists of the standard Grover iterations for the whole
database. Local search consists of Grover iterations in each individual block
made simultaneously in all blocks. Efficiency of an algorithm is measured by
number of queries to the oracle.


title: Einstein and the Quantum

abstract:
  We review here the main contributions of Einstein to the quantum theory. To
put them in perspective we first give an account of Physics as it was before
him. It is followed by a brief account of the problem of black body radiation
which provided the context for Planck to introduce the idea of quantum.
Einstein's revolutionary paper of 1905 on light-quantum hypothesis is then
described as well as an application of this idea to the photoelectric effect.
We next take up a discussion of Einstein's other contributions to old quantum
theory. These include (i) his theory of specific heat of solids, which was the
first application of quantum theory to matter, (ii) his discovery of
wave-particle duality for light and (iii) Einstein's A and B coefficients
relating to the probabilities of emission and absorption of light by atomic
systems and his discovery of radiation stimulated emission of light which
provides the basis for laser action. We then describe Einstein's contribution
to quantum statistics viz Bose-Einstein Statistics and his prediction of
Bose-Einstein condensation of a boson gas. Einstein played a pivotal role in
the discovery of Quantum mechanics and this is briefly mentioned. After 1925
Einstein's contributed mainly to the foundations of Quantum Mechanics. We
choose to discuss here (i) his Ensemble (or Statistical) Interpretation of
Quantum Mechanics and (ii) the discovery of Einstein-Podolsky-Rosen (EPR)
correlations and the EPR theorem on the conflict between Einstein-Locality and
the completeness of the formalism of Quantum Mechanics. We end with some
comments on later developments.


title:
Characterization of several kinds of quantum analogues of relative
  entropy

abstract:
  Quantum relative entropy $D(\rho\|\sigma)\defeq\Tr \rho (\log \rho- \log
\sigma)$ plays an important role in quantum information and related fields.
However, there are many quantum analogues of relative entropy. In this paper,
we characterize these analogues from information geometrical viewpoint. We also
consider the naturalness of quantum relative entropy among these analogues.


title: Quantum deletion: Beyond the no-deletion principle

abstract:
  Suppose we are given two identical copies of an unknown quantum state and we
wish to delete one copy from among the given two copies. The quantum
no-deletion principle restricts us from perfectly deleting a copy but it does
not prohibit us from deleting a copy approximately. Here we construct two types
of a universal quantum deletion machine which approximately deletes a copy such
that the fidelity of deletion does not depend on the input state. The two types
of universal quantum deletion machines are (1) a conventional deletion machine
described by one unitary operator and (2) a modified deletion machine described
by two unitary operators. Here it is shown that modified deletion machine
deletes a qubit with fidelity 0.75, which is the maximum limit for deleting an
unknown quantum state. In addition to this we also show that the modified
deletion machine retains the qubit in the first mode with average fidelity 0.77
(approx.) which is slightly greater than the fidelity of measurement for two
given identical state, showing how precisely one can determine its state [13].
We also show that the deletion machine itself is input state independent i.e.
the information is not hidden in the deleting machine, and hence we can delete
the information completely from the deletion machine.


title: General error estimate for adiabatic quantum computing

abstract:
  Most investigations devoted to the conditions for adiabatic quantum computing
are based on the first-order correction ${\bra{\Psi_{\rm ground}(t)}\dot
H(t)\ket{\Psi_{\rm excited}(t)} /\Delta E^2(t)\ll1}$. However, it is
demonstrated that this first-order correction does not yield a good estimate
for the computational error. Therefore, a more general criterion is proposed,
which includes higher-order corrections as well and shows that the
computational error can be made exponentially small -- which facilitates
significantly shorter evolution times than the above first-order estimate in
certain situations. Based on this criterion and rather general arguments and
assumptions, it can be demonstrated that a run-time $T$ of order of the inverse
minimum energy gap $\Delta E_{\rm min}$ is sufficient and necessary, i.e.,
$T=\ord(\Delta E_{\rm min}^{-1})$. For some examples, these analytical
investigations are confirmed by numerical simulations. PACS: 03.67.Lx,
03.67.-a.


title: Geometric phase for open quantum systems and stochastic unravellings

abstract:
  We analyze the geometric phase for an open quantum system when computed by
resorting to a stochastic unravelling of the reduced density matrix (quantum
jump approach or stochastic Schrodienger equations). We show that the resulting
phase strongly depends on the type of unravelling used for the calculations: as
such, this phase is 'not' a geometric object since it depends on non-physical
parameters which are not related to the path followed by the density matrix
during the evolution of the system.


title:
On the quantum hardness of solving isomorphism problems as nonabelian
  hidden shift problems

abstract:
  We consider an approach to deciding isomorphism of rigid n-vertex graphs (and
related isomorphism problems) by solving a nonabelian hidden shift problem on a
quantum computer using the standard method. Such an approach is arguably more
natural than viewing the problem as a hidden subgroup problem. We prove that
the hidden shift approach to rigid graph isomorphism is hard in two senses.
First, we prove that Omega(n) copies of the hidden shift states are necessary
to solve the problem (whereas O(n log n) copies are sufficient). Second, we
prove that if one is restricted to single-register measurements, an exponential
number of hidden shift states are required.


title:
Energy and multipartite entanglement in multidimensional and frustrated
  spin models

abstract:
  We investigate the relation between the entanglement properties of a quantum
state and its energy for macroscopic spin models. To this aim, we develop a
general method to compute energy bounds for states without certain forms of
multipartite entanglement. Violation of these bounds implies the presence of
these types of multipartite entanglement. As examples, we investigate the
Heisenberg model in different dimensions, the Ising model and the XX model in
the presence of a magnetic field. Finally, by studying the Heisenberg model on
a triangular lattice, we demonstrate that our techniques can be applied also to
frustrated systems.


title: Optimal estimation of quantum observables

abstract:
  We consider the problem of estimating the ensemble average of an observable
on an ensemble of equally prepared identical quantum systems. We show that,
among all kinds of measurements performed jointly on the copies, the optimal
unbiased estimation is achieved by the usual procedure that consists in
performing independent measurements of the observable on each system and
averaging the measurement outcomes.


title: Useful entanglement can be extracted from all nonseparable states

abstract:
  We consider entanglement distillation from a single-copy of a multipartite
state, and instead of rates we analyze the "quality" of the distilled
entanglement. This "quality" is quantified by the fidelity with the GHZ-state.
We show that each not fully-separable state $\sigma$ can increase the "quality"
of the entanglement distilled from other states, no matter how weakly entangled
is $\sigma$. We also generalize this to the case where the goal is distilling
states different than the GHZ. These results provide new insights on the
geometry of the set of separable states and its dual (the set of entanglement
witnesses).


title: Entanglement distillation using particle statistics

abstract:
  We extend the idea of entanglement concentration for pure states(Phys. Rev.
Lett. {\bf 88}, 187903) to the case of mixed states. The scheme works only with
particle statistics and local operations, without the need of any other
interactions. We show that the maximally entangled state can be distilled out
when the initial state is pure, otherwise the entanglement of the final state
is less than one. The distillation efficiency is a product of the diagonal
elements of the initial state, it takes the maximum 50%, the same as the case
for pure states.


abstract:
  The role of geometry on dispersive forces is investigated by calculating the
energy between different spheroidal particles and planar surfaces, both with
arbitrary dielectric properties. The energy is obtained in the non-retarded
limit using a spectral representation formalism and calculating the interaction
between the surface plasmons of the two macroscopic bodies. The energy is a
power-law function of the separation of the bodies, where the exponent value
depends on the geometrical parameters of the system, like the separation
distance between bodies, and the aspect ratio among minor and major axes of the
spheroid.


title: Minimal disturbance measurement for coherent states is non-Gaussian

abstract:
  In standard coherent state teleportation with shared two-mode squeezed vacuum
(TMSV) state there is a trade-off between the teleportation fidelity and the
fidelity of estimation of the teleported state from results of the Bell
measurement. Within the class of Gaussian operations this trade-off is optimal,
i.e. there is not a Gaussian operation which would give for a given output
fidelity a larger estimation fidelity. We show that this trade-off can be
improved by up to 2.77% if we use a suitable non-Gaussian operation. This
operation can be implemented by the standard teleportation protocol in which
the shared TMSV state is replaced with a suitable non-Gaussian entangled state.
We also demonstrate that this operation can be used to enhance the transmission
fidelity of a certain noisy channel.


title:
Influence of a repump laser on a nearly degenerate four-wave-mixing
  spectrum in atomic vapors

abstract:
  The influence of a repump laser on a nearly degenerate four-wave-mixing
(NDFWM) spectrum was investigated. We found the amplitude and line shape of the
NDFWM depended strongly on the detuning of the repump field. A five-peak
structure was observed. And at some certain repump detuning a dip appeared at
the central peak. A rough analysis was proposed to explain this effect.


title:
Convergent Iterative Solutions for a Sombrero-Shaped Potential in Any
  Space Dimension and Arbitrary Angular Momentum

abstract:
  We present an explicit convergent iterative solution for the lowest energy
state of the Schroedinger equation with an $N$-dimensional radial potential
$V=\frac{g^2}{2}(r^2-1)^2$ and an angular momentum $l$. For $g$ large, the rate
of convergence is similar to a power series in $g^{-1}$.


title: Beam Splitter for Spin Waves in Quantum Spin Network

abstract:
  We theoretically design and analytically study a controllable beam splitter
for the spin wave propagating in a star-shaped (e.g., a $Y$-shaped beam) spin
network. Such a solid state beam splitter can display quantum interference and
quantum entanglement by the well-aimed controls of interaction on nodes. It
will enable an elementary interferometric device for scalable quantum
information processing based on the solid system.


title:
Experimental demonstration of coherent state estimation with minimal
  disturbance

abstract:
  We investigate the optimal tradeoff between information gained about an
unknown coherent state and the state disturbance caused by the measurement
process. We propose several optical schemes that can enable this task, and we
implement one of them, a scheme which relies on only linear optics and homodyne
detection. Experimentally we reach near optimal performance, limited only by
detection inefficiencies. In addition we show that such a scheme can be used to
enhance the transmission fidelity of a class of noisy channels.


title: Programmable quantum state discriminator by Nuclear Magnetic Resonance

abstract:
  In this paper a programmable quantum state discriminator is implemented by
using nuclear magnetic resonance. We use a two qubit spin-1/2 system, one for
the data qubit and one for the ancilla (programme) qubit. This device does the
unambiguous (error free) discrimination of pair of states of the data qubit
that are symmetrically located about a fixed state. The device is used to
discriminate both, linearly polarized states and elliptically polarized states.
The maximum probability of the successful discrimination is achieved by
suitably preparing the ancilla qubit. It is also shown that, the probability of
discrimination depends on angle of unitary operator of the protocol and
ellipticity of the data qubit state.


title:
Markov property and strong additivity of von Neumann entropy for graded
  quantum systems

abstract:
  It is easy to verify the equivalence of the quantum Markov property and the
strong additivity of entropy for graded quantum systems as well. However, the
structure of Markov states for graded systems is different from that for tensor
product systems. For three-composed graded systems there are U(1)-gauge
invariant Markov states whose restriction to the pair of marginal subsystems is
non-separable.


title: Local Distinguishability and Schmidt Number of Orthogonal States

abstract:
  Now, the known ensembles of orthogonal states which are distinguishable by
local operators and classical communication (LOCC) satisfy the condition that
the sum of Schmidit numbers of the orthogonal states is not bigger than the
dimensions of the whole space. A natural question is whether an arbitary
ensembles of LOCC-distinguishable orthogonal states satisfies the condition. We
first show that, in this paper, the answer is positive. Then we generalize it
into multipartite systems, and show that a necessary condition for
LOCC-distinguishability of multipartite orthogonal quantum states is that the
sum of the least numbers of the product states (For bipartite system, the least
number of product states is Schmidit number) of the orthogonal states is not
bigger than the dimensions of the Hilbert space of the multipartite system.
This necessary condition is very simple and general, and one can get many cases
of indistinguishability by it. It means that the least number of the product
states acts an important role in distinguishablity of states, and implies that
the least number of the product states may be an good manifestion of quantum
nonlocality in some sense. In fact, entanglement emphases the "amount" of
nonlocality, but the least number of the product states emphases the types of
nonlocality. For example, the known W states and GHZ states have different
least number of the product states, and are different in type.


title: Truth and Completeness in Quantum Mechanics: A Semantic Viewpoint

abstract:
  The Einstein, Podolski and Rosen (EPR) argument aiming to prove the
incompleteness of quantum mechanics (QM) was opposed by most EPR's contemporary
physicists and is not accepted within the standard interpretation of QM, which
maintains that QM is a complete theory. An analysis of the semantic
implications of the opponent positions shows that they imply different notions
of truth. The introduction of a nonclassical notion of truth within the
standard interpretation is usually justified by referring to known theorems
that should prove that QM is a contextual and nonlocal theory. However, these
theorems are based on a doubtful implicit epistemological assumption. If one
renounces it, one can provide an alternative interpretation of QM that it
realistic in a semantic sense. Within this interpretation the EPR viewpoint is
recovered and QM is considered a (semantically) incomplete, noncontextual and
local theory. Furthermore, the new interpretation provides several suggestions
for constructing a more general theory embedding QM and for connecting QM with
classical physics and relativity.


title: Equi-entangled bases in arbitrary dimensions

abstract:
  For the space of two identical systems of arbitrary dimensions, we introduce
a continuous family of bases with the following properties: i) the bases are
orthonormal, ii) in each basis, all the states have the same values of
entanglement, and iii) they continuously interpolate between the product basis
and the maximally entangled basis. The states thus constructed may find
applications in many areas related to quantum information science including
quantum cryptography, optimal Bell tests and investigation of enhancement of
channel capacity due to entanglement.


title:
A Bell Theorem Without Inequalities for Two Particles, Using Efficient
  Detectors

abstract:
  We consider an entangled two-particle state that is produced from two
independent down-conversion sources by the process of "entanglement-swapping",
so that the particles have never met. We prove a Greenberger-Horne-Zeilinger
(GHZ) type theorem, showing that the quantum mechanical perfect correlations
for such a state are inconsistent with any deterministic, local, realistic
theory. This theorem holds for individual events with no inequalities, for
detectors of 100% efficiency.


title: Hybrid quantum repeater using bright coherent light

abstract:
  We describe a quantum repeater protocol for long-distance quantum
communication. In this scheme, entanglement is created between qubits at
intermediate stations of the channel by using a weak dispersive light-matter
interaction and distributing the outgoing bright coherent light pulses among
the stations. Noisy entangled pairs of electronic spin are then prepared with
high success probability via homodyne detection and postselection. The local
gates for entanglement purification and swapping are deterministic and
measurement-free, based upon the same coherent-light resources and weak
interactions as for the initial entanglement distribution. Finally, the
entanglement is stored in a nuclear-spin-based quantum memory. With our system,
qubit-communication rates approaching 100 Hz over 1280 km with fidelities near
99% are possible for reasonable local gate errors.


title: Bicomplex Quantum Mechanics: II. The Hilbert Space

abstract:
  Using the bicomplex numbers $\mathbb{T}$ which is a commutative ring with
zero divisors defined by $\mathbb{T}=\{w_0 + w_1 i_1 + w_2 i_2 + w_3 j | w_0,
w_1, w_2, w_3 \in \mathbb{R}\}$ where $i_{1}^{2} = -1, i_{2}^{2} = -1, j^2 = 1,
i_1 i_2 = j = i_2 i_1$, we construct hyperbolic and bicomplex Hilbert spaces.
Linear functionals and dual spaces are considered and properties of linear
operators are obtained; in particular it is established that the eigenvalues of
a bicomplex self-adjoint operator are in the set of hyperbolic numbers.


title: Entanglement of Fermi gases in a harmonic trap

abstract:
  For both cases with and without interactions, bipartite entanglement of
two-fermions from a Fermi gas in a trap is investigated. We show how the
entanglement depends on the locations of the two fermions and the total number
of particles. Fermions at the verge of trap have longer entanglement distance
(beyond it, the entanglement disappears) than those in the center. We derive a
lower limitation to the average overlapping for two entangled fermions in the
BCS ground state, it is shown to be $\sqrt{Q/2M}$, a function of Cooper pair
number $Q$ and total number of occupied energy levels $M$.


title:
Quantum key distribution using superposition of the vacuum and single
  photon states

abstract:
  B92-type and BB84-type quantum cryptography schemes using superposed states
of the vacuum and single particle states which are robust against PNS attacks
are studied. The number of securely transferred classical bits per particle
(not per qubit) sent in these schemes is calculated and found to have upper
bounds. Possible experimental realizations using the cavity QED or linear
optics are suggested.


title: Quantum mechanical corrections to the Alfven waves

abstract:
  The hydrodynamical model of quantum mechanics based on the Schroedinger
equation is combined with the magnetohydrodynamical term to form so called
quantum magnetohydrodynamic equation. It is shown that the quantum correction
to the Alfven waves follows from this new equation. The possible generalization
is considered for the so called nonlinear Schroedinger equation and for the
situation where dissipation is described by the Navier-Stokes equation.


title:
A Bell Theorem Without Inequalities for Two Particles, Using Inefficient
  Detectors

abstract:
  We again consider (as in a companion paper) an entangled two-particle state
that is produced from two independent down-conversion sources by the process of
"entanglement-swapping", so that the particles have never met. We show that
there is a natural extension of the Einstein-Pololsky-Rosen discussion of
"elements of reality" to include inefficient detectors. We consider inefficient
deterministic, local, realistic models of quantum theory that are "robust",
which we consider to be the minimum requirement for them to be taken seriously.
By robust, we mean they satisfy the following three criteria: (a) they
reproduce the quantum results for perfect correlations, if all particles are
detected; (b) they produce some counts for every setting of the angles (so they
don't describe some experiments that can easily be performed as "impossible");
(c) all their hidden variables are relevant (they must each produce a
detectable result in some experiment). For such models we prove a
Greenberger-Horne-Zeilinger (GHZ) type theorem for arbitrary detection
efficiencies, showing that any such theory is inconsistent with the quantum
mechanical perfect correlations. This theorem holds for individual events with
no inequalities. As a result, the theorem is also independent of any random
sampling hypothesis.


title: Quantum key distribution protocols using entangled state

abstract:
  We present three quantum key distribution protocols using entangled state. In
the first two protocols, all Einstein-Podolsky-Rosen pairs are used to
distribute a secret key except those chosen for eavesdropping check, because
the communication parties measure each of their particles in an invariable
measuring basis. The first protocol is based on the ideal of qubit transmission
in blocks. Although it need quantum memory, its theoretic efficiency
approximates to 100%. The second protocol does not need quantum memory and its
efficiency for qubits can achieve 100%. In the third protocol, we present a
controlled quantum key distribution using three-particle entangled state to
solve a special cryptographic task. Only with the controller's permission could
the communication parties establish their sharing key and the sharing key is
secret to the controller. We also analyze the security and the efficiency of
the present protocols.


title:
Remote implementations of partially unknown quantum operations of
  multiqubits

abstract:
  We propose and prove the protocol of remote implementations of partially
unknown quantum operations of multiqubits belonging to the restricted sets.
Moreover, we obtain the general and explicit forms of restricted sets and
present evidence of their uniqueness and optimization. In addition, our
protocol has universal recovery operations that can enhance the power of remote
implementations of quantum operations.


title:
Controlled and combined remote implementations of partially unknown
  quantum operations of multiqubits using GHZ states

abstract:
  We propose and prove protocols of controlled and combined remote
implementations of partially unknown quantum operations belonging to the
restricted sets [An Min Wang: PRA, \textbf{74}, 032317(2006)] using GHZ states.
We detailedly describe the protocols in the cases of one qubit, respectively,
with one controller and with two senders. Then we extend the protocols to the
cases of multiqubits with many controllers and two senders. Because our
protocols have to demand the controller(s)'s startup and authorization or two
senders together working and cooperations, the controlled and combined remote
implementations of quantum operations definitely can enhance the security of
remote quantum information processing and potentially have more applications.
Moreover, our protocol with two senders is helpful to farthest arrive at the
power of remote implementations of quantum operations in theory since the
different senders perhaps have different operational resources and different
operational rights in practice.


title:
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems
  driven by a classical flow

abstract:
  We generalize the definition of quantum Anosov properties and the related
Lyapunov exponents to the case of quantum systems driven by a classical flow,
i.e. skew-product systems. We show that the skew Anosov properties can be
interpreted as regular Anosov properties in an enlarged Hilbert space, in the
framework of a generalized Floquet theory. This extension allows us to describe
the hyperbolicity properties of almost-periodic quantum parametric oscillators
and we show that their upper Lyapunov exponents are positive and equal to the
Lyapunov exponent of the corresponding classical parametric oscillators. As
second example, we show that the configurational quantum cat system satisfies
quantum Anosov properties.


title:
Efficient multiparty quantum secret sharing of secure direct
  communication

abstract:
  In this paper, we present an (n, n) threshold quantum secret sharing scheme
of secure direct communication using Greenberger-Horne-Zeilinger state. The
present scheme is efficient in that all the Greenberger-Horne-Zeilinger states
used in the quantum secret sharing scheme are used to generate shared secret
messages except those chosen for checking eavesdropper. In our scheme, the
measuring basis of communication parties is invariable and the classical
information used to check eavesdropping needs only the results of measurements
of the communication parties. Another nice feature of our scheme is that the
sender transmit her secret messages to the receivers directly and the receivers
recover the sender's secret by combining their results, different from the QSS
scheme whose object is essentially to allow a sender to establish a shared key
with the receivers. This feature of our scheme is similar to that of quantum
secret direct communication.


title:
Design of a High Power Continuous Source of Broadband Down-Converted
  Light

abstract:
  We present the design and experimental proof of principle of a low threshold
optical parametric oscillator (OPO) that continuously oscillates over a large
bandwidth allowed by phase matching. The large oscillation bandwidth is
achieved with a selective two-photon loss that suppresses the inherent mode
competition, which tends to narrow the bandwidth in conventional OPOs. Our
design performs pairwise mode-locking of many frequency pairs, in direct
equivalence to passive mode-locking of ultrashort pulsed lasers. The ability to
obtain high powers of continuous \textit{and} broadband down-converted light
enables the optimal exploitation of the correlations within the down-converted
spectrum, thereby strongly affecting two-photon interactions even at
classically high power levels, and opening new venues for applications such as
two-photon spectroscopy and microscopy and optical spread spectrum
communication.


title: Zeno and Anti Zeno effect for a two level system in a squeezed bath

abstract:
  We discuss the appearance of Zeno (QZE) or anti-Zeno (QAE) effect in an
exponentially decaying system. We consider the quantum dynamics of a
continuously monitored two level system interacting with a squeezed bath. We
find that the behavior of the system depends critically on the way in which the
squeezed bath is prepared. For specific choices of the squeezing phase the
system shows Zeno or anti-Zeno effect in conditions for which it would decay
exponentially if no measurements were done. This result allows for a clear
interpretation in terms of the equivalent spin system interacting with a
fictitious magnetic field.


title:
Long-Term Stability of an Area-Reversible Atom-Interferometer Sagnac
  Gyroscope

abstract:
  We report on a study of the long-term stability and absolute accuracy of an
atom interferometer gyroscope. This study included the implementation of an
electro-optical technique to reverse the vector area of the interferometer for
reduced systematics and a careful study of systematic phase shifts. Our data
strongly suggests that drifts less than 96 $\mu$deg/hr are possible after
empirically removing shifts due to measured changes in temperature, laser
intensity, and several other experimental parameters.


title: Transmitting qudits through larger quantum channels

abstract:
  We address the problem of transmitting states belonging to finite dimensional
Hilbert space through a quantum channel associated with a larger (even infinite
dimensional) Hilbert space.