title: Coherent states with elliptical polarization

abstract:
  Coherent states of the two dimensional harmonic oscillator are constructed as
superpositions of energy and angular momentum eigenstates. It is shown that
these states are Gaussian wave-packets moving along a classical trajectory,
with a well defined elliptical polarization. They are coherent correlated
states with respect to the usual cartesian position and momentum operators. A
set of creation and annihilation operators is defined in polar coordinates, and
it is shown that these same states are precisely coherent states with respect
to such operators.


title:
Holonomic Quantum Computation Using Rf-SQUIDs Coupled Through A
  Microwave Cavity

abstract:
  We propose a new scheme to realize holonomic quantum computation with
rf-SQUID qubits in a microwave cavity. In this scheme associated with the
non-Abelian holonomies, the single-qubit gates and a two-qubit control-Phase
gate as well as a control-NOT gate can be easily constructed by tuning
adiabatically the Rabi frequencies of classical microwave pulses coupled to the
SQUIDs. The fidelity of these gates is estimated to be possibly higher than 90
% with the current technology.


title: Comment on Complex Extension of Quantum Mechanics

abstract:
  In their Erratum [Phys. Rev. Lett. {\bf 92}, 119902 (2004),
quant-ph/0208076], written in reaction to [quant-ph/0310164], Bender, Brody and
Jones propose a revised definition for a physical observable in PT-symmetric
quantum mechanics. We show that although this definition avoids the dynamical
inconsistency revealed in quant-ph/0310164, it is still not a physically viable
definition. In particular, we point out that a general proof that this
definition is consistent with the requirements of the quantum measurement
theory is lacking, give such a proof for a class of PT-symmetric systems by
establishing the fact that this definition implies that the observables are
pseudo-Hermitian operators, and show that for all the cases that this
definition is consistent with the requirements of measurement theory it reduces
to a special case of a more general definition given in [quant-ph/0310164]. The
latter is the unique physically viable definition of observables in
PT-symmetric quantum mechanics.


title:
The non-linear field theory III: Geometrical illustration of the
  electromagnetic representation of Dirac's electron theory

abstract:
  The present paper is the continuity of the previous papers "Non-linear field
theory" I and II. Here on the basis of the electromagnetic representation of
Dirac's electron theory we consider the geometrical distribution of the
electromagnetic fields of the electron-positron. This gives the posibility to
obtain the explanation and solution of many fundamental problems of the QED.


title: A question in the axiomatic approach to Quantum Mechanics

abstract:
  The classical Hilbert space formulation of the axioms of Quantum Mechanics
appears to leave open the question whether the Hermitian operators which are
associated with the observables of a finite non-relativistic quantum system are
uniquely determined.


title: Thermal entanglement of spins in a nonuniform magnetic field

abstract:
  We study the effect of inhomogeneities in the magnetic field on the thermal
entanglement of a two spin system. We show that in the ferromagnetic case a
very small inhomogeneity is capable to produce large values of thermal
entanglement. This shows that the absence of entanglement in the ferromagnetic
Heisenberg system is highly unstable against inhomogeneoity of magnetic fields
which is inevitably present in any solid state realization of qubits.


title: What does quantum chaos mean?

abstract:
  We discuss how the concept of the quantum action can be used to characterize
quantum chaos. As an example we study quantum mechanics of the inverse square
potential in order to test some questions related to quantum action. Quantum
chaos is discussed for the 2-D hamiltonian system of harmonic oscillators with
anharmonic coupling.


title:
Entanglement in spin chains and lattices with long-range Ising-type
  interactions

abstract:
  We consider N initially disentangled spins, embedded in a ring or
d-dimensional lattice of arbitrary geometry, which interact via some
long--range Ising--type interaction. We investigate relations between
entanglement properties of the resulting states and the distance dependence of
the interaction in the limit N to infinity. We provide a sufficient condition
when bipartite entanglement between blocks of L neighboring spins and the
remaining system saturates, and determine S_L analytically for special
configurations. We find an unbounded increase of S_L as well as diverging
correlation and entanglement length under certain circumstances. For
arbitrarily large N, we can efficiently calculate all quantities associated
with reduced density operators of up to ten particles.


title:
Reply to "comment on Geometric phases for mixed states during cyclic
  evolutions"

abstract:
  We show that the geometric phase for mixed state during a cyclic evolution
suggested in 2004 J. Phys. A 37 3699 is U(1) invariant and can be observed by
nowaday techniques.


title: Wave Functions and Bohmian Trajectories in Interference Phenomena

abstract:
  In the last few years the hydrodynamic formulation of quantum mechanics,
equivalent to the Bohmian equations of motion, has been used to obtain
numerical solutions of the Schrodinger equation. Problems, however, have been
experienced near wave function nodes (or low probability regions). Here we
attempt to compute wave functions and Bohmian trajectories for the interference
of one particle or of two identical particles. It turns out that the large
number of nodes (i.e. interference minima) makes the hydrodynamic equations
impractical, whereas a more straightforward solution of the Schrodinger
equation gives very good results.


title: On PSI-complete and PSIR-complete measurements

abstract:
  I construct a POVM which has 2d rank-one elements and which is
informationally complete for generic pure states in d dimensions, thus
confirming a conjecture made by Flammia, Silberfarb, and Caves
(quant-ph/0404137). I show that if a rank-one POVM is required to be
informationally complete for all pure states in d dimensions, it must have at
least 3d-2 elements. I also show that, in a POVM which is informationally
complete for all pure states in d dimensions, for any vector there must be at
least 2d-1 POVM elements which do not annihilate that vector.


title: Implementation of analytic functions with quantum gates

abstract:
  In order to realize a Quantum CPU some schemes for executing fundamental
mathematical tasks are needed. In this paper we present some quantum circuits
which, using elementary arithmetic operations, allow an approximated
calculation of continuous functions. Furthermore, we give an explicit example
of our procedure applied to the exponential function.


title:
Quantum Entanglement and the Self-Trapping Transition in Polaronic
  Systems

abstract:
  We revisit from a quantum-information perspective a classic problem of
polaron theory in one dimension. In the context of the Holstein model we show
that a simple analysis of quantum entanglement between excitonic and phononic
degrees of freedom allows one to effectively characterize both the small and
large polaron regimes as well as the crossover in between. The small (large)
polaron regime corresponds to a high (low) degree of bipartite quantum
entanglement between the exciton and the phonon cloud that clothes the exciton.
Moreover, the self-trapping transition is clearly displayed by a sharp drop of
exciton-phonon entanglement.


title: New Construction of Mutually Unbiased Bases in Square Dimensions

abstract:
  We show that k=w+2 mutually unbiased bases can be constructed in any square
dimension d=s^2 provided that there are w mutually orthogonal Latin squares of
order s. The construction combines the design-theoretic objects (k,s)-nets
(which can be constructed from w mutually orthogonal Latin squares of order s
and vice versa) and generalized Hadamard matrices of size s. Using known lower
bounds on the asymptotic growth of the number of mutually orthogonal Latin
squares (based on number theoretic sieving techniques), we obtain that the
number of mutually unbiased bases in dimensions d=s^2 is greater than s^1/14.8
for all s but finitely many exceptions. Furthermore, our construction gives
more mutually orthogonal bases in many non-prime-power dimensions than the
construction that reduces the problem to prime power dimensions.


title: Efficient Quantum Circuits for Schur and Clebsch-Gordan Transforms

abstract:
  The Schur basis on n d-dimensional quantum systems is a generalization of the
total angular momentum basis that is useful for exploiting symmetry under
permutations or collective unitary rotations. We present efficient (size
poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur
transform, which is the change of basis between the computational and the Schur
bases. These circuits are based on efficient circuits for the Clebsch-Gordan
transformation. We also present an efficient circuit for a limited version of
the Schur transform in which one needs only to project onto different Schur
subspaces. This second circuit is based on a generalization of phase estimation
to any nonabelian finite group for which there exists a fast quantum Fourier
transform.


title: Dynamics of initially entangled open quantum systems

abstract:
  Linear maps of matrices describing evolution of density matrices for a
quantum system initially entangled with another are identified and found to be
not always completely positive. They can even map a positive matrix to a matrix
that is not positive, unless we restrict the domain on which the map acts.
Nevertheless, their form is similar to that of completely positive maps. Only
some minus signs are inserted in the operator-sum representation. Each map is
the difference of two completely positive maps. The maps are first obtained as
maps of mean values and then as maps of basis matrices. These forms also prove
to be useful. An example for two entangled qubits is worked out in detail.
Relation to earlier work is discussed.


title:
Towards Quantum Superpositions of a Mirror: an Exact Open Systems
  Analysis - Calculational Details

abstract:
  We give details of calculations analyzing the proposed mirror superposition
experiment of Marshall, Simon, Penrose, and Bouwmeester within different
stochastic models for state vector collapse. We give two methods for exactly
calculating the fringe visibility in these models, one proceeding directly from
the equation of motion for the expectation of the density matrix, and the other
proceeding from solving a linear stochastic unravelling of this equation. We
also give details of the calculation that identifies the stochasticity
parameter implied by the small displacement Taylor expansion of the CSL model
density matrix equation. The implications of the two results are briefly
discussed. Two pedagogical appendices review mathematical apparatus needed for
the calculations.


title: Bell's Theorem - Why Inequalities, Correlations?

abstract:
  It is shown that Bell's counterfactuals admit joint quasiprobability
distributions (i.e. joint distributions exist, but may not be non-negative). A
necessary and sufficient condition for the existence among them of a true
probability distribution (i.e. no-nnegative) is Bell's inequalities. This, in
turn, is a necessary condition for the existence of local hidden variables. The
treatment is amenable to generalization to examples of 'nonlocality without
inequalities'.


title: Simulation of Slow Light with Electronics Circuits

abstract:
  We present an electronic circuit which simulates wave propagation in
dispersive media. The circuit is an array of phase shifter composed of
operational amplifiers and can be described with a discretized version of
one-dimensional wave equation for envelopes. The group velocity can be changed
both spatially and temporarily. It is used to emulate slow light or stopped
light, which has been realized in a medium with electromagnetically induced
transparency (EIT). The group-velocity control of optical pulses is expected to
be a useful tool in the field of quantum information and communication.


title: Quantum Mechanical Hysteresis and the Electron Transfer Problem

abstract:
  We study a simple quantum mechanical symmetric donor-acceptor model for
electron transfer (ET) with coupling to internal deformations. The model
contains several basic properties found in biological ET in enzymes and
photosynthetic centers; it produces tunnelling with hysteresis thus providing a
simple explanation for the slowness of the reversed rate and the near 100%
efficiency of ET in many biological systems. The model also provides a
conceptual framework for the development of molecular electronics memory
elements based on electrostatic architectures.


title: Stark Effect in Lax-Phillips Theory

abstract:
  The scattering theory of Lax and Phillips, originally developed to describe
resonances associated with classical wave equations, has been recently extended
to apply as well to the case of the Schroedinger equation in the case that the
wave operators for the corresponding Lax-Phillips theory exist. It is known
that the bound state levels of an atom become resonances (spectral
enhancements) in the continuum in the presence of an electric field (in all
space) in the quantum mechanical Hilbert space. Such resonances appear as
states in the extended Lax-Phillips Hilbert space. We show that for a simple
version of the Stark effect, these states can be explicitly computed, and
exhibit the (necessarily) semigroup property of decay in time. The widths and
location of the resonances are those given by the poles of the resolvent of the
standard quantum mechanical form.


title:
A relativistically covariant version of Bohm's quantum field theory for
  the scalar field

abstract:
  We give a relativistically covariant, wave-functional formulation of Bohm's
quantum field theory for the scalar field based on a general foliation of
space-time by space-like hypersurfaces. The wave functional, which guides the
evolution of the field, is space-time-foliation independent but the field
itself is not. Hence, in order to have a theory in which the field may be
considered a beable, some extra rule must be given to determine the foliation.
We suggest one such rule based on the eigen vectors of the energy-momentum
tensor of the field itself.


title:
An anatomy of a quantum adiabatic algorithm that transcends the Turing
  computability

abstract:
  We give an update on a quantum adiabatic algorithm for the Turing
noncomputable Hilbert's tenth problem, and briefly go over some relevant issues
and misleading objections to the algorithm.


title:
Implementing Grover's Quantum Search on a Para-Hydrogen based Pure State
  NMR Quantum Computer

abstract:
  We demonstrate the implementation of Grover's quantum search algorithm on a
liquid state nuclear magnetic resonance (NMR) quantum computer using
essentially pure states. This was achieved using a two qubit device where the
initial state is an essentially pure ($\epsilon=1.06\pm0.04$) singlet nuclear
spin state of a pair of 1H nuclei arising from a chemical reaction involving
para-hydrogen. We have implemented Grover's search to find one of four inputs
which satisfies a function.


title: Some basics of $su(1,1)$

abstract:
  A basic introduction to the $su(1,1)$ algebra is presented, in which we
discuss the relation with canonical transformations, the realization in terms
of quantized radiation field modes and coherent states. Instead of going into
details of these topics, we rather emphasize the existing connections between
them. We discuss two parametrizations of the coherent states manifold
$SU(1,1)/U(1)$: as the Poincar{\'e} disk in the complex plane and as the
pseudosphere (a sphere in a Minkowskian space), and show that it is a natural
phase space for quantum systems with SU(1,1) symmetry.


title: Nonadiabatic geometric phase induced by a counterpart of the Stark shift

abstract:
  We analyse the geometric phase due to the Stark shift in a system composed of
a bosonic field, driven by time-dependent linear amplification, interacting
dispersively with a two-level (fermionic) system. We show that a geometric
phase factor in the joint state of the system, which depends on the fermionic
state (resulting form the Stark shift), is introduced by the amplification
process. A clear geometrical interpretation of this phenomenon is provided. We
also show how to measure this effect in an interferometric experiment and to
generate geometric "Schrodinger cat"-like states. Finally, considering the
currently available technology, we discuss a feasible scheme to control and
measure such geometric phases in the context of cavity quantum electrodynamics.


title:
Collective states in highly symmetric atomic configurations, and
  single-photon traps

abstract:
  Abbreviated Abstract: We study correlated states in a circular and
linear-chain configuration of identical two-level atoms containing the energy
of a single quasi-resonant photon in the form of a collective excitation, where
the collective behaviour is mediated by exchange of transverse photons between
the atoms. For a circular configuration of atoms the effective Hamiltonian on
the radiationless subspace of the system can be diagonalized analytically. In
this case, the radiationless energy eigenstates carry a $\mathbb{Z}_N$ quantum
number $p=0,1, ..., N$ which is analogous to the angular momentum quantum
number $l= 0, 1, ...$, carried by particles propagating in a central potential,
such as a hydrogen-like system. Just as the hydrogen s-states are the only
electronic wave functions which can occupy the central region of the Coulomb
potential, the quasi-particle corresponding to a collective excitation of the
circular atomic sample can occupy the central atom only for vanishing
$\mathbb{Z}_N$ quantum number $p$. For large numbers of atoms in a maximally
subradiant state, a critical interatomic distance of $\lambda/2$ emerges both
in the linear-chain and the circular configuration of atoms. The spontaneous
decay rate of the linear configuration exhibits a jump-like "critical"
behaviour for next-neighbour distances close to a half-wavelength. Furthermore,
both the linear-chain and the circular configuration exhibit exponential photon
trapping once the next-neighbour distance becomes less than a half-wavelength,
with the suppression of spontaneous decay being particularly pronounced in the
circular system. In this way, circular configurations containing sufficiently
many atoms may be natural candidates for {\it single-photon traps}.


title:
Optimized quantum implementation of elliptic curve arithmetic over
  binary fields

abstract:
  Shor's quantum algorithm for discrete logarithms applied to elliptic curve
groups forms the basis of a "quantum attack" of elliptic curve cryptosystems.
To implement this algorithm on a quantum computer requires the efficient
implementation of the elliptic curve group operation. Such an implementation
requires we be able to compute inverses in the underlying field. In [PZ03],
Proos and Zalka show how to implement the extended Euclidean algorithm to
compute inverses in the prime field GF(p). They employ a number of
optimizations to achieve a running time of O(n^2), and a space-requirement of
O(n) qubits (there are some trade-offs that they make, sacrificing a few extra
qubits to reduce running-time). In practice, elliptic curve cryptosystems often
use curves over the binary field GF(2^m). In this paper, we show how to
implement the extended Euclidean algorithm for polynomials to compute inverses
in GF(2^m). Working under the assumption that qubits will be an `expensive'
resource in realistic implementations, we optimize specifically to reduce the
qubit space requirement, while keeping the running-time polynomial. Our
implementation here differs from that in [PZ03] for GF(p), and we are able to
take advantage of some properties of the binary field GF(2^m). We also optimize
the overall qubit space requirement for computing the group operation for
elliptic curves over GF(2^m) by decomposing the group operation to make it
"piecewise reversible" (similar to what is done in [PZ03] for curves over
GF(p)).


title: The Emergence of Classical Dynamics in a Quantum World

abstract:
  Ever since the advent of quantum mechanics, it has been clear that the atoms
composing matter do not obey Newton's laws. Instead, their behavior is
described by the Schroedinger equation. Surprisingly though, until recently, no
clear explanation was given for why everyday objects, which are merely
collections of atoms, are observed to obey Newton's laws. It would seem that,
if quantum mechanics explains all the properties of atoms accurately, they,
too, should obey quantum mechanics. This reasoning led some scientists to
believe in a distinct macroscopic, or ``big and complicated,'' world in which
quantum mechanics fails and classical mechanics takes over, although there has
never been experimental evidence for such a failure. Even those who insisted
that Newtonian mechanics would somehow emerge from the underlying quantum
mechanics as the system became increasingly macroscopic were hindered by the
lack of adequate experimental and theoretical tools. In the last decade,
however, this quantum-to-classical transition has become accessible to
experimental study and quantitative description, and the resulting insights are
the subject of this article.


title:
On validity of the original Bell inequality for the Werner nonseparable
  state

abstract:
  In quant-ph/0406139, we have introduced in a very general setting the new
class of quantum states, density source-operator states, satisfying any
classical CHSH-form inequality, and shown that any separable state belongs to
this class. In the present paper, we prove that the Werner nonseparable state
also belongs to the class of density source-operator states. Moreover, for any
dimension d>2, the Werner state is in such a subclass of this class where each
density source-operator state satisfies also the perfect correlation form of
the original Bell inequality regardless of whether or not the Bell perfect
correlation restriction is fulfilled. The latter earlier unknown property of
the Werner state can be verified experimentally.


title: Dynamical Imperfections in quantum computers

abstract:
  We study the effects of dynamical imperfections in quantum computers. By
considering an explicit example, we identify different regimes ranging from the
low-frequency case, where the imperfections can be considered as static but
with renormalized parameters, to the high frequency fluctuations, where the
effects of imperfections are completely wiped out. We generalize our results by
proving a theorem on the dynamical evolution of a system in the presence of
dynamical perturbations.


title:
Initial state maximizing the nonexponentially decaying survival
  probability for unstable multilevel systems

abstract:
  The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.


title: Exact Numerical Solution of the BCS Pairing Problem

abstract:
  We propose a new simulation computational method to solve the reduced BCS
Hamiltonian based on spin analogy and submatrix diagonalization. Then we
further apply this method to solve superconducting energy gap and the results
are well consistent with those obtained by Bogoliubov transformation method.
The exponential problem of 2^{N}-dimension matrix is reduced to the polynomial
problem of N-dimension matrix. It is essential to validate this method on a
real quantum


title:
Effective-mass Schroedinger equation and generation of solvable
  potentials

abstract:
  A one-dimensional Schr\"odinger equation with position-dependent effective
mass in the kinetic energy operator is studied in the framework of an $so(2,1)$
algebra. New mass-deformed versions of Scarf II, Morse and generalized
P\"oschl-Teller potentials are obtained. Consistency with an intertwining
condition is pointed out.


title: Quantum Networks for Generating Arbitrary Quantum States

abstract:
  Quantum protocols often require the generation of specific quantum states. We
describe a quantum algorithm for generating any prescribed quantum state. For
an important subclass of states, including pure symmetric states, this
algorithm is efficient.


title: Economical Phase-Covariant Cloning of Qudits

abstract:
  We derive the optimal N to M phase-covariant quantum cloning for equatorial
states in dimension d with M=kd+N, k integer. The cloning maps are optimal for
both global and single-qudit fidelity. The map is achieved by an ``economical''
cloning machine, which works without ancilla.


title:
Multiple Round Quantum Dense Coding And Its Implementation Using Nuclear
  Magnetic Resonance

abstract:
  A multiple round quantum dense coding (MRQDC) scheme based on the quantum
phase estimation algorithm is proposed. Using an $m+1$ qubit system, Bob can
transmit $2^{m+1}$ messages to Alice, through manipulating only one qubit and
exchanging it between Alice and Bob for $m$ rounds. The information capacity is
enhanced to $m+1$ bits. We have implemented the scheme in a three- qubit
nuclear magnetic resonance (NMR) quantum computer. The experimental results
show a good agreement between theory and experiment.


title: Probing the evolution of Stark wave packets by a weak half cycle pulse

abstract:
  We probe the dynamic evolution of a Stark wave packet in cesium using weak
half-cycle pulses (HCP's). The state-selective field ionization(SSFI) spectra
taken as a function of HCP delay reveal wave packet dynamics such as Kepler
beats, Stark revivals and fractional revivals. A quantum-mechanical simulation
explains the results as multi-mode interference induced by the HCP.


title:
Superconducting Phase Qubit Coupled to a Nanomechanical Resonator:
  Beyond the Rotating-Wave Approximation

abstract:
  We consider a simple model of a Josephson junction phase qubit coupled to a
solid-state nanoelectromechanical resonator. This and many related
qubit-resonator models are analogous to an atom in an electromagnetic cavity.
When the systems are weakly coupled and nearly resonant, the dynamics is
accurately described by the rotating-wave approximation (RWA) or the
Jaynes-Cummings model of quantum optics. However, the desire to develop faster
quantum-information-processing protocols necessitates approximate, yet analytic
descriptions that are valid for more strongly coupled qubit-resonator systems.
Here we present a simple theoretical technique, using a basis of dressed
states, to perturbatively account for the leading-order corrections to the RWA.
By comparison with exact numerical results, we demonstrate that the method is
accurate for moderately strong coupling, and provides a useful theoretical tool
for describing fast quantum information processing. The method applies to any
quantum two-level system linearly coupled to a harmonic oscillator or
single-mode boson field.


title:
Atom waveguide using a two-color evanescent light field around a
  subwavelength-diameter optical fiber

abstract:
  We suggest using a two-color evanescent light field around a
subwavelength-diameter fiber to trap and guide atoms. The optical fiber carries
a red-detuned light and a blue-detuned light, with both modes far from
resonance. When both input light fields are circularly polarized, a set of
trapping minima of the total potential in the transverse plane is formed as a
ring around the fiber. This design allows confinement of atoms to a cylindrical
shell around the fiber. When one or both of the input light fields are linearly
polarized, the total potential has two local minimum points in the transverse
plane. This design allows confinement of atoms to two straight lines parallel
to the fiber axis. Due to the thin thickness of the fiber, we can use
far-off-resonance fields with substantially differing evanescent decay lengths
to produce a net potential with a large depth, a large coherence time, and a
large trap lifetime. For example, a 0.2-$\mu$m-radius silica fiber carrying 30
mW of 1.06-$\mu$m-wavelength light and 29 mW of 700-nm-wavelength light, both
fields are circularly polarized at the input, gives for cesium atoms a trap
depth of 2.9 mK, a coherence time of 32 ms, and a recoil-heating-limited trap
lifetime of 541 s.


title:
Super controlled gates and controlled gates in two-qubit gate
  simulations

abstract:
  In two-qubit gate simulations an entangling gate is used several times
together with single qubit gates to simulate another two-qubit gate. We show
how a two-qubit gate's simulation power is related to the simulation power of
its mirror gate. And we show that an arbitrary two-qubit gate can be simulated
by three applications of a super controlled gate together with single qubit
gates. We also give the gates set that can be simulated by n applications of a
controlled gate in a constructive way. In addition we give some gates which can
be used four times to simulate an arbitrary two-qubit gate.


title:
Ensemble Algorithm for the Selection Problem by NMR Ensemble Quantum
  Computers

abstract:
  In this paper, we present an ensemble algorithm for selection problem to find
the k-th smallest element in the unsorted database. We will search the k-th
smallest element by using "divide-and-conquer" strategy. We first divide D, the
domain of the database, into two parts, determine which of the two parts the
object element sought belongs to, and then concentrate on that part. We repeat
divide that part until object element is found. The determination of which part
depends on the output of ensemble counting scheme, which outputs the number of
assignments satisfying the value of the oracle query function is set to one.
Our algorithm modifies the ensemble counting scheme by constructing a new
oracle query function g_y(j). We set g_y(j) to one if the j-th element is less
than or equal to y. At first, we set y to the middle value of D and perform the
ensemble counting scheme with the oracle query function g_y(.) to compute the
number C, the number of j satisfying g_y(j)=1. If C>k, the object element lies
in the first half of D. If C<=k, then it must be in the second half of D. We
recursively apply this method by adapting y until the object element is found.
Our algorithm thus requires O(ln|D|) oracle queries for adequate measure
accuracy to find the k-th smallest element, where |D| denotes the size of D.


title: Maximal violation of the Ardehali's inequality of $n$ qubits

abstract:
  In this paper, we characterize the maximal violation of Ardehali's inequality
of $n$ qubits by showing that GHZ's states and the states obtained from them by
local unitary transformations are the unique states that maximally violate the
Ardehali's inequalities. This concludes that Ardehali's inequalities can be
used to characterize maximally entangled states of $n$ qubits, as the same as
Mermin's and Bell-Klyshko's inequalities.


title:
Operator-sum representation of time-dependent density operators and its
  applications

abstract:
  We show that any arbitrary time-dependent density operator of an open system
can always be described in terms of an operator-sum representation regardless
of its initial condition and the path of its evolution in the state space, and
we provide a general expression of Kraus operators for arbitrary time-dependent
density operator of an $N$-dimensional system. Moreover, applications of our
result are illustrated through several examples.


title: A quantum model for collective recoil lasing

abstract:
  Free Electron Laser (FEL) and Collective Atomic Recoil Laser (CARL) are
described by the same model of classical equations for properly defined scaled
variables. These equations are extended to the quantum domain describing the
particle's motion by a Schr\"{o}dinger equation coupled to a self-consistent
radiation field. The model depends on a single collective parameter $\bar \rho$
which represents the maximum number of photons emitted per particle. We
demonstrate that the classical model is recovered in the limit $\bar \rho\gg
1$, in which the Wigner function associated to the Schr\"{o}dinger equation
obeys to the classical Vlasov equation. On the contrary, for $\bar \rho\le 1$,
a new quantum regime is obtained in which both FELs and CARLs behave as a
two-state system coupled to the self-consistent radiation field and described
by Maxwell-Bloch equations.


title: Efficient fiber coupling of down-conversion photon pairs

abstract:
  We develop and apply an effective analytic theory of a non-collinear,
broadband type-I parametric down-conversion to study a coupling efficiency of
the generated photon pairs into single mode optical fibers. We derive
conditions necessary for highly efficient coupling for single and double type-I
crystal producing polarization entangled states of light. We compare the
obtained approximate analytic expressions with the exact numerical solutions
and discuss the results for a case of BBO crystals.


title:
Nonergodicity of entanglement and its complementary behavior to
  magnetization in infinite spin chain

abstract:
  We consider the problem of the validity of a statistical mechanical
description of two-site entanglement in an infinite spin chain described by the
XY model Hamiltonian. We show that the two-site entanglement of the state,
evolved from the initial equilibrium state, after a change of the magnetic
field, does not approach its equilibrium value. This suggests that two-site
entanglement, like (single-site) magnetization, is a nonergodic quantity in
this model. Moreover we show that these two nonergodic quantities behave in a
complementary way.


title: Caianiello's maximal acceleration. Recent developments

abstract:
  A quantum mechanical upper limit on the value of particle accelerations is
consistent with the behavior of a class of superconductors and well known
particle decay rates. It also sets limits on the mass of the Higgs boson and
affects the stability of compact stars. In particular, type-I superconductors
in static conditions offer an example of a dynamics in which acceleration has
an upper limit.


title: Bell-Type Quantum Field Theories

abstract:
  In [Phys. Rep. 137, 49 (1986)] John S. Bell proposed how to associate
particle trajectories with a lattice quantum field theory, yielding what can be
regarded as a |Psi|^2-distributed Markov process on the appropriate
configuration space. A similar process can be defined in the continuum, for
more or less any regularized quantum field theory; such processes we call
Bell-type quantum field theories. We describe methods for explicitly
constructing these processes. These concern, in addition to the definition of
the Markov processes, the efficient calculation of jump rates, how to obtain
the process from the processes corresponding to the free and interaction
Hamiltonian alone, and how to obtain the free process from the free Hamiltonian
or, alternatively, from the one-particle process by a construction analogous to
"second quantization." As an example, we consider the process for a second
quantized Dirac field in an external electromagnetic field.


title: Parts of Quantum States

abstract:
  It is shown that generic N-party pure quantum states (with equidimensional
subsystems) are uniquely determined by their reduced states of just over half
the parties; in other words, all the information in almost all N-party pure
states is in the set of reduced states of just over half the parties. For N
even, the reduced states in fewer than N/2 parties are shown to be an
insufficient description of almost all states (similar results hold when N is
odd). It is noted that Real Algebraic Geometry is a natural framework for any
analysis of parts of quantum states: two simple polynomials, a quadratic and a
cubic, contain all of their structure. Algorithmic techniques are described
which can provide conditions for sets of reduced states to belong to pure or
mixed states.


title: Unitarity as preservation of entropy and entanglement in quantum systems

abstract:
  The logical structure of Quantum Mechanics (QM) and its relation to other
fundamental principles of Nature has been for decades a subject of intensive
research. In particular, the question whether the dynamical axiom of QM can be
derived from other principles has been often considered. In this contribution,
we show that unitary evolutions arise as a consequences of demanding
preservation of entropy in the evolution of a single pure quantum system, and
preservation of entanglement in the evolution of composite quantum systems.


title: Spin network setting of topological quantum computation

abstract:
  The spin network simulator model represents a bridge between (generalised)
circuit schemes for standard quantum computation and approaches based on
notions from Topological Quantum Field Theories (TQFTs). The key tool is
provided by the fiber space structure underlying the model which exhibits
combinatorial properties closely related to SU(2) state sum models, widely
employed in discretizing TQFTs and quantum gravity in low spacetime dimensions.


title: Optimal conclusive discrimination of two states can be achieved locally

abstract:
  This paper constructs a LOCC protocol that achieves the global optimality in
conclusive discrimination of any two states with arbitrary a priori
probability. This can be interpreted that there is no ``non-locality'' in the
conclusive discrimination of two multipartite states.


title: Quantum information and triangular optical lattices

abstract:
  The regular structures obtained by optical lattice technology and their
behaviour are analysed from the quantum information perspective. Initially, we
demonstrate that a triangular optical lattice of two atomic species, bosonic or
fermionic, can be employed to generate a variety of novel spin-1/2 models that
include effective three-spin interactions. Such interactions can be employed to
simulate specific one or two dimensional physical systems that are of
particular interest for their condensed matter and entanglement properties. In
particular, connections between the scaling behaviour of entanglement and the
entanglement properties of closely spaced spins are drawn. Moreover, three-spin
interactions are well suited to support quantum computing without the need to
manipulate individual qubits. By employing Raman transitions or the interaction
of the atomic electric dipole moment with magnetic field gradients, one can
generate Hamiltonians that can be used for the physical implementation of
geometrical or topological objects. This work serves as a review article that
also includes many new results.


title: Is partial quantum search of a database any easier?

abstract:
  In this paper, we consider the partial database search problem where given a
database on N items, we are required to determine the first k bits of an
address x such that f(x)=1. We derive an algorithm and a lower bound for this
problem in the quantum circuits model. Let q(k,N) be the minimum number of
queries needed to find the first k bits of the required address x. We show that
there exist constants c_k and d_k such that (pi/4) (1 - d_k/sqrt{K}) sqrt{N} <=
q(k,n) <= (pi/4) (1 - c_k/sqrt{K}) sqrt{N}, where K=2^k. Thus, it is always
easier to determine a few bits of the target address than to find the entire
address, but as k becomes large this advantage reduces rapidly.


title:
Quantum versus classical scattering of Dirac particles by a solenoidal
  magnetic field and the correspondence principle

abstract:
  We present a detailed analysis of the scattering of charged particles by the
magnetic field of a long solenoid of constant magnetic flux and finite radius.
We study the relativistic and non-relativistic quantum and classical scenarios.
The classical limit of the perturbative quantum expressions, understood as the
Planck's limit (making $\hbar$ going to zero) is analyzed and compared with the
classical result. The classical cross section shows a general non-symmetric
behavior with respect to the scattering angle in contradistinction to the
quantum calculations performed so far. The various regimes analyzed show that
the quantum cross sections do not satisfy the correspondence principle: they do
not reduce to the classical result in any considered limit, an argument in
favor of the interpretation of the process as a purely quantum phenomenon. We
conclude that in order to restore the classical correspondence of the
phenomenon, a complete non-perturbative quantum calculation for a finite
solenoid radius is required.


title:
Explicit formula for the external driving field used to eliminate the
  decoherence of a two-state system coupled to a noise field

abstract:
  The elimination of decoherence of a multiphoton two-state quantum system by
using an appropriate external driving field is considered. The multiphoton
process caused by the noise field has a supersymmetric Lie algebraic structure.
The time-evolution equations for the off-diagonal elements of the density
operator of the two-state system are derived in the interaction picture. A
simple explicit formula is given for the time-dependent external driving field
used to eliminate the decoherence of the multiphoton two-state system.


title:
Implementing fanout, parity, and Mod gates via spin exchange
  interactions

abstract:
  We show that, for any n > 0, the Heisenberg interaction among 2n qubits (as
spin-1/2 particles) can be used to exactly implement an n-qubit parity gate,
which is equivalent in constant depth to an n-qubit fanout gate. Either
isotropic or nonisotropic versions of the interaction can be used. We
generalize our basic results by showing that any Hamiltonian (acting on
suitably encoded logical qubits), whose eigenvalues depend quadratically on the
Hamming weight of the logical qubit values, can be used to implement
generalized Mod_q gates for any q > 1.
  This paper is a sequel to quant-ph/0309163, and resolves a question left open
in that paper.


title:
Breaking Classical Public Key Cryptosystems by Using a Novel Ensemble
  Search Algorithm

abstract:
  In this paper, we improve Bruschweiler's algorithm such that only one query
is needed for searching the single object z from N=2^n unsorted elements. Our
algorithm construct the new oracle query function g(.) satisfying g(x)=0 for
all input x, except for one, say x=z, where g(z)=z. To store z, our algorithm
extends from one ancillary qubit to n ancillary qubits. We then measure these
ancillary qubits to discover z. We further use our ensemble search algorithm to
attack classical public key cryptosystems. Given the ciphertext C=Ek(m, r)
which is generated by the encryption function Ek(), a public key k, a message
m, and a random number r, we can construct an oracle query function h(.)
satisfying h(m', r')=0 if Ek(m', r')!=C and h(m', r')= (m', r') if Ek(m',
r')=C. There is only one object, say (m, r), can be discovered in decryption of
C. By preparing the input with all possible states of (m', r'), we can thus use
our ensemble search algorithm to find the wanted object (m, r). Obviously, we
break the classical public key cryptosystems under the ciphertext attack by
performing the oracle query function only one time.


title: Quantum and classical correlated imaging

abstract:
  We outline the potential gains of quantum correlated imaging and compare it
to classical correlated imaging. As shown earlier by A. Gatti, E. Bambilla, M.
Bache, and L. A. Lugiato, ArXive:quant-ph/0405056, classical correlated imaging
can mimic most features of quantum imaging but at lower signal-to-noise ratio
for a given mean photon number (or intensity). In this paper we specifically
investigate coherent correlated imaging, and show that while it is possible to
perform such imaging using a thermal source, a coherent light-source provides a
less demanding experimental setup. We also compare the performance to what can
be obtained by using non-classical light.


title: Quasiperiodic dynamics of coherent diffusion: a quantum walk approach

abstract:
  We study the dynamics of a generalization of quantum coin walk on the line
which is a natural model for a diffusion modified by quantum or interference
effects. In particular, our results provide surprisingly simple explanations to
phenomena observed by Bouwmeester et al. (Phys. Rev. A, 61, 13410 (1999)) in
their optical Galton board experiment, and a description of a stroboscopic
quantum walks given by Buershaper and Burnett (quant-ph/0406039) through
numerical simulations. We also provide heuristic explanations for the behavior
of our model which show, in particular, that its dynamics can be viewed as a
discrete version of Bloch oscillations.


title: On the goodness of "quantum blobs" in phase space quantization

abstract:
  We replace the usual notion of quantum cell from statistical mechanics by
that of "quantum blob". A quantum blob is the transform, by a linaer symplectic
transformation, of a phase space ball with radius equal to the square root of
h-bar. The intersection of a quantum blob with any symplectic plane is an
ellipse with area one half of h. This very special property, which is closed
related to the principle of the symplectic camel, leads to a symplectic
invariant statement of the uncertainty principle. We moreover prove that the
average of a phase space Gaussian over a quantum blob is the Wigner transform
of a minimum uncertainty Gaussian.


title:
Cryptanalysis of a Practical Quantum Key Distribution With
  Polarization-Entangled Photons

abstract:
  Recently, a quantum key exchange protocol has been described, which served as
basis for securing an actual bank transaction by means of quantum cryptography
[quant-ph/0404115]. Here we show, that the authentication scheme applied is
insecure in the sense that an attacker can provoke a situation where initiator
and responder of a key exchange end up with different keys. Moreover, it may
happen that an attacker can decrypt a part of the plaintext protected with the
derived encryption key.


title:
A Novel Protocol-Authentication Algorithm Ruling Out a Man-in-the-Middle
  Attack in Quantum Cryptography

abstract:
  In this work we review the security vulnerability of Quantum Cryptography
with respect to "man-in-the-middle attacks" and the standard authentication
methods applied to counteract these attacks. We further propose a modified
authentication algorithm which features higher efficiency with respect to
consumption of mutual secret bits.


title: The Physical Interpretation of PT-invariant Potentials

abstract:
  A purely imaginary potential can provide a phenomenological description of
creation and absorption of quantum mechanical particles. PT-invariance of such
a potential ensures that the non-unitary phenomena occur in a balanced manner.
In spite of wells and sinks which locally violate the conservation of quantum
probability, there is no net get loss or gain of particles. This, in turn, is
intuitively consistent with real energy eigenvalues.


title:
Efficient classical-communication-assisted local simulation of n-qubit
  GHZ correlations

abstract:
  We present a local hidden-variable model supplemented by classical
communication that reproduces the quantum-mechanical predictions for
measurements of all products of Pauli operators on an n-qubit GHZ state (or
"cat state"). The simulation is efficient since the required amount of
communication scales linearly with the number of qubits, even though there are
Bell-type inequalities for these states for which the amount of violation grows
exponentially with n. The structure of our model yields insight into the
Gottesman-Knill theorem by demonstrating that, at least in this limited case,
the correlations in the set of nonlocal hidden variables represented by the
stabilizer generators are captured by an appropriate set of local hidden
variables augmented by n-2 bits of classical communication.


title:
Rigorous derivation of coherent resonant tunneling time and velocity in
  finite periodic systems

abstract:
  The velocity $v_{res}$ of resonant tunneling electrons in finite periodic
structures is analytically calculated in two ways. The first method is based on
the fact that a transmission of unity leads to a coincidence of all still
competing tunneling time definitions. Thus, having an indisputable resonant
tunneling time $\tau_{res},$ we apply the natural definition
$v_{res}=L/\tau_{res}$ to calculate the velocity. For the second method we
combine Bloch's theorem with the transfer matrix approach to decompose the wave
function into two Bloch waves. Then the expectation value of the velocity is
calculated. Both different approaches lead to the same result, showing their
physical equivalence. The obtained resonant tunneling velocity $v_{res}$ is
smaller or equal to the group velocity times the magnitude of the complex
transmission amplitude of the unit cell. Only at energies where the unit cell
of the periodic structure has a transmission of unity $v_{res}$ equals the
group velocity. Numerical calculations for a GaAs/AlGaAs superlattice are
performed. For typical parameters the resonant velocity is below one third of
the group velocity.


title:
Complete hierarchies of efficient approximations to problems in
  entanglement theory

abstract:
  We investigate several problems in entanglement theory from the perspective
of convex optimization. This list of problems comprises (A) the decision
whether a state is multi-party entangled, (B) the minimization of expectation
values of entanglement witnesses with respect to pure product states, (C) the
closely related evaluation of the geometric measure of entanglement to quantify
pure multi-party entanglement, (D) the test whether states are multi-party
entangled on the basis of witnesses based on second moments and on the basis of
linear entropic criteria, and (E) the evaluation of instances of maximal output
purities of quantum channels. We show that these problems can be formulated as
certain optimization problems: as polynomially constrained problems employing
polynomials of degree three or less. We then apply very recently established
known methods from the theory of semi-definite relaxations to the formulated
optimization problems. By this construction we arrive at a hierarchy of
efficiently solvable approximations to the solution, approximating the exact
solution as closely as desired, in a way that is asymptotically complete. For
example, this results in a hierarchy of novel, efficiently decidable sufficient
criteria for multi-particle entanglement, such that every entangled state will
necessarily be detected in some step of the hierarchy. Finally, we present
numerical examples to demonstrate the practical accessibility of this approach.


title: Single-photon two-qubit SWAP gate for entanglement manipulation

abstract:
  A SWAP operation between different types of qubits of single photons is
essential for manipulating hyperentangled photons for a variety of
applications. We have implemented an efficient SWAP gate for the momentum and
polarization degrees of freedom of single photons. The SWAP gate was utilized
in a single-photon two-qubit quantum logic circuit to deterministically
transfer momentum entanglement between a pair of down-converted photons to
polarization entanglement. The polarization entanglement thus obtained violates
Bell's inequality by more than 150 standard deviations.


title:
Quantum teleportation via two qubit Heisenberg XY chain - Effects of
  anisotropy and magnetic field

abstract:
  In this paper, we study the influence of anisotropy on the usefulness, of the
entanglement in a two-qubit Heisenberg XY chain at thermal equilibrium in the
presence of an external magnetic field, as resource for quantum teleportation
via the standard teleportation protocol. We show that the nonzero thermal
entanglement produced by adjusting the external magnetic field strength beyond
some critical strength is a useful resource. We also considered entanglement
teleportation via two two-qubit Heisenberg XY chains.


title:
Two-Way Quantum Number Distribution Based on Entanglement and Bell-State
  Measurements

abstract:
  A scheme is proposed by which two parties, Alice and Bob, can securely
exchange real numbers. The scheme requires Alice and Bob to share entanglement
and both to perform Bell-state measurements. With a qubit system two real
numbers can each be sent by Alice and Bob, resulting in four real numbers
shared by them. The number of real numbers that can be shared increases if
higher-dimensional systems are utilized. The number of significant figures of
each shared real number depends upon the number of Bell-state measurements that
Alice and Bob perform. The security of the scheme against individual
eavesdropping attacks is analyzed and the effects of channel losses and errors
discussed.


title:
Advantages of high-speed technique for quantum key distribution; reply
  to quant-ph/0407050

abstract:
  We respond to a comment on our high-speed technique for the implementation of
free-space quantum key distribution (QKD). The model used in the comment
assigns inappropriately high link losses to the technique in question. We show
that the use of reasonable loss parameters in the model invalidates the
comment's main conclusion and highlights the benefits of increased transmission
rates.


title:
Implementing high dimensional unitary representations of SU(2) on a
  Quantum Computer

abstract:
  In this note we consider a system with a large angular momentum l whose state
we can store using some log_2(l) qubits. The problem then is how to carry out
spatial rotations of the system in this representation. In other words we are
looking at a unitary representation of SU(2) with dimension 2l+1 and want to
implement these transformations with resources polynomial in log(l). We only
give a sketch of our solution which involves ``storing'' discretised spherical
harmonic functions Y_{l,m}(Theta,phi) in a quantum register. Also there are
some technical gaps in the construction, but they are based on plausible
assumptions. Our approach is rather cumbersome and we hope somebody will find a
nicer solution. For a nice, elementary explanation of what we are trying to do
(not involving physics or representation theory) see section 4.6.2.


title: An iterative method for extreme optics of two-level systems

abstract:
  We formulate the problem of a two-level system in a linearly polarized laser
field in terms of a nonlinear Riccati-type differential equation and solve the
equation analytically in time intervals much shorter than half the optical
period. The analytical solutions for subsequent intervals are then stuck
together in an iterative procedure to cover the scale time of the laser pulse.
This approach is applicable to pulses of arbitrary (nonrelativistic) strengths,
shapes and durations, thus covering the whole region of light-matter couplings
from weak through moderate to strong ones. The method allows quick insight into
different problems from the field of light--matter interaction. Very good
quality of the method is shown by recovering with it a number of subtle effects
met in earlier numerically calculated photon-emission spectra from model
molecular ions, double quantum wells, atoms and semiconductors. The method
presented is an efficient mathematical tool to describe novel effects in the
region of, e.g., extreme nonlinear optics, i.e., when two--level systems are
exposed to pulses of only a few cycles in duration and strength ensuring the
Rabi frequency to approach and even exceed the laser light frequence.


title: Manipulation of optical solitons in Bose-Einstein condensates

abstract:
  We propose a method to control the optical transparency of a Bose-Einstein
condensate with working energy levels of the Lambda-type. The reported effects
are essentially nonlinear and are considered in the framework of an exactly
solvable model describing the interaction of light with a Lambda-type medium.
We show how the complicated nonlinear interplay between fast and slow solitons
in the $\Lambda$-type medium points to a possibility to create optical gates as
well as to a possibility to store optical information.


title: Detecting multipartite entanglement

abstract:
  We discuss the problem of determining whether the state of several quantum
mechanical subsystems is entangled. As in previous work on two subsystems we
introduce a procedure for checking separability that is based on finding state
extensions with appropriate properties and may be implemented as a semidefinite
program. The main result of this work is to show that there is a series of
tests of this kind such that if a multiparty state is entangled this will
eventually be detected by one of the tests. The procedure also provides a means
of constructing entanglement witnesses that could in principle be measured in
order to demonstrate that the state is entangled.


title:
Decomposition of time-covariant operations on quantum systems with
  continuous and/or discrete energy spectrum

abstract:
  Every completely positive map G that commutes which the Hamiltonian time
evolution is an integral or sum over (densely defined) CP-maps G_\sigma where
\sigma is the energy that is transferred to or taken from the environment. If
the spectrum is non-degenerated each G_\sigma is a dephasing channel followed
by an energy shift. The dephasing is given by the Hadamard product of the
density operator with a (formally defined) positive operator. The Kraus
operator of the energy shift is a partial isometry which defines a translation
on R with respect to a non-translation-invariant measure.
  As an example, I calculate this decomposition explicitly for the rotation
invariant gaussian channel on a single mode.
  I address the question under what conditions a covariant channel destroys
superpositions between mutually orthogonal states on the same orbit. For
channels which allow mutually orthogonal output states on the same orbit, a
lower bound on the quantum capacity is derived using the Fourier transform of
the CP-map-valued measure (G_\sigma).


title: Tracing the bounds on Bell-type inequalities

abstract:
  Bell-type inequalities and violations thereof reveal the fundamental
differences between standard probability theory and its quantum counterpart. In
the course of previous investigations ultimate bounds on quantum mechanical
violations have been found. For example, Tsirelson's bound constitutes a global
upper limit for quantum violations of the Clauser-Horne-Shimony-Holt (CHSH) and
the Clauser-Horne (CH) inequalities. Here we investigate a method for
calculating the precise quantum bounds on arbitrary Bell-type inequalities by
solving the eigenvalue problem for the operator associated with each Bell-type
inequality. Thereby, we use the min-max principle to calculate the norm of
these self-adjoint operators from the maximal eigenvalue yielding the upper
bound for a particular set of measurement parameters. The eigenvectors
corresponding to the maximal eigenvalues provide the quantum state for which a
Bell-type inequality is maximally violated.


title:
Squeezing spectra from s-ordered quasiprobability distributions.
  Application to dispersive optical bistability

abstract:
  It is well known that the squeezing spectrum of the field exiting a nonlinear
cavity can be directly obtained from the fluctuation spectrum of normally
ordered products of creation and annihilation operators of the cavity mode. In
this article we show that the output field squeezing spectrum can be derived
also by combining the fluctuation spectra of any pair of s-ordered products of
creation and annihilation operators. The interesting result is that the
spectrum obtained in this way from the linearized Langevin equations is exact,
and this occurs in spite of the fact that no s-ordered quasiprobability
distribution verifies a true Fokker-Planck equation, i.e., the Langevin
equations used for deriving the squeezing spectrum are not exact. The
(linearized) intracavity squeezing obtained from any s-ordered distribution is
also exact. These results are exemplified in the problem of dispersive optical
bistability.


title: Jensen-Shannon divergence, Fisher information, and Wootters' hypothesis

abstract:
  We discuss different statistical distances in probability space, with
emphasis on the Jensen-Shannon divergence, vis-a-vis {\it metrics} in Hilbert
space and their relationship with Fisher's information measure. This study
provides further reconfirmation of Wootters' hypothesis concerning the
possibility that statistical fluctuations in the outcomes of measurements be
regarded (at least partly) as responsible for the Hilbert-space structure of
quantum mechanics.


title:
Collective attacks and unconditional security in continuous variable
  quantum key distribution

abstract:
  We present here an information theoretic study of Gaussian collective attacks
on the continuous variable key distribution protocols based on Gaussian
modulation of coherent states. These attacks, overlooked in previous security
studies, give a finite advantage to the eavesdropper in the experimentally
relevant lossy channel, but are not powerful enough to reduce the range of the
reverse reconciliation protocols. Secret key rates are given for the ideal case
where Bob performs optimal collective measurements, as well as for the
realistic cases where he performs homodyne or heterodyne measurements. We also
apply the generic security proof of Christiandl et. al. [quant-ph/0402131] to
obtain unconditionally secure rates for these protocols.


title: Security bounds for continuous variables quantum key distribution

abstract:
  Security bounds for key distribution protocols using coherent and squeezed
states and homodyne measurements are presented. These bounds refer to (i)
general attacks and (ii) collective attacks where Eve interacts individually
with the sent states, but delays her measurement until the end of the
reconciliation process. For the case of a lossy line and coherent states, it is
first proven that a secure key distribution is possible up to 1.9 dB of losses.
For the second scenario, the security bounds are the same as for the completely
incoherent attack.


title:
Towards a quantum evolutionary scheme: violating Bell's inequalities in
  language

abstract:
  We show the presence of genuine quantum structures in human language. The
neo-Darwinian evolutionary scheme is founded on a probability structure that
satisfies the Kolmogorovian axioms, and as a consequence cannot incorporate
quantum-like evolutionary change. In earlier research we revealed quantum
structures in processes taking place in conceptual space. We argue that the
presence of quantum structures in language and the earlier detected quantum
structures in conceptual change make the neo-Darwinian evolutionary scheme
strictly too limited for Evolutionary Epistemology. We sketch how we believe
that evolution in a more general way should be implemented in epistemology and
conceptual change, but also in biology, and how this view would lead to another
relation between both biology and epistemology.


title: Thermodynamical Cost of Accessing Quantum Information

abstract:
  Thermodynamics is a macroscopic physical theory whose two very general laws
are independent of any underlying dynamical laws and structures. Nevertheless,
its generality enables us to understand a broad spectrum of phenomena in
physics, information science and biology. Recently, it has been realised that
information storage and processing based on quantum mechanics can be much more
efficient than their classical counterpart. What general bound on storage of
quantum information does thermodynamics imply? We show that thermodynamics
implies a weaker bound than the quantum mechanical one (the Holevo bound). In
other words, if any post-quantum physics should allow more information storage
it could still be under the umbrella of thermodynamics.


title: Multiparty data hiding of quantum information

abstract:
  We present protocols for multiparty data hiding of quantum information that
implement all possible threshold access structures. Closely related to secret
sharing, data hiding has a more demanding security requirement: that the data
remain secure against unrestricted LOCC attacks. In the limit of hiding a large
amount of data, our protocols achieve an asymptotic rate of one hidden qubit
per local physical qubit. That is, each party holds a share that is the same
size as the hidden state to leading order, with accuracy and security
parameters incurring an overhead that is asymptotically negligible. The data
hiding states have very unusual entanglement properties, which we briefly
discuss.


title: Casimir force between designed materials: what is possible and what not

abstract:
  We establish strict upper limits for the Casimir interaction between
multilayered structures of arbitrary dielectric or diamagnetic materials. We
discuss the appearance of different power laws due to frequency-dependent
material constants. Simple analytical expressions are in good agreement with
numerical calculations based on Lifshitz theory. We discuss the improvements
required for current (meta) materials to achieve a repulsive Casimir force.


title: Gaussian-random Ensembles of Pseudo-Hermitian Matrices

abstract:
  Attention has been brought to the possibility that statistical fluctuation
properties of several complex spectra, or, well-known number sequences may
display strong signatures that the Hamiltonian yielding them as eigenvalues is
PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of
pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing
distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call
the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian
Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic
Riemann-zeros (${1 \over 2}\pm i t_n)$ would rather correspond to some
PT-symmetric (pseudo-Hermitian) Hamiltonian.


title:
Direct measurement of superluminal group velocity and of signal velocity
  in an optical fiber

abstract:
  We present an easy way of observing superluminal group velocities using a
birefringent optical fiber and other standard devices. In the theoretical
analysis, we show that the optical properties of the setup can be described
using the notion of "weak value". The experiment shows that the group velocity
can indeed exceed c in the fiber; and we report the first direct observation of
the so-called "signal velocity", the speed at which information propagates and
that cannot exceed c.


title: Purifications Without Entanglement, State Reconstructions and Entropy

abstract:
  In this paper we have analysed in detail two different purification
protocols. The first one, proposed by Sudarshan, is based on the preservation
of probabilities.We have constructed a second protocol here based on
optimisation of fidelities. We have considered both complete and partial
measurements and have established bounds and inequalities for various
fidelities. For every type of measurement, we have analysed post-measurement
states based on the Maximum entropy principle as well as what we have proposed
as unbiased states. We show that our purification protocol always leads to
better state reconstruction. These schemes can be thought of as operations in
the sense of Kraus and we have explicitly constructed the Kraus operators for
these. We have also shown that the entropy either increases or remains the same
depending on the choice of the purification basis.


title: On the control of the lateral Casimir force between corrugated surfaces

abstract:
  The general perturbative expression for the lateral Casimir force between two
plates covered by longitudinal corrugations of arbitrary shape is obtained.
This expression is applicable for corrugation periods larger than the
separation distance. The cases of asymmetric corrugations are considered, which
allow to increase the maximum to minimum force ratio and affect the character
of equilibrium points. This opens new opportunities to control the lateral
Casimir forces for use in microelectromechanical devices based entirely on the
vacuum fluctuation properties.


title: Alternative Descriptions in Quaternionic Quantum Mechanics

abstract:
  We characterize the quasianti-Hermitian quaternionic operators in QQM by
means of their spectra; moreover, we state a necessary and sufficient condition
for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian
with respect to a uniquely defined positive scalar product in a infinite
dimensional (right) quaternionic Hilbert space. According to such results we
obtain two alternative descriptions of a quantum optical physical system, in
the realm of quaternionic quantum mechanics, while no alternative can exist in
complex quantum mechanics, and we discuss some differences between them.


title: Quantum States from Tangent Vectors

abstract:
  We argue that tangent vectors to classical phase space give rise to quantum
states of the corresponding quantum mechanics. This is established for the case
of complex, finite-dimensional, compact, classical phase spaces C, by
explicitly constructing Hilbert-space vector bundles over C. We find that these
vector bundles split as the direct sum of two holomorphic vector bundles: the
holomorphic tangent bundle T(C), plus a complex line bundle N(C). Quantum
states (except the vacuum) appear as tangent vectors to C. The vacuum state
appears as the fibrewise generator of N(C). Holomorphic line bundles N(C) are
classified by the elements of Pic(C), the Picard group of C. In this way Pic(C)
appears as the parameter space for nonequivalent vacua. Our analysis is
modelled on, but not limited to, the case when C is complex projective space.


title:
An Algebraic Construction of Generalized Coherent States for
  Shape-Invariant Potentials

abstract:
  Generalized coherent states for shape invariant potentials are constructed
using an algebraic approach based on supersymmetric quantum mechanics. We show
this generalized formalism is able to: a) supply the essential requirements
necessary to establish a connection between classical and quantum formulations
of a given system (continuity of labeling, resolution of unity, temporal
stability, and action identity); b) reproduce results already known for
shape-invariant systems, like harmonic oscillator, double anharmonic,
Poschl-Teller and self-similar potentials and; c) point to a formalism that
provides an unified description of the different kind of coherent states for
quantum systems.


title: Multi-splitter interaction for entanglement distribution

abstract:
  In protocols of distributed quantum information processing, a network of
bilateral entanglement is a key resource for efficient communication and
computation. We propose a model, efficient both in finite and infinite Hilbert
spaces, that performs entanglement distribution among the elements of a network
without local control. In the establishment of entangled channels, our setup
requires only the proper preparation of a single elected element. We suggest a
setup of electromechanical systems to implement our proposal.


title: The Lorentz-Dirac force from QED for linear acceleration

abstract:
  We investigate the motion of a wave packet of a charged scalar particle
linearly accelerated by a static potential in quantum electrodynamics. We
calculate the expectation value of the position of the charged particle after
the acceleration to first order in the fine structure constant in the hbar -> 0
limit. We find that the change in the expectation value of the position (the
position shift) due to radiation reaction agrees exactly with the result
obtained using the Lorentz-Dirac force in classical electrodynamics. We also
point out that the one-loop correction to the potential may contribute to the
position change in this limit.


title: Mapping of Euclidean resonance on static resonant tunneling

abstract:
  Quantum tunneling through an almost classical potential barrier can be
strongly enhanced by a nonstationary field so that the penetration through the
barrier becomes not exponentially small. This constitutes an extremely unusual
phenomenon of quantum physics called Euclidean resonance. A certain
nonstationary barrier is proposed with a very low WKB tunneling rate. The
quantum dynamics of this barrier is mapped on resonant tunneling across a
static double barrier with a resonant level inside. The real penetration
through the dynamical barrier is not exponentially small providing an example
of Euclidean resonance. Therefore, the Schoedinger equation allows solutions of
the type of Euclidean resonance. The counterintuitive phenomenon of Euclidean
resonance is a dynamical analogue of static resonant tunneling.


title: Remote spectral measurement using entangled photons

abstract:
  By utilizing the frequency anticorrelation of two-photon states produced via
spontaneous parametric down conversion (SPDC), the working principle of a novel
remote spectrometer is demonstrated. With the help of a local scanning
monochromator, the spectral transmission function of an optical element (or
atmosphere) at remote locations can be characterized for wide range of
wavelengths with expected high resolution.


title:
Quantum parallelism of the controlled-NOT operation: an experimental
  criterion for the evaluation of device performance

abstract:
  It is shown that a quantum controlled-NOT gate simultaneously performs the
logical functions of three distinct conditional local operations. Each of these
local operations can be verified by measuring a corresponding truth table of
four local inputs and four local outputs. The quantum parallelism of the gate
can then be observed directly in a set of three simple experimental tests, each
of which has a clear intuitive interpretation in terms of classical logical
operations. Specifically, quantum parallelism is achieved if the average
fidelity of the three classical operations exceeds 2/3. It is thus possible to
evaluate the essential quantum parallelism of an experimental controlled-NOT
gate by testing only three characteristic classical operations performed by the
gate.


title: Depolarization channels with zero-bandwidth noises

abstract:
  A simple model describing depolarization channels with zero-bandwidth
environment is presented and exactly solved. The environment is modelled by
Lorentzian, telegraphic and Gaussian zero-bandwidth noises. Such channels can
go beyond the standard Markov dynamics and therefore can illustrate the
influence of memory effects of the noisy communication channel on the
transmitted information. To quantify the disturbance of quantum states the
entanglement fidelity between arbitrary input and output states is
investigated.


title:
A pseudo-unitary ensemble of random matrices, PT-symmetry and the
  Riemann Hypothesis

abstract:
  An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that
possesses real eigenvalues with level-spacing distribution exactly as for the
Gaussian Unitary Ensemble found by Wigner. By a re-interpretation of Connes'
spectral interpretation of the zeros of the Riemann zeta function, we propose
to enlarge the scope of search of the Hamiltonian connected with the celebrated
Riemann Hypothesis by suggesting that the Hamiltonian could also be
PT-symmetric (or pseudo-Hermitian).


title: Local copying of orthogonal entangled quantum states

abstract:
  In classical information theory one can, in principle, produce a perfect copy
of any input state. In quantum information theory, the no cloning theorem
prohibits exact copying of nonorthogonal states. Moreover, if we wish to copy
multiparticle entangled states and can perform only local operations and
classical communication (LOCC), then further restrictions apply. We investigate
the problem of copying orthogonal, entangled quantum states with an entangled
blank state under the restriction to LOCC. Throughout, the subsystems have
finite dimension D. We show that if all of the states to be copied are
non-maximally entangled, then novel LOCC copying procedures based on
entanglement catalysis are possible. We then study in detail the LOCC copying
problem where both the blank state and at least one of the states to be copied
are maximally entangled. For this to be possible, we find that all the states
to be copied must be maximally entangled. We obtain a necessary and sufficient
condition for LOCC copying under these conditions. For two orthogonal,
maximally entangled states, we provide the general solution to this condition.
We use it to show that for D=2,3, any pair of orthogonal, maximally entangled
states can be locally copied using a maximally entangled blank state. However,
we also show that for any D which is not prime, one can construct pairs of such
states for which this is impossible.


title: Ghost Interference with Optical Parametric Amplifier

abstract:
  The 'Ghost' interference experiment is analyzed when the source of entangled
photons is a multimode Optical Parametric Amplifier(OPA) whose weak limit is
the two-photon Spontaneous Parametric Downconversion(SPDC) beam. The visibility
of the double-slit pattern is calculated, taking the finite coincidence time
window of the photon counting detectors into account. It is found that the
coincidence window and the bandwidth of light reaching the detectors play a
crucial role in the loss of visibility on coincidence detection, not only in
the 'Ghost' interference experiment but in all experiments involving
coincidence detection. The differences between the loss of visibility with
two-mode and multimode OPA sources is also discussed.
  PACS: 42.65.Yj, 42.50.Dv, 42.65.Lm


title:
Quantum spin tunneling in a soluble quasi-spin model: An angle-based
  potential description

abstract:
  We propose an approach which allows to construct and use a potential function
written in terms of an angle variable to describe interacting spin systems. We
show how this can be implemented in the Lipkin-Meshkov-Glick, here considered a
paradigmatic spin model. It is shown how some features of the energy gap can be
interpreted in terms of a spin tunneling. A discrete Wigner function is
constructed for a symmetric combination of two states of the model and its time
evolution is obtained. The physical information extracted from that function
reinforces our description of phase oscillations in a potential.


title:
Thermodynamic and noise considerations for the detection of microscopic
  particles in a gas by Photoacoustic Raman spectroscopy

abstract:
  We develop a simple thermodynamic model to describe the heat transfer
mechanisms and generation of acoustic waves in photoacoustic Raman spectroscopy
by small particulate suspensions in a gas. Using Langevin methods to describe
the thermal noise we study the signal and noise properties, and from the noise
equivalent power we determine the minimum number density of the suspended
particles that can be detected. We find that for some relevant cases, as few as
100 particles per cubic meter can be detected.


title: Mixed state sensitivity of several quantum information benchmarks

abstract:
  We investigate an imbalance between the sensitivity of the common state
measures--fidelity, trace distance, concurrence, tangle, von Neumann entropy
and linear entropy--when acted on by a depolarizing channel. Further, in this
context we explore two classes of two-qubit entangled mixed states.
Specifically, we illustrate a sensitivity imbalance between three of these
measures for depolarized (i.e., Werner-state like) nonmaximally entangled and
maximally entangled mixed states, noting that the size of the imbalance depends
on the state's tangle and linear entropy.


title:
Adiabatic pulse propagation in coherent atomic media with the tripod
  level configuration

abstract:
  We investigate the problem of propagation of three-component resonant light
pulses with adiabatically varying amplitudes through a medium consisting of
atoms with the tripod level configuration. By means of both analytic and
numerical methods we found the two modes of shape-preserving pulse propagation.
The pulse propagation velocity is found to be either equal to the speed of
light or significantly slowed down, depending on a particular propagation mode.


title: Implementable Quantum Bit-String Commitment Protocol

abstract:
  Quantum bit-string commitment[A.Kent, Phys.Rev.Lett., 90, 237901 (2003)] or
QBSC is a variant of bit commitment (BC). In this paper, we propose a new QBSC
protocol that can be implemented using currently available technology, and
prove its security under the same security criteria as discussed by Kent. QBSC
is a generalization of BC, but has slightly weaker requirements, and our
proposed protocol is not intended to break the no-go theorem of quantum BC.


title: Quantum channel based on correlated twin laser beams

abstract:
  This work is the development and analysis of the recently proposed quantum
cryptographic protocol, based on the use of the two-mode coherently correlated
states. The protocol is supplied with the cyrptographic control procedures. The
channel error properties and stability against eavesdropping are examined.
State detection features are proposed.


title:
Realization of Universal Optimal Quantum Machines by Projective
  Operators and Stochastic Maps

abstract:
  Optimal quantum machines can be implemented by linear projective operations.
In the present work a general qubit symmetrization theory is presented by
investigating the close links to the qubit purification process and to the
programmable teleportation of any generic optimal anti-unitary map. In
addition, the contextual realization of the N ->M cloning map and of the
teleportation of the N->(M-N) universal NOT gate is analyzed by a novel and
very general angular momentum theory. An extended set of experimental
realizations by state symmetrization linear optical procedures is reported.
These include the 1->2 cloning process, the UNOT gate and the quantum
tomographic characterization of the optimal partial transpose map of
polarization encoded qubits.


title: Geometric quantum gates robust against stochastic control errors

abstract:
  We analyze a scheme for quantum computation where quantum gates can be
continuously changed from standard dynamic gates to purely geometric ones.
These gates are enacted by controlling a set of parameters that are subject to
unwanted stochastic fluctuations. This kind of noise results in a departure
from the ideal case that can be quantified by a gate fidelity. We find that the
maximum of this fidelity corresponds to quantum gates with a vanishing
dynamical phase.


title:
Broadband Relaxation-Optimized Polarization Transfer in Magnetic
  Resonance

abstract:
  Many applications of magnetic resonance are limited by rapid loss of spin
coherence caused by large transverse relaxation rates. In nuclear magnetic
resonance (NMR) of large proteins, increased relaxation losses lead to poor
sensitivity of experiments and increased measurement time. In this paper we
develop broadband relaxation optimized pulse sequences (BB-CROP) which approach
fundamental limits of coherence transfer efficiency in the presence of very
general relaxation mechanisms that include cross-correlated relaxation. These
broadband transfer schemes use new techniques of chemical shift refocusing
(STAR echoes) that are tailored to specific trajectories of coupled spin
evolution. We present simulations and experimental data indicating significant
enhancement in the sensitivity of multi-dimensional NMR experiments of large
molecules by use of these methods.


title: A two-way algorithm for the entanglement problem

abstract:
  We propose an algorithm which proves a given bipartite quantum state to be
separable in a finite number of steps. Our approach is based on the search for
a decomposition via a countable subset of product states, which is dense within
all product states. Performing our algorithm simultaneously with the algorithm
by Doherty, Parrilo and Spedalieri (which proves a quantum state to be
entangled in a finite number of steps) leads to a two-way algorithm that
terminates for any input state. Only for a set of arbitrary small measure near
the border between separable and entangled states the result is inconclusive.


title: Controlling a group velocity of light by magnetic field

abstract:
  We have shown that quantum interference in a driven quasi-degenerate
two-level atomic system can be controlled by an externally applied magnetic
field. We demonstrate that the mechanism of optical control is based on quantum
interference, which allows one to implement both electromagnetically induced
transparency and electromagnetically induced absorption in one atomic system.
Dispersion of such the medium allows one to control group velocity of
propagation of light pulses be ultra-slow or superluminal via applied magnetic
field.


title:
Loophole-free test of quantum non-locality using high-efficiency
  homodyne detectors

abstract:
  We provide a detailed analysis of the recently proposed setup for a
loophole-free test of Bell inequality using conditionally generated
non-Gaussian states of light and balanced homodyning. In the proposed scheme, a
two-mode squeezed vacuum state is de-gaussified by subtracting a single photon
from each mode with the use of an unbalanced beam splitter and a standard
low-efficiency single-photon detector. We thoroughly discuss the dependence of
the achievable Bell violation on the various relevant experimental parameters
such as the detector efficiencies, the electronic noise and the mixedness of
the initial Gaussian state. We also consider several alternative schemes
involving squeezed states, linear optical elements, conditional photon
subtraction and homodyne detection.


title:
A new approach to the logarithmic perturbation theory for the spherical
  anharmonic oscillator

abstract:
  The explicit semiclassical treatment of the logarithmic perturbation theory
for the bound-state problem for the spherical anharmonic oscillator is
developed. Based upon the $\hbar$-expansions and suitable quantization
conditions a new procedure for deriving perturbation expansions is offered.
Avoiding disadvantages of the standard approach, new handy recursion formulae
with the same simple form both for ground and excited states have been
obtained. As an example, the perturbation expansions for the energy eigenvalues
of the quartic anharmonic oscillator are considered.


title: Classical mechanics is not h=0 limit of quantum mechanics

abstract:
  Both the set of quantum states and the set of classical states described by
symplectic tomographic probability distributions (tomograms) are studied. It is
shown that the sets have common part but there exist tomograms of classical
states which are not admissible in quantum mechanics and vica versa, there
exist tomograms of quantum states which are not admissible in classical
mechanics. Role of different transformations of reference frames in phase space
of classical and quantum systems (scaling and rotation) determining the
admissibility of the tomograms as well as the role of quantum uncertainty
relations is elucidated. Union of all admissible tomograms of both quantum and
classical states is discussed in context of interaction of quantum and
classical systems. Negative probabilities in classical mechanics and in quantum
mechanics corresponding to the tomograms of classical states and quantum states
are compared with properties of nonpositive and nonnegative density operators,
respectively.


title: Quantum polarization properties of two-mode energy eigenstates

abstract:
  We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to
two can be transformed into an orthogonal state using only linear optics.
According to a recently suggested definition of polarization degree, this
implies that all such states are fully polarized. This is also found to be true
for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2)
orbit. Complete two- and three-photon bases whose basis states are related by
only phase shifts or geometrical rotations are also derived.


title: Macroscopic quantum tunneling with decoherence

abstract:
  The tunneling probability for a system modelling macroscopic quantum
tunneling is computed. We consider an open quantum system with one degree of
freedom consisting of a particle trapped in a cubic potential interacting with
an environment characterized by a dissipative and a diffusion parameter. A
representation based on the energy eigenfunctions of the isolated system, i. e.
the system uncoupled to the environment, is used to write the dynamical master
equation for the reduced Wigner function of the open quantum system. This
equation becomes very simple in that representation. The use of the WKB
approximation for the eigenfunctions suggests an approximation which allows an
analytic computation of the tunneling rate, in this real time formalism, when
the system is initially trapped in the false ground state. We find that the
decoherence produced by the environment suppresses tunneling in agreement with
results in other macroscopic quantum systems with different potentials. We
confront our analytical predictions with an experiment where the escape rate
from the zero voltage state was measured for a current-biased Josephson
junction shunted with a resistor.


title: Spontaneous emission of light from atoms: the model

abstract:
  We investigate (non-relativistic) atomic systems interacting with quantum
electromagnetic field (QEF). The resulting model describes spontaneous emission
of light from a two-level atom surrounded by various initial states of the QEF.
We assume, that the quantum field interacts with the atom via the standard,
minimal-coupling Hamiltonian, with the $A^2$ term neglected. We also assume,
that there will appear at most single excitations (photons). By conducting the
analysis on a general level we allow for an arbitrary initial state of the QEF
(which can be for instance: the vacuum, the ground state in a cavity, or the
squeezed state). We derive a Volterra-type equation which governs the time
evolution of the amplitude of the excited state. The two-point function of the
initial state of the QEF, integrated with a combination of atomic
wavefunctions, forms the kernel of this equation.


title: The "Forgotten" Process : the emission stimulated by matter waves

abstract:
  In a famous paper where he introduces the A and B coefficients, Einstein
considered that atomic decays of excited atoms can be stimulated by light
waves. Here we consider that atomic decays can also be stimulated by atomic
waves. It is however necessary to change the Maxwell-Boltzmann statistics of
thermal equilibrium into Bose-Einstein statistics and to introduce a
coefficient C which complements the list of the coefficients introduced by
Einstein. Stimulated emission of light can be considered as the first step
towards the laser. Similarly, stimulated production of matter waves can be
considered as the basic phenomenon for an atom-laser. Most of the results that
we obtain here are not new. However, the method that we use remains very close
to elementary classical physics and emphasizes the symmetry between
electromagnetic and matter waves from various points of view.


title:
Quantum theory of a polarization phase-gate in an atomic tripod
  configuration

abstract:
  We present the quantum theory of a polarization phase-gate that can be
realized in a sample of ultracold rubidium atoms driven into a tripod
configuration. The main advantages of this scheme are in its relative
simplicity and inherent symmetry. It is shown that the conditional phase shifts
of order $\pi$ can be attained.


title: Four-photon correction in two-photon Bell experiments

abstract:
  Correlated photons produced by spontaneous parametric down-conversion are an
essential tool for quantum communication, especially suited for long-distance
connections. To have a reasonable count rate after all the losses in the
propagation and the filters needed to improve the coherence, it is convenient
to increase the intensity of the laser that pumps the non-linear crystal. By
doing so, however, the importance of the four-photon component of the
down-converted field increases, thus degrading the quality of two-photon
interferences. In this paper, we present an easy derivation of this nuisance
valid for any form of entanglement generated by down-conversion, followed by a
full study of the problem for time-bin entanglement. We find that the
visibility of two-photon interferences decreases as V=1-2\rho, where \rho is,
in usual situations, the probability per pulse of creating a detectable photon
pair. In particular, the decrease of V is independent of the coherence of the
four-photon term. Thanks to the fact that \rho can be measured independently of
V, the experimental verification of our prediction is provided for two
different configuration of filters.


title:
A Proposal for an Optical Implementation of an Universal Quantum Phase
  Gate

abstract:
  Large optical nonlinearities occurring in a coherently prepared atomic system
are shown to produce phase shifts of order $\pi$. Such an effect may be
observed in ultracold rubidium atoms where it could be feasibly exploited
toward the realization of a polarization phase gate.


title:
Coherently-assisted incoherent population transfer in a five-level
  system

abstract:
  A novel effect of population transfer in a five-level system is analyzed.
This population transfer effect is found to be a version of a Raman process,
which is facilitated and assisted by coherence effects, acting to close other
available decay channels.


title: Bellman equations for optimal feedback control of qubit states

abstract:
  Using results from quantum filtering theory and methods from classical
control theory, we derive an optimal control strategy for an open two-level
system (a qubit in interaction with the electromagnetic field) controlled by a
laser. The aim is to optimally choose the laser's amplitude and phase in order
to drive the system into a desired state. The Bellman equations are obtained
for the case of diffusive and counting measurements for vacuum field states. A
full exact solution of the optimal control problem is given for a system with
simpler, linear, dynamics. These linear dynamics can be obtained physically by
considering a two-level atom in a strongly driven, heavily damped, optical
cavity.


title: Superdense coding using multipartite states

abstract:
  We show that with the fourpartite quantum channel used to teleport an
arbitrary two qubit state, we can construct a superdense coding protocol where
it is possible to transmit 4 bits of classical information sending only 2
qubits. Alice and Bob initially share a four qubit maximally entangled state
and by locally manipulating her two qubits Alice can generate 16 orthogonal
maximally entangled states, which are used to encode the message transmitted to
Bob. He reads the 4 bit message by a generalized Bell state measurement. A
generalized protocol in which 2N bits of classical information is transmitted
via N qubits is also presented. We also show that this four(2N-)partite channel
is equivalent to two(N) Bell states, which proves that we need two(N) Bell
states to teleport a two(N) qubit system.


title:
A simple method for the preparation of pseudopure states in NMR quantum
  information processing

abstract:
  The use of nuclear magnetic resonance (NMR) to carry out quantum information
processing (QIP) often requires the preparation, transformation, and detection
of pseudopure states. In our previous work, it was shown that the use of pairs
of pseudopure states (POPS) as a basis for QIP is very convenient because of
the simplicity in experimental execution. It is now further demonstrated that
the product of the NMR spectra corresponding to two sets of POPS that share a
common pseudopure state has the same peak frequencies as those of the common
(single) pseudopure state. Examples of applying two different quantum logic
gates to a 5-qubit system are given.


abstract:
  The rigged Hilbert space of the algebra of the one-dimensional rectangular
barrier potential is constructed. The one-dimensional rectangular potential
provides another opportunity to show that the rigged Hilbert space fully
accounts for Dirac's bra-ket formalism. The analogy between Dirac's formalism
and Fourier methods is pointed out.


title:
Polarization statistical properties of the emission from the single mode
  Vertical-Cavity Surface-Emitting Lasers with the equally living laser levels

abstract:
  The full quantum-statistical theory of the Vertical-Cavity Surface-Emitting
Laser (VCSEL) in the form of the Langevin equations is constructed for
arbitrary relations between the frequency parameters. The same theoretical
treatment as in Ref.[1,2] are used. For detailed analysis the theory is applied
for lasers with equally living laser levels and on this basis the analytical
expressions for the spectral densities of the Stokes parameter fluctuations are
obtained in the explicit dependence on the physical phenomena, including the
spin-flip and the optical anisotropy. It is demonstrated the arbitrary
distribution of electrons between the sub-levels under pumping does not
restrict a possibility to achieve the noise reduction below the quantum limit.
Under comparison with phenomenological treatment Ref.[3] it is shown this
approach turns out to be not quite satisfied.


title: Tomographic measurements on superconducting qubit states

abstract:
  We propose an approach to reconstruct any superconducting charge qubit state
by using quantum state tomography. This procedure requires a series of
measurements on a large enough number of identically prepared copies of the
quantum system. The experimental feasibility of this procedure is explained and
the time scales for different quantum operations are estimated according to
experimentally accessible parameters. Based on the state tomography, we also
investigate the possibility of the process tomography.