title:
Quantum Equilibrium and the Role of Operators as Observables in Quantum
  Theory

abstract:
  Bohmian mechnaics is the most naively obvious embedding imaginable of
Schr\"odingers's equation into a completely coherent physical theory. It
describes a world in which particles move in a highly non-Newtonian sort of
way, one which may at first appear to have little to do with the spectrum of
predictions of quantum mechanics. It turns out, however, that as a consequence
of the defining dynamical equations of Bohmian mechanics, when a system has
wave function $\psi$ its configuration is typically random, with probability
density $\rho$ given by $|\psi|^2$, the quantum equilibrium distribution. It
also turns out that the entire quantum formalism, operators as observables and
all the rest, naturally emerges in Bohmian mechanics from the analysis of
``measurements.'' This analysis reveals the status of operators as observables
in the description of quantum phenomena, and facilitates a clear view of the
range of applicability of the usual quantum mechanical formulas.


title: Quantum Equilibrium and the Origin of Absolute Uncertainty

abstract:
  The quantum formalism is a ``measurement'' formalism--a phenomenological
formalism describing certain macroscopic regularities. We argue that it can be
regarded, and best be understood, as arising from Bohmian mechanics, which is
what emerges from Schr\"odinger's equation for a system of particles when we
merely insist that ``particles'' means particles. While distinctly
non-Newtonian, Bohmian mechanics is a fully deterministic theory of particles
in motion, a motion choreographed by the wave function. We find that a Bohmian
universe, though deterministic, evolves in such a manner that an {\it
appearance} of randomness emerges, precisely as described by the quantum
formalism and given, for example, by ``$\rho=|\psis|^2$.'' A crucial ingredient
in our analysis of the origin of this randomness is the notion of the effective
wave function of a subsystem, a notion of interest in its own right and of
relevance to any discussion of quantum theory. When the quantum formalism is
regarded as arising in this way, the paradoxes and perplexities so often
associated with (nonrelativistic) quantum theory simply evaporate.


title: Classical vs Quantum Mechanics: role of elementary excitations

abstract:
  Simple theorems relating a quantum mechanical system to the corresponding
classical one at equilibrium and connecting the quantum eigenvalues to the
frequencies of normal modes oscillations are presented. Corresponding to each
quantum eigenfunction, a ` classical eigenfunction' is associated. Those
belonging to `elementary excitations' play an important role.


title: Three level atom optics via the tunneling interaction

abstract:
  Three level atom optics (TLAO) is introduced as a simple, efficient and
robust method to coherently manipulate and transport neutral atoms. The
tunneling interaction among three trapped states allows to realize the spatial
analog of the stimulated Raman adiabatic passage (STIRAP), coherent population
trapping (CPT), and electromagnetically induced transparency (EIT) techniques.
We investigate a particular implementation in optical microtrap arrays and show
that under realistic parameters the coherent manipulation and transfer of
neutral atoms among dipole traps could be realized in the millisecond range.


title: Adiabatic quantum computation and quantum phase transitions

abstract:
  We analyze the ground state entanglement in a quantum adiabatic evolution
algorithm designed to solve the NP-complete Exact Cover problem. The entropy of
entanglement seems to obey linear and universal scaling at the point where the
mass gap becomes small, suggesting that the system passes near a quantum phase
transition. Such a large scaling of entanglement suggests that the effective
connectivity of the system diverges as the number of qubits goes to infinity
and that this algorithm cannot be efficiently simulated by classical means. On
the other hand, entanglement in Grover's algorithm is bounded by a constant.


title: Quantum tensor product structures are observable-induced

abstract:
  It is argued that the partition of a quantum system into subsystems is
dictated by the set of operationally accessible interactions and measurements.
The emergence of a multi-partite tensor product structure of the state-space
and the associated notion of quantum entanglement are then relative and
observable-induced. We develop a general algebraic framework aimed to formalize
this concept. We discuss several cases relevant to quantum information
processing and decoherence control.


title: A family of quantum protocols

abstract:
  We introduce two dual, purely quantum protocols: for entanglement
distillation assisted by quantum communication (``mother'' protocol) and for
entanglement assisted quantum communication (``father'' protocol). We show how
a large class of ``children'' protocols (including many previously known ones)
can be derived from the two by direct application of teleportation or
super-dense coding. Furthermore, the parent may be recovered from most of the
children protocols by making them ``coherent''. We also summarize the various
resource trade-offs these protocols give rise to.


title:
Recognizing Small-Circuit Structure in Two-Qubit Operators and Timing
  Hamiltonians to Compute Controlled-Not Gates

abstract:
  This work proposes numerical tests which determine whether a two-qubit
operator has an atypically simple quantum circuit. Specifically, we describe
formulae, written in terms of matrix coefficients, characterizing operators
implementable with exactly zero, one, or two controlled-not (CNOT) gates and
all other gates being one-qubit. We give an algorithm for synthesizing
two-qubit circuits with optimal number of CNOT gates, and illustrate it on
operators appearing in quantum algorithms by Deutsch-Josza, Shor and Grover. In
another application, our explicit numerical tests allow timing a given
Hamiltonian to compute a CNOT modulo one-qubit gates, when this is possible.


title: Intensity Interferometry with Anyons

abstract:
  A pairwise correlation function in relative momentum space is discussed as a
tool to characterize the properties of an incoherent source of non-interacting
Abelian anyons. This is analogous to the Hanbury--Brown Twiss effect for
particles with fractional statistics in two dimensions. In particular, using a
flux tube model for anyons, the effects of source shape and quantum statistics
on a two-particle correlation function are examined. Such a tool may prove
useful in the context of quantum computing and other experimental applications
where studying anyon sources are of interest.


title: Noise induced loss of entanglement

abstract:
  The disentangling effect of repeated applications of the bit flip channel
(I\otimes\sigma_x) on bipartite qubit systems is analyzed. It is found that the
rate of loss of entanglement is not uniform over all states. The distillable
entanglement of maximally entangled states decreases faster than that of less
entangled states. The analysis is also generalized to noise channels of the
form n.sigma.


title:
Unconditional Security of the Bennett 1992 quantum key-distribution over
  lossy and noisy channel

abstract:
  We show that the security proof of the Bennett 1992 protocol over loss-free
channel in (K. Tamaki, M. Koashi, and N. Imoto, Phys. Rev. Lett. 90, 167904
(2003)) can be adapted to accommodate loss. We assumed that Bob's detectors
discriminate between single photon states on one hand and vacuum state or
multi-photon states on the other hand.


title: How far apart are classical and quantum systems?

abstract:
  As is well known, classical systems approximate quantum ones -- but how well?
We introduce a definition of a "distance" on classical and quantum phase spaces
that offers a measure of their separation. Such a distance scale provides a
means to measure the quality of approximate solutions to various problems. A
few simple applications are discussed.


title: Quantum Decoys

abstract:
  Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$,
the canonical orthonormal basis. Sometimes however Alice interleaves quantum
decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such
pairwise superpositions of possible words cannot be distinguished from the
message words. Thus as malevolent Eve observes the quantum channel, she runs
the risk of damaging the superpositions (by causing a collapse). At the
receiving end honest Bob, whom we assume is warned of the quantum decoys'
distribution, checks upon their integrity with a measurement. The present work
establishes, in the case of individual attacks, the tradeoff between Eve's
information gain (her chances, if a message word was sent, of guessing which)
and the disturbance she induces (Bob's chances, if a quantum decoy was sent, to
detect tampering). Besides secure channel protocols, quantum decoys seem a
powerful primitive for constructing n-dimensional quantum cryptographic
applications. Moreover the methods employed in this article should be of strong
interest to anyone concerned with the old but fundamental problem of how much
information may be gained about a system, versus how much this will disturb the
system, in quantum mechanics. Keywords: d-level systems cryptography


title: Universal Measure of Entanglement

abstract:
  A general framework is developed for separating classical and quantum
correlations in a multipartite system. Entanglement is defined as the
difference in the correlation information encoded by the state of a system and
a suitably defined separable state with the same marginals. A generalization of
the Schmidt decomposition is developed to implement the separation of
correlations for any pure, multipartite state. The measure based on this
decomposition is a generalization of the entanglement of formation to
multipartite systems, provides an upper bound for the relative entropy of
entanglement, and is directly computable on pure states. The example of pure
three-qubit states is analyzed in detail, and a classification based on
minimal, four-term decompositions is developed.


title: Exact quantum jump approach to open systems in Bosonic and spin baths

abstract:
  A general method is developed which enables the exact treatment of the
non-Markovian quantum dynamics of open systems through a Monte Carlo simulation
technique. The method is based on a stochastic formulation of the von Neumann
equation of the composite system and employs a pair of product states following
a Markovian random jump process. The performance of the method is illustrated
by means of stochastic simulations of the dynamics of open systems interacting
with a Bosonic reservoir at zero temperature and with a spin bath in the strong
coupling regime.


title: Thermofield Dynamics of Time-Dependent Boson and Fermion Systems

abstract:
  We formulate the thermofield dynamics for time-dependent systems by combining
the Liouville-von Neumann equation, its invariant operators, and the basic
notions of thermofield dynamics. The new formulation is applied to
time-dependent bosons and fermions by using the time-dependent annihilation and
creation operators that satisfy the Liouville-von Neumann equation. It is shown
that the thermal state is the time- and temperature-dependent vacuum state and
a general formula is derived to calculate the thermal expectation value of
operators.


title:
High Efficiency Photon Number Detection for Quantum Information
  Processing

abstract:
  The Visible Light Photon Counter (VLPC) features high quantum efficiency and
low pulse height dispersion. These properties make it ideal for efficient
photon number state detection. The ability to perform efficient photon number
state detection is important in many quantum information processing
applications, including recent proposals for performing quantum computation
with linear optical elements. In this paper we investigate the unique
capabilities of the VLPC. The efficiency of the detector and cryogenic system
is measured at 543nm wavelengths to be 85%. A picosecond pulsed laser is then
used to excite the detector with pulses having average photon numbers ranging
from 3-5. The output of the VLPC is used to discriminate photon numbers in a
pulse. The error probability for number state discrimination is an increasing
function of the number of photons, due to buildup of multiplication noise. This
puts an ultimate limit on the ability of the VLPC to do number state detection.
For many applications, it is sufficient to discriminate between 1 and more than
one detected photon. The VLPC can do this with 99% accuracy.


title: Generation of photon number states

abstract:
  The Visible Light Photon Counter (VLPC) has the capability to discriminate
photon number states, in contrast to conventional photon counters which can
only detect the presence or absence of photons. We use this capability, along
with the process of parametric down-conversion, to generate photon number
states. We experimentally demonstrate generation of states containing 1,2,3 and
4 photons with high fidelity. We then explore the effect the detection
efficiency of the VLPC has on the generation rate and fidelity of the created
states.


title: Binegativity and geometry of entangled states in two qubits

abstract:
  We prove that the binegativity is always positive for any two-qubit state. As
a result, as suggested by the previous works, the asymptotic relative entropy
of entanglement in two qubits does not exceed the Rains bound, and the
PPT-entanglement cost for any two-qubit state is determined to be the
logarithmic negativity of the state. Further, the proof reveals some
geometrical characteristics of the entangled states, and shows that the partial
transposition can give another separable approximation of the entangled state
in two qubits.


title: Quantum key distribution with 2-bit quantum codes

abstract:
  We propose a prepare-and-measure scheme for quantum key distribution with
2-bit quantum codes. The protocol is unconditionally secure under whatever type
of intercept-and-resend attack. Given the symmetric and independent errors to
the transmitted qubits, our scheme can tolerate a bit error rate up to 26% in
4-state protocol and 30% in 6-state protocol, respectively. These values are
higher than all currently known threshold values for prepare-and-measure
protocols. A specific realization with linear optics is given.


title: Quantum Cloning of Mixed States in Symmetric Subspace

abstract:
  Quantum cloning machine for arbitrary mixed states in symmetric subspace is
proposed. This quantum cloning machine can be used to copy part of the output
state of another quantum cloning machine and is useful in quantum computation
and quantum information. The shrinking factor of this quantum cloning achieves
the well-known upper bound. When the input is identical pure states, two
different fidelities of this cloning machine are optimal.


title:
Generation and purification of maximally-entangled atomic states in
  optical cavities

abstract:
  We present a probabilistic scheme for generating and purifying
maximally-entangled states of two atoms inside an optical cavity via no-photon
detection in the output cavity mode, where ideal detectors may not be required.
The intermediate mixed states can be continuously "filtered" so as to violate
Bell inequalities in a parametrized manner. The scheme relies on an additional
strong-driving field that yields unusual dynamics in cavity QED experiments,
simultaneously realizing Jaynes-Cummings and anti-Jaynes-Cummings interactions.


title: A new adiabatic quantum search algorithm

abstract:
  We present a new adiabatic quantum algorithm for searching over structured
databases. The new algorithm is optimized using a simplified complexity
analysis.


title: Comments on some papers by M. Koashi and N. Imoto

abstract:
  This paper has been withdrawn by the author. My counter-example to the
Koashi-Imoto decomposition can be avoided by setting j=1 for all states, at
fixed l.


title:
The Darboux transformation and algebraic deformations of shape-invariant
  potentials

abstract:
  We investigate the backward Darboux transformations (addition of a lowest
bound state) of shape-invariant potentials on the line, and classify the
subclass of algebraic deformations, those for which the potential and the bound
states are simple elementary functions. A countable family, $m=0,1,2,...$, of
deformations exists for each family of shape-invariant potentials. We prove
that the $m$-th deformation is exactly solvable by polynomials, meaning that it
leaves invariant an infinite flag of polynomial modules
$\mathcal{P}^{(m)}_m\subset\mathcal{P}^{(m)}_{m+1}\subset...$, where
$\mathcal{P}^{(m)}_n$ is a codimension $m$ subspace of $<1,z,...,z^n>$. In
particular, we prove that the first ($m=1$) algebraic deformation of the
shape-invariant class is precisely the class of operators preserving the
infinite flag of exceptional monomial modules $\mathcal{P}^{(1)}_n = <
1,z^2,...,z^n>$. By construction, these algebraically deformed Hamiltonians do
not have an $\mathfrak{sl}(2)$ hidden symmetry algebra structure.


title:
Optimization of Bell's Inequality Violation For Continuous Variable
  Systems

abstract:
  Two mode squeezed vacuum states allow Bell's inequality violation (BIQV) for
all non-vanishing squeezing parameter $(\zeta)$. Maximal violation occurs at
$\zeta \to \infty$ when the parity of either component averages to zero. For a
given entangled {\it two spin} system BIQV is optimized via orientations of the
operators entering the Bell operator (cf. S. L. Braunstein, A. Mann and M.
Revzen: Phys. Rev. Lett. {\bf68}, 3259 (1992)). We show that for finite $\zeta$
in continuous variable systems (and in general whenever the dimensionality of
the subsystems is greater than 2) additional parameters are present for
optimizing BIQV. Thus the expectation value of the Bell operator depends, in
addition to the orientation parameters, on configuration parameters.
Optimization of these configurational parameters leads to a unique maximal BIQV
that depends only on $\zeta.$ The configurational parameter variation is used
to show that BIQV relation to entanglement is, even for pure state, not
monotonic.


title: Gaussian quantum operator representation for bosons

abstract:
  We introduce the Gaussian quantum operator representation, using the most
general multi-mode Gaussian operator basis. The representation unifies and
substantially extends existing phase-space representations of density matrices
for Bose systems, and also includes generalized squeezed-state and thermal
bases. It enables first-principles dynamical or equilibrium calculations in
quantum many-body systems, with quantum uncertainties appearing as dynamical
objects. Any quadratic Liouville equation for the density operator results in a
purely deterministic time evolution. Any cubic or quartic master equation can
be treated using stochastic methods.


title: Boundary Quantum Mechanics

abstract:
  A reformulation of a physical theory in which measurements at the initial and
final moments of time are treated independently is discussed, both on the
classical and quantum levels. Methods of the standard quantum mechanics are
used to quantize boundary phase space to obtain boundary quantum mechanics -- a
theory that does not depend on the distinction between the initial and final
moments of time, a theory that can be formulated without reference to the
causal structure. As a supplementary material, the geometrical description of
quantization of a general (e.g. curved) configuration space is presented.


title: A formula for the Bloch vector of some Lindblad quantum systems

abstract:
  Using the Bloch representation of an N-dimensional quantum system and
immediate results from quantum stochastic calculus, we establish a closed
formula for the Bloch vector, hence also for the density operator, of a quantum
system following a Lindblad evolution with selfadjoint Lindblad operators.


title: A geometric phase gate without dynamical phases

abstract:
  A general scheme for an adiabatic geometric phase gate is proposed which is
maximally robust against parameter fluctuations. While in systems with SU(2)
symmetry geometric phases are usually accompanied by dynamical phases and are
thus not robust, we show that in the more general case of a SU(2) x SU(2)
symmetry it is possible to obtain a non-vanishing geometric phase without
dynamical contributions. The scheme is illustrated for a phase gate using two
systems with dipole-dipole interactions in external laser fields which form an
effective four-level system.


title:
Controlling dipole-dipole frequency shifts in a lattice-based optical
  atomic clock

abstract:
  Motivated by the ideas of using cold alkaline earth atoms trapped in an
optical lattice for realization of optical atomic clocks, we investigate
theoretically the perturbative effects of atom-atom interactions on a clock
transition frequency. These interactions are mediated by the dipole fields
associated with the optically excited atoms. We predict resonance-like features
in the frequency shifts when constructive interference among atomic dipoles
occur. We theoretically demonstrate that by fine-tuning the coherent
dipole-dipole couplings in appropriately designed lattice geometries, the
undesirable frequency shifts can be greatly suppressed.


title: Classical Limit of Quantum Dynamical Entropies

abstract:
  Two non-commutative dynamical entropies are studied in connection with the
classical limit. For systems with a strongly chaotic classical limit, the
Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in
the quantisation parameter. The model of the quantised hyperbolic automorphisms
of the 2-torus is examined in detail.


title:
Probing the dispersive and spatial properties of planar photonic crystal
  waveguide modes via highly efficient coupling from optical fiber tapers

abstract:
  The demonstration of an optical fiber based probe for efficiently exciting
the waveguide modes of high-index contrast planar photonic crystal (PC) slabs
is presented. Utilizing the dispersion of the PC, fiber taper waveguides formed
from standard silica single-mode optical fibers are used to evanescently couple
light into the guided modes of a patterned silicon membrane. A coupling
efficiency of approximately 95% is obtained between the fiber taper and a PC
waveguide mode suitably designed for integration with a previously studied
ultra-small mode volume high-Q PC resonant cavity [1]. The micron-scale lateral
extent and dispersion of the fiber taper is also used as a near-field spatial
and spectral probe to study the profile and dispersion of PC waveguide modes.
The mode selectivity of this wafer-scale probing technique, together with its
high efficiency, suggests that it will be useful in future quantum and
non-linear optics experiments employing planar PCs.


title:
Comparison of LOQC C-sign gates with ancilla inefficiency and an
  improvement to functionality under these conditions

abstract:
  We compare three proposals for non-deterministic C-sign gates implemented
using linear optics and conditional measurements with non-ideal ancilla mode
production and detection. The simplified KLM gate [Ralph et al, Phys.Rev.A {\bf
65}, 012314 (2001)] appears to be the most resilient under these conditions. We
also find that the operation of this gate can be improved by adjusting the
beamsplitter ratios to compensate to some extent for the effects of the
imperfect ancilla.


title: Computational Complexity Measures of Multipartite Quantum Entanglement

abstract:
  We shed new light on entanglement measures in multipartite quantum systems by
taking a computational-complexity approach toward quantifying quantum
entanglement with two familiar notions--approximability and distinguishability.
Built upon the formal treatment of partial separability, we measure the
complexity of an entangled quantum state by determining (i) how hard to
approximate it from a fixed classical state and (ii) how hard to distinguish it
from all partially separable states. We further consider the
Kolmogorovian-style descriptive complexity of approximation and distinction of
partial entanglement.


title: A note on graphs resistant to quantum uniform mixing

abstract:
  Continuous-time quantum walks on graphs is a generalization of
continuous-time Markov chains on discrete structures. Moore and Russell proved
that the continuous-time quantum walk on the $n$-cube is instantaneous exactly
uniform mixing but has no average mixing property. On complete (circulant)
graphs $K_{n}$, the continuous-time quantum walk is neither instantaneous
(except for $n=2,3,4$) nor average uniform mixing (except for $n=2$). We
explore two natural {\em group-theoretic} generalizations of the $n$-cube as a
$G$-circulant and as a bunkbed $G \rtimes \Int_{2}$, where $G$ is a finite
group. Analyses of these classes suggest that the $n$-cube might be special in
having instantaneous uniform mixing and that non-uniform average mixing is
pervasive, i.e., no memoryless property for the average limiting distribution;
an implication of these graphs having zero spectral gap. But on the bunkbeds,
we note a memoryless property with respect to the two partitions. We also
analyze average mixing on complete paths, where the spectral gaps are nonzero.


title: Probability amplitude in quantum like games

abstract:
  Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude are given. The first game is described by
the quantum formalism of spin one half system for which two noncommuting
observables are measured.
  The second game corresponds to the spin one case.
  Quantum logical orthocomplemented nondistributive lattices for these two
games are presented. Interference terms for the probability amplitudes are
analyzed by using so called contextual approach to probability (in the von
Mises frequency approach). We underline that our games are not based on using
of some microscopic systems. The whole scenario is macroscopic.


title: Theory of Plasmon-assisted Transmission of Entangled Photons

abstract:
  The recent surface plasmon entanglement experiment [E. Altewischer et al.,
Nature (London) 418, 304 (2002)] is theoretically analyzed. The entanglement
preservation upon transmission in the non-focused case is found to provide
information about the interaction of the biphoton and the metallic film. The
entanglement degradation in the focused case is explained in the framework of a
fully multimode model. This phenomenon is a consequence of the
polarization-selective filtering behavior of the metallic nanostructured film.


title: Testing quantum duality using cold Rydberg atoms

abstract:
  Classically, the dynamics of the chiral oscillator (CO) may be described by
the Landau model (LM) through a well established mathematical procedure known
as duality mapping. In this letter we show how this duality is broken in
quantum mechanics due to the presence of a $Z_2$-anomaly in the CO. We give the
theoretical basis for an experimental setup displaying the possibility to
measure this global anomaly using cold Rydberg atoms.


title: Can there be a Fock state of the radiation field?

abstract:
  We analyze possible hurdles in generating a Fock state of the radiation field
in a micromaser cavity.


title:
Wigner's inequality for conditional probabilities and nonexistence of a
  realistic model for the two dimensional Hilbert space

abstract:
  We perform the analysis of probabilistic assumptions of Bell's approach. We
emphasize that J. Bell wrote about probability without to specify the concrete
axiomatics of probability theory. The careful analysis demonstrated that
(surprisingly) J. Bell did not apply the classical probability model
(Kolmogorov) to describe ``classical physical framework.'' In fact, he created
his own probabilistic model and compared it with the quantum one. The crucial
point is that J. Bell did not pay attention to {\it conditional probabilities.}
We show that conditional probability in his model cannot be defined by
classical Bayes' formula. We also use the approach based on Bell-type
inequalities in the conventional probabilistic approach, Kolmogorov model. We
prove an analog of Wigner's inequality for conditional probabilities and by
using this inequality show that predictions of the conventional and quantum
probability models disagree already in the case of noncomposite systems (even
in the two dimensional case).


title:
Engineering quantum pure states of a trapped cold ion beyond the
  Lamb-Dicke limit

abstract:
  Based on the conditional quantum dynamics of laser-ion interaction, we
propose an efficient theoretical scheme to deterministically generate quantum
pure states of a single trapped cold ion without performing the Lamb-Dicke
approximation. An arbitrary quantum state can be created by using a series of
classical laser beams with selected frequencies, initial phases and durations.
As special examples, we further show how to create or approximate several
typical macroscopic quantum states, such as the phase state and (even/odd)
coherent states. Unlike previous schemes operated in the Lamb-Dicke regime, the
present one does well for arbitrary strength coupling between the internal and
external degrees of freedom of the ion. The experimental realizability of this
approach is also discussed.


title:
Controlled Collisions for Multiparticle Entanglement of Optically
  Trapped Atoms

abstract:
  Entanglement lies at the heart of quantum mechanics and in recent years has
been identified as an essential resource for quantum information processing and
computation. Creating highly entangled multi-particle states is therefore one
of the most challenging goals of modern experimental quantum mechanics,
touching fundamental questions as well as practical applications. Here we
report on the experimental realization of controlled collisions between
individual neighbouring neutral atoms trapped in the periodic potential of an
optical lattice. These controlled interactions act as an array of quantum gates
between neighbouring atoms in the lattice and their massively parallel
operation allows the creation of highly entangled states in a single
operational step, independent of the size of the system. In the experiment, we
observe a coherent entangling-disentangling evolution in the many-body system
depending on the phase shift acquired during the collision between neighbouring
atoms. This dynamics is indicative of highly entangled many-body states that
present novel opportunities for theory and experiment.


title:
Structure of multiphoton quantum optics. I. Canonical formalism and
  homodyne squeezed states

abstract:
  We introduce a formalism of nonlinear canonical transformations for general
systems of multiphoton quantum optics. For single-mode systems the
transformations depend on a tunable free parameter, the homodyne local
oscillator angle; for n-mode systems they depend on n heterodyne mixing angles.
The canonical formalism realizes nontrivial mixings of pairs of conjugate
quadratures of the electromagnetic field in terms of homodyne variables for
single-mode systems; and in terms of heterodyne variables for multimode
systems. In the first instance the transformations yield nonquadratic model
Hamiltonians of degenerate multiphoton processes and define a class of non
Gaussian, nonclassical multiphoton states that exhibit properties of coherence
and squeezing. We show that such homodyne multiphoton squeezed states are
generated by unitary operators with a nonlinear time evolution that realizes
the homodyne mixing of a pair of conjugate quadratures. Tuning of the local
oscillator angle allows to vary at will the statistical properties of such
states. We discuss the relevance of the formalism for the study of degenerate
(up-)down-conversion processes. In a companion paper, ``Structure of
multiphoton quantum optics. II. Bipartite systems, physical processes, and
heterodyne squeezed states'', we provide the extension of the nonlinear
canonical formalism to multimode systems, we introduce the associated
heterodyne multiphoton squeezed states, and we discuss their possible
experimental realization.

categories: quant-ph cond-mat hep-th math-ph math.MP physics.optics


title: Finite size effects in entangled rings of qubits

abstract:
  We study translationally invariant rings of qubits with a finite number of
sites N, and find the maximal nearest-neighbor entanglement for a fixed z
component of the total spin. For small numbers of sites our results are
analytical. The use of a linearized version of the concurrence allows us to
relate the maximal concurrence to the ground state energy of an XXZ spin model,
and to calculate it numerically for N<25. We point out some interesting
finite-size effects. Finally, we generalize our results beyond nearest
neighbors.


title:
Entanglement, correlations, and the energy gap in many-body quantum
  systems

abstract:
  What correlations are present in the ground state of a many-body Hamiltonian?
We study the relationship between ground-state correlations, especially
entanglement, and the energy gap between the ground and first excited states.
We prove several general inequalities which show quantitatively that
ground-state correlations between systems not directly coupled by the
Hamiltonian necessarily imply a small energy gap.


title: Detailed Balance and Intermediate Statistics

abstract:
  We present a theory of particles, obeying intermediate statistics ("anyons"),
interpolating between Bosons and Fermions, based on the principle of Detailed
Balance. It is demonstrated that the scattering probabilities of identical
particles can be expressed in terms of the basic numbers, which arise naturally
and logically in this theory. A transcendental equation determining the
distribution function of anyons is obtained in terms of the statistics
parameter, whose limiting values 0 and 1 correspond to Bosons and Fermions
respectively. The distribution function is determined as a power series
involving the Boltzmann factor and the statistics parameter and we also express
the distribution function as an infinite continued fraction. The last form
enables one to develop approximate forms for the distribution function, with
the first approximant agreeing with our earlier investigation.


title:
Quantum dynamical correlations: Effective potential analytic
  continuation approach

abstract:
  We propose a new quantum dynamics method called the effective potential
analytic continuation (EPAC) to calculate the real time quantum correlation
functions at finite temperature. The method is based on the effective action
formalism which includes the standard effective potential. The basic notions of
the EPAC are presented for a one-dimensional double well system in comparison
with the centroid molecular dynamics (CMD) and the exact real time quantum
correlation function. It is shown that both the EPAC and the CMD well reproduce
the exact short time behavior, while at longer time their results deviate from
the exact one. The CMD correlation function damps rapidly with time because of
ensemble dephasing. The EPAC correlation function, however, can reproduce the
long time oscillation inherent in the quantum double well systems. It is also
shown that the EPAC correlation function can be improved toward the exact
correlation function by means of the higher order derivative expansion of the
effective action.


title: Entangled two atoms through different couplings and the thermal noise

abstract:
  The entanglement of two atoms is studied when the two atoms are coupled to a
single-mode thermal field with different couplings. The different couplings of
two atoms are in favor of entanglement preparation: it not only makes the case
of absence entanglement with same coupling appear entanglement, but also
enhances the entanglement with the increasing of the relative difference of two
couplings. We also show that the diversity of coupling can improved the
critical temperature. If the optical cavity is leaky during the time evolution,
the dissipative thermal environment is benefit to produce the entanglement.


title: Quantum arrival times and operator normalization

abstract:
  A recent approach to arrival times used the fluorescence of an atom entering
a laser illuminated region and the resulting arrival-time distribution was
close to the axiomatic distribution of Kijowski, but not exactly equal, neither
in limiting cases nor after compensation of reflection losses by normalization
on the level of expectation values. In this paper we employ a normalization on
the level of operators, recently proposed in a slightly different context. We
show that in this case the axiomatic arrival time distribution of Kijowski is
recovered as a limiting case. In addition, it is shown that Allcock's complex
potential model is also a limit of the physically motivated fluorescence
approach and connected to Kijowski's distribution through operator
normalization.


title: "Squashed Entanglement" - An Additive Entanglement Measure

abstract:
  In this paper, we present a new entanglement monotone for bipartite quantum
states. Its definition is inspired by the so-called intrinsic information of
classical cryptography and is given by the halved minimum quantum conditional
mutual information over all tripartite state extensions. We derive certain
properties of the new measure which we call "squashed entanglement": it is a
lower bound on entanglement of formation and an upper bound on distillable
entanglement. Furthermore, it is convex, additive on tensor products, and
superadditive in general.
  Continuity in the state is the only property of our entanglement measure
which we cannot provide a proof for. We present some evidence, however, that
our quantity has this property, the strongest indication being a conjectured
Fannes type inequality for the conditional von Neumann entropy. This inequality
is proved in the classical case.


title: Unital quantum operators on the Bloch ball and Bloch region

abstract:
  For one qubit systems, we present a short, elementary argument characterizing
unital quantum operators in terms of their action on Bloch vectors. We then
show how our approach generalizes to multi-qubit systems, obtaining
inequalities that govern when a ``diagonal'' superoperator on the Bloch region
is a quantum operator. These inequalities are the n-qubit analogue of the
Algoet-Fujiwara conditions. Our work is facilitated by an analysis of
operator-sum decompositions in which negative summands are allowed.


title: Teleportation of continuous variable polarisation states

abstract:
  This paper discusses methods for the optical teleportation of continuous
variable polarisation states. We show that using two pairs of entangled beams,
generated using four squeezed beams, perfect teleportation of optical
polarisation states can be performed. Restricting ourselves to 3 squeezed
beams, we demonstrate that polarisation state teleportation can still exceed
the classical limit. The 3-squeezer schemes involve either the use of quantum
non-demolition measurement or biased entanglement generated from a single
squeezed beam. We analyse the efficacies of these schemes in terms of fidelity,
signal transfer coefficients and quantum correlations.


title: A measurable entanglement criterion for two qubits

abstract:
  We propose a directly measurable criterion for the entanglement of two
qubits. We compare the criterion with other criteria, and we find that for pure
states, and some mixed states, it coincides with the state's concurrency. The
measure can be obtained with a Bell state analyser and the ability to make
general local unitary transformations. However, the procedure fails to measure
the entanglement of a general mixed two-qubit state.


title: On quantum key distribution in decoherence-free subspace

abstract:
  We propose easy implementable protocols for robust quantum key distribution
with the collective dephasing channel or collective rotating channel.
  In these protocols, Bob only takes passive photon detection to measure the
polarization qubits in the random bases. The source for the protocol with
collective rotating channel is made by type 2 spontaneous parametric down
conversion with random unitary rotation and phase shifter, no quantum
disentangler is required.
  A simple proof for unconditionally security is shown.


title: Angular Momentum of Photons Emitted by Atoms

abstract:
  It is shown that the spin and orbital angular momentum of electric dipole
photons have the same operator structure and may differ from each other only by
spatial dependence in the very vicinity of the atom. It is shown that the
photon twins created by a dipole forbidden transition can manifest the maximum
entanglement with respect to the angular momentum. It is shown that the states
of photons with projection of angular momentum $m=0$ are less stable than those
with $m= \pm 1$.


title:
Structure of multiphoton quantum optics. II. Bipartite systems, physical
  processes, and heterodyne squeezed states

abstract:
  Extending the scheme developed for a single mode of the electromagnetic field
in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical
formalism and homodyne squeezed states'', we introduce two-mode nonlinear
canonical transformations depending on two heterodyne mixing angles. They are
defined in terms of hermitian nonlinear functions that realize heterodyne
superpositions of conjugate quadratures of bipartite systems. The canonical
transformations diagonalize a class of Hamiltonians describing non degenerate
and degenerate multiphoton processes. We determine the coherent states
associated to the canonical transformations, which generalize the non
degenerate two--photon squeezed states. Such heterodyne multiphoton squeezed
are defined as the simultaneous eigenstates of the transformed, coupled
annihilation operators. They are generated by nonlinear unitary evolutions
acting on two-mode squeezed states. They are non Gaussian, highly non
classical, entangled states. For a quadratic nonlinearity the heterodyne
multiphoton squeezed states define two--mode cubic phase states. The
statistical properties of these states can be widely adjusted by tuning the
heterodyne mixing angles, the phases of the nonlinear couplings, as well as the
strength of the nonlinearity. For quadratic nonlinearity, we study the
higher-order contributions to the susceptibility in nonlinear media and we
suggest possible experimental realizations of multiphoton conversion processes
generating the cubic-phase heterodyne squeezed states.


title: Photon polarisation entanglement from distant dipole sources

abstract:
  It is commonly believed that photon polarisation entanglement can only be
obtained via pair creation within the same source or via postselective
measurements on photons that overlapped within their coherence time inside a
linear optics setup. In contrast to this, we show here that polarisation
entanglement can also be produced by distant single photon sources in free
space and without the photons ever having to meet, if the detection of a photon
does not reveal its origin -- the which way information. In the case of two
sources, the entanglement arises under the condition of two emissions in
certain spatial directions and leaves the dipoles in a maximally entangled
state.


title: The Heisenberg versus the Schrodinger picture in quantum field theory

abstract:
  The Heisenberg picture and Schrodinger picture are supposed to be equivalent
representations of quantum mechanics. However this idea has been challenged by
P.A.M. Dirac. Also, it has been recently shown by A. J. Faria et al that this
is not necessarily the case. In this article a simple problem will be worked
out in quantum field theory in which the Heisenberg picture and Schrodinger
picture give different results.


title:
Coulomb-Oscillator Duality and Scattering Problem in 5-Dimensional
  Coulomb Field

abstract:
  It is shown that the Hurwitz transformation connects the eight-dimensional
repulsive oscillator problem with the five-dimensional Coulomb problem for
continuous spectrum. The hyperspherical and parabolic bases for this system are
calculated. The quantum mechanical scattering problem of charged particles in
the 5-dimensional Coulomb field is solved.


title:
Quantum circuits for single-qubit measurements corresponding to platonic
  solids

abstract:
  Each platonic solid defines a single-qubit positive operator valued measure
(POVM) by interpreting its vertices as points on the Bloch sphere. We construct
simple circuits for implementing this kind of measurements and other simple
types of symmetric POVMs on one qubit. Each implementation consists of a
discrete Fourier transform and some elementary quantum operations followed by
an orthogonal measurement in the computational basis.


title:
Semiclassical time-evolution of the reduced density matrix and
  dynamically assisted generation of entanglement for bipartite quantum systems

abstract:
  Two particles, initially in a product state, become entangled when they come
together and start to interact. Using semiclassical methods, we calculate the
time evolution of the corresponding reduced density matrix $\rho_1$, obtained
by integrating out the degrees of freedom of one of the particles. To quantify
the generation of entanglement, we calculate the purity ${\cal P}(t)={\rm
Tr}[\rho_1(t)^2]$. We find that entanglement generation sensitively depends (i)
on the interaction potential, especially on its strength and range, and (ii) on
the nature of the underlying classical dynamics. Under general statistical
assumptions, and for short-scaled interaction potentials, we find that ${\cal
P}(t)$ decays exponentially fast if the two particles are required to interact
in a chaotic environment, whereas it decays only algebraically in a regular
system. In the chaotic case, the decay rate is given by the golden rule
spreading of one-particle states due to the two-particle coupling, but cannot
exceed the system's Lyapunov exponent.


title: Resonance Fluorescence Squeezing Spectra from Photonic Bandgap Crystals

abstract:
  The fluorescence intensity and quadrature spectra from a two-level atom
embedded in a photonic bandgap crystal and resonantly driven by a classical
pump light are calculated. The non-Markovian nature of the problem caused by
the non-uniform distribution of the photonic density of states is handled by
linearizing the generalized optical Bloch equations with the Liouville operator
expansion. Unlike the case in free space, we find that the bandgap effects will
not only modify the fluorescence spectral shape but also cause squeezing in the
in-phase quadrature spectra.


title: Time and Geometric Quantization

abstract:
  In this paper we briefly review the functional version of the Koopman-von
Neumann operatorial approach to classical mechanics. We then show that its
quantization can be achieved by freezing to zero two Grassmannian partners of
time. This method of quantization presents many similarities with the one known
as Geometric Quantization.


title:
Unifying Entanglement and Nonlocality as a Single Concept: Quantum
  Wholeness

abstract:
  Although entanglement is widely recognized as one of the most fascinating
characteristics of quantum mechanics, nonlocality remains to be a big
labyrinth. The proof of existence of nonlocality is as yet not much convincing
because of its strong reliance on Bell's theorem where the assumption of
realism weakens the proof. We demonstrate that entanglement and quantum
nonlocality are two equivalent aspects of the same quantum wholeness for
spacelike separated quantum systems. This result implies that quantum mechanics
is indeed a nonlocal theory and lays foundation of understanding quantum
nonlocality beyond Bell's theorem.


title:
Resonance of Minimizers for $n$-level Quantum Systems with an Arbitrary
  Cost

abstract:
  We consider an optimal control problem describing a laser-induced population
transfer on a $n$-level quantum system.
  For a convex cost depending only on the moduli of controls (i.e. the lasers
intensities), we prove that there always exists a minimizer in resonance. This
permits to justify some strategies used in experimental physics. It is also
quite important because it permits to reduce remarkably the complexity of the
problem (and extend some of our previous results for $n=2$ and $n=3$): instead
of looking for minimizers on the sphere $S^{2n-1}\subset\C^n$ one is reduced to
look just for minimizers on the sphere $S^{n-1}\subset \R^n$. Moreover, for the
reduced problem, we investigate on the question of existence of strict abnormal
minimizer.


title: Phase-space approach to the study of decoherence in quantum walks

abstract:
  We analyze the quantum walk on a cycle using discrete Wigner functions as a
way to represent the states and the evolution of the walker. The method
provides some insight on the nature of the interference effects that make
quantum and classical walks different. We also study the behavior of the system
when the quantum coin carried by the walker interacts with an environment. We
show that for this system quantum coherence is robust for initially delocalized
states of the walker. The use of phase-space representation enables us to
develop an intuitive description of the nature of the decoherence process in
this system.


title: Spin-dependent Bohm trajectories for hydrogen eigenstates

abstract:
  The Bohm trajectories for several hydrogen atom eigenstates are determined,
taking into account the additional momentum term that arises from the Pauli
current. Unlike the original Bohmian result, the spin-dependent term yields
nonstationary trajectories. The relationship between the trajectories and the
standard visualizations of orbitals is discussed. The trajectories for a model
problem that simulates a 1s-2p transition in hydrogen are also examined.


title:
Fluorescence Spectra of a Two-Level Atom Embedded in a Three-Dimensional
  Photonic Crystal

abstract:
  Steady-state fluorescence spectra of a two-level atom embedded in a
three-dimensional photonic bandgap crystal and driven by a monochromatic
classical electrical field is calculated theoretically for the first time as we
know. The non-Markovian noises caused by the non-uniform distribution of photon
density of states near the photonic bandgap are handled by a new approach in
which the Liouville operator expansion is utilized to linearize the generalized
optical Bloch equations. The fluorescence spectra are then directly solved by
the linearized Bloch equations in the frequency domain. We find that if the
atomic energy level is far from the bandgap, fluorescence spectra with Mollow's
triplets are observed. However, when the atomic energy level is near the
bandgap, the relative magnitude and the number of the fluorescence peaks are
found to be varied according to the wavelength offset.


title:
No information flow using statistical fluctuations, and quantum
  cryptography

abstract:
  The communication protocol of Home and Whitaker [Phys. Rev. A 67, 022306
(2003)] is examined in some detail, and found to work equally well using a
separable state. The protocol is in fact completely classical, based on simple
post-selection of suitable experimental runs. The quantum cryptography protocol
proposed in the same publication is also examined, and is found to indeed need
quantum properties for the system to be secure. However, the security test
proposed in the mentioned paper is found to be insufficient, and a modification
is proposed here that will ensure security.


title:
Comment on "Measurement of quantum states of neutrons in the Earth's
  gravitational field"

abstract:
  In the paper by V.V. Nesvizhevsky et al., Phys. Rev. D 67, 102002 (2003), it
is argued that the lowest quantum state of neutrons in the Earth's
gravitational field has been experimentally identified. While this is most
likely correct, it is imperative to investigate all alternative explanations of
the result in order to close all loopholes, as it is the first experiment ever
claimed to have observed gravitational quantum states. Here we show that
geometrical effects in the experimental setup can mimic the results attributed
to gravity. Modifications of the experimental setup to close these possible
loopholes are suggested.


title:
p-adic CCR: Galois group representations, cyclic dynamics, and
  zeta-functions

abstract:
  We consider a model of cyclic time evolution for Kochubei's p-adic
realization of the canonical commutation relations (CCR). Connections to
Kubota-Leopoldt p-adic zeta-functions and to arithmetic quantum theories such
as the Bost-Connes model are examined.


title:
Quantum information via state partitions and the context translation
  principle

abstract:
  For many-particle systems, quantum information in base n can be defined by
partitioning the set of states according to the outcomes of n-ary (joint)
observables. Thereby, k particles can carry k nits. With regards to the
randomness of single outcomes, a context translation principle is proposed.
Quantum randomness is related to the uncontrollable degrees of freedom of the
measurement interface, thereby translating a mismatch between the state
prepared and the state measured.


title: Probabilistic quantum multimeters

abstract:
  We propose quantum devices that can realize probabilistically different
projective measurements on a qubit. The desired measurement basis is selected
by the quantum state of a program register. First we analyze the
phase-covariant multimeters for a large class of program states, then the
universal multimeters for a special choice of program. In both cases we start
with deterministic but erroneous devices and then proceed to devices that never
make a mistake but from time to time they give an inconclusive result. These
multimeters are optimized (for a given type of a program) with respect to the
minimum probability of inconclusive result. This concept is further generalized
to the multimeters that minimize the error rate for a given probability of an
inconclusive result (or vice versa). Finally, we propose a generalization for
qudits.


title: Quantum Reversibility: Is there an Echo?

abstract:
  We study the possibility to undo the quantum mechanical evolution in a time
reversal experiment. The naive expectation, as reflected in the common
terminology ("Loschmidt echo"), is that maximum compensation results if the
reversed dynamics extends to the same time as the forward evolution. We
challenge this belief, and demonstrate that the time $t_r$ for maximum return
probability is in general shorter. We find that $t_r$ depends on $lambda =
eps_evol/eps_prep$, being the ratio of the error in setting the parameters
(fields) for the time reversed evolution to the perturbation which is involved
in the preparation process. Our results should be observable in spin-echo
experiments where the dynamical irreversibility of quantum phases is measured.


title: Quantum error correction in globally controlled arrays

abstract:
  An interesting concept in quantum computation is that of global control (GC),
where there is no need to manipulate qubits individually. One can implement a
universal set of quantum gates on a one-dimensional array purely via signals
that target the entire structure indiscriminately. But large-scale quantum
computation imposes several requirements in terms of noise level, time, space
(scaling) and in particular parallelism. Keeping in mind these requirements, we
prove GC can support error-correction, by implementing two simple codes. This
opens the way to fault-tolerant computation with this type of architecture.


title: The Bell-Kochen-Specker Theorem

abstract:
  Meyer, Kent and Clifton (MKC) claim to have nullified the Bell-Kochen-Specker
(Bell-KS) theorem. It is true that they invalidate KS's account of the
theorem's physical implications. However, they do not invalidate Bell's point,
that quantum mechanics is inconsistent with the classical assumption, that a
measurement tells us about a property previously possessed by the system. This
failure of classical ideas about measurement is, perhaps, the single most
important implication of quantum mechanics. In a conventional colouring there
are some remaining patches of white. MKC fill in these patches, but only at the
price of introducing patches where the colouring becomes ''pathologically''
discontinuous. The discontinuities mean that the colours in these patches are
empirically unknowable. We prove a general theorem which shows that their
extent is at least as great as the patches of white in a conventional approach.
The theorem applies, not only to the MKC colourings, but also to any other such
attempt to circumvent the Bell-KS theorem (Pitowsky's colourings, for example).
We go on to discuss the implications. MKC do not nullify the Bell-KS theorem.
They do, however, show that we did not, hitherto, properly understand the
theorem. For that reason their results (and Pitowsky's earlier results) are of
major importance.


title: Measuring Controlled-NOT and two-qubit gate operation

abstract:
  Accurate characterisation of two-qubit gates will be critical for any
realisation of quantum computation. We discuss a range of measurements aimed at
characterising a two-qubit gate, specifically the CNOT gate. These measurements
are architecture-independent, and range from simple truth table measurements,
to single figure measures such as the fringe visibility, parity, fidelity, and
entanglement witnesses, through to whole-state and whole-gate measures achieved
respectively via quantum state and process tomography. In doing so, we examine
critical differences between classical and quantum gate operation.


title: Bipartite entanglement and localization of one-particle states

abstract:
  We study bipartite entanglement in a general one-particle state, and find
that the linear entropy, quantifying the bipartite entanglement, is directly
connected to the paricitpation ratio, charaterizing the state localization. The
more extended the state is, the more entangled the state. We apply the general
formalism to investigate ground-state and dynamical properties of entanglement
in the one-dimensional Harper model.


title:
Quantum dot single photon sources: Prospects for applications in linear
  optics quantum information processing

abstract:
  An optical source that produces single photon pulses on demand has potential
applications in linear optics quantum computation, provided that stringent
requirements on indistinguishability and collection efficiency of the generated
photons are met. We show that these are conflicting requirements for anharmonic
emitters that are incoherently pumped via reservoirs. As a model for a
coherently pumped single photon source, we consider cavity-assisted spin-flip
Raman transitions in a single charged quantum dot embedded in a microcavity. We
demonstrate that using such a source, arbitrarily high collection efficiency
and indistinguishability of the generated photons can be obtained
simultaneously with increased cavity coupling. We analyze the role of errors
that arise from distinguishability of the single photon pulses in linear optics
quantum gates by relating the gate fidelity to the strength of the two-photon
interference dip in photon cross-correlation measurements. We find that
performing controlled phase operations with error < 1% requires nano-cavities
with Purcell factors F_P >= 40 in the absence of dephasing, without
necessitating the strong coupling limit.


title:
Mode entanglement of electrons in the one-dimensional Frenkel-Kontorova
  model

abstract:
  We study the mode entanglement in the one-dimensional Frenkel-Kontorova
model, and found that behaviors of quantum entanglement are distinct before and
after the transition by breaking of analyticity. We show that the more extended
the electron is, the more entangled the corresponding state. Finally, a
quantitative relation is given between the average square of the concurrence
quantifying the degree of entanglement and the participation ratio
characterizing the degree of localization.


title: Phase-space path-integral calculation of the Wigner function

abstract:
  The Wigner function W(q,p) is formulated as a phase-space path integral,
whereby its sign oscillations can be seen to follow from interference between
the geometrical phases of the paths. The approach has similarities to the
path-centroid method in the configuration-space path integral. Paths can be
classified by the mid-point of their ends; short paths where the mid-point is
close to (q,p) and which lie in regions of low energy (low P function of the
Hamiltonian) will dominate, and the enclosed area will determine the sign of
the Wigner function. As a demonstration, the method is applied to a sequence of
density matrices interpolating between a Poissonian number distribution and a
number state, each member of which can be represented exactly by a discretized
path integral with a finite number of vertices. Saddle point evaluation of
these integrals recovers (up to a constant factor) the WKB approximation to the
Wigner function of a number state.


title:
Multiplicativity of Accessible Fidelity and Quantumness for Sets of
  Quantum States

abstract:
  Two measures of sensitivity to eavesdropping for alphabets of quantum states
were recently introduced by Fuchs and Sasaki in quant-ph/0302092. These are the
accessible fidelity and quantumness. In this paper we prove an important
property of both measures: They are multiplicative under tensor products. The
proof in the case of accessible fidelity shows a connection between the measure
and characteristics of entanglement-breaking quantum channels.


title: Quantum-state extraction from high-Q cavities

abstract:
  The problem of extraction of a single-mode quantum state from a high-Q cavity
is studied for the case in which the time of preparation of the quantum state
of the cavity mode is short compared with its decay time. The temporal
evolution of the quantum state of the field escaping from the cavity is
calculated in terms of phase-space functions. A general condition is derived
under which the quantum state of the pulse built up outside the cavity is a
nearly perfect copy of the quantum state the cavity field was initially
prepared in. The results show that unwanted losses prevent the realization of a
nearly perfect extraction of nonclassical quantum states from high-Q optical
microcavities with presently available technology.


title:
Qubit Assisted Probing of Coherence Between States of a Macroscopic
  Apparatus

abstract:
  I present a general scheme through which the evidence of a superposition
involving distinct classical-like states of a macroscopic system can be probed.
The scheme relies on a qubit being coupled to a macroscopic harmonic oscillator
in such a way that it can be used to both prepare and probe a macroscopic
superposition. Two potentially realizable implementations, one with a flux
qubit coupled to a LC circuit, and the other with an ion-trap qubit coupled to
the collective motion of several ions, are proposed.


title: Comment on "Conservative Quantum Computing"

abstract:
  A Comment on the paper "Conservative Quantum Computing" by M. Ozawa, Phys.
Rev. Lett. 89, 057902 (2002). The author replies in Phys. Rev. Lett. 91, 089802
(2003).


title:
Comment on "Quantum waveguide array generator for performing Fourier
  transforms: Alternate route to quantum computing"

abstract:
  A Comment on the paper "Quantum waveguide array generator for performing
Fourier transforms: Alternate route to quantum computing" by R. Akis and D.K.
Ferry, Appl. Phys. Lett. 79, 2823 (2001). The authors reply in Appl. Phys.
Lett. 80, 2420 (2002).


title: Quantum NP and a Quantum Hierarchy

abstract:
  The complexity class NP is quintessential and ubiquitous in theoretical
computer science. Two different approaches have been made to define "Quantum
NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA
by Knill, Kitaev, and Watrous. From an operator point of view, NP can be viewed
as the result of the exists-operator applied to P. Recently, Green, Homer,
Moore, and Pollett proposed its quantum version, called the N-operator, which
is an abstraction of NQP. This paper introduces the exists^{Q}-operator, which
is an abstraction of QMA, and its complement, the forall^{Q}-operator. These
operators not only define Quantum NP but also build a quantum hierarchy,
similar to the Meyer-Stockmeyer polynomial hierarchy, based on two-sided
bounded-error quantum computation.


title:
Entanglement and nonlocality versus spontaneous emission in two-atom
  system

abstract:
  We study evolution of entanglement of two two-level atoms in the presence of
dissipation caused by spontaneous emission. We find explicit fromulas for the
amount of entanglement as a function of time, in the case of destruction of the
initial entanglement and possible creation of a transient entanglement between
atoms. We also discuss how spontaneous emission influences nonlocality of
states expressed by violation of Bell - CHSH inequality. It is shown that
evolving system very quickly becomes local, even if entanglement is still
present or produced.


title:
Remote preparation of a single-mode photonic qubit by measuring field
  quadrature noise

abstract:
  An electromagnetic field quadrature measurement, performed on one of the
modes of the nonlocal single-photon state $a|1,0>-b|0,1>$, collapses it into a
superposition of the single-photon and vacuum states in the other mode. We use
this effect to implement remote preparation of arbitrary single-mode photonic
qubits conditioned on observation of a preselected quadrature value. The
quantum efficiency of the prepared qubit can be higher than that of the initial
single photon.


title: New exact treatment of the perturbed Coulomb interactions

abstract:
  A novel method for the exact solvability of quantum systems is discussed and
used to obtain closed analytical expressions in arbitrary dimensions for the
exact solutions of the hydrogenic atom in the external potential $\Delta
V(r)=br+cr^{2}$, which is based on the recently introduced supersymmetric
perturbation theory.


title:
Single Atom Cooling by Superfluid Immersion: A Non-Destructive Method
  for Qubits

abstract:
  We present a scheme to cool the motional state of neutral atoms confined in
sites of an optical lattice by immersing the system in a superfluid. The motion
of the atoms is damped by the generation of excitations in the superfluid, and
under appropriate conditions the internal state of the atom remains unchanged.
This scheme can thus be used to cool atoms used to encode a series of entangled
qubits non-destructively. Within realisable parameter ranges, the rate of
cooling to the ground state is found to be sufficiently large to be useful in
experiments.


title:
Implementation for Solving Random Satisfiability Problems through
  CNOT-based circuits in a NMR Quantum Processor

abstract:
  We give a general method of construting quantum circuit for random
\QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as
multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are
almost the same as the sizes of the SAT formulas. Further, a parallelization
scheme is described to solve random SAT problems efficiently through these
quantum circuits in \QTR{it}{nuclear magnetic resonance} (NMR) ensemble quantum
computing. This scheme exploits truly mixed states as input states rather than
pseudo-pure states, and combines with the topological nanture of the NMR
spectrum to identify the solutions to SAT problems in a parallel way. Several
typical SAT problems have been experimentally demonstrated by this scheme with
good performances.


title: Quantum entangling power of adiabatically connected hamiltonians

abstract:
  The space of quantum Hamiltonians has a natural partition in classes of
operators that can be adiabatically deformed into each other. We consider
parametric families of Hamiltonians acting on a bi-partite quantum state-space.
When the different Hamiltonians in the family fall in the same adiabatic class
one can manipulate entanglement by moving through energy eigenstates
corresponding to different value of the control parameters. We introduce an
associated notion of adiabatic entangling power. This novel measure is analyzed
for general $d\times d$ quantum systems and specific two-qubits examples are
studied


title:
Universal quantum control in irreducible state sectors: application to
  bosonic and spin-boson systems

abstract:
  This paper has been withdrawn by the authors because it was just an early
submission of quant-ph/0308133 with the wrong title. Sorry.


title:
Universal quantum control in irreducible state-space sectors:
  application to bosonic and spin-boson systems

abstract:
  We analyze the dynamical-algebraic approach to universal quantum control
introduced in P. Zanardi, S. Lloyd, quant-ph/0305013. The quantum state-space
$\cal H$ encoding information decomposes into irreducible sectors and
subsystems associated to the group of available evolutions. If this group
coincides with the unitary part of the group-algebra $\CC{\cal K}$ of some
group $\cal K$ then universal control is achievable over the ${\cal
K}$-irreducible components of $\cal H$. This general strategy is applied to
different kind of bosonic systems. We first consider massive bosons in a
double-well and show how to achieve universal control over all
finite-dimensional
  Fock sectors. We then discuss a multi-mode massless case giving the
conditions for generating the whole infinite-dimensional multi-mode
Heisenberg-Weyl enveloping-algebra. Finally we show how to use an auxiliary
bosonic mode coupled to finite-dimensional systems to generate high-order
non-linearities needed for universal control.


title: Experimental nonlinear sign shift for linear optics quantum computation

abstract:
  We have realized the nonlinear sign shift (NS) operation for photonic
qubits.This operation shifts the phase of two photons reflected by a beam
splitter using an extra single photon and measurement. We show that the
conditional phase shift is $(1.05\pm 0.06) \pi $ in clear agreement with
theory. Our results show that by using an ancilla photon and conditional
detection, nonlinear optical effects can be implemented using only linear
optical elements. This experiment represents an essential step for linear
optical implementations of scalable quantum computation.


title:
Demonstration of superluminal effects in an absorptionless,
  non-reflective system

abstract:
  We present an experimental and theoretical study of a simple, passive system
consisting of a birefringent, two-dimensional photonic crystal and a polarizer
in series, and show that superluminal dispersive effects can arise even though
no incident radiation is absorbed or reflected. We demonstrate that a vector
formulation of the Kramers-Kronig dispersion relations facilitates an
understanding of these counter-intuitive effects.


title:
Proton Zemach radius from measurements of the hyperfine splitting of
  hydrogen and muonic hydrogen

abstract:
  While measurements of the hyperfine structure of hydrogen-like atoms are
traditionally regarded as test of bound-state QED, we assume that theoretical
QED predictions are accurate and discuss the information about the
electromagnetic structure of protons that could be extracted from the
experimental values of the ground state hyperfine splitting in hydrogen and
muonic hydrogen. Using recent theoretical results on the proton polarizability
effects and the experimental hydrogen hyperfine splitting we obtain for the
Zemach radius of the proton the value 1.040(16) fm. We compare it to the
various theoretical estimates the uncertainty of which is shown to be larger
that 0.016 fm. This point of view gives quite convincing arguments in support
of projects to measure the hyperfine splitting of muonic hydrogen.


title: What is the value of an observable between pre- and postselection?

abstract:
  Hall's recent derivation of an exact uncertainty relation [Phys. Rev. A64,
052103 (2001)] is revisited. It is found that the Bayes estimator of an
observable between pre- and postselection equals the real part of the weak
value. The quadratic loss function equals the expectation of the squared
imaginary part of the weak value.


title:
New criteria of separability for tripartite and more high dimensional
  multipartite qubit density matrixes

abstract:
  In this Letter we find the new criteria of separability of multipartite qubit
density matrixes. Especially, we discuss in detail the criteria of separability
for tripartite qubit density matrixes. We find the sufficient and necessary
conditions of separability for tripartite qubit density matrixes, and give two
corollaries. The second corollary can be taken as the criterion of existence of
entanglement for tripartite qubit density matrixes. In concrete application,
its steps are quite simple and easy to operate. Some examples, discussions and
the generalization to more high dimensional multipartite qubit density matrixes
are given.


title: Concurrence Vectors for Entanglement of High-dimensional Systems

abstract:
  The concurrence vectors are proposed by employing the fundamental
representation of $A_n$ Lie algebra, which provides a clear criterion to
evaluate the entanglement of bipartite system of arbitrary dimension for both
pure and mixed states. Accordingly, a state is separable if the norm of its
concurrence vector vanishes. The state vectors related to SU(3) states and
SO(3) states are discussed in detail. The sign situation of nonzero components
of concurrence vectors of entangled bases presents a simple criterion to judge
whether the whole Hilbert subspace spanned by those bases is entangled, or
there exists entanglement edge. This is illustrated in terms of the concurrence
surfaces of several concrete examples.


title: Approximation of Various Quantum Query Types

abstract:
  Query complexity measures the amount of information an algorithm needs about
a problem to compute a solution. On a quantum computer there are different
realizations of a query and we will show that these are not always equivalent.
Our definition of equivalence is based on the ability to simulate (or
approximate) one query type by another. We show that a bit query can always
approximate a phase query with just two queries, while there exist problems for
which the number of phase queries which are necessary to approximate a bit
query must grow exponentially with the precision of the bit query. This result
follows from the query complexity bounds for the evaluation problem, for which
we establish a strong lower bound for the number of phase queries by exploiting
a relation between quantum algorithms and trigonometric polynomials.


title: High-Multipolar Effects on Dispersive Forces

abstract:
  We show that the dispersive force between a spherical nanoparticle (with a
radius $\le$ 100 nm) and a substrate is enhanced by several orders of magnitude
when the sphere is near to the substrate. We calculate exactly the dispersive
force in the non-retarded limit by incorporating the contributions to the
interaction from of all the multipolar electromagnetic modes. We show that as
the sphere approaches the substrate, the fluctuations of the electromagnetic
field, induced by the vacuum and the presence of the substrate, the dispersive
force is enhanced by orders of magnitude. We discuss this effect as a function
of the size of the sphere.


title: Mutually Unbiased Bases, Generalized Spin Matrices and Separability

abstract:
  A collection of orthonormal bases for a complex dXd Hilbert space is called
mutually unbiased (MUB) if for any two vectors v and w from different bases the
square of the inner product equals 1/d: |<v,w>| ^{2}=1/d. The MUB problem is to
prove or disprove the the existence of a maximal set of d+1 bases. It has been
shown in [W. K. Wootters, B. D. Fields, Annals of Physics, 191, no. 2, 363-381,
(1989)] that such a collection exists if d is a power of a prime number p. We
revisit this problem and use dX d generalizations of the Pauli spin matrices to
give a constructive proof of this result. Specifically we give explicit
representations of commuting families of unitary matrices whose eigenvectors
solve the MUB problem. Additionally we give formulas from which the orthogonal
bases can be readily computed. We show how the techniques developed here
provide a natural way to analyze the separability of the bases. The techniques
used require properties of algebraic field extensions, and the relevant part of
that theory is included in an Appendix.


title:
Generalized remote state preparation: Trading cbits, qubits and ebits in
  quantum communication

abstract:
  We consider the problem of communicating quantum states by simultaneously
making use of a noiseless classical channel, a noiseless quantum channel and
shared entanglement. We specifically study the version of the problem in which
the sender is given knowledge of the state to be communicated. In this setting,
a trade-off arises between the three resources, some portions of which have
been investigated previously in the contexts of the quantum-classical trade-off
in data compression, remote state preparation and superdense coding of quantum
states, each of which amounts to allowing just two out of these three
resources. We present a formula for the triple resource trade-off that reduces
its calculation to evaluating the data compression trade-off formula. In the
process, we also construct protocols achieving all the optimal points. These
turn out to be achievable by trade-off coding and suitable time-sharing between
optimal protocols for cases involving two resources out of the three mentioned
above.


title:
Photon generation from vacuum in nondegenerate cavities with regular and
  random periodic displacements of boundaries

abstract:
  We study the influence of fluctuations in periodic motion of boundaries of an
ideal three-dimensional cavity on the rate of photon generation from vacuum due
to the nonstationary Casimir effect.


title: Capacitive coupling of atomic systems to mesoscopic conductors

abstract:
  We describe a technique that enables a strong, coherent coupling between
isolated neutral atoms and mesoscopic conductors. The coupling is achieved by
exciting atoms trapped above the surface of a superconducting transmission line
into Rydberg states with large electric dipole moments, that induce voltage
fluctuations in the transmission line. Using a mechanism analogous to cavity
quantum electrodynamics an atomic state can be transferred to a long-lived mode
of the fluctuating voltage, atoms separated by millimeters can be entangled, or
the quantum state of a solid state device can be mapped onto atomic or photonic
states.


title: Sealing quantum message by quantum code

abstract:
  Quantum error correcting code is a useful tool to combat noise in quantum
computation. It is also an important ingredient in a number of unconditionally
secure quantum key distribution schemes. Here, I am going to show that quantum
code can also be used to seal a quantum message. Specifically, every one can
still read the content of the sealed quantum message. But, any such attempt can
be detected by an authorized verifier with an exponentially close to one
probability


title: Entropic uncertainty relations for the ground state of a coupled system

abstract:
  There is a renewed interest in the uncertainty principle, reformulated from
the information theoretic point of view, called the entropic uncertainty
relations. They have been studied for various integrable systems as a function
of their quantum numbers. In this work, focussing on the ground state of a
nonlinear, coupled Hamiltonian system, we show that approximate eigenstates can
be can be constructed within the framework of adiabatic theory. Using the
adiabatic eigenstates, we estimate the information entropies and their sum as a
function of the the nonlinearity parameter. We also briefly look at the
information entropies for the highly excited states in the system.


title: Control-target inversion property on Abelian groups

abstract:
  We show that the quantum Fourier transform on finite fields used to solve
query problems is a special case of the usual quantum Fourier transform on
finite abelian groups. We show that the control/target inversion property holds
in general. We apply this to get a sharp query complexity separation between
classical and quantum algorithms for a hidden homomorphism problem on finite
Abelian groups.


title: Quantum error-correction codes on Abelian groups

abstract:
  We prove a general form of bit flip formula for the quantum Fourier transform
on finite abelian groups and use it to encode some general CSS codes on these
groups.


title: Statistical Model with Measurement Degree of Freedom and Quantum Physics

abstract:
  This is an English translation of the manuscript which appeared in
Surikaiseki Kenkyusho Kokyuroku No. 1055 (1998). The asymptotic efficiency of
statistical estimate of unknown quantum states is discussed, both in adaptive
and collective settings. Aaptive bounds are written in sigle letterized form,
and collective bounds are written in limitting expression. Our arguments
clarify mathematical regularity conditions.


title:
Graphical description of the action of local Clifford transformations on
  graph states

abstract:
  We translate the action of local Clifford operations on graph states into
transformations on their associated graphs - i.e. we provide transformation
rules, stated in purely graph theoretical terms, which completely characterize
the evolution of graph states under local Clifford operations. As we will show,
there is essentially one basic rule, successive application of which generates
the orbit of any graph state under local unitary operations within the Clifford
group.


title:
A Pulse Shaping Algorithm of a Coherent Matter Wave. Controlling
  Reaction Dynamics

abstract:
  A pulse shaping algorithm for a matter wave with the purpose of controlling a
binary reaction has been designed. The scheme is illustrated for an Eley-Rideal
reaction where an impinging matter-wave atom recombines with an adsorbed atom
on a metal surface. The wave function of the impinging atom is shaped such that
the desorbing molecule leaves the surface in a specific vibrational state.


title: Limit to non-destructive optical detection of atoms

abstract:
  All optical techniques used to probe the properties of Bose-Einstein
condensates have been based on dispersion and absorption that can be described
by a two-level atom. Both phenomena lead to spontaneous emission that is
destructive. Recently, both were shown to lead to the same limit to the signal
to noise ratio for a given destruction. We generalise this result to show that
no single-pass optical technique using classical light, based on any number of
lasers or coherences between any number of levels, can exceed the limit imposed
by the two-level atom. This puts significant restrictions on potential
non-destructive measurement schemes.


title:
Crossover from classical to quantum behavior of Duffing oscillator
  through "pseudo-Lyapunov exponent"

abstract:
  We discuss the quantum--classical correspondence in a specific dissipative
chaotic system, Duffing oscillator. We quantize it on the basis of quantum
state diffusion (QSD) which is a certain formulation for open quantum systems
and an effective tool for analyzing complex problems numerically. We consider a
sensitivity to initial conditions, `` pseudo-Lyapunov exponent '', and
investigate it in detail, varying Planck constant effectively. We show that in
a dissipative system there exists a certain critical stage in which the
crossover from classical to quantum behavior occurs. Furthermore, we show that
an effect of dissipation suppresses the occurrence of chaos in the quantum
region, while it, combined with the periodic external force, plays a crucial
role in the chaotic behaviors of classical system.


title:
Coherent interaction of laser pulses in a resonant optically dense
  extended medium under the regime of strong field-matter coupling

abstract:
  Nonstationary pump-probe interaction between short laser pulses propagating
in a resonant optically dense coherent medium is considered. A special
attention is paid to the case, where the density of two-level particles is high
enough that a considerable part of the energy of relatively weak external
laser-fields can be coherently absorbed and reemitted by the medium. Thus, the
field of medium reaction plays a key role in the interaction processes, which
leads to the collective behavior of an atomic ensemble in the strongly coupled
light-matter system. Such behavior results in the fast excitation interchanges
between the field and a medium in the form of the optical ringing, which is
analogous to polariton beating in the solid-state optics. This collective
oscillating response, which can be treated as successive beats between light
wave-packets of different group velocities, is shown to significantly affect
propagation and amplification of the probe field under its nonlinear
interaction with a nearly copropagating pump pulse. Depending on the probe-pump
time delay, the probe transmission spectra show the appearance of either
specific doublet or coherent dip. The widths of these features are determined
by the density-dependent field-matter coupling coefficient and increase during
the propagation. Besides that, the widths of the coherent features, which
appear close to the resonance in the broadband probe-spectrum, exceed the
absorption-line width, since, under the strong-coupling regime, the frequency
of the optical ringing exceeds the rate of incoherent relaxation. Contrary to
the stationary strong-field effects, the density- and coordinate-dependent
transmission spectra of the probe manifest the importance of the collective
oscillations and cannot be obtained in the framework of the single-atom model.


title: Quantum Entanglement under Lorentz Boost

abstract:
  In order to understand the characteristics of quantum entanglement of massive
particles under Lorentz boost, we first introduce a relevant relativistic spin
observable, and evaluate its expectation values for the Bell states under
Lorentz boost. Then we show that maximal violation of the Bell's inequality can
be achieved by properly adjusting the directions of the spin measurement even
in a relativistically moving inertial frame.
  Based on this we infer that the entanglement information is preserved under
Lorentz boost as a form of correlation information determined by the
transformation characteristic of the Bell state in use.


title: Novel Identification of Symmetric and Anti-Symmetric Quantum Functions

abstract:
  Procedures are given below to construct symmetric and anti-symmetric quantum
functions. If hidden in an oracle, such functions can be identified exactly,
without iterative interrogation. This is another example of quantum search. The
resulting positive (or negative) functions also serve to uniquely reorganize a
superposition of states to give a basis state for testing purposes.


title: New Approachs to Quantum Computer Simulaton in a Classical Supercomputer

abstract:
  Classical simulation is important because it sets a benchmark for quantum
computer performance. Classical simulation is currently the only way to
exercise larger numbers of qubits. To achieve larger simulations, sparse matrix
processing is emphasized below while trading memory for processing. It
performed well within NCSA supercomputers, giving a state vector in convenient
continuous portions ready for post processing.


title: Separability and entanglement in 2x3xN composite quantum systems

abstract:
  The separability and entanglement of quantum mixed states in $\Cb^2 \otimes
\Cb^3 \otimes \Cb^N$ composite quantum systems are investigated. It is shown
that all quantum states $\rho$ with positive partial transposes and rank
$r(\rho)\leq N$ are separable.


title: Indistinguishability and the external correlation of mixtures

abstract:
  Experimental evidence, the heuristics of indistinguishability, and its
logical inconsistency with quantum formalism all argue against the existence of
a quantum mixture uncorrelated with the exterior, that is, argue for the
postulate "The state of a system uncorrelated with its exterior is pure." This
is shown to be equivalent with "The state of a system describable in terms of
indistinguishable pure states is pure," and with "The state of the universe is
pure"; further, it yields a quantitative expression of the traditional relation
of welcher Weg information to partial coherence. It is concluded that all
mixtures are "improper," the trace-reduction of a composite system's pure
state.


title: Nonclassical degree of states of single and bipartite systems

abstract:
  We consider experimental routes to determine the nonclassical degree of
states of a field mode. We adopt a distance-type criterium based on the
Hilbert-Schmidt metric to quantify the nonclassicality. The concept of
nonclassical degree is extended for states of bipartite systems, allowing us to
discuss a possible connection between nonclassicality and entanglement
measures.


title:
Intrinsic Decoherence and Irreversibility in the Quasiperiodic Kicked
  Rotor

abstract:
  We show that some classically chaotic quantum systems uncoupled from noisy
environments may generate intrinsic decoherence with all its associated
effects. In particular, we have observed time irreversibility and high
sensitivity to small perturbations in the initial conditions in a quasiperiodic
version of the kicked rotor. The existence of simple quantum systems with
intrinsic decoherence clarifies the quantum--classical correspondence in
chaotic systems.


title: Quantum Darwinism and Envariance

abstract:
  Effective classicality of a property of a quantum system can be defined using
redundancy of its record in the environment. This allows quantum physics to
approximate the situation encountered in the classical world: The information
about a classical system can exist independently from its state. In quantum
theory this is no longer possible: In an isolated quantum system the state and
the information about it are inextricably linked, and any measurement may --
and usually will -- reset that state. However, when the information about the
state of a quantum system is spread throughout the environment, it can be
treated (almost) as in classical physics.


title: Estimation of the Local Density of States on a Quantum Computer

abstract:
  We report an efficient quantum algorithm for estimating the local density of
states (LDOS) on a quantum computer. The LDOS describes the redistribution of
energy levels of a quantum system under the influence of a perturbation.
Sometimes known as the ``strength function'' from nuclear spectroscopy
experiments, the shape of the LDOS is directly related to the survivial
probability of unperturbed eigenstates, and has recently been related to the
fidelity decay (or ``Loschmidt echo'') under imperfect motion-reversal. For
quantum systems that can be simulated efficiently on a quantum computer, the
LDOS estimation algorithm enables an exponential speed-up over direct classical
computation.


title: Quantum entanglement and fixed-point bifurcations

abstract:
  How does the classical phase space structure for a composite system relate to
the entanglement characteristics of the corresponding quantum system? We
demonstrate how the entanglement in nonlinear bipartite systems can be
associated with a fixed point bifurcation in the classical dynamics. Using the
example of coupled giant spins we show that when a fixed point undergoes a
supercritical pitchfork bifurcation, the corresponding quantum state - the
ground state - achieves its maximum amount of entanglement near the critical
point. We conjecture that this will be a generic feature of systems whose
classical limit exhibits such a bifurcation.


title: No "No-Go"

abstract:
  In spite of the very common opinion we show that QM is not complete and that
it is possible to create prequantum models providing finer description of
physical reality than QM. There exists (at least in theoretical models)
dispersion free states and the Heisenberg uncertainty principle can be
violated. Thus in spite of all ``No-Go'' theorems (e.g., von Neumann, Kochen
and Specker,..., Bell) we found a realist basis of quantum mechanics. I think
that our model would totally satisfy A. Einstein who was sure that QM is not
complete and a finer description is possible.


title: Optimal quantum circuit synthesis from Controlled-U gates

abstract:
  From a geometric approach, we derive the minimum number of applications
needed for an arbitrary Controlled-Unitary gate to construct a universal
quantum circuit. A new analytic construction procedure is presented and shown
to be either optimal or close to optimal. This result can be extended to
improve the efficiency of universal quantum circuit construction from any
entangling gate. Specifically, for both the Controlled-NOT and Double-CNOT
gates, we develop simple analytic ways to construct universal quantum circuits
with three applications, which is the least possible.


title: On the additivity conjecture for channels with arbitrary constraints

abstract:
  Recently Shor proved equivalence of several open (sub)additivity problems
related to the Holevo capacity and the entanglement of formation [15]. In our
previous note [6] equivalence of these to the additivity of the Holevo capacity
for channels with arbitrary linear constraints was shown. This note is the
development of the previous one in the direction of channels with general
constraints. Introducing input constraints provides greater flexibility in the
treatment of the additivity conjecture. The Holevo capacity of arbitrarily
constrained channel is considered and the characteristic property of an optimal
ensemble for such channel is derived, generalizing the maximal distance
property of Schumacher and Westmoreland (proposition 1). It is shown that the
additivity conjecture for two channels with single linear constraints is
equivalent to the similar conjecture for two arbitrarily constrained channels
and, hence, to an interesting subadditivity property of the $\chi$-function for
the tensor product of these channels (theorem 1). We also propose an
alternative way of proving that the additivity conjecture for any two
unconstrained channels implies strong superadditivity of the entanglement of
formation. The arguments from the convex analysis provide another
characterization of channels for which subadditivity of the $\chi $-function
holds (theorem 3). This characterization and some modification of Shor's
channel extension provide a simple way of proving that global additivity of the
minimum output entropy for unconstrained channels implies global subadditivity
of the $\chi $-function and strong superadditivity of the entanglement of
formation.


title: Resonance fluorescence of a trapped three-level atom

abstract:
  We investigate theoretically the spectrum of resonance fluorescence of a
harmonically trapped atom, whose internal transitions are $\Lambda$--shaped and
driven at two-photon resonance by a pair of lasers, which cool the
center--of--mass motion. For this configuration, photons are scattered only due
to the mechanical effects of the quantum interaction between light and atom. We
study the spectrum of emission in the final stage of laser--cooling, when the
atomic center-of-mass dynamics is quantum mechanical and the size of the wave
packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use
the spectral decomposition of the Liouville operator of the master equation for
the atomic density matrix and apply second order perturbation theory. We find
that the spectrum of resonance fluorescence is composed by two narrow sidebands
-- the Stokes and anti-Stokes components of the scattered light -- while all
other signals are in general orders of magnitude smaller. For very low
temperatures, however, the Mollow--type inelastic component of the spectrum
becomes visible. This exhibits novel features which allow further insight into
the quantum dynamics of the system. We provide a physical model that interprets
our results and discuss how one can recover temperature and cooling rate of the
atom from the spectrum. The behaviour of the considered system is compared with
the resonance fluorescence of a trapped atom whose internal transition consists
of two-levels.


title:
L'argument Einstein Podolsky Rosen (EPR) : Paradoxe, Alternative,
  Demonstration

abstract:
  The EPR (Einstein, Podolsky, Rosen) argument and the Schrodinger cat paradox
are revisited in relation with modern quantum optics and atomic physics and
with the concept of decoherence. It is shown that the questions raised fifty
years ago are still at the heart of our understanding of quantum physics today.


title: Implementing Shor's algorithm on Josephson Charge Qubits

abstract:
  We investigate the physical implementation of Shor's factorization algorithm
on a Josephson charge qubit register. While we pursue a universal method to
factor a composite integer of any size, the scheme is demonstrated for the
number 21. We consider both the physical and algorithmic requirements for an
optimal implementation when only a small number of qubits is available. These
aspects of quantum computation are usually the topics of separate research
communities; we present a unifying discussion of both of these fundamental
features bridging Shor's algorithm to its physical realization using Josephson
junction qubits. In order to meet the stringent requirements set by a short
decoherence time, we accelerate the algorithm by decomposing the quantum
circuit into tailored two- and three-qubit gates and we find their physical
realizations through numerical optimization.


title: Controlled order rearrangement encryption for quantum key distribution

abstract:
  A novel technique is devised to perform orthogonal state quantum key
distribution. In this scheme, entangled parts of a quantum information carrier
are sent from Alice to Bob through two quantum channels. However before the
transmission, the orders of the quantum information carrier in one channel is
reordered so that Eve can not steal useful information. At the receiver's end,
the order of the quantum information carrier is restored. The order
rearrangement operation in both parties is controlled by a prior shared control
key which is used repeatedly in a quantum key distribution session.