title: Continuous-Variable Quantum Games

abstract:
  We investigate the quantization of games in which the players can access to a
continuous set of classical strategies, making use of continuous-variable
quantum systems. For the particular case of the Cournot's Duopoly, we find
that, even though the two players both act as "selfishly" in the quantum game
as they do in the classical game, they are found to virtually cooperate due to
the quantum entanglement between them. We also find that the original
Einstein-Podolksy-Rosen state contributes to the best profits that the two
firms could ever attain. Moreover, we propose a practical experimental setup
for the implementation of such quantum games.


title: Quantum Information Processing by NMR using strongly coupled spins

abstract:
  The enormous theoretical potential of Quantum Information Processing (QIP) is
driving the pursuit for its practical realization by various physical
techniques. Currently Nuclear Magnetic Resonance (NMR) has been the forerunner
by demonstrating a majority of quantum algorithms. In NMR, spin systems
consisting of coupled nuclear spins are utilized as qubits. In order to carry
out QIP, a spin system has to meet two major requirements: (i) qubit
addressability and (ii) mutual coupling among the qubits. It has been
demonstrated that the magnitude of the mutual coupling among qubits can be
increased by orienting the spin-systems in a liquid crystal matrix and
utilizing the residual dipolar couplings. While utilizing residual dipolar
couplings may be useful to increase the number of qubits, nuclei of same
species (homonuclei) might become strongly coupled. In strongly coupled
spin-systems, spins loose their individual identity of being qubits. We propose
that even such strongly coupled spin-systems can be used for QIP and the
qubit-manipulation can be achieved by transition-selective pulses. We
demonstrate experimental preparation of pseudopure states, creation of
maximally entangled states, implementation logic gates and implementation of
Deutsch-Jozsa (DJ) algorithm in strongly coupled 2,3 and 4 spin systems. The
energy levels of the strongly coupled 3 and 4 spin systems were obtained by
using a Z-COSY experiment.


title: Foundations of quantum theory and quantum information applications

abstract:
  This thesis establishes a number of connections between foundational issues
in quantum theory, and some quantum information applications. It starts with a
review of quantum contextuality and non-locality, multipartite entanglement
characterisation, and of a few quantum information protocols.
  Quantum non-locality and contextuality are shown to be essential for
different implementations of quantum information protocols known as quantum
random access codes and quantum communication complexity protocols. I derive
sufficient experimental conditions for tests of these quantum properties.
  I also discuss how the distribution of quantum information through quantum
cloning processes can be useful in quantum computing. Regarding entanglement
characterisation, some results are obtained relating two problems, that of
additivity of the relative entropy of entanglement, and that of identifying
different types of tripartite entanglement in the asymptotic regime of
manipulations of many copies of a given state.
  The thesis ends with a description of an information processing task in which
a single qubit substitutes for an arbitrarily large amount of classical
communication. This result is interpreted in different ways: as a gap between
quantum and classical computation space complexity; as a bound on the amount of
classical communication necessary to simulate entanglement; and as a basic
result on hidden-variable theories for quantum mechanics. I also show that the
advantage of quantum over classical communication can be established in a
feasible experiment.


title:
Does the Transverse Electric Zero Mode Contribute to the Casimir Effect
  for a Metal?

abstract:
  The finite temperature Casimir free energy, entropy, and internal energy are
considered anew for a conventional parallel-plate configuration, in the light
of current discussions in the literature. In the case of an "ideal" metal,
characterized by a refractive index equal to infinity for all frequencies, we
recover, via a somewhat unconventional method, conventional results for the
temperature dependence, meaning that the zero-frequency transverse electric
mode contributes the same as the transverse magnetic mode. For a real metal,
however, approximately obeying the Drude dispersive model at low frequencies,
we find that the zero-frequency transverse electric mode does not contribute at
all. This would appear to lead to an observable temperature dependence and a
violation of the third law of thermodynamics. It had been suggested that the
source of the difficulty was the behaviour of the reflection coefficient for
perpendicular polarization but we show that this is not the case. By
introducing a simplified model for the Casimir interaction, consisting of two
harmonic oscillators interacting via a third one, we illustrate the behavior of
the transverse electric field. Numerical results are presented based on the
refractive index for gold. A linear temperature correction to the Casimir force
between parallel plates is indeed found which should be observable in
room-temperature experiments, but this does not entail any thermodynamic
inconsistency.


title: Seven Principles of Quantum Mechanics

abstract:
  The list of basic axioms of quantum mechanics as it was formulated by von
Neumann includes only the mathematical formalism of the Hilbert space and its
statistical interpretation. We point out that such an approach is too general
to be considered as the foundation of quantum mechanics. In particular in this
approach any finite-dimensional Hilbert space describes a quantum system.
Though such a treatment might be a convenient approximation it can not be
considered as a fundamental description of a quantum system and moreover it
leads to some paradoxes like Bell's theorem.
  I present a list from seven basic postulates of axiomatic quantum mechanics.
In particular the list includes the axiom describing spatial properties of
quantum system. These axioms do not admit a nontrivial realization in the
finite-dimensional Hilbert space. One suggests that the axiomatic quantum
mechanics is consistent with local realism.


title: Local Realism, Contextualism and Loopholes in Bell`s Experiments

abstract:
  It is currently widely accepted, as a result of Bell's theorem and related
experiments, that quantum mechanics is inconsistent with local realism and
there is the so called quantum non-locality. We show that such a claim can be
justified only in a simplified approach to quantum mechanics when one neglects
the fundamental fact that there exist space and time. Mathematical definitions
of local realism in the sense of Bell and in the sense of Einstein are given.
We demonstrate that if we include into the quantum mechanical formalism the
space-time structure in the standard way then quantum mechanics might be
consistent with Einstein's local realism. It shows that loopholes are
unavoidable in experiments aimed to establish a violation of Bell`s
inequalities. We show how the space-time structure can be considered from the
contextual point of view. A mathematical framework for the contextual approach
is outlined.


title: On a Possible Physical Metatheory of Consciousness

abstract:
  We show that the modern quantum mechanics, and particularly the theory of
decoherence, allows formulating a sort of a physical metatheory of
consciousness. Particularly, the analysis of the necessary conditions for the
occurrence of decoherence, along with the hypothesis that consciousness bears
(more-or-less) well definable physical origin, leads to a wider physical
picture naturally involving consciousness. This can be considered as a sort of
a psycho-physical parallelism, but on very wide scales bearing some
cosmological relevance.


title: Quantum Parallelism in Quantum Information Processing

abstract:
  We investigate distinguishability (measured by fidelity) of the initial and
the final state of a qubit, which is an object of the so-called nonideal
quantum measurement of the first kind. We show that the fidelity of a nonideal
measurement can be greater than the fidelity of the corresponding ideal
measurement. This result is somewhat counterintuitive, and can be traced back
to the quantum parallelism in quantum operations, in analogy with the quantum
parallelism manifested in the quantum computing theory. In particular, while
the quantum parallelism in quantum computing underlies efficient quantum
algorithms, the quantum parallelism in quantum information theory underlies
this, classically unexpected, increase of the fidelity.


title: Time Asymmetric Quantum Theory - I Modifying an Axiom of Quantum Physics

abstract:
  A slight modification of one axiom of quantum theory changes a reversible
theory into a time asymmetric theory. Whereas the standard Hilbert space axiom
does not distinguish mathematically between the space of states (in-states of
scattering theory) and the space of observables (out-``states'' of scattering
theory) the new axiom associates states and observables to two different Hardy
subspaces which are dense in the same Hilbert space and analytic in the lower
and upper complex energy plane, respectively. As a consequence of this new
axiom the dynamical equations (Schr\"{o}dinger or Heisenberg) integrate to a
semigroup evolution. Extending this new Hardy space axiom to a relativistic
theory provides a relativistic theory of resonance scattering and decay with
Born probablilities that fulfill Einstein causality and the exponential decay
law.


title: Non-Empty Quantum Dot as a Spin-Entangler

abstract:
  We consider a three-port single-level quantum dot system with one input and
two output leads. Instead of considering an empty dot, we study the situations
that two input electrons co-tunnel through the quantum dot occupied by one or
two dot electrons. We show that electron entanglement can be generated via the
co-tunneling processes when the dot is occupied by two electrons, yielding
non-local spin-singlet states at the output leads. When the dot is occupied by
a single electron, net spin-singlet final states could be generated by
injecting polarized electrons to the dot system. When the input electrons are
unpolarized, we show that by carefully arranging model parameters non-local
spin-triplet electrons can also be obtained at the output leads if the
dot-electron spin remains unchanged in the final state.


title: Hydrogen atom in phase space. The Kirkwood-Rihaczek representation

abstract:
  We present a phase-space representation of the hydrogen atom using the
Kirkwood-Rikaczek distribution function. This distribution allows us to obtain
analytical results, which is quite unique because an exact analytical form of
the Wigner functions corresponding to the atom states is not known. We show how
the Kirkwood-Rihaczek distribution reflects properties of the hydrogen atom
wave functions in position and momentum representations.


title: Geometric Phases and Topological Quantum Computation

abstract:
  In the first part of this review we introduce the basics theory behind
geometric phases and emphasize their importance in quantum theory. The subject
is presented in a general way so as to illustrate its wide applicability, but
we also introduce a number of examples that will help the reader understand the
basic issues involved. In the second part we show how to perform a universal
quantum computation using only geometric effects appearing in quantum phases.
It is then finally discussed how this geometric way of performing quantum gates
can lead to a stable, large scale, intrinsically fault-tolerant quantum
computer.


title:
Experimental application of decoherence-free subspaces in a
  quantum-computing algorithm

abstract:
  For a practical quantum computer to operate, it will be essential to properly
manage decoherence. One important technique for doing this is the use of
"decoherence-free subspaces" (DFSs), which have recently been demonstrated.
Here we present the first use of DFSs to improve the performance of a quantum
algorithm. An optical implementation of the Deutsch-Jozsa algorithm can be made
insensitive to a particular class of phase noise by encoding information in the
appropriate subspaces; we observe a reduction of the error rate from 35% to
essentially its pre-noise value of 8%.


title:
A Note on the correspondence between Qubit Quantum Operations and
  Special Relativity

abstract:
  We exploit a well-known isomorphism between complex hermitian $2\times 2$
matrices and $\mathbb{R}^4$, which yields a convenient real vector
representation of qubit states. Because these do not need to be normalized we
find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose
vertical cross-sections are nothing but Bloch spheres. Pure states are
represented by light-like vectors, unitary operations correspond to special
orthogonal transforms about the axis of the cone, positive operations
correspond to pure Lorentz boosts. We formalize the equivalence between the
generalized measurement formalism on qubit states and the Lorentz
transformations of special relativity, or more precisely elements of the
restricted Lorentz group together with future-directed null boosts. The note
ends with a discussion of the equivalence and some of its possible
consequences.


title: Entangled multiplet by angular momentum addition

abstract:
  We present the visible entangled states of 4-qubit system which can be
observed easily in physical laboratories. This was motivated from the fact that
the entangled state of 2-qubit system comes from singlet and triplet states
which are constructed through the angular momentum addition formalism. We show
that 4-qubit system has the new entangled states different from GHZ or W types
entangled states


title: Analytic Solution of Strongly Coupling Schroedinger Equations

abstract:
  A recently developed expansion method for analytically solving the ground
states of strongly coupling Schr\"odinger equations by Friedberg, Lee and Zhao
is extended to excited states and applied to the pedagogically important
problems of power-law central forces. With the extended method, the Hydrogen
atom problem is resolved and the low-lying states of Yukawa potential are
approximately obtained.


title: Energy spectrum of the equal spin-spin interactions Hamiltonian

abstract:
  The energy spectrum of eigenvalues of the equal spin-spin interactions (ESSI)
Hamiltonian has been found. The obtained spectrum is free from limitations
imposed on number of spins and parameters of the ESSI Hamiltonian. This model
can be used for consideration of spin dynamics of mesoscopic systems and
molecules with large number of nuclei spins.


title: How to Complete the Quantum-Mechanical Description?

abstract:
  If the statement by Einstein, Podolsky and Rosen on incompleteness of
Quantum-Mechanical description of nature is correct, then we can regard Quantum
Mechanics as a Method of Indirect Computation. The problem is, whether the
theory is incomplete or the nature itself does not allow complete description?
And if the first option is correct, how is it possible to complete the
Quantum-Mechanical description? Here we try to complement de-Broglie's idea on
wave-pilot the stochastic gravitation gives origin to. We assume that
de-Broglie's wave-pilots are gravitational stochastic ones, and we shall regard
micro-objects as test classical particles being subject to the influence of
de-Broglie's waves stochastic gravitation.


title: Entanglement and Relativity

abstract:
  In this paper we survey, in an elementary fashion, some of the questions that
arise when one considers how entanglement and relativity are related via the
notion of non-locality. We begin by reviewing the role of entangled states in
Bell inequality violation and question whether the associated notions of
non-locality lead to problems with relativity. The use of entanglement and
wavefunction collapse in Einstein's famous incompleteness argument is then
considered, before we go on to see how the issue of non-locality is transformed
if one considers quantum mechanics without collapse to be a complete theory, as
in the Everett interpretation. The opportunity is taken to consider whether
teleportation and dense coding might constitute a source of non-locality within
the Everett interpretation.


title: Entanglement in the Process of Stimulated Brillouin Scattering of Light

abstract:
  The process of stimulated Brillouin scattering is described by the model of
two-dimensional oscillator. The phenomenon of entanglement which appears in the
photon-phonon modes after the interaction with matter is discussed.


title:
Optical implementation of Deutsch-Jozsa and Bernstein-Vazirani quantum
  algorithms in eight dimensions

abstract:
  We report on a fiber-optics implementation of the Deutsch-Jozsa and
Bernstein-Vazirani quantum algorithms for 8-point functions. The measured
visibility of the 8-path interferometer is about 97.5%. Potential applications
of our setup to quantum communication or cryptographic protocols using several
qubits are discussed.


title: Symmetrization and Entanglement of Arbitrary States of Qubits

abstract:
  Given two arbitrary pure states $ |\phi>$ and $ |\psi>$ of qubits or higher
level states, we provide arguments in favor of states of the form $
\frac{1}{\sqrt{2}}(|\psi> |\phi> + i |\phi> |\psi>) $ instead of symmetric or
anti-symmetric states, as natural candidates for optimally entangled states
constructed from these states. We show that such states firstly have on the
average a high value of concurrence, secondly can be constructed by a universal
unitary operator independent of the input states. We also show that these
states are the only ones which can be produced with perfect fidelity by any
quantum operation designed for intertwining two pure states with a relative
phase. A probabilistic method is proposed for producing any pre-determined
relative phase into the combination of any two arbitrary states.


title:
Comment on "Quasideterministic Generation of Entangled Atoms in a Cavity
  "

abstract:
  This paper has been withdrawn by the author(s), due a crucial sign error in
conclusion .


title:
Do the Robertson-SCHR\"{O}DINGER and the Heisenberg Uncertainty
  Relations Imply a General Physical Principle ?

abstract:
  It is explicitly shown that there exist physical states (normalized to 1) in
which the Robertson- Schr\"{o}dinger and Heisenberg uncertainty relations are
invalid, namely, the mean values of the physical operators are infinite.
Consequently, these relations cannot imply a general physical principle. The
explanation by the theory of functional analysis is given : for these states
even the definition of the uncertainty notion through the dispersion notion in
the probability theory is irrelevant.


title: Multipartite Entanglement and Hyperdeterminants

abstract:
  We classify multipartite entanglement in a unified manner, focusing on a
duality between the set of separable states and that of entangled states.
Hyperdeterminants, derived from the duality, are natural generalizations of
entanglement measures, the concurrence, 3-tangle for 2, 3 qubits respectively.
Our approach reveals how inequivalent multipartite entangled classes of pure
states constitute a partially ordered structure under local actions,
significantly different from a totally ordered one in the bipartite case.
Moreover, the generic entangled class of the maximal dimension, given by the
nonzero hyperdeterminant, does not include the maximally entangled states in
Bell's inequalities in general (e.g., in the 4 or more qubits), contrary to the
widely known bipartite or 3-qubit cases. It suggests that not only are they
never locally interconvertible with the majority of multipartite entangled
states, but they would have no grounds for the canonical n-partite entangled
states. Our classification is also useful for that of mixed states.


title:
Positive operator valued measures covariant with respect to an Abelian
  group

abstract:
  Given a unitary representation $U$ of an Abelian group $G$ and a subgroup
$H$, we characterise the positive operator valued quotient group $G/H$ and
covariant with respect to $U$.


title: Does decoherence in the thermodynamic limit exist?

abstract:
  Paper withdrawn due to an error into the equations of the probability
amplitudes.


title: Implement Quantum Random Walks with Linear Optics Elements

abstract:
  The quantum random walk has drawn special interests because its remarkable
features to the classical counterpart could lead to new quantum algorithms. In
this paper, we propose a feasible scheme to implement quantum random walks on a
line using only linear optics elements. With current single-photon interference
technology, the steps that could be experimentally implemented can be extended
to very large numbers. We also show that, by decohering the quantum states, our
scheme for quantum random walk tends to be classical.


title:
Realization of symmetric sharing of entanglement in semiconductor
  microcrystallites coupled by a cavity field

abstract:
  The entanglement of excitonic states in a system of $N$ spatially separated
semiconductor microcrystallites is investigated. The interaction among the
different microcrystallites is mediated by a single-mode cavity field. It is
found that the symmetric sharing of the entanglement (measured by the
concurrence) between any pair of the excitonic state with $N$ qubits defined by
the number states (vacuum and a single-exciton states) or the coherent states
(odd and even coherent states) can be prepared by the cavity field for this
system.


title:
The Born rule from a consistency requirement on hidden measurements in
  complex Hilbert space

abstract:
  We formalize the hidden measurement approach within the very general notion
of an interactive probability model. We narrow down the model by assuming the
state space of a physical entity is a complex Hilbert space and introduce the
principle of consistent interaction which effectively partitions the space of
apparatus states. The normalized measure of the set of apparatus states that
interact with a pure state giving rise to a fixed outcome is shown to be in
accordance with the probability obtained using the Born rule.


title:
Characterization of entanglement transformation via group representation
  theory

abstract:
  Entanglement transformation of composite quantum systems is investigated in
the context of group representation theory. Representation of the direct
product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on
the binary composite system, is realized in the four-dimensional complex space
in terms of a set of novel bases that are pseudo orthonormalized. The
two-to-one homomorphism is then established for the group $SL(2,C)\otimes
SL(2,C)$ onto the $SO(4,C)$. It is shown that the resulting representation
theory leads to the complete characterization for the entanglement
transformation of the binary composite system.


title:
Decoherence from a Chaotic Environment: An Upside Down "Oscillator" as a
  Model

abstract:
  Chaotic evolutions exhibit exponential sensitivity to initial conditions.
This suggests that even very small perturbations resulting from weak coupling
of a quantum chaotic environment to the position of a system whose state is a
non-local superposition will lead to rapid decoherence. However, it is also
known that quantum counterparts of classically chaotic systems lose exponential
sensitivity to initial conditions, so this expectation of enhanced decoherence
is by no means obvious. We analyze decoherence due to a "toy" quantum
environment that is analytically solvable, yet displays the crucial phenomenon
of exponential sensitivity to perturbations. We show that such an environment,
with a single degree of freedom, can be far more effective at destroying
quantum coherence than a heat bath with infinitely many degrees of freedom.
This also means that the standard "quantum Brownian motion" model for a
decohering environment may not be as universally applicable as it once was
conjectured to be.


title: Three-dimensional Casimir force between absorbing multilayer dielectrics

abstract:
  Recently the influence of dielectric and geometrical properties on the
Casimir force between dispersing and absorbing multilayered plates in the
zero-temperature limit has been studied within a 1D quantization scheme for the
electromagnetic field in the presence of causal media [R. Esquivel-Sirvent, C.
Villarreal, and G.H. Cocoletzi, Phys. Rev. Lett. 64, 052108 (2001)]. In the
present paper a rigorous 3D analysis is given, which shows that for complex
heterostructures the 1D theory only roughly reflects the dependence of the
Casimir force on the plate separation in general. Further, an extension of the
very recently derived formula for the Casimir force at zero temperature [M.S.
Toma\v{s}, Phys. Rev. A 66, 052103 (2002)] to finite temperatures is given, and
analytical expressions for specific distance laws in the zero-temperature limit
are derived. In particular, it is shown that the Casimir force between two
single-slab plates behaves asymptotically like $d^{-6}$ in place of $d^{-4}$
($d$, plate separation).


title: Quantum description of classical apparatus: Zeno effect and decoherence

abstract:
  We study the measurement process by treating classical detectors entirely
quantum mechanically. As a generic model we use a point-contact detector
coupled to an electron in a quantum dot and tunneling into the continuum.
Transition to the classical description and the mechanism of decoherence are
investigated. We concentrate on the influence of the measurement on the
electron decay rate to the continuum. We demonstrate that the Zeno (or the
anti-Zeno) effect requires a nonuniform density of states in the continuum. In
this case we show that the anti-Zeno effect relates only to the average decay
rate, whereas for sufficiently small time the Zeno effect always takes place.
We discuss the experimental consequences of our results and the role of the
projection postulate in a measurement process.


title:
Stochastic resonance in periodic potentials: realization in a
  dissipative optical lattice

abstract:
  We have observed the phenomenon of stochastic resonance on the Brillouin
propagation modes of a dissipative optical lattice. Such a mode has been
excited by applying a moving potential modulation with phase velocity equal to
the velocity of the mode. Its amplitude has been characterized by the
center-of-mass (CM) velocity of the atomic cloud. At Brillouin resonance, we
studied the CM-velocity as a function of the optical pumping rate at a given
depth of the potential wells. We have observed a resonant dependence of the CM
velocity on the optical pumping rate, corresponding to the noise strength. This
corresponds to the experimental observation of stochastic resonance in a
periodic potential in the low-damping regime.


title: Dark propagation modes in optical lattices

abstract:
  We examine the stimulated light scattering onto the propagation modes of a
dissipative optical lattice. We show that two different pump-probe
configurations may lead to the excitation, via different mechanisms, of the
same mode. We found that in one configuration the scattering on the propagation
mode results in a resonance in the probe transmission spectrum while in the
other configuration no modification of the scattering spectrum occurs, i.e. the
mode is dark. A theoretical explanation of this behaviour is provided.


title: Limits of noise squeezing in Kerr effect

abstract:
  It is well known that the optical Kerr effect can be a source of highly
squeezed light, however the analytical limit of the noise suppression has not
been found yet. The process is reconsidered and an analytical estimation of the
optimal quadrature noise level is presented. The validity of the new scaling
law is checked numerically and analytically.


title: Superselection Rules in Quantum Cryptography

abstract:
  It is believed that superselection rules in quantum mechanics can restrict
the possible operation on a qbit. If this was true, the model used by Mayers
for the impossibility of bit commitment and by Kitaev for the impossibility of
coin flipping would be inadequate. We explain why this is not the case. We show
that a charge superselection rule implies no restriction on the operations that
can be executed on any individual qbit.


title:
Local Spectral Density for a Periodically Driven System of Coupled
  Quantum States with Strong Imperfection in Unperturbed Energies

abstract:
  A random matrix theory approach is applied in order to analyze the
localization properties of local spectral density for a generic system of
coupled quantum states with strong static imperfection in the unperturbed
energy levels. The system is excited by an external periodic field, the
temporal profile of which is close to monochromatic one. The shape of local
spectral density is shown to be well described by the contour obtained from a
relevant model of periodically driven two-states system with irreversible
losses to an external thermal bath. The shape width and the inverse
participation ratio are determined as functions both of the Rabi frequency and
of parameters specifying the localization effect for our system in the absence
of external field.


title:
Security of the Bennett 1992 quantum-key distribution against individual
  attack over a realistic channel

abstract:
  The security of two-state quantum key distribution against individual attack
is estimated when the channel has losses and noises. We assume that Alice and
Bob use two nonorthogonal single-photon polarization states. To make our
analysis simple, we propose a modified B92 protocol in which Alice and Bob make
use of inconclusive results and Bob performs a kind of symmetrization of
received states. Using this protocol, Alice and Bob can estimate Eve's
information gain as a function of a few parameters which reflect the
imperfections of devices or Eve's disturbance. In some parameter regions, Eve's
maximum information gain shows counter-intuitive behavior, namely, it decreases
as the amount of disturbances increases. For a small noise rate Eve can extract
perfect information in the case where the angle between Alice's two states is
small or large, while she cannot extract perfect information for intermediate
angles. We also estimate the secret key gain which is the net growth of the
secret key per one pulse. We show the region where the modified B92 protocol
over a realistic channel is secure against individual attack.


title:
Unconditionally Secure Key Distribution Based on Two Nonorthogonal
  States

abstract:
  We prove the unconditional security of the Bennett 1992 protocol, by using a
reduction to an entanglement distillation protocol initiated by a local
filtering process. The bit errors and the phase errors are correlated after the
filtering, and we can bound the amount of phase errors from the observed bit
errors by an estimation method involving nonorthogonal measurements. The angle
between the two states shows a trade-off between accuracy of the estimation and
robustness to noises.


title: Time-dependent Casimir-Polder forces and partially dressed states

abstract:
  A time-dependent Casimir-Polder force is shown to arise during the time
evolution of a partially dressed two-level atom. The partially dressed atom is
obtained by a rapid change of an atomic parameter such as its transition
frequency, due to the action of some external agent. The electromagnetic field
fluctuations around the atom, averaged over the solid angle for simplicity, are
calculated as a function of time, and it is shown that the interaction energy
with a second atom yields a dynamical Casimir-Polder potential between the two
atoms.


title: Remote state preparation and measurement of single photon

abstract:
  Quantum information theory has revolutionized the way in which information is
processed using quantum resources such as entangled states, local operations
and classical communications. Two important protocols in quantum communications
are quantum teleportation and remote state preparation. In quantum
teleportation neither the sender nor the receiver know the identity of a state.
In remote state preparation the sender knows the state which is to be remotely
prepared without ever physically sending the object or the complete classical
description of it. Using one unit of entanglement and one classical bit Alice
can remotely prepare a photon (from special ensemble) of her choice at Bob's
laboratory. In remote state measurement Alice asks Bob to simulate any single
particle measurement statistics on an arbitrary photon. In this talk we will
present these ideas and discuss the latest developments and future open
problems.


title: Qubit versus bit for measuring an integral of a classical field

abstract:
  Methods for measuring an integral of a classical field via local interaction
of classical bits or local interaction of qubits passing through the field one
at a time are analyzed. A quantum method, which has an exponentially better
precision than any classical method we could see, is described.


title:
Localization and pattern formation in Wigner representation via
  multiresolution

abstract:
  We present an application of variational-wavelet analysis to quasiclassical
calculations of solutions of Wigner equations related to nonlinear (polynomial)
dynamical problems. (Naive) deformation quantization, multiresolution
representations and variational approach are the key points. Numerical
calculations demonstrates pattern formation from localized eigenmodes and
transition from chaotic to localized (waveleton) types of behaviour.


title: Contextual objectivity and quantum holism

abstract:
  In our effort to restate a "realistic" approach to quantum mechanics, that
would fully acknowledge that local realism is untenable, we add a few more
questions and answers to the list presented in quant-ph/0203131. We also
suggest to replace the very misleading wording "quantum non-locality" by
"quantum holism", that conveys a much better intuitive idea of the physical
content of entanglement.


title: The direction of time: from the global arrow to the local arrow

abstract:
  In this paper we discuss the traditional approaches to the problem of the
arrow of time. On the basis of this discussion we adopt a global and
non-entropic approach, according to which the arrow of time has a global origin
and is an intrinsic, geometrical feature of space-time. Finally, we show how
the global arrow is translated into local terms as a local time-asymmetric flux
of energy


title: Explicit, analytical solution of scaling quantum graphs

abstract:
  Based on earlier work on regular quantum graphs we show that a large class of
scaling quantum graphs with arbitrary topology are explicitly analytically
solvable. This is surprising since quantum graphs are excellent models of
quantum chaos and quantum chaotic systems are not usually explicitly
analytically solvable.


title: The G\"odelizing Quantum-Mechanical Automata

abstract:
  Using Albert results we argue that we don't need new physics to understand
G\"odelization. Albert quantum automaton can "understand" both a formal system
and a G\"odel proposition which can't be obtained within this system. There are
two significant conclusions. The first speaks "against Penrose" whereas the
second speaks for him.


title: Quantum dissipation induced noncommutative geometry

abstract:
  The quantum statistical dynamics of a position coordinate x coupled to a
reservoir requires theoretically two copies of the position coordinate within
the reduced density matrix description. One coordinate moves forward in time
while the other coordinate moves backward in time. It is shown that quantum
dissipation induces, in the plane of the forward and backward motions, a
noncommutative geometry. The noncommutative geometric plane is a consequence of
a quantum dissipation induced phase interference which is closely analogous to
the Aharanov-Bohm effect.


title: Targeting qubit states using open-loop control

abstract:
  We present an open-loop (bang-bang) scheme which drives an open two-level
quantum system to any target state, while maintaining quantum coherence
throughout the process. The control is illustrated by a realistic simulation
for both adiabatic and thermal decoherence. In the thermal decoherence regime,
the control achieved by the proposed scheme is qualitatively similar, at the
ensemble level, to the control realized by the quantum feedback scheme of Wang,
Wiseman, and Milburn [Phys. Rev. A 64, #063810 (2001)] for the spontaneous
emission of a two-level atom. The performance of the open-loop scheme compares
favorably against the quantum feedback scheme with respect to robustness,
target fidelity and transition times.


title:
Constant-time solution to the Global Optimization Problem using
  Bruschweiler's ensemble search algorithm

abstract:
  A constant-time solution of the continuous Global Optimization Problem (GOP)
is obtained by using an ensemble algorithm. We show that under certain
assumptions, the solution can be guaranteed by mapping the GOP onto a discrete
unsorted search problem, whereupon Bruschweiler's ensemble search algorithm is
applied. For adequate sensitivities of the measurement technique, the query
complexity of the ensemble search algorithm depends linearly on the size of the
function's domain. Advantages and limitations of an eventual NMR implementation
are discussed.


title: On the Role of Locality Condition in Bell's Theorem

abstract:
  For a special stochastic realistic model in certain spin-correlation
experiments and without imposing the locality condition, an inequality is
found. Then, it is shown that quantum theory is able (is possible) to violate
this inequality. This shows that, irrelevance of the locality condition, the
quantum entanglement of the spin singlet-state is the reason for the violation
of Bell's inequality in Bell's theorem.


title: Quantum memory for individual polarization photon

abstract:
  Here we present an experimentally feasible quantum memory for individual
polarization photon with long-lived atomic ensembles excitations. Based a
process similar to teleportation, the memory is reversible. And the storage
information can be effortlessly read out and transferred back to photon.
Although it successes with only a probability of 1/4, it is expected valuable
in various quantum information processing, especially those cases where
polarized photons are employed. The physical requirements are moderate and fit
the presest technique.


title: Observer Created Violation of Bell's Inequalities

abstract:
  Local systems may appear to violate Bell's inequalities if they are observed
through suitable filters. The nonlocality leading to violation is outside the
system and comprises the observer comparing the outcomes of the typical two
wing Bell experiment. An example based on a well known gedanken experiment by
Mermin is presented, and implications for the interpretation of Bell tests are
discussed.


title:
Additivity of Entanglement of Formation of Two Three-level-antisymmetric
  States

abstract:
  Quantum entanglement is the quantum information processing resource. Thus it
is of importance to understand how much of entanglement particular quantum
states have, and what kinds of laws entanglement and also transformation
between entanglement states subject to. Therefore, it is essentialy important
to use proper measures of entanglement which have nice properties. One of the
major candidates of such measures is "entanglement of formation", and whether
this measurement is additive or not is an important open problem. We aim at
certain states so-called "antisymmetric states" for which the additivity are
not solved as far as we know, and show the additivity for two of them.
  Keywords: quantum entanglement, entanglement of formation, additivity of
entanglement measures, antisymmetric states.


title: A Quantum Computer Architecture using Nonlocal Interactions

abstract:
  Several authors have described the basic requirements essential to build a
scalable quantum computer. Because many physical implementation schemes for
quantum computing rely on nearest neighbor interactions, there is a hidden
quantum communication overhead to connect distant nodes of the computer. In
this paper we propose a physical solution to this problem which, together with
the key building blocks, provides a pathway to a scalable quantum architecture
using nonlocal interactions. Our solution involves the concept of a quantum bus
that acts as a refreshable entanglement resource to connect distant memory
nodes providing an architectural concept for quantum computers analogous to the
von Neumann architecture for classical computers.


title: A Practical Quantum Mechanism for the Public Goods Game

abstract:
  Quantum generalizations of conventional games broaden the range of available
strategies, which can help improve outcomes for the participants. With many
players, such quantum games can involve entanglement among many states which is
difficult to implement, especially if the states must be communicated over some
distance. This paper describes a quantum mechanism for the economically
significant $n$-player public goods game that requires only two-particle
entanglement and is thus much easier to implement than more general quantum
mechanisms. In spite of the large temptation to free ride on the efforts of
others in this game, two-particle entanglement is sufficient to give near
optimal expected payoff when players use a simple mixed strategy for which no
player can benefit by making different choices. This mechanism can also address
some heterogeneous preferences among the players.


title:
Requirements for compatibility between local and multipartite quantum
  states

abstract:
  We consider a partial trace transformation which maps a multipartite quantum
state to collection of local density matrices. We call this collection a mean
field state. The necessary and sufficient conditions under which a mean field
state is compatible with at least one multipartite pure state are found for the
system of $n$ qubits and for the tripartite system with the Hilbert space of
dimension 2x2x4. Compatibility of mean field states with more general classes
of multipartite quantum states is discussed.


title: Lower Bound on Entanglement of Formation for the Qubit-Qudit System

abstract:
  Wootters [PRL 80, 2245 (1998)] has derived a closed formula for the
entanglement of formation (EOF) of an arbitrary mixed state in a system of two
qubits. There is no known closed form expression for the EOF of an arbitrary
mixed state in any system more complicated than two qubits. This paper, via a
relatively straightforward generalization of Wootters' original derivation,
obtains a closed form lower bound on the EOF of an arbitary mixed state of a
system composed of a qubit and a qudit (a d-level quantum system, with d
greater than or equal to 3). The derivation of the lower bound is detailed for
a system composed of a qubit and a qutrit (d = 3); the generalization to d
greater than 3 then follows readily.


title: Uncollapsing the wave function

abstract:
  The space quantization induced by a Stern-Gerlach experiment is normally
explained by invoking the ``collapse of the wave function.'' This is a rather
mysterious idea; it would be better to explain the Stern-Gerlach results
without using it. We re-analyze the Stern-Gerlach experiment using path
integrals. We find if we model explicitly the finite width of the beam,
coherent interference within the beam itself provides the space quantization --
without need to invoke the collapse. If we insist on employing only wave
functions with the space and spin parts kept forcibly disentangled, we recreate
the need to invoke the collapse. The collapse-free approach makes more specific
predictions about the shape and position of the scattered beams; if the
interaction region has finite length, these may be testable. Pending
experimental disambiguation, the chief arguments in favor of the collapse-free
approach are that it is simpler and less mysterious, has no adjustable
parameters, and requires the invocation of no new forces.


title: On Interferometric Duality in Multibeam Experiments

abstract:
  We critically analyze the problem of formulating duality between fringe
visibility and which-way information, in multibeam interference experiments. We
show that the traditional notion of visibility is incompatible with any
intuitive idea of complementarity, but for the two-beam case. We derive a
number of new inequalities, not present in the two-beam case, one of them
coinciding with a recently proposed multibeam generalization of the inequality
found by Greenberger and YaSin. We show, by an explicit procedure of
optimization in a three-beam case, that suggested generalizations of Englert's
inequality, do not convey, differently from the two-beam case, the idea of
complementarity, according to which an increase of visibility is at the cost of
a loss in path information, and viceversa.


title: Thermally induced spin flips above an atom chip

abstract:
  We describe an experiment in which Bose-Einstein condensates and cold atom
clouds are held by a microscopic magnetic trap near a room temperature metal
wire 500 $\mu$m in diameter. The ensemble of atoms breaks into fragments when
it is brought close to the ceramic-coated aluminum surface of the wire, showing
that fragmentation is not peculiar to copper surfaces. The lifetime for atoms
to remain in the microtrap is measured over a range of distances down to $27
\mu$m from the surface of the metal. We observe the loss of atoms from the
microtrap due to spin flips. These are induced by radio-frequency thermal
fluctuations of the magnetic field near the surface, as predicted but not
previously observed.


title:
Robust quantum information processing with techniques from liquid state
  NMR

abstract:
  While Nuclear Magnetic Resonance (NMR) techniques are unlikely to lead to a
large scale quantum computer they are well suited to investigating basic
phenomena and developing new techniques. Indeed it is likely that many existing
NMR techniques will find uses in quantum information processing. Here I
describe how the composite rotation (composite pulse) method can be used to
develop quantum logic gates which are robust against systematic errors.


title: Understanding Permutation Symmetry

abstract:
  \noindent In our contribution to this volume we deal with \emph{discrete}
symmetries: these are symmetries based upon groups with a discrete set of
elements (generally a set of elements that can be enumerated by the positive
integers). In physics we find that discrete symmetries frequently arise as
`internal', non-spacetime symmetries. Permutation symmetry is such a discrete
symmetry arising as the mathematical basis underlying the statistical behaviour
of ensembles of certain types of indistinguishable quantum particle (e.g.,
fermions and bosons). Roughly speaking, if such an ensemble is invariant under
a permutation of its constituent particles (i.e., permutation symmetric) then
one doesn't `count' those permutations which merely `exchange'
indistinguishable particles; rather, the exchanged state is identified with the
original state. This principle of invariance is generally called the
`indistinguishability postulate' [IP], but we prefer to use the term
`permutation invariance' [PI]. It is this symmetry principle that is typically
taken to underpin and explain the nature of (fermionic and bosonic) quantum
statistics (although, as we shall see, this characterisation is not
uncontentious), and it is this principle that has important consequences
regarding the metaphysics of identity and individuality for particles
exhibiting such statistical behaviour.


title: A note on the Lorentz force, magnetic charges and the Casimir effect

abstract:
  We show that in order to account for the repulsive Casimir effect in the
parallel plate geometry in terms of the quantum version of the Lorentz force,
virtual surface densities of magnetic charges and currents must be introduced.
The quantum version of the Lorentz force expressed in terms of the correlators
of the electric and magnetic fields for planar geometries yields then correctly
the Casimir pressure.


title:
Transmission through a potential barrier in quantum mechanics of
  multiple degrees of freedom: complex way to the top

abstract:
  A semiclassical method for the calculation of tunneling exponent in systems
with many degrees of freedom is developed. We find that corresponding classical
solution as function of energy form several branches joint by bifurcation
points. A regularization technique is proposed, which enables one to choose
physically relevant branches of solutions everywhere in the classically
forbidden region and also in the allowed region. At relatively high energy the
physical branch describes tunneling via creation of a classical state, close to
the top of the barrier. The method is checked against exact solutions of the
Schrodinger equation in a quantum mechanical system of two degrees of freedom.


title: Adiabatic Quantum State Generation and Statistical Zero Knowledge

abstract:
  The design of new quantum algorithms has proven to be an extremely difficult
task. This paper considers a different approach to the problem, by studying the
problem of 'quantum state generation'. This approach provides intriguing links
between many different areas: quantum computation, adiabatic evolution,
analysis of spectral gaps and groundstates of Hamiltonians, rapidly mixing
Markov chains, the complexity class statistical zero knowledge, quantum random
walks, and more.
  We first show that many natural candidates for quantum algorithms can be cast
as a state generation problem. We define a paradigm for state generation,
called 'adiabatic state generation' and develop tools for adiabatic state
generation which include methods for implementing very general Hamiltonians and
ways to guarantee non negligible spectral gaps. We use our tools to prove that
adiabatic state generation is equivalent to state generation in the standard
quantum computing model, and finally we show how to apply our techniques to
generate interesting superpositions related to Markov chains.


title: Objectivism and Irreversibility in Quantum Mechanics

abstract:
  A hypothetical formulation of quantum mechanics is presented so as to
reconcile it with macro-realism. On the analogy drawn from thermodynamics, an
objective description of wave packet reduction is postulated, in which a
characteristic energy scale and a time scale are introduced to separate the
quantum and classical conceptions.


title: Quantum Guessing via Deutsch-Jozsa

abstract:
  We examine the "Guessing Secrets" problem arising in internet routing, in
which the goal is to discover two or more objects from a known finite set. We
propose a quantum algorithm using O(1) calls to an O(logN) oracle. This
improves upon the best known classical result, which uses O(logN) questions and
requires an additional O(logN^3) steps to produce the answer. In showing the
possibilities of this algorithm, we extend the types of questions and function
oracles that the Deutsch-Jozsa algorithm can be used to solve.


title: Purification through Zeno-like Measurements

abstract:
  A series of frequent measurements on a quantum system (Zeno-like
measurements) is shown to result in the ``purification'' of another quantum
system in interaction with the former. Even though the measurements are
performed on the former system, their effect drives the latter into a pure
state, irrespectively of its initial (mixed) state, provided certain conditions
are satisfied.


title: Quantum measurements and Kolmogorovian probability theory

abstract:
  We establish connections between the requirement of measurability of a
probability space and the principle of complimentarity in quantum mechanics. It
is shown that measurability of a probability space implies the dependence of
results of quantum measurement not only on the properties of a quantum object
under consideration, but also on the classical characteristics of the measuring
device which is used. We show that if one takes into account the requirement of
measurability in a quantum case, the Bell inequality does not follow from the
hypothesis about the existence of an objective reality.


title: Efficient sharing of a continuous-variable quantum secret

abstract:
  We propose an efficient scheme for sharing a continuous variable quantum
secret using passive optical interferometry and squeezers: this efficiency is
achieved by showing that a maximum of two squeezers is required to replicate
the secret state, and we obtain the cheapest configuration in terms of total
squeezing cost. Squeezing is a cost for the dealer of the secret as well as for
the receivers, and we quantify limitations to the fidelity of the replicated
secret state in terms of the squeezing employed by the dealer.


title:
Scheme for the implementation of a universal quantum cloning machine via
  cavity-assisted atomic collisions in cavity QED

abstract:
  We propose a scheme to implement the $1\to2$ universal quantum cloning
machine of Buzek et.al [Phys. Rev.A 54, 1844(1996)] in the context of cavity
QED. The scheme requires cavity-assisted collision processes between atoms,
which cross through nonresonant cavity fields in the vacuum states. The cavity
fields are only virtually excited to face the decoherence problem. That's why
the requirements on the cavity quality factor can be loosened.


title: Perfect Test of Entanglement for Two-level Systems

abstract:
  A 3-setting Bell-type inequality enforced by the indeterminacy relation of
complementary local observables is proposed as an experimental test of the
2-qubit entanglement. The proposed inequality has an advantage of being a
sufficient and necessary criterion of the separability. Therefore any entangled
2-qubit state cannot escape the detection by this kind of tests. It turns out
that the orientation of the local testing observables plays a crucial role in
our perfect detection of the entanglement.


title: Dissipation, Emergent Quantization and Quantum Fluctuations

abstract:
  We review some aspects of the quantization of the damped harmonic oscillator.
We derive the exact action for a damped mechanical system in the frame of the
path integral formulation of the quantum Brownian motion problem developed by
Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of
freedom for dissipative systems and thermal field theories is discussed and the
doubled variables are related to quantum noise effects. The 't Hooft proposal,
according to which the loss of information due to dissipation in a classical
deterministic system manifests itself in the quantum features of the system, is
analyzed and the quantum spectrum of the harmonic oscillator is shown to be
originated from the dissipative character of the original classical
deterministic system.


title: Decoherence-Free Subspaces and Subsystems

abstract:
  Decoherence is the phenomenon of non-unitary dynamics that arises as a
consequence of coupling between a system and its environment. It has important
harmful implications for quantum information processing, and various solutions
to the problem have been proposed. Here we provide a detailed a review of the
theory of decoherence-free subspaces and subsystems, focusing on their
usefulness for preservation of quantum information.


title: NMR implementation of a quantum scheduling algorithm

abstract:
  The improved quantum scheduling algorithm proposed by Grover has been
generalized using the generalized quantum search algorithm, in which a unitary
operator replaces the Walsh-Hadamard transform, and $\pi/2$ phase rotations
replace the selective inversions, in order to make the quantum scheduling
algorithm suitable for more cases. Our scheme is realized on a nuclear magnetic
resonance (NMR) quantum computer. Experimental results show a good agreement
between theory and experiment.


title: Anisotropic velocity distributions in 3D dissipative optical lattices

abstract:
  We present a direct measurement of velocity distributions in two dimensions
by using an absorption imaging technique in a 3D near resonant optical lattice.
The results show a clear difference in the velocity distributions for the
different directions. The experimental results are compared with a numerical 3D
semi-classical Monte-Carlo simulation. The numerical simulations are in good
qualitative agreement with the experimental results.


title:
Temperature correction to the Casimir force in cryogenic range and
  anomalous skin effect

abstract:
  Temperature correction to the Casimir force is considered for real metals at
low temperatures. With the temperature decrease the mean free path for
electrons becomes larger than the field penetration depth. In this condition
description of metals with the impedance of anomalous skin effect is shown to
be more appropriate than with the permittivity. The effect is crucial for the
temperature correction. It is demonstrated that in the zero frequency limit the
reflection coefficients should coincide with those of ideal metal if we demand
the entropy to be zero at T=0. All the other prescriptions discussed in the
literature for the $n=0$ term in the Lifshitz formula give negative entropy. It
is shown that the temperature correction in the region of anomalous skin effect
is not suppressed as it happens in the plasma model. This correction will be
important in the future cryogenic measurements of the Casimir force.


title:
Robust quantum gates and a bus architecture for quantum computing with
  rare-earth-ion doped crystals

abstract:
  We present a composite pulse controlled phase gate which together with a bus
architecture improves the feasibility of a recent quantum computing proposal
based on rare-earth-ion doped crystals. Our proposed gate operation is tolerant
to variations between ions of coupling strengths, pulse lengths, and frequency
shifts, and it achieves worst case fidelities above 0.999 with relative
variations in coupling strength as high as 10% and frequency shifts up to
several percent of the resonant Rabi frequency of the laser used to implement
the gate. We outline an experiment to demonstrate the creation and detection of
maximally entangled states in the system.


title: Geometric phase in open systems

abstract:
  We calculate the geometric phase associated to the evolution of a system
subjected to decoherence through a quantum-jump approach. The method is general
and can be applied to many different physical systems. As examples, two main
source of decoherence are considered: dephasing and spontaneous decay. We show
that the geometric phase is completely insensitive to the former, i.e. it is
independent of the number of jumps determined by the dephasing operator.


title: Entanglement transformations of pure Gaussian states

abstract:
  We present a theory of entanglement transformations of Gaussian pure states
with local Gaussian operations and classical communication. This is the
experimentally accessible set of operations that can be realized with optical
elements such as beam splitters, phase shifts and squeezers, together with
homodyne measurements. We provide a simple necessary and sufficient condition
for the possibility to transform a pure bipartite Gaussian state into another
one. We contrast our criterion with what is possible if general local
operations are available.


title: Master-equations for the study of decoherence

abstract:
  Different structures of master-equation used for the description of
decoherence of a microsystem interacting through collisions with a surrounding
environment are considered and compared. These results are connected to the
general expression of the generator of a quantum dynamical semigroup in
presence of translation invariance recently found by Holevo.


title: A Simple Proof that Toffoli and Hadamard are Quantum Universal

abstract:
  Recently Shi proved that Toffoli and Hadamard are universal for quantum
computation. This is perhaps the simplest universal set of gates that one can
hope for, conceptually; It shows that one only needs to add the Hadamard gate
to make a 'classical' set of gates quantum universal. In this note we give a
few lines proof of this fact relying on Kitaev's universal set of gates, and
discuss the meaning of the result.


title:
NMR experimental realization of seventh-order coupling transformations
  and the seven-qubit modified Deutsch-Jozsa algorithm

abstract:
  We propose a scalable method on the basis of nth-order coupling operators to
construct f-dependent phase transformations in the n-qubit modified
Deutsch-Jozsa (D-J) quantum algorithm. The novel n-qubit entangling
transformations are easily implemented via J-couplings between neighboring
spins. The seven-qubit modified D-J quantum algorithm and seventh-order
coupling transformations are then experimentally demonstrated with liquid state
nuclear magnetic resonance (NMR) techniques. The method may offer the
possibility of creating generally entangled states of n qubits and simulating
n-body interactions on n-qubit NMR quantum computers.


title: Playing Prisoner's Dilemma with Quantum Rules

abstract:
  Quantum game theory is a recently developing field of physical research. In
this paper, we investigate quantum games in a systematic way. With the famous
instance of the Prisoner's Dilemma, we present the fascinating properties of
quantum games in different conditions, i.e. different number of the players,
different strategic space of the players and different amount of the
entanglement involved.


title: The Data Compression Theorem for Ergodic Quantum Information Sources

abstract:
  We extend the data compression theorem to the case of ergodic quantum
information sources. Moreover, we provide an asymptotically optimal compression
scheme which is based on the concept of high probability subspaces. The rate of
this compression scheme is equal to the von Neumann entropy rate.


title:
Mixing quantum and classical mechanics and uniqueness of Planck's
  constant

abstract:
  Observables of quantum or classical mechanics form algebras called quantum or
classical Hamilton algebras respectively (Grgin E and Petersen A (1974) {\it J
Math Phys} {\bf 15} 764\cite{grginpetersen}, Sahoo D (1977) {\it Pramana} {\bf
8} 545\cite{sahoo}). We show that the tensor-product of two quantum Hamilton
algebras, each characterized by a different Planck's constant is an algebra of
the same type characterized by yet another Planck's constant. The algebraic
structure of mixed quantum and classical systems is then analyzed by taking the
limit of vanishing Planck's constant in one of the component algebras. This
approach provides new insight into failures of various formalisms dealing with
mixed quantum-classical systems. It shows that in the interacting mixed
quantum-classical description, there can be no back-reaction of the quantum
system on the classical. A natural algebraic requirement involving restriction
of the tensor product of two quantum Hamilton algebras to their components
proves that Planck's constant is unique.


title: Continuous-Variable Quantum Teleportation with a Conventional Laser

abstract:
  We give a description of balanced homodyne detection (BHD) using a
conventional laser as a local oscillator (LO), where the laser field outside
the cavity is a mixed state whose phase is completely unknown. Our description
is based on the standard interpretation of the quantum theory for measurement,
and accords with the experimental result in the squeezed state generation
scheme. We apply our description of BHD to continuous-variable quantum
teleportation (CVQT) with a conventional laser to analyze the CVQT experiment
[A. Furusawa et al., Science 282, 706 (1998)], whose validity has been
questioned on the ground of intrinsic phase indeterminacy of the laser field
[T. Rudolph and B.C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)]. We show that
CVQT with a laser is valid only if the unknown phase of the laser field is
shared among sender's LOs, the EPR state, and receiver's LO. The CVQT
experiment is considered valid with the aid of an optical path other than the
EPR channel and a classical channel, directly linking between a sender and a
receiver. We also propose a method to probabilistically generate a strongly
phase-correlated quantum state via continuous measurement of independent
lasers, which is applicable to realizing CVQT without the additional optical
path.


title: Decoherence and quantum trajectories

abstract:
  Decoherence is the process by which quantum systems interact and become
correlated with their external environments; quantum trajectories are a
powerful technique by which decohering systems can be resolved into stochastic
evolutions, conditioned on different possible ``measurements'' of the
environment. By calling on recently-developed tools from quantum information
theory, we can analyze simplified models of decoherence, explicitly quantifying
the flow of information and randomness between the system, the environment, and
potential observers.


title: Pancharatnam and Berry Phases in Three-Level Photonic Systems

abstract:
  A theoretical analysis of Pancharatnam and Berry phases is made for biphoton
three-level systems, which are produced via frequency degenerate co-linear
spontaneous parametric down conversion (SPDC). The general theory of
Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in
Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical
phases are derived for the transformations produced by linear phase-converters.
The problem of gauge invariance is treated along all the article.


title:
Deterministic Secure Direct Communication Using Ping-pong protocol
  without public channel

abstract:
  Based on an EPR pair of qubits and allowing asymptotically secure key
distribution, a secure communication protocol is presented. Bob sends either of
the EPR pair qubits to Alice. Alice receives the travel qubit. Then she can
encode classical information by local unitary operations on this travel qubit.
Alice send the qubit back to Bob. Bob can get Alice's information by
measurement on the two photons in Bell operator basis. If Eve in line, she has
no access to Bob's home qubit. All her operations are restricted to the travel
qubit. In order to find out which opeartion Alice performs, Eve's operation
must include measurements. The EPR pair qubits are destroyed. Bob's measurement
on the two photons in Bell operator basis can help him to judge whether Eve
exist in line or not. In this protocal, a public channel is not necessary.


title: Quantizing Time

abstract:
  A quantum mechanical theory is proposed which abandons an external parameter
``time'' in favor of a self-adjoint operator on a Hilbert space whose elements
represent measurement events rather than system states. The standard quantum
mechanical description is obtained in the idealized case of measurements of
infinitely short duration. A theory of perturbation is developped. As a sample
application Fermi's Golden Rule and the S-matrix are derived. The theory also
offers a solution to the controversal issue of the time-energy uncertainty
relation.


title: Decoherence in Phase Space

abstract:
  Much of the discussion of decoherence has been in terms of a particle moving
in one dimension that is placed in an initial superposition state (a
Schr\"{o}dinger "cat" state) corresponding to two widely separated wave
packets. Decoherence refers to the destruction of the interference term in the
quantum probability function. Here, we stress that a quantitative measure of
decoherence depends not only on the specific system being studied but also on
whether one is considering coordinate, momentum or phase space. We show that
this is best illustrated by considering Wigner phase space where the measure is
again different. Analytic results for the time development of the Wigner
distribution function for a two-Gaussian Schrodinger "cat" state have been
obtained in the high-temperature limit (where decoherence can occur even for
negligible dissipation) which facilitates a simple demonstration of our
remarks.


title: What is really "quantum" in quantum theory?

abstract:
  By analysing probabilistic foundations of quantum theory we understood that
the so called quantum calculus of probabilities (including Born's rule) is not
the main distinguishing feature of "quantum". This calculus is just a special
variant of a contextual probabilistic calculus. In particular, we analysed the
EPR-Bohm-Bell approach by using contextual probabilistic models (e.g., the
frequency von Mises model). It is demonstrated that the EPR-Bohm-Bell
consideration are not so much about "quantum", but they are merely about
contextual. Our conjecture is that the "fundamental quantum element" is the
Schr\"odinger evolution describing the very special dependence of probabilities
on contexts. The main quantum mystery is neither the probability calculus in a
Hilbert space nor the nonncommutative (Heisenberg) representation of physical
observables, but the Schr\"odinger evolution of contextual probabilities.


title: Measurement-based quantum computation with cluster states

abstract:
  We give a detailed account of the one-way quantum computer, a scheme of
quantum computation that consists entirely of one-qubit measurements on a
particular class of entangled states, the cluster states. We prove its
universality, describe why its underlying computational model is different from
the network model of quantum computation and relate quantum algorithms to
mathematical graphs. Further we investigate the scaling of required resources
and give a number of examples for circuits of practical interest such as the
circuit for quantum Fourier transformation and for the quantum adder. Finally,
we describe computation with clusters of finite size.


title: Exact solution of the Hu-Paz-Zhang master equation

abstract:
  The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a
linear passive bath. It is exact within the assumption that the oscillator and
bath are initially uncoupled . Here an exact general solution is obtained in
the form of an expression for the Wigner function at time t in terms of the
initial Wigner function. The result is applied to the motion of a Gaussian wave
packet and to that of a pair of such wave packets. A serious divergence arising
from the assumption of an initially uncoupled state is found to be due to the
zero-point oscillations of the bath and not removed in a cutoff model. As a
consequence, worthwhile results for the equation can only be obtained in the
high temperature limit, where zero-point oscillations are neglected. In that
limit closed form expressions for wave packet spreading and attenuation of
coherence are obtained. These results agree within a numerical factor with
those appearing in the literature, which apply for the case of a particle at
zero temperature that is suddenly coupled to a bath at high temperature. On the
other hand very different results are obtained for the physically consistent
case in which the initial particle temperature is arranged to coincide with
that of the bath.


title: Decoherence without dissipation

abstract:
  The prototypical Schr\"{o}dinger cat state, i.e., an initial state
corresponding to two widely separated Gaussian wave packets, is considered. The
decoherence time is calculated solely within the framework of elementary
quantum mechanics and equilibrium statistical mechanics. This is at variance
with common lore that irreversible coupling to a dissipative environment is the
mechanism of decoherence. Here, we show that, on the contrary, decoherence can
in fact occur at high temperature even for vanishingly small dissipation.


title: Quantum measurement and decoherence

abstract:
  Distribution functions defined in accord with the quantum theory of
measurement are combined with results obtained from the quantum Langevin
equation to discuss decoherence in quantum Brownian motion. Closed form
expressions for wave packet spreading and the attenuation of coherence of a
pair of wave packets are obtained. The results are exact within the context of
linear passive dissipation. It is shown that, contrary to widely accepted
current belief, decoherence can occur at high temperature in the absence of
dissipation. Expressions for the decoherence time with and without dissipation
are obtained that differ from those appearing in earlier discussions.


title: How to project qubits faster using quantum feedback

abstract:
  When one performs a continuous measurement, whether on a classical or quantum
system, the measurement provides a certain average rate at which one becomes
certain about the state of the system. For a quantum system this is an average
rate at which the system is projected onto a pure state. We show that for a
standard kind of continuous measurement, for a qubit this rate may be increased
by applying unitary operations during the measurement (that is, by using
Hamiltonian feedback), in contrast to the equivalent measurement on a classical
bit, where reversible operations cannot be used to enhance the rate of entropy
reduction. We determine the optimal feedback algorithm and discuss the
Hamiltonian resources required.


title:
Wave Packet Spreading: Temperature and Squeezing Effects with
  Applications to Quantum Measurement and Decoherence

abstract:
  A localized free particle is represented by a wave packet and its motion is
discussed in most quantum mechanics textbooks. Implicit in these discussions is
the assumption of zero temperature. We discuss how the effects of finite
temperature and squeezing can be incorporated in an elementary manner. The
results show how the introduction of simple tools and ideas can bring the
reader into contact with topics at the frontiers of research in quantum
mechanics. We discuss the standard quantum limit, which is of interest in the
measurement of small forces, and decoherence of a mixed (``Schrodinger cat'')
state, which has implications for current research in quantum computation,
entanglement, and the quantum-classical interface.


title: Checking $2 \times M$ separability via semidefinite programming

abstract:
  In this paper we propose a sequence of tests which gives a definitive test
for checking $2\times M$ separability. The test is definitive in the sense that
each test corresponds to checking membership in a cone, and that the closure of
the union of all these cones consists exactly of {\it all} $2 \times M$
separable states. Membership in each single cone may be checked via
semidefinite programming, and is thus a tractable problem. This sequential test
comes about by considering the dual problem, the characterization of all
positive maps acting ${\mathbb C}^{2 \times 2} \to {\mathbb C}^{M\times M}$.
The latter in turn is solved by characterizing all positive quadratic matrix
polynomials in a complex variable.


title: Time, Finite Statistics, and Bell's Fifth Position

abstract:
  I discuss three issues connected to Bell's theorem and Bell-CHSH-type
experiments: time and the memory loophole, finite statistics (how wide are the
error bars Under Local Realism), and the question of whether a loophole-free
experiment is feasible, a surprising omission on Bell's list of four positions
to hold in the light of his results. Levy's (1935) theory of martingales, and
Fisher's (1935) theory of randomization in experimental design, take care of
time and of finite statistics. I exploit a (classical) computer network
metaphor for local realism to argue that Bell's conclusions are independent of
how one likes to interpret probability, and give a critique of some recent
anti-Bellist literature.


title:
Coalescence and Anti-Coalescence Interference of Two-Photon Wavepacket
  in a Beam Splitter

abstract:
  We study a general theory on the interference of two-photon wavepacket in a
beam splitter (BS). We find that the perfect coalescence interference requires
a symmetric spectrum of two-photon wavepacket which can be entangled or
un-entangled. Furthermore, we introduce a two-photon wavepacket with
anti-symmetric spectrum, which is related with photon entanglement and shows a
perfect anti-coalescence effect. The theory present uniform and complete
explanation to two-photon interference.


title:
An Elementary Aharonov-Bohm System in Three Space Dimensions: Quantum
  Attraction With No Classical Force

abstract:
  As a consequence of the Aharonov-Bohm effect, there is a quantum-induced
attraction between a charged particle and a rigid, impenetrable hoop made from
an arbitrarily thin tube containing a superconductor quantum of magnetic flux.
This is remarkable because in classical physics there is no force between the
two objects, and quantum-mechanical effects (associated with uncertainty
principle energy) generally are repulsive rather than attractive. For an
incident spinless charged particle in a P wave (in a configuration with total
angular momentum zero) we verify a resonance just above threshold using the
Kohn variational principle in its S-matrix form. Even if optimistic choices of
parameters describing a model system with these properties turned out to be
feasible, the temperature required to observe the resonance would be far lower
than has yet been attained in the laboratory.


title: Quantum Game with Restricted Matrix Strategies

abstract:
  We study a quantum game played by two players with restricted multiple
strategies. It is found that in this restricted quantum game Nash equilibrium
does not always exist when the initial state is entangled. At the same time, we
find that when Nash equilibrium exists the pay off function is usually
different from that in the classical counterpart except in some special cases.
This presents an explicit example where quantum game and classical game may
differ. When designing a quantum game with limited strategies, the allowed
strategy should be carefully chosen according to the type of initial state.


title:
Efficient classical simulation of slightly entangled quantum
  computations

abstract:
  We present a scheme to efficiently simulate, with a classical computer, the
dynamics of multipartite quantum systems on which the amount of entanglement
(or of correlations in the case of mixed-state dynamics) is conveniently
restricted. The evolution of a pure state of n qubits can be simulated by using
computational resources that grow linearly in n and exponentially in the
entanglement. We show that a pure-state quantum computation can only yield an
exponential speed-up with respect to classical computations if the entanglement
increases with the size n of the computation, and gives a lower bound on the
required growth.


title:
Quantum nondemolition measurement of a single electron spin in a quantum
  dot

abstract:
  We propose a scheme for the quantum nondemolition (QND) measurement of a
single electron spin in a single quantum dot (QD). Analytical expressions are
obtained for the optical Faraday effect between a quantum dot exciton and
microcavity field. The feasibility of the QND measurement of a single electron
spin is discussed for a GaAs/AlAs microcavity with an InAs QD.


title: Quantum information and special relativity

abstract:
  Relativistic effects affect nearly all notions of quantum information theory.
The vacuum behaves as a noisy channel, even if the detectors are perfect. The
standard definition of a reduced density matrix fails for photon polarization
because the transversality condition behaves like a superselection rule. We can
however define an effective reduced density matrix which corresponds to a
restricted class of positive operator-valued measures. There are no pure photon
qubits, and no exactly orthogonal qubit states. Reduced density matrices for
the spin of massive particles are well-defined, but are not covariant under
Lorentz transformations. The spin entropy is not a relativistic scalar and has
no invariant meaning. The distinguishability of quantum signals and their
entanglement depend on the relative motion of observers.


title: Remarks on entanglement assisted classical capacity

abstract:
  The property of the optimal signal ensembles of entanglement assisted channel
capacity is studied. A relationship between entanglement assisted channel
capacity and one-shot capacity of unassisted channel is obtained. The data
processing inequalities, convexity and additivity of the entanglement assisted
channel capacity are reformulated by simple methods.


title: A loophole in Cabello's proof to Bell's theorem without inequalities

abstract:
  Cabello proved Bell's theorem without using inequalities. A loophole of
Cabello's proof is pointed out in this work.


title: Optimization of a Neutron-Spin Test of the Quantum Zeno Effect

abstract:
  A neutron-spin experimental test of the quantum Zeno effect (QZE) is
discussed from a practical point of view, when the nonideal efficiency of the
magnetic mirrors, used for filtering the spin state, is taken into account. In
the idealized case the number N of (ideal) mirrors can be indefinitely
increased, yielding an increasingly better QZE. By contrast, in a practical
situation with imperfect mirrors, there is an optimal number of mirrors, N_opt,
at which the QZE becomes maximum: more frequent measurements would deteriorate
the performance. However, a quantitative analysis shows that a good
experimental test of the QZE is still feasible. These conclusions are of
general validity: in a realistic experiment, the presence of losses and
imperfections leads to an optimal frequency N_opt, which is in general finite.
One should not increase N beyond N_opt. A convenient formula for N_opt, valid
in a broad framework, is derived as a function of the parameters characterizing
the experimental setup.


title: Diffraction of Weakly Bound Clusters: Spectroscopy and Size Effects

abstract:
  Exciting experiments in the field of atom and molecule optics have lately
drawn much attention to the effects involved in the coherent diffraction of
particle beams. We review the influence of the finite size of the particles and
of their energy level spectrum on the diffraction pattern. In turn, we
demonstrate how experimental diffraction measurements allow to determine these
quantities of weakly bound molecules by considering the diffraction of the
dimer and trimer of helium, and the deuterium molecule dimer.


title: On Metric of Quantum States with Lorentzian Signature

abstract:
  In this note we comment on yet another way of describing metric of quantum
states with the Lorentzian signature. For this, we consider the metric of
quantum states and make successive transformations, exploiting the relationship
between S3 and SU(2).


title: The nilpotent Dirac equation and its applications in particle physics

abstract:
  The nilpotent Dirac formalism has been shown, in previous publications, to
generate new physical explanations for aspects of particle physics, with the
additional possibility of calculating some of the parameters involved in the
Standard Model. The applications so far obtained are summarised, with an
outline of some more recent developments.


title: On the irreversibility of entanglement distillation

abstract:
  We investigate the irreversibility of entanglement distillation for a
symmetric d-1 parameter family of mixed bipartite quantum states acting on
Hilbert spaces of arbitrary dimension d x d. We prove that in this family the
entanglement cost is generically strictly larger than the distillable
entanglement, such that the set of states for which the distillation process is
asymptotically reversible is of measure zero. This remains true even if the
distillation process is catalytically assisted by pure state entanglement and
every operation is allowed, which preserves the positivity of the partial
transpose. It is shown, that reversibility occurs only in cases where the state
is quasi-pure in the sense that all its pure state entanglement can be revealed
by a simple operation on a single copy. The reversible cases are shown to be
completely characterized by minimal uncertainty vectors for entropic
uncertainty relations.


title: Note on the derivative of the hyperbolic cotangent

abstract:
  In a letter to Nature (Ford G W and O'Connell R F 1996 Nature 380 113) we
presented a formula for the derivative of the hyperbolic cotangent that differs
from the standard one in the literature by an additional term proportional to
the Dirac delta function. Since our letter was necessarily brief, shortly after
its appearance we prepared a more extensive unpublished note giving a detailed
explanation of our argument. Since this note has been referenced in a recent
article (Estrada R and Fulling S A 2002 J. Phys. A: Math. Gen. 35 3079) we
think it appropriate that it now appear in print. We have made no alteration to
the original note.


title: The generalized Kochen-Specker theorem

abstract:
  A proof of the generalized Kochen-Specker theorem in two dimensions due to
Cabello and Nakamura is extended to all higher dimensions. A set of 18 states
in four dimensions is used to give closely related proofs of the generalized
Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the
relationship between these three theorems.


title: Selective pressures on genomes in molecular evolution

abstract:
  We describe the evolution of macromolecules as an information transmission
process and apply tools from Shannon information theory to it. This allows us
to isolate three independent, competing selective pressures that we term
compression, transmission, and neutrality selection. The first two affect
genome length: the pressure to conserve resources by compressing the code, and
the pressure to acquire additional information that improves the channel,
increasing the rate of information transmission into each offspring. Noisy
transmission channels (replication with mutations) gives rise to a third
pressure that acts on the actual encoding of information; it maximizes the
fraction of mutations that are neutral with respect to the phenotype. This
neutrality selection has important implications for the evolution of
evolvability. We demonstrate each selective pressure in experiments with
digital organisms.

categories: quant-ph cs.NE nlin.AO physics.bio-ph q-bio.PE


title: Maxwell's Demon, Szilard's Engine and Quantum Measurements

abstract:
  We propose and analyze a quantum version of Szilard's ``one-molecule
engine.'' In particular, we recover, in the quantum context, Szilard's
conclusion concerning the free energy ``cost'' of measurements: $\Delta F \geq
k_B T\ln2$ per bit of information.


title: Stochastic Simulation of Grover's Algorithm

abstract:
  We simulate Grover's algorithm in a classical computer by means of a
stochastic method using the Hubbard-Stratonovich decomposition of n-qubit gates
into one-qubit gates integrated over auxiliary fields. The problem reduces to
finding the fixed points of the associated system of Langevin differential
equations. The equations are obtained automatically for any number of qubits by
employing a computer algebra program. We present the numerical results of the
simulation for a small search space.


title: On the Monomiality of Nice Error Bases

abstract:
  Unitary error bases generalize the Pauli matrices to higher dimensional
systems. Two basic constructions of unitary error bases are known: An algebraic
construction by Knill, which yields nice error bases, and a combinatorial
construction by Werner, which yields shift-and-multiply bases. An open problem
posed by Schlingemann and Werner (see
http://www.imaph.tu-bs.de/qi/problems/6.html) relates these two constructions
and asks whether each nice error basis is equivalent to a shift-and-multiply
basis. We solve this problem and show that the answer is negative. However, we
also show that it is always possible to find a fairly sparse representation of
a nice error basis.


title: Grover's Algorithm: Quantum Database Search

abstract:
  We review Grover's algorithm by means of a detailed geometrical
interpretation and a worked out example. Some basic concepts of Quantum
Mechanics and quantum circuits are also reviewed. This work is intended for
non-specialists which have basic knowledge on undergraduate Linear Algebra.


title: Phase shifts of atomic de Broglie waves at an evanescent wave mirror

abstract:
  A detailed theoretical investigation of the reflection of an atomic de
Broglie wave at an evanescent wave mirror is presented. The classical and the
semiclassical descriptions of the reflection process are reviewed, and a full
wave-mechanical approach based on the analytical soution of the corresponding
Schr\"odinger equation is presented. The phase shift at reflection is
calculated exactly and interpreted in terms of instantaneous reflection of the
atom at an effective mirror. Besides the semiclassical regime of reflection
describable by the WKB method, a pure quantum regime of reflection is
identified in the limit where the incident de Broglie wavelength is large
compared to the evanescent wave decay length.


title: Perturbatively Defined Effective Classical Potential in Curved Space

abstract:
  The partition function of a quantum statistical system in flat space can
always be written as an integral over a classical Boltzmann factor $\exp[
-\beta V^{\rm eff cl({\bf x}_0)]$, where $V^{\rm eff cl({\bf x}_0)$ is the
so-called effective classical potential containing the effects of all quantum
fluctuations. The variable of integration is the temporal path average ${\bf
x_0\equiv \beta ^{-1}\int_0^ \beta d\tau {\bf x}(\tau)$. We show how to
generalize this concept to paths $q^\mu(\tau)$ in curved space with metric
$g_{\mu \nu (q)$, and calculate perturbatively the high-temperature expansion
of $V^{\rm eff cl(q_0)$. The requirement of independence under coordinate
transformations $q^\mu(\tau)\to q'^\mu(\tau)$ introduces subtleties in the
definition and treatment of the path average $q_0^\mu$, and covariance is
achieved only with the help of a suitable Faddeev-Popov procedure.


title: Supersymmetrically transformed periodic potentials

abstract:
  The higher order supersymmetric partners of a stationary periodic potential
are studied. The transformation functions associated to the band edges do not
change the spectral structure. However, when the transformation is implemented
for factorization energies inside of the forbidden bands, the final potential
will have again the initial band structure but it can have bound states
encrusted into the gaps, giving place to localized periodicity defects.


title:
Construction and Characterization of Symmetrical States for Multiqubit
  Systems

abstract:
  A general method in constructing a complete set of wave functions for
multipartite identical qubits is presented based on the irreducible
representations of the permutation group and the nth rank tensors. Particular
examples for n =2, 3, and 4 are derived and the entanglement behavior for each
state is examined from several criteria. It is found that the states so
constructed are all bound entangled states. For the case of even n, all the
states are found to have maximum "n-tangle". The symmetry in spin space is
found to increase the n-tangle in general. The "n-tangle" for n = 4 is found
not always representing 4-way entanglement. It measures the degree of
spin-space symmetry instead. A useful relationship in the classification
between systems containing different number of qubits is given in terms of the
Young's Tableaux based on our analysis.


title: Quantum Computation with a One-Dimensional Optical Lattice

abstract:
  We present an economical dynamical control scheme to perform quantum
computation on a one dimensional optical lattice, where each atom encodes one
qubit. The model is based on atom tunneling transitions between neighboring
sites of the lattice. They can be activated by external laser beams resulting
in a two-qubit phase gate or in an exchange interaction. A realization of the
Toffoli gate is presented which requires only a single laser pulse and no
individual atom addressing.


title: Quantum data hiding with spontaneous parameter down-conversion

abstract:
  Here we analyze the practical implication of the existing quantum data hiding
protocol with Bell states produced with optical downconverter. We show that the
uncertainty for the producing of the Bell states with spontaneous parameter
down-conversion should be taken into account, because it will cause serious
trouble to the hider encoding procedure. A set of extended Bell states and a
generalized Bell states analyzer are proposed to describe and analyze the
possible states of two photons distributing in two paths. Then we present a
method to integrate the above uncertainty of Bell states preparation into the
dating hiding procedure, when we encode the secret with the set of extended
Bell states. These modifications greatly simplify the hider's encoding
operations, and thus paves the way for the implementation of quantum data
hiding with present-day quantum optics.


title:
Entanglement versus relaxation and decoherence in a quantum algorithm
  for quantum chaos

abstract:
  We study analytically and numerically the behavior of quantum entanglement in
a quantum computer operating an efficient algorithm for quantum chaos. Our
results show that in an ideal algorithm the entanglement decays exponentially
with the diffusive relaxation rate induced by classical chaos. This decay goes
down to a residual level which drops exponentially with the number of qubits
n_q. Decoherence destroys the residual entanglement with a rate exponential in
n_q.


title: The 2-local Hamiltonian problem encompasses NP

abstract:
  We show that the NP complete problems MAX CUT and INDEPENDENT SET can be
formulated as the 2-local Hamiltonian problem as defined by Kitaev. He
introduced the quantum complexity class BQNP as the quantum analog of NP, and
showed that the 5-local Hamiltonian problem is BQNP-complete. It is not known
whether the s-local Hamiltonian problem is BQNP-complete for s smaller than 5.
Therefore it is interesting to determine what problems can be reduced to the
s-local Hamiltonian problem. Kitaev showed that 3-SAT can be formulated as a
3-local Hamiltonian problem. We extend his result by showing that 2-locality is
sufficient in order to encompass NP.


title: Concurrence and foliations induced by some 1-qubit channels

abstract:
  We start with a short introduction to the roof concept. An elementary
discussion of phase-damping channels shows the role of anti-linear operators in
representing their concurrence. A general expression for some concurrences is
derived. We apply it to 1-qubit channels of length two, getting induced
foliations of the state space, the optimal decompositions, and the entropy of a
state with respect to these channels. For amplitude-damping channels one
obtains an expression for the Holevo capacity allowing for easy numerical
calculations.


title: Non-adiabatic geometrical quantum gates in semiconductor quantum dots

abstract:
  In this paper we study the implementation of non-adiabatic geometrical
quantum gates with in semiconductor quantum dots. Different quantum information
enconding/manipulation schemes exploiting excitonic degrees of freedom are
discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the
limitations of adiabatic schemes relying on adiabatic Berry phase; fast
geometrical quantum gates can be in principle implemented


title: Holonomic quantum gates: A semiconductor-based implementation

abstract:
  We propose an implementation of holonomic (geometrical) quantum gates by
means of semiconductor nanostructures. Our quantum hardware consists of
semiconductor macroatoms driven by sequences of ultrafast laser pulses ({\it
all optical control}). Our logical bits are Coulomb-correlated electron-hole
pairs (excitons) in a four-level scheme selectively addressed by laser pulses
with different polarization. A universal set of single and two-qubit gates is
generated by adiabatic change of the Rabi frequencies of the lasers and by
exploiting the dipole coupling between excitons.


title: Dynamics of two atoms coupled to a cavity field

abstract:
  We investigate the interaction of two two-level atoms with a single mode
cavity field. One of the atoms is exactly at resonance with the field, while
the other is well far from resonance and hence is treated in the dispersive
limit. We find that the presence of the non-resonant atom produces a shift in
the Rabi frequency of the resonant atom, as if it was detuned from the field.
We focus on the discussion of the evolution of the state purity of each atom.


title:
Unitary time-dependent superconvergent technique for pulse-driven
  quantum dynamics

abstract:
  We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation
theory for time-dependent Hamiltonians. It is strictly unitary upon truncation
at an arbitrary order and not restricted to periodic or quasiperiodic
Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the
KAM transformations involved in the iterative procedure. The technique is
illustrated on a two-level model perturbed by a pulsed interaction for which we
obtain convergence all the way from the sudden regime to the opposite adiabatic
regime.


title: Exact quantum Fourier transforms and discrete logarithm algorithms

abstract:
  We show how the quantum fast Fourier transform (QFFT) can be made exact for
arbitrary orders (first for large primes). For most quantum algorithms only the
quantum Fourier transform of order $2^n$ is needed, and this can be done
exactly. Kitaev \cite{kitaev} showed how to approximate the Fourier transform
for any order. Here we show how his construction can be made exact by using the
technique known as ``amplitude amplification''. Although unlikely to be of any
practical use, this construction e.g. allows to make Shor's discrete logarithm
quantum algorithm exact. Thus we have the first example of an exact non black
box fast quantum algorithm, thereby giving more evidence that ``quantum'' need
not be probabilistic. We also show that in a certain sense the family of
circuits for the exact QFFT is uniform. Namely the parameters of the gates can
be calculated efficiently.