title:
A Robust Method for Estimating the Lindblad Operators of a Dissipative
  Quantum Process from Measurements of the Density Operator at Multiple Time
  Points

abstract:
  We present a robust method for quantum process tomography, which yields a set
of Lindblad operators that optimally fit the measured density operators at a
sequence of time points. The benefits of this method are illustrated using a
set of liquid-state Nuclear Magnetic Resonance (NMR) measurements on a molecule
containing two coupled hydrogen nuclei, which are sufficient to fully determine
its relaxation superoperator. It was found that the complete positivity
constraint, which is necessary for the existence of the Lindblad operators, was
also essential for obtaining a robust fit to the measurements. The general
approach taken here promises to be broadly useful in studying dissipative
quantum processes in many of the diverse experimental systems currently being
developed for quantum information processing purposes.


title: Time in Quantum Mechanics and Quantum Field Theory

abstract:
  W. Pauli pointed out that the existence of a self-adjoint time operator is
incompatible with the semibounded character of the Hamiltonian spectrum. As a
result, people have been arguing a lot about the time-energy uncertainty
relation and other related issues. In this article, we show in details that
Pauli's definition of time operator is erroneous in several respects.


title: The challenge of non-hermitian structures in physics

abstract:
  We present a brief review of physical problems leading to indefinite Hilbert
spaces and non-hermitian Hamiltonians. With the exception of pseudo-Riemannian
manifolds in GR, the problem of a consistent physical interpretation of these
structures still waits to be faced.
  In print in Rev. Mex. Fis.


title: MGP versus Kochen-Specker condition in hidden variables theories

abstract:
  Hidden variables theories for quantum mechanics are usually assumed to
satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these
theories are necessarily contextual. But the KS condition can be criticized
from an operational viewpoint, which suggests that a weaker condition (MGP)
should be adopted in place of it. This leads one to introduce a class of hidden
parameters theories in which contextuality can, in principle, be avoided, since
the proofs of the Bell-Kochen-Specker theorem break down. A simple model
recently provided by the author for an objective interpretation of quantum
mechanics can be looked at as a noncontextual hidden parameters theory, which
shows that such theories actually exist.


title: Unitary Solutions to the Yang-Baxter Equation in Dimension Four

abstract:
  In this paper, we determine all unitary solutions to the Yang-Baxter equation
in dimension four. Quantum computation motivates this study.
  This set of solutions will assist in clarifying the relationship between
quantum entanglement and topological entanglement.
  We present a variety of facts about the Yang-Baxter equation for the reader
unfamiliar with the equation.


title:
Lewenstein-Sanpera decomposition of a generic 2x2 density matrix by
  using Wootters's basis

abstract:
  The Lewenstein-Sanpera decomposition for a generic two-qubit density matrix
is obtained by using Wootters's basis. It is shown that the average concurrence
of the decomposition is equal to the concurrence of the state. It is also shown
that all the entanglement content of the state is concentrated in the
Wootters's state $|x_1>$ associated with the largest eigenvalue $\lambda_1$ of
the Hermitian matrix $\sqrt{\sqrt{\rho}\tilde{\rho}\sqrt{\rho}}$ >. It is shown
that a given density matrix $\rho$ with corresponding set of positive numbers
$\lambda_i$ and Wootters's basis can transforms under $SO(4,c)$ into a generic
$2\times2$ matrix with the same set of positive numbers but with new Wootters's
basis, where the local unitary transformations correspond to $SO(4,r)$
transformations, hence, $\rho$ can be represented as coset space
$SO(4,c)/SO(4,r)$ together with positive numbers $\lambda_i$. By giving an
explicit parameterization we characterize a generic orbit of group of local
unitary transformations.


title: Schmidt numbers of low rank bipartite mixed states

abstract:
  We prove a lower bound for Schmidt numbers of bipartite mixed states. This
lower bound can be applied easily to low rank bipartite mixed states. From this
lower bound it is known that generic low rank bipartite mixed states have
relatively high Schmidt numbers and thus entangled. We can compute Schmidt
numbers exactly for some mixed states by this lower bound as shown in Examples.
This lower bound can also be used effectively to determine that some mixed
states cannot be convertible to other mixed states by local operations and
classical communication.
  The results in this paper are proved by ONLY using linear algebra, thus the
results and proof are easy to understand.


title: Quantum mechanics as a complete physical theory

abstract:
  We show that the principles of a ''complete physical theory'' and the
conclusions of the standard quantum mechanics do not irreconcilably contradict
each other as is commonly believed. In the algebraic approach, we formulate
axioms that allow constructing a renewed mathematical scheme of quantum
mechanics. This scheme involves the standard mathematical formalism of quantum
mechanics. Simultaneously, it contains a mathematical object that adequately
describes a single experiment. We give an example of the application of the
proposed scheme.


title: A Fixed Point Result for Environment-Induced Semigroups

abstract:
  Based on the environment induced semigroup approach to the quantum
measurement process, we show that a certain class of these semigroups, referred
to as contractive uniformly $k$-Lipschitzian semigroups, exhibit a fixed point
property. With regard to the quantum measurement problem, semigroups of this
kind ensure decoherence and the selection of a single state from the familiy of
pointer states. In fact, the common fixed point is the selected state.


title:
Dynamics of entanglement for coherent excitonic states in a system of
  two coupled quantum dots and cavity QED

abstract:
  The dynamics of the entanglement for coherent excitonic states in the system
of two coupled large semiconductor quantum dots ($R/a_{B}\gg 1$) mediated by a
single-mode cavity field is investigated. Maximally entangled coherent
excitonic states can be generated by cavity field initially prepared in odd
coherent state. The entanglement of the excitonic coherent states between two
dots reaches maximum when no photon is detected in the cavity. The effects of
the zero-temperature environment on the entanglement of excitonic coherent
state are also studied using the concurrence for two subsystems of the excitons


title:
Quantum coherence in a degenerate two-level atomic ensemble: for a
  transition $F_e=0\leftrightarrow F_g=1$

abstract:
  For a transition $F_e=0\leftrightarrow F_g=1$ driven by a linearly polarized
light and probed by a circularly light, quantum coherence effects are
investigated. Due to the coherence between the drive Rabi frequency and Zeeman
splitting, electromagnetically induced transparency, electromagnetically
induced absorption, and the transition from positive to negative dispersion are
obtained, as well as the populations coherently oscillating in a wide spectral
region. At the zero pump-probe detuning, the subluminal and superluminal light
propagation is predicted. Finally, coherent population trapping states are not
highly sensitive to the refraction and absorption in such ensemble.


title: Recursive Weak- and Strong Coupling Expansions in a Cosine Potential

abstract:
  For the Cos(2x)-Potential the coefficients of the weak- and strong coupling
perturbation series of the ground state energy are constructed recursively.
They match the well-known expansion coefficients of the Mathieu equation's
characteristic values. However presently there is no physically intuitive
method to extract the coefficients of the strong coupling series from those of
the weak one. The standard rule while giving exellent results for the
anharmonic oscillator fails completely in this case.


title: The non-negativity of probabilities and the collapse of state

abstract:
  The dynamical equation of hybrid systems, being the combination of
Schr\"odinger and Liouville equations, produces noncausal evolution when the
initial state of interacting quantum and classical mechanical systems is as it
is demanded in discussions regarding the problem of measurement. It is found
that state of quantum mechanical system instantaneously collapses due to the
non-negativity of probabilities.


title: Coherence of qubits based on single Ca$^+$ ions

abstract:
  Two-level ionic systems, where quantum information is encoded in long lived
states (qubits), are discussed extensively for quantum information processing.
We present a collection of measurements which characterize the stability of a
qubit based on the $S_{1/2}$--$D_{5/2}$ transition of single $^{40}$Ca$^+$ ions
in a linear Paul trap. We find coherence times of $\simeq$1 ms, discuss the
main technical limitations and outline possible improvements.


title: Laser cooling of trapped Fermi gases

abstract:
  The collective Raman cooling of trapped one- and two-component Fermi gases is
considered. We obtain the quantum master equation that describes the laser
cooling in the festina lente regime, for which the heating due to photon
reabsorption can be neglected. For the two-component case the collisional
processes are described within the formalism of quantum Boltzmann master
equation. The inhibition of the spontaneous emission can be overcome by
properly adjusting the spontaneous Raman rate during the cooling. Our numerical
results based in Monte Carlo simulations of the corresponding rate equations,
show that three-dimensional temperatures of the order of $0.08 T_F$
(single-component) and $0.03 T_F$ (two-component) can be achieved. We
investigate the statistical properties of the equilibrium distribution of the
laser-cooled gas, showing that the number fluctuations are enhanced compared
with the thermal distribution close to the Fermi surface. Finally, we analyze
the heating related to the background losses, concluding that our laser-cooling
scheme should maintain the temperature of the gas without significant
additional losses.


title: Coherent State Measures and the Extended Dobinski relations

abstract:
  Conventional Bell and Stirling numbers arise naturally in the normal ordering
of simple monomials in boson operators. By extending this process we obtain
generalizations of these combinatorial numbers, defined as coherent state
matrix elements of arbitrary monomials, as well as the associated Dobinski
relations. These Bell-type numbers may be considered as power moments and give
rise to positive measures which allow the explicit construction of new classes
of coherent states.


title:
Asymptotic phase shifts and Levinson theorem for 2D potentials with
  inverse square singularities

abstract:
  The Levinson theorem for two-dimensional scattering is generalized for
potentials with inverse square singularities. By this theorem, the number of
bound states in a given m-th partial wave is related to the phase shift and the
singularity strength of the potential. For the m-wave phase shift the
asymptotic behaviour is calculated for short wavelengths.


title: Classifying N-qubit Entanglement via Bell's Inequalities

abstract:
  All the states of N qubits can be classified into N-1 entanglement classes
from 2-entangled to N-entangled (fully entangled) states. Each class of
entangled states is characterized by an entanglement index that depends on the
partition of N. The larger the entanglement index of an state, the more
entangled or the less separable is the state in the sense that a larger maximal
violation of Bell's inequality is attainable for this class of state.


title: Coexistence and Joint Measurability in Quantum Mechanics

abstract:
  This talk is a survey of the question of joint measurability of coexistent
observables and its is based on the monograph Operational Quantum Physics [1]
and on the papers [2,3,4].


title:
Inhibition of electromagnetically induced absorption due to excited
  state decoherence in Rb vapor

abstract:
  The explanation presented in [Taichenachev et al, Phys. Rev. A {\bf 61},
011802 (2000)] according to which the electromagnetically induced absorption
(EIA) resonances observed in degenerate two level systems are due to coherence
transfer from the excited to the ground state is experimentally tested in a
Hanle type experiment observing the parametric resonance on the $% D1$ line of
$^{87}$Rb. While EIA occurs in the $F=1\to F^{\prime}=2 $ transition in a cell
containing only $Rb$ vapor, collisions with a buffer gas ($30 torr$ of $Ne$)
cause the sign reversal of this resonance as a consequence of collisional
decoherence of the excited state. A theoretical model in good qualitative
agreement with the experimental results is presented.


title: Single atoms in a standing-wave dipole trap

abstract:
  We trap a single cesium atom in a standing-wave optical dipole trap. Special
experimental procedures, designed to work with single atoms, are used to
measure the oscillation frequency and the atomic energy distribution in the
dipole trap. These methods rely on unambiguously detecting presence or loss of
the atom using its resonance fluorescence in the magneto-optical trap.


title:
Maximal Violation of Bell Inequalities using Continuous Variables
  Measurements

abstract:
  We propose a whole family of physical states that yield a violation of the
Bell CHSH inequality arbitrarily close to its maximum value, when using
quadrature phase homodyne detection. This result is based on a new binning
process called root binning, that is used to transform the continuous variables
measurements into binary results needed for the tests of quantum mechanics
versus local realistic theories. A physical process in order to produce such
states is also suggested. The use of high-efficiency spacelike separated
homodyne detections with these states and this binning process would result in
a conclusive loophole-free test of quantum mechanics.


title: Macroscpoic Quantum Game

abstract:
  The game in which acts of participants don't have an adequate description in
terms of Boolean logic and classical theory of probabilities is considered. The
model of the game interaction is constructed on the basis of a non-distributive
orthocomplemented lattice. Mixed strategies of the participants are calculated
by the use of probability amplitudes according to the rules of quantum
mechanics. A scheme of quantization of the payoff function is proposed and an
algorithm for the search of Nash equilibrium is given. It is shown that
differently from the classical case in the quantum situation a discrete set of
equilibrium is possible.


title: Energy-Information Coupling From Classical To Quantum

abstract:
  It is known that there is no possibility of transmitting information without
a certain amount of energy. This is arbitrarily small in Classical Physics, due
to the continuous nature of the energy parameter, while one cannot reduce that
amount below Planck's energy quanta in Quantum Physics. In short, one cannot
send less than a photon from a place to another when transmitting a minimum of
information. However, as single photons are never completely defined
simultaneously in all their parameters as position and momentum, their exact
contribution to the information transmitted cannot be known in advance, but
only probabilistically predicted. So the information transmitted is always
blurred before one can - in a way that is only probabilistically predictable -
localize or, alternatively, determine the momenta of the photons transporting
it. In order to enhance the information content of a message, is it then really
possible to exploit the situation by considering the information contained in a
superposition state before localization or, alternatively, determination of
momenta? It would be so if such blurred information were richer than a defined
one, the former being vaguer than the latter as it would be compatible with
more possible outputs, and only in this sense more extensive. But if one
defines the information content of a state as the negative logarithm of the
probability of the state itself, it is not possible to identify the more a
priori probable blurred information pertaining to that state with the bigger
one. Then the idea of exploiting a supposedly enhanced information content of
superposition states in Quantum Computation seems to contradict directly - but,
as we will se, without necessity - the classical probabilistic definition of
information.


title: Numerical study of induced vortex tunneling

abstract:
  Tunneling of vortex-antivortex pairs across a superconducting film can be
controlled via inductive coupling of the film to an external circuit. We study
this process numerically in a toroidal film (periodic boundary conditions in
both directions) by using the dual description of vortices, in which they are
represented by a fundamental quantum field. We compare the results to those
obtained in the instanton approach.


title: Simulating the Effects of Quantum Error-correction Schemes

abstract:
  It is important to protect quantum information against decoherence and
operational errors, and quantum error-correcting (QEC) codes are the keys to
solving this problem. Of course, just the existence of codes is not efficient.
It is necessary to perform operations fault-tolerantly on encoded states
because error-correction process (i.e., encoding, decoding, syndrome
measurement and recovery) itself induces an error. By using simulation, this
paper investigates the effects of some important QEC codes (the five qubit
code, the seven qubit code and the nine qubit code) and their fault-tolerant
operations when the error-correction process itself induces an error. The
corresponding results, statistics and analyses are presented in this paper.


title: A simple quantum heat engine

abstract:
  Quantum heat engines employ as working agents multi-level systems instead of
gas-filled cylinders. We consider particularly two-level agents such as
electrons immersed in a magnetic field. Work is produced in that case when the
electrons are being carried from a high-magnetic-field region into a
low-magnetic-field region. In watermills, work is produced instead when some
amount of fluid drops from a high-altitude reservoir to a low-altitude
reservoir. We show that this purely mechanical engine may in fact be considered
as a two-level quantum heat engine, provided the fluid is viewed as consisting
of n molecules of weight one and N-n molecules of weight zero. Weight-one
molecules are analogous to electrons in their higher energy state, while
weight-zero molecules are analogous to electrons in their lower energy state.
More generally, fluids consist of non-interacting molecules of various weights.
It is shown that, not only the average value of the work produced per cycle,
but also its fluctuations, are the same for mechanical engines and quantum
(Otto) heat engines. The reversible Carnot cycles are approached through the
consideration of multiple sub-reservoirs.


title: Local realist (but contextual) derivation of the EPR-Bohm correlations

abstract:
  The probabilistic structure of quantum mechanics is investigated in the
frequency framework. Such an approach can be interpreted as a contextual
approach to quantum probabilities. By using rather complicated frequency
calculations we reproduce the EPR-Bohm correlation function which is typically
derived by using the calculus of probabilities in a Hilbert space. Our
frequency probabilistic model of the EPR-Bohm experiment is a realist model --
physical observables are considered as objective properties of physical
systems. It is also local -- a measurement over one part of a composite system
does not disturb another part of this system. Nevertheless, our result does not
contradict to the well known Bell's ``NO-GO'' theorem. J. Bell used the
conventional (Kolmogorov) measure-theoretical approach. We use the frequency
approach. In the latter approach there are no reasons to assume that the
simultaneous probability distribution exists: corresponding frequencies may
fluctuate and not approach any definite limit (which Bell would like to use as
the probability). The frequency probabilistic derivation demonstrated that
incompatibility of observables under consideration plays the crucial role in
producing of the EPR-Bohm correlations.


title: Entanglement in quantum critical phenomena

abstract:
  Quantum phase transitions occur at zero temperature and involve the
appearance of long-range correlations. These correlations are not due to
thermal fluctuations but to the intricate structure of a strongly entangled
ground state of the system. We present a microscopic computation of the scaling
properties of the ground-state entanglement in several 1D spin chain models
both near and at the quantum critical regimes. We quantify entanglement by
using the entropy of the ground state when the system is traced down to $L$
spins. This entropy is seen to scale logarithmically with $L$, with a
coefficient that corresponds to the central charge associated to the conformal
theory that describes the universal properties of the quantum phase transition.
Thus we show that entanglement, a key concept of quantum information science,
obeys universal scaling laws as dictated by the representations of the
conformal group and its classification motivated by string theory. This
connection unveils a monotonicity law for ground-state entanglement along the
renormalization group flow. We also identify a majorization rule possibly
associated to conformal invariance and apply the present results to interpret
the breakdown of density matrix renormalization group techniques near a
critical point.


title: All-Versus-Nothing Violation of Local Realism for Two Entangled Photons

abstract:
  It is shown that the Greenberger-Horne-Zeilinger theorem can be generalized
to the case with only two entangled particles. The reasoning makes use of two
photons which are maximally entangled both in polarization and in spatial
degrees of freedom. In contrast to Cabello's argument of "all versus nothing"
nonlocality with four photons [Phys. Rev. Lett. 87, 010403 (2001)], our
proposal to test the theorem can be implemented with linear optics and thus is
well within the reach of current experimental technology.


title: Inelastic Diffraction and Spectroscopy of Very Weakly Bound Clusters

abstract:
  We study the coherent inelastic diffraction of very weakly bound two body
clusters from a material transmission grating. We show that internal
transitions of the clusters can lead to new separate peaks in the diffraction
pattern whose angular positions determine the excitation energies. Using a
quantum mechanical approach to few body scattering theory we determine the
relative peak intensities for the diffraction of the van der Waals dimers
(D_2)_2 and H_2-D_2. Based on the results for these realistic examples we
discuss the possible applications and experimental challenges of this coherent
inelastic diffraction technique.


title:
A Combinatory-Algebraic Perspective on Multipartiteness, Entanglement
  and Quantum Localization

abstract:
  We claim that both multipartiteness and localization of subsystems of
compound quantum systems are of an essentially relative nature crucially
depending on the set of operationalistically available states. In a more
general setting, to capture the relativity and variability of our structures
with respect to the observation means, sheaves of algebras may need be
introduced. We provide the general formalism based on algebras which exhibits
the relativity of multipartiteness and localization.


title: Einstein, Podolsky and Rosen versus Bohm and Bell

abstract:
  There is an opinion that the Bohm reformulation of the EPR paradox in terms
of spin variables is equivalent to the original one. In this note we show that
such an opinion is not justified. We apply to the original EPR problem the
method which was used by Bell for the Bohm reformulation. He has shown that
correlation function of two spins cannot be represented by classical
correlation of separated bounded random processes. This Bell`s theorem has been
interpreted as incompatibility of local realism with quantum mechanics. We show
that, in contrast to Bell`s theorem for spin or polarization correlation
functions, the correlation of positions (or momenta) of two particles,
depending on the rotation angles, in the original EPR model always admits a
representation in the form of classical correlation of separated random
processes. In this sense there exists a local realistic representation for the
original EPR model but there is no such a representation for the Bohm spin
reformulation of the EPR paradox. It shows also that the phenomena of quantum
nonlocality is based not only on the properties of entangled states but also on
the using of particular bounded observables.


title:
Phonon-phonon interactions due to non-linear effects in a linear ion
  trap

abstract:
  We examine in detail the theory of the intrinsic non-linearities in the
dynamics of trapped ions due to the Coulomb interaction. In particular the
possibility of mode-mode coupling, which can be a source of decoherence in
trapped ion quantum computation, or, alternatively, can be exploited for
parametric down-conversion of phonons, is discussed and conditions under which
such coupling is possible are derived.


title:
Quantum computation in the neuronal microtubules: quantum gates, ordered
  water and superradiance

abstract: This paper was withdrawn by the author because severe errors were discovered.


title:
Dynamical Decoupling Using Slow Pulses: Efficient Suppression of 1/f
  Noise

abstract:
  The application of dynamical decoupling pulses to a single qubit interacting
with a linear harmonic oscillator bath with $1/f$ spectral density is studied,
and compared to the Ohmic case. Decoupling pulses that are slower than the
fastest bath time-scale are shown to drastically reduce the decoherence rate in
the $1/f$ case. Contrary to conclusions drawn from previous studies, this shows
that dynamical decoupling pulses do not always have to be ultra-fast. Our
results explain a recent experiment in which dephasing due to $1/f$ charge
noise affecting a charge qubit in a small superconducting electrode was
successfully suppressed using spin-echo-type gate-voltage pulses.


title: A revised de Broglie relation in discrete space-time

abstract:
  We introduce a revised de Broglie relation in discrete space-time, and
analyze some possible inferences of the relation.


title: Correlations and entanglement in probability theory

abstract:
  We generalize the classical probability frame by adopting a wider family of
random variables that includes nondeterministic ones. The frame that emerges is
known to host a ''classical'' extension of quantum mechanics. We discuss the
notion of probabilistic correlation and show that it includes two kinds of
correlation: a classical one, which occurs for both deterministic and
indeterministic observables, and a nonclassical one, which occurs only for
indeterministic observables. The latter will be called probabilistic
entanglement and represents a property of intrinsically random systems, not
necessarily quantum. It appears possible to separate the two kinds of
correlation and characterize them by numerical functions which satisfy a simple
product rule.


title: Quantum channels with correlated noise and entanglement teleportation

abstract:
  Motivated by the results of C. Macchiavello and G. M. Palma on
entanglement-enhanced information transmission over a quantum channel with
correlated noise, we demonstrate how the entanglement teleportation scheme of
J. Lee and M. S. Kim gives rise to two uncorrelated generalized depolarizing
channels. In an attempt to find a teleportation scheme which yields two
correlated generalized depolarizing channels, we discover a novel teleportation
scheme, which allows one to learn about the entanglement in an entangled pure
input state, but without decreasing the amount of entanglement associated with
it.


title: Towards a Theory of Conservative Computing

abstract:
  We extend the notion of conservativeness, given by Fredkin and Toffoli in
1982, to generic gates whose input and output lines may assume a finite number
d of truth values. A physical interpretation of conservativeness in terms of
conservation of the energy associated to the data used during the computation
is given. Moreover, we define conservative computations, and we show that they
naturally induce a new NP-complete decision problem. Finally, we present a
framework that can be used to explicit the movement of energy occurring during
a computation, and we provide a quantum implementation of the primitives of
such framework using creation and annihilation operators on the Hilbert space
C^d, where d is the number of energy levels considered in the framework.


title:
Quantum Error Models and Error Mitigation for Long-Distance
  Teleportation Architectures

abstract:
  A quantum communication architecture is being developed for long-distance,
high-fidelity qubit teleportation. It uses an ultrabright narrowband source of
polarization-entangled photons, plus trapped-atom quantum memories, and it is
compatible with long-distance transmission over standard telecommunication
fiber. This paper reports error models for the preceding teleportation
architecture, and for an extension thereto which enables long-distance
transmission and storage of Greenberger-Horne-Zeilinger states. The use of
quantum error correction or entanglement purification to improve the
performance of these quantum communication architectures is also discussed.


title: On preparation of the W-states from atomic ensembles

abstract:
  A scheme, where three atomic ensembles can be prepared in the states of the
W-class via Raman type interaction of strong classical field and a projection
measurement involved three single-photon detectors and two beamsplitters, are
considered. The obtained atomic entanglement consists of the Dicke or W-states
of each of the ensembles.


title:
Encoded Recoupling and Decoupling: An Alternative to Quantum Error
  Correcting Codes, Applied to Trapped Ion Quantum Computation

abstract:
  A recently developed theory for eliminating decoherence and design
constraints in quantum computers, ``encoded recoupling and decoupling'', is
shown to be fully compatible with a promising proposal for an architecture
enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature
417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates
are implemented using the Sorensen-Molmer (SM) scheme applied to pairs of ions
at a time. The encoding offers continuous protection against collective
dephasing. Decoupling pulses, that are also implemented using the SM scheme
directly to the encoded qubits, are capable of further reducing various other
sources of qubit decoherence, such as due to differential dephasing and due to
decohered vibrational modes. The feasibility of using the relatively slow SM
pulses in a decoupling scheme quenching the latter source of decoherence
follows from the observed 1/f spectrum of the vibrational bath.


title:
Characterizing quantum theory in terms of information-theoretic
  constraints

abstract:
  We show that three fundamental information-theoretic constraints--the
impossibility of superluminal information transfer between two physical systems
by performing measurements on one of them, the impossibility of broadcasting
the information contained in an unknown physical state, and the impossibility
of unconditionally secure bit commitment--suffice to entail that the
observables and state space of a physical theory are quantum-mechanical. We
demonstrate the converse derivation in part, and consider the implications of
alternative answers to a remaining open question about nonlocality and bit
commitment.


title: Global and Local Aspects of Exceptional Point

abstract:
  Exceptional points are singularities of eigenvalues and eigenvectors for
complex values of, say, an interaction parameter. They occur universally and
are square root branch point singularities of the eigenvalues in the vicinity
of level repulsions. The intricate connection between the distribution of
exceptional points and particular fluctuation properties of level spacing is
discussed. The distribution of the exceptional points of the problem
$H_0+\lambda H_1$ is given for the situation of hard chaos. Theoretical
predictions of local properties of exceptional points have recently been
confirmed experimentally. This relates to the specific topological structure of
an exceptional point as well as to the chiral properties of the wave functions
associated with exceptional points.


title: Hidden Translation and Translating Coset in Quantum Computing

abstract:
  We give efficient quantum algorithms for the problems of Hidden Translation
and Hidden Subgroup in a large class of non-abelian solvable groups including
solvable groups of constant exponent and of constant length derived series. Our
algorithms are recursive. For the base case, we solve efficiently Hidden
Translation in $\Z_{p}^{n}$, whenever $p$ is a fixed prime. For the induction
step, we introduce the problem Translating Coset generalizing both Hidden
Translation and Hidden Subgroup, and prove a powerful self-reducibility result:
Translating Coset in a finite solvable group $G$ is reducible to instances of
Translating Coset in $G/N$ and $N$, for appropriate normal subgroups $N$ of
$G$. Our self-reducibility framework combined with Kuperberg's subexponential
quantum algorithm for solving Hidden Translation in any abelian group, leads to
subexponential quantum algorithms for Hidden Translation and Hidden Subgroup in
any solvable group.


title: A strange feature of Bohm's Theory of quantum motion

abstract:
  In the Bohm picture and one-dimensional case, we show that given an
adequately chosen potential for characterising obstacles, one can derive laws
of motion formally identical to that of special relativity. In such a
hypothetical scheme, superluminal velocities are not forbidden, but a particle
cannot collide with an obstacle with an average, superluminal velocity.


title:
The Holevo-Schumacher-Westmoreland Channel Capacity for a Class of Qudit
  Unital Channels

abstract:
  The Holevo-Schumacher-Westmoreland (HSW) classical (entanglement-unassisted)
channel capacity for a class of qudit unital channels is shown to be C =
log2(d) - Smin, where d is the dimension of the qudit, and Smin is the minimum
possible von Neumann entropy at the channel output. The HSW channel capacity
for tensor products of this class of unital qudit channels is shown to obey the
same formula.


title: A Geometrical Representation of Entanglement as Internal Constraint

abstract:
  We study a system of two entangled spin 1/2, were the spin's are represented
by a sphere model developed within the hidden measurement approach which is a
generalization of the Bloch sphere representation, such that also the
measurements are represented. We show how an arbitrary tensor product state can
be described in a complete way by a specific internal constraint between the
ray or density states of the two spin 1/2. We derive a geometrical view of
entanglement as a 'rotation' and 'stretching' of the sphere representing the
states of the second particle as measurements are performed on the first
particle. In the case of the singlet state entanglement can be represented by a
real physical constraint, namely by means of a rigid rod.


title: State property systems and orthogonality

abstract:
  The structure of a state property system was introduced to formalize in a
complete way the operational content of the Geneva-Brussels approach to the
foundations of quantum mechanics, and the category of state property systems
was proven to be equivalence to the category of closure spaces. The first
axioms of standard quantum axiomatics (state determination and atomisticity)
have been shown to be equivalent to the $T_0$ and $T_1$ axioms of closure
spaces, and classical properties to correspond to clopen sets, leading to a
decomposition theorem into classical and purely nonclassical components for a
general state property system. The concept of orthogonality, very important for
quantum axiomatics, had however not yet been introduced within the formal
scheme of the state property system. In this paper we introduce orthogonality
in a operational way, and define ortho state property systems. Birkhoff's well
known biorthogonal construction gives rise to an orthoclosure and we study the
relation between this orthoclosure and the operational orthogonality that we
introduced.


title:
Decoherence of quantum states and its suppression in ensemble
  large-scale solid state NMR quantum computers

abstract:
  It is discussed the decoherence problems in ensemble large-scale solid state
NMR quantum computer based on the array of P donor atoms having nuclear spin I
= 1/2. It is considered here, as main mechanisms of decoherence for low
temperature (< 0.1 K), the adiabatic processes of random modulation of qubit
resonance frequency determined by secular part of nuclear spin interaction with
electron spin of the basic atoms, with impurity paramagnetic atoms and also
with nuclear spins of impurity diamagnetic atoms. It was made estimations of
allowed concentrations of magnetic impurities and of spin temperature whereby
the required decoherence suppression is obtained. It is discussed the random
phase error suppression in the ensemble quantum register basic states.


title: The generalized Fenyes-Nelson model for free scalar field theory

abstract:
  The generalized Fenyes--Nelson model of quantum mechanics is applied to the
free scalar field. The resulting Markov field is equivalent to the Euclidean
Markov field with the times scaled by a common factor which depends on the
diffusion parameter. This result is consistent between Guerra's earlier work on
stochastic quantization of scalar fields. It suggests a deep connection between
Euclidean field theory and the stochastic interpretation of quantum mechanics.
The question of Lorentz covariance is also discussed.


title:
Deterministic and Highly Efficient Quantum Cryptography with Entangled
  Photon Pairs

abstract:
  We present a protocol for deterministic and highly efficient quantum
cryptography with entangled photon pairs in a 4x4-dimentional Hilbert space.
Two communicating parties, Alice and Bob first share a both polarization- and
path-entangled photon pair, and then each performs a complete Bell-state
measurement on their own photon in one of two complementary Bell-state bases.
It is demonstrated that each measurement in which both Alice and Bob register a
photon can build certain perfect correlation and generate 1.5 key bits on
average. The security of our protocol is guaranteed by the non-cloning theorem.


title: Quantization of the classical action and eigenvalue problem

abstract:
  The eigenvalue problem in quantum mechanics is reduced to quantization of the
classical action of the physical system. State function of the system,
$\psi_0(\phi)$, is written in the form of superposition of two plane waves in
the phase space. Quantization condition is derived from the basic requirements
of continuity and finiteness for $\psi_0(\phi)$ in the whole region.


title: Classical Concepts in Quantum Programming

abstract:
  The rapid progress of computer technology has been accompanied by a
corresponding evolution of software development, from hardwired components and
binary machine code to high level programming languages, which allowed to
master the increasing hardware complexity and fully exploit its potential.
  This paper investigates, how classical concepts like hardware abstraction,
hierarchical programs, data types, memory management, flow of control and
structured programming can be used in quantum computing. The experimental
language QCL will be introduced as an example, how elements like irreversible
functions, local variables and conditional branching, which have no direct
quantum counterparts, can be implemented, and how non-classical features like
the reversibility of unitary transformation or the non-observability of quantum
states can be accounted for within the framework of a procedural programming
language.


title: Decoherence control in microwave cavities

abstract:
  We present a scheme able to protect the quantum states of a cavity mode
against the decohering effects of photon loss. The scheme preserves quantum
states with a definite parity, and improves previous proposals for decoherence
control in cavities. It is implemented by sending single atoms, one by one,
through the cavity. The atomic state gets first correlated to the photon number
parity. The wrong parity results in an atom in the upper state. The atom in
this state is then used to inject a photon in the mode via adiabatic transfer,
correcting the field parity. By solving numerically the exact master equation
of the system, we show that the protection of simple quantum states could be
experimentally demonstrated using presently available experimental apparatus.


title:
Macroscopic mechanical oscillators at the quantum limit using
  optomechanical cooling

abstract:
  We discuss how the optomechanical coupling provided by radiation pressure can
be used to cool macroscopic collective degrees of freedom, as vibrational modes
of movable mirrors. Cooling is achieved using a phase-sensitive feedback-loop
which effectively overdamps the mirrors motion without increasing the thermal
noise. Feedback results able to bring macroscopic objects down to the quantum
limit. In particular, it is possible to achieve squeezing and entanglement.


title:
Scattering theory of plasmon-assisted entanglement transfer and
  distillation

abstract:
  We analyse the quantum mechanical limits to the plasmon-assisted entanglement
transfer observed by E. Altewischer, M.P. van Exter, and J.P. Woerdman [Nature,
418, 304 (2002)]. The maximal violation S of Bell's inequality at the
photodetectors behind two linear media (such as the perforated metal films in
the experiment) can be described by two ratio's tau_1, tau_2 of
polarization-dependent transmission probabilities. A fully entangled incident
state is transferred without degradation for tau_1=tau_2, but a relatively
large mismatch of tau_1 and tau_2 can be tolerated with a small reduction of S.
We predict that fully entangled Bell pairs can be distilled out of partially
entangled radiation if tau_1 and tau_2 satisfy a pair of inequalities.


title: Quantum Probability and Decision Theory, Revisited

abstract:
  An extended analysis is given of the program, originally suggested by
Deutsch, of solving the probability problem in the Everett interpretation by
means of decision theory. Deutsch's own proof is discussed, and alternatives
are presented which are based upon different decision theories and upon
Gleason's Theorem. It is argued that decision theory gives Everettians most or
all of what they need from `probability'. Some consequences of (Everettian)
quantum mechanics for decision theory itself are also discussed.


title: Quantum morphogenesis: A variation on Thom's catastrophe theory

abstract:
  Non-commutative propositions are characteristic of both quantum and
non-quantum (sociological, biological, psychological) situations. In a Hilbert
space model states, understood as correlations between all the possible
propositions, are represented by density matrices. If systems in question
interact via feedback with environment their dynamics is nonlinear. Nonlinear
evolutions of density matrices lead to phenomena of morphogenesis which may
occur in non-commutative systems. Several explicit exactly solvable models are
presented, including `birth and death of an organism' and `development of
complementary properties'.


title: Harmonic Oscillator, Coherent States, and Feynman Path Integral

abstract:
  The Feynman path integral for the generalized harmonic oscillator is
reviewed, and it is shown that the path integral can be used to find a complete
set of wave functions for the oscillator. Harmonic oscillators with different
(time-dependent) parameters can be related through unitary transformations. The
existence of generalized coherent states for a simple harmonic oscillator can
then be interpreted as the result of a (formal) {\em invariance} under a
unitary transformation which relates the same harmonic oscillator. In the path
integral formalism, the invariance is reflected in that the kernels do not
depend on the choice of classical solutions.


title:
Unitary transformation for the system of a particle in a linear
  potential

abstract:
  A unitary operator which relates the system of a particle in a linear
potential with time-dependent parameters to that of a free particle, has been
given. This operator, closely related to the one which is responsible for the
existence of coherent states for a harmonic oscillator, is used to find a
general wave packet described by an Airy function. The kernel (propagator) and
a complete set of Hermite-Gaussian type wave functions are also given.


title:
Path Integrals over Measurement Amplitudes: Practical Quantum
  Foundations for Signal Processing and Control

abstract:
  It is shown that classical control diagrams can be mapped one-to-one onto
quantum path integrals over measurement amplitudes. To show the practical
utility of this method, exact closed-form expressions are derived for the
control dynamics and quantum noise levels of a test mass observed by a
Fabry-Perot interferometer. This formalism provides an efficient yet rigorous
method for analyzing complex systems such as interferometric gravity wave
detectors and magnetic resonance force microscopy (MRFM) experiments. Quantum
limits are conjectured for the sensitivity of interferometric observation of
test mass trajectories.


title:
Casimir Forces and Boundary Conditions in One Dimension: Attraction,
  Repulsion, Planck Spectrum, and Entropy

abstract:
  Quantities associated with Casimir forces are calculated in a model wave
system of one spatial dimension with Dirichlet or Neumann boundary conditions.
1)Due to zero-point fluctuations, a partition is attracted to the walls of a
box if the wave boundary conditions are alike for the partition and the walls,
but is repelled if the conditions are different. 2)The use of Casimir energies
in the presence of zero-point radiation introduces a natural maximum-entropy
principle which is satisfied only by the Planck spectrum for both like and
unlike boundary conditions between the box and partition. 3)The Casimir forces
are attractive and increasing with temperature for like boundary conditions,
but are repulsive and decreasing with temperature for unlike conditions. 4)In
the high-temperature limit, there is a temperature-independent Casimir entropy
for like but not for unlike boundary conditions. These results have
3-dimensional electromagnetic counterparts.


title: Dynamical aspects of quantum entanglement for weakly coupled kicked tops

abstract:
  We investigate how the dynamical production of quantum entanglement for
weakly coupled, composite quantum systems is influenced by the chaotic dynamics
of the corresponding classical system, using coupled kicked tops. The linear
entropy for the subsystem (a kicked top) is employed as a measure of
entanglement. A perturbative formula for the entanglement production rate is
derived. The formula contains a correlation function that can be evaluated only
from the information of uncoupled tops. Using this expression and the
assumption that the correlation function decays exponentially which is
plausible for chaotic tops, it is shown that {\it the increment of the strength
of chaos does not enhance the production rate of entanglement} when the
coupling is weak enough and the subsystems (kicked tops) are strongly chaotic.
The result is confirmed by numerical experiments. The perturbative approach is
also applied to a weakly chaotic region, where tori and chaotic sea coexist in
the corresponding classical phase space, to reexamine a recent numerical study
that suggests an intimate relationship between the linear stability of the
corresponding classical trajectory and the entanglement production rate.


title: Optimal Detection of Symmetric Mixed Quantum States

abstract:
  We develop a sufficient condition for the least-squares measurement (LSM), or
the square-root measurement, to minimize the probability of a detection error
when distinguishing between a collection of mixed quantum states. Using this
condition we derive the optimal measurement for state sets with a broad class
of symmetries.
  We first consider geometrically uniform (GU) state sets with a possibly
nonabelian generating group, and show that if the generator satisfies a certain
constraint, then the LSM is optimal. In particular, for pure-state GU ensembles
the LSM is shown to be optimal. For arbitrary GU state sets we show that the
optimal measurement operators are GU with generator that can be computed very
efficiently in polynomial time, within any desired accuracy.
  We then consider compound GU (CGU) state sets which consist of subsets that
are GU. When the generators satisfy a certain constraint, the LSM is again
optimal. For arbitrary CGU state sets the optimal measurement operators are
shown to be CGU with generators that can be computed efficiently in polynomial
time.


title:
Supersymmetric approach to exactly solvable systems with
  position-dependent effective masses

abstract:
  We discuss the relationship between exact solvability of the Schr\"{o}dinger
equation with a position-dependent mass and the ordering ambiguity in the
Hamiltonian operator within the frame of supersymmetric quantum mechanics. The
one-dimensional Schr\"{o}dinger equation, derived from the general form of the
effective mass Hamiltonian, is solved exactly for a system with exponentially
changing mass in the presence of a potential with similar behaviour, and the
corresponding supersymmetric partner Hamiltonians are related to the
effective-mass Hamiltonians proposed in the literature.


title: Exact solutions of effective-mass Schrodinger equations

abstract:
  We outline a general method for obtaining exact solutions of Schr\"{o}dinger
equations with a position dependent effective mass and compare the results with
those obtained within the frame of supersymmetric quantum theory. We observe
that the distinct effective mass Hamiltonians proposed in the literature in
fact describe exactly equivalent systems having identical spectra and wave
functions as far as exact solvability is concerned. This observation clarifies
the Hamiltonian dependence of the band-offset ratio for quantum wells.


title: Two-mode squeezed vacuum state coupled to the common thermal reservoir

abstract:
  Entangled states play a crucial role in quantum information protocols, thus
the dynamical behavior of entanglement is of a great importance. In this paper
we consider a two-mode squeezed vacuum state coupled to one thermal reservoir
as a model of an entangled state embedded in an environment. As a criterion for
entanglement we use a continuous-variable equivalent of the Peres-Horodecki
criterion, namely the Simon criterion. To quantify entanglement we use the
logarithmic negativity. We derive a condition, which assures that the state
remains entangled in spite of the interaction with the reservoir. Moreover for
the case of interaction with vacuum as an environment we show that a state of
interest after intinitely long interaction is not only entangled, but also
pure. For comparison we also consider a model in which each of both modes is
coupled to its own reservoir.


title:
Autonomous generation of all Wigner functions and marginal probability
  densities of Landau levels

abstract:
  Generation of Wigner functions of Landau levels and determination of their
symmetries and generic properties are achieved in the autonomous framework of
deformation quantization. Transformation properties of diagonal Wigner
functions under space inversion, time reversal and parity transformations are
specified and their invariance under a four-parameter subgroup of symplectic
transformations are established. A generating function for all Wigner functions
is developed and this has been identified as the phase-space coherent state for
Landau levels. Integrated forms of generating function are used in generating
explicit expressions of marginal probability densities on all possible two
dimensional phase-space planes. Phase-space realization of unitary similarity
and gauge transformations as well as some general implications for the Wigner
function theory are presented.


title:
Evolution of an open system as a continuous measurement of this system
  by its environment

abstract:
  The restricted-path-integral (RPI) description of a continuous quantum
measurement is rederived starting from the description of an open system by the
Feynman-Vernon influence functional. For this end the total evolution operator
of the compound system consisting of the open system and its environment is
decomposed into the sum of partial evolution operators. Accordingly, the
influence functional of the open system is decomposed into the integral of
partial influence functionals (PIF). If the partial evolution operators or PIF
are chosen in such a way that they decohere (do not interfere with each other),
then the formalism of RPI effectively arises. The evolution of the open system
may then be interpreted as a continuous measurement of this system by its
environment. This is possible if the environment is macroscopic or mesoscopic.


title:
Time and setting dependent instrument parameters and proofs of Bell-type
  inequalities

abstract:
  We show that all proofs of Bell-type inequalities, as discussed in Bell's
well known book and as claimed to be relevant to Einstein-Podolsky-Rosen type
experiments, come to a halt when Einstein-local time and setting dependent
instrument parameters are included.


title: Time Operator for a Quantum Singular Oscillator

abstract:
  The problem of existence of a self-adjoint time operator conjugate to a
Hamiltonian with SU(1,1) dynamical symmetry is investigated. In the space
spanned by the eigenstates of the generator $K_3$ of the SU(1,1) group, the
time operator for the quantum singular harmonic potential of the form $\omega
^2x2 + g/x2$ is constructed explicitly, and shown that it is related to the
time-of-arrival operator of Aharonov and Bohm. Our construction is fully
algebraic, involving only the generators of the SU(1,1) group.


title: Response to Comment by Myrvold and Appleby

abstract:
  Myrvold and Appleby claim that our model for EPR experiments is non-local and
that previous proofs of the Bell theorem go through even if our setting and
time dependent instrument parameters are included. We show that their claims
are false.


title: Two-photon imaging and quantum holography

abstract:
  It has been claimed that ``the use of entangled photons in an imaging system
can exhibit effects that cannot be mimicked by any other two-photon source,
whatever strength of the correlations between the two photons'' [A. F.
Abouraddy, B. E. A. Saleh, A. V. Sergienko, and M. C. Teich, Phys. Rev. Lett.
87, 123602 (2001)]. While we believe that the cited statement is true, we show
that the method proposed in that paper, with ``bucket detection'' of one of the
photons, will give identical results for entangled states as for appropriately
prepared classically correlated states.


title: Mixed quantum state detection with inconclusive results

abstract:
  We consider the problem of designing an optimal quantum detector with a fixed
rate of inconclusive results that maximizes the probability of correct
detection, when distinguishing between a collection of mixed quantum states. We
develop a sufficient condition for the scaled inverse measurement to maximize
the probability of correct detection for the case in which the rate of
inconclusive results exceeds a certain threshold. Using this condition we
derive the optimal measurement for linearly independent pure-state sets, and
for mixed-state sets with a broad class of symmetries. Specifically, we
consider geometrically uniform (GU) state sets and compound geometrically
uniform (CGU) state sets with generators that satisfy a certain constraint.
  We then show that the optimal measurements corresponding to GU and CGU state
sets with arbitrary generators are also GU and CGU respectively, with
generators that can be computed very efficiently in polynomial time within any
desired accuracy by solving a semidefinite programming problem.


title:
Configuration of separability and tests for multipartite entanglement in
  Bell-type experiments

abstract:
  We derive tight quadratic inequalities for all kinds of hybrid
separable-inseparable $n$-particle density operators on an arbitrary
dimensional space. This methodology enables us to truly derive a tight
quadratic inequality as tests for full $n$-partite entanglement in various
Bell-type correlation experiments on the systems that may not be identified as
a collection of qubits, e.g., those involving photons measured by incomplete
detectors. It is also proved that when the two measured observables are assumed
to precisely anti-commute, a stronger quadratic inequality can be used as a
witness of full $n$-partite entanglement.


title: All Hermitian Hamiltonians Have Parity

abstract:
  It is shown that if a Hamiltonian $H$ is Hermitian, then there always exists
an operator P having the following properties: (i) P is linear and Hermitian;
(ii) P commutes with H; (iii) P^2=1; (iv) the nth eigenstate of H is also an
eigenstate of P with eigenvalue (-1)^n. Given these properties, it is
appropriate to refer to P as the parity operator and to say that H has parity
symmetry, even though P may not refer to spatial reflection. Thus, if the
Hamiltonian has the form H=p^2+V(x), where V(x) is real (so that H possesses
time-reversal symmetry), then it immediately follows that H has PT symmetry.
This shows that PT symmetry is a generalization of Hermiticity: All Hermitian
Hamiltonians of the form H=p^2+V(x) have PT symmetry, but not all PT-symmetric
Hamiltonians of this form are Hermitian.


title:
The Hidden Subgroup Problem in Affine Groups: Basis Selection in Fourier
  Sampling

abstract:
  Many quantum algorithms, including Shor's celebrated factoring and discrete
log algorithms, proceed by reduction to a hidden subgroup problem, in which a
subgroup H of a group G must be determined from a quantum state y uniformly
supported on a left coset of H. These hidden subgroup problems are then solved
by Fourier sampling: the quantum Fourier transform of y is computed and
measured. When the underlying group is non-Abelian, two important variants of
the Fourier sampling paradigm have been identified: the weak standard method,
where only representation names are measured, and the strong standard method,
where full measurement occurs. It has remained open whether the strong standard
method is indeed stronger, that is, whether there are hidden subgroups that can
be reconstructed via the strong method but not by the weak, or any other known,
method. In this article, we settle this question in the affirmative. We show
that hidden subgroups of semidirect products of Z_p by Z_q, where q divides
(p-1) and q = p / polylog(p), can be efficiently determined by the strong
standard method. Furthermore, the weak standard method and the ``forgetful''
Abelian method are insufficient for these groups. We extend this to an
information-theoretic solution for the hidden subgroup problem over semidirect
products of Z_p by \Z_q where q divides (p-1) and, in particular, the Affine
groups A_p. Finally, we prove a closure property for the class of groups over
which the hidden subgroup problem can be solved efficiently.


title: Degree of entanglement for bipartite pure states

abstract: This paper has been withdrawn.


title: Evolution of twin-beam in active optical media

abstract:
  We study the evolution of twin-beam propagating inside active media that may
be used to establish a continuous variable entangled channel between two
distant users. In particular, we analyze how entanglement is degraded during
propagation, and determine a threshold value for the interaction time, above
which the state become separable, and thus useless for entanglement based
manipulations. We explicitly calculate the fidelity for coherent state
teleportation and show that it is larger than one half for the whole range of
parameters preserving entanglemenent.


title: Quantum state engineering assisted by entanglement

abstract:
  We suggest a general scheme for quantum state engineering based on
conditional measurements carried out on entangled twin-beam of radiation.
Realistic detection schemes such as {\sc on/off} photodetection, homodyne
detection and joint measurement of two-mode quadratures are analyzed in
details. Imperfections of the apparatuses, such as nonunit quantum efficiency
and finite resolution, are taken into account. We show that conditional {\sc
on/off} photodetection provides a reliable scheme to verify nonclassicality,
whereas conditional homodyning represents a tunable and robust source of
squeezed light. We also describe optical teleportation as a conditional
measurement, and evaluate the degrading effects of finite amount of
entanglement, decoherence due to losses, and nonunit quantum efficiency.


title: Time Scale and Completely Positive Dynamical Evolutions

abstract:
  It is argued that in the description of macroscopic systems inside quantum
mechanics the study of the dynamics of selected degrees of freedom slowly
varying on a suitable time scale, corresponding to relevant observables for the
given reduced description, is particularly meaningful. A formalism developing
these ideas in the more simple case of a microsystem interacting with a
macroscopic system is briefly outlined, together with an application to the
field of neutron optics. The obtained reduced description relies on a T-matrix
formalism and has the property of complete positivity.


title: Complete positivity and subdynamics in quantum field theory

abstract:
  The relevance that the property of complete positivity has had in the
determination of quantum structures is briefly reviewed, together with recent
applications to neutron optics and quantum Brownian motion. A possible useful
application and generalization of this property to the description of
macroscopic systems inside quantum mechanics is discussed on the basis of
recent work on the derivation of subdynamics in Heisenberg picture of slowly
varying degrees of freedom inside nonrelativistic quantum field theory.


title:
Decoherence Versus the Idealization of Microsystems as Correlation
  Carriers Between Macrosystems

abstract:
  It is argued that the appropriate framework to describe a microsystem as a
correlation carrier between a source and a detector is non-equilibrium
statistical mechanics for the compound source-detector system. An attempt is
given to elucidate how this idealized notion of microsystem might arise inside
a field theoretical description of isolated macrosystems: then decoherence
appears as the natural limit of this idealization.


title:
Quantum cryptography protocols robust against photon number splitting
  attacks for weak laser pulses implementations

abstract:
  We introduce a new class of quantum quantum key distribution protocols,
tailored to be robust against photon number splitting (PNS) attacks. We study
one of these protocols, which differs from the BB84 only in the classical
sifting procedure. This protocol is provably better than BB84 against PNS
attacks at zero error.


title: Mapping of non-central potentials under point canonical transformations

abstract:
  Motivated by the observation that all known exactly solvable shape invariant
central potentials are inter-related via point canonical transformations, we
develop an algebraic framework to show that a similar mapping procedure is also
exist between a class of non-central potentials. As an illustrative example, we
discuss the inter-relation between the generalized Coulomb and oscillator
systems.


title:
Imprinting a complete information about a quantum channel on its output
  state

abstract:
  We introduce a novel property of bipartite quantum states, which we call
"faithfulness", and we say that a state is faithful when acting with a channel
on one of the two quantum systems, the output state carries a complete
information about the channel. The concept of faithfulness can also be extended
to sets of states, when the output states patched together carry a complete
imprinting of the channel.


title: Determinisitic Optical Fock State Generation

abstract:
  We present a scheme for the deterministic generation of N-photon Fock states
from N three-level atoms in a high-finesse optical cavity. The method applies
an external laser pulsethat generates an $N$-photon output state while
adiabatically keeping the atom-cavity system within a subspace of optically
dark states. We present analytical estimates of the error due to amplitude
leakage from these dark states for general N, and compare it with explicit
results of numerical simulations for N \leq 5. The method is shown to provide a
robust source of N-photon states under a variety of experimental conditions and
is suitable for experimental implementation using a cloud of cold atoms
magnetically trapped in a cavity. The resulting N-photon states have potential
applications in fundamental studies of non-classical states and in quantum
information processing.


title: Generalized Spherical Harmonics

abstract:
  We generalize the spherical harmonics for l=1 and give the differential
equation that the generalized forms satisfy. The new forms have an obvious
interpretation in the context of quantum mechanics.


title: A note on quantum entropy inequalities and channel capacities

abstract:
  Quantum entropy inequalities are studied. Some quantum entropy inequalities
are obtained by several methods. For entanglement breaking channel, we show
that the entanglement-assisted classical capacity is upper bounded by $\log d$.
A relationship between entanglement-assisted and one-shot unassisted capacities
is obtained. This relationship shows the entanglement-assisted channel capacity
is upper bounded by the sum of $\log d$ and the one-shot unassisted classical
capacity.


title: Two-object remote quantum control

abstract:
  We consider the two-object remote quantum control for a special case in which
all the object qubits are in a telecloning state. We propose a scheme which
achieves the two-object remote quantum control by using two particular
four-particle entangled states.


title: Derivation of the Born Rule from Operational Assumptions

abstract:
  The Born rule is derived from operational assumptions, independent of the
normalization of the state. Unlike Gleason's theorem, the argument applies even
if probabilities are defined for only a single resolution of the identity, so
it applies to all the major foundational approaches to quantum mechanics. There
are important points of contact with Deutsch's program for deducing the
probabilistic interpretation of quantum mechanics from decision thoery, as
recently completed by Wallace. Decision theory can be used to supplement the
present derivation, in application to the Everett interpretation, but it is
otherwise unnecessary.


title: N-qubit Entanglement Index and Classification

abstract:
  We show that all the N-qubit states can be classified as N entanglement
classes each of which has an entanglement index $E=N-p=0,1,...,N-1$(E=0
corresponds to a fully separate class) where $p$ denotes number of groups for a
partition of the positive integer N. In other words, for any partition
$(n_1,n_2,...,n_p)$ of N with $n_j\ge 1$ and $N=\sum_{j=1}^{p}n_j$, the
entanglement index for the corresponding state
$\rho_{n_1}\bigotimes\rho_{n_2}...\bigotimes \rho_{n_p}$ with $\rho_{n_j}$
denoting a fully entangled state of $n_j-$qubits is
$E(\rho_{n_1}\bigotimes\rho_{n_2}...\bigotimes
\rho_{n_p})=\sum_{j=1}^{p}(n_j-1)=N-p$.


title: Quantum Algorithms for some Hidden Shift Problems

abstract:
  Almost all of the most successful quantum algorithms discovered to date
exploit the ability of the Fourier transform to recover subgroup structure of
functions, especially periodicity. The fact that Fourier transforms can also be
used to capture shift structure has received far less attention in the context
of quantum computation.
  In this paper, we present three examples of ``unknown shift'' problems that
can be solved efficiently on a quantum computer using the quantum Fourier
transform. We also define the hidden coset problem, which generalizes the
hidden shift problem and the hidden subgroup problem. This framework provides a
unified way of viewing the ability of the Fourier transform to capture subgroup
and shift structure.


title: Quantum billiards and constrained random wave correlations

abstract:
  We study chaotic eigenfunctions in wedge-shaped and rectangular regions using
a generalization of Berry's conjecture. An expression for the two-point
correlation function is derived and verified numerically.


title:
Control of photodissociation branching using the complete reflection
  phenomenon: Application to HI molecule

abstract:
  The laser control of photodissociation branching in a diatomic molecule is
demonstrated to be effectively achieved with use of the complete reflection
phenomenon. The phenomenon and the control condition can be nicely formulated
by the semiclassical (Zhu-Nakamura) theory. The method is applied to the
branching between I($^2 P_{3/2}$) (HI $\to$ H + I) and I$^*(^2 P_{1/2})$ (HI
$\to$ H + I$^*$) formation, and nearly complete control is shown to be possible
by appropriately choosing an initial vibrational state and laser frequency in
spite of the fact that there are three electronically excited states involved.
Numerical calculations of the corresponding wavepacket dynamics confirm the
results.


title: On the number-phase problem

abstract:
  The known approaches of number-phase problem (for a quantum oscillator) are
mutually contradictory. All of them are subsequent in respect with the
Robertson-Schr\"{o}dinger uncertainty relation (RSUR). In oposition here it is
proposed a new approacch aimed to be aboriginal as regard RSRUR. From the new
perspective the Dirac's operators for vibrational number and phase appear as
correct mathematical tools while the alluded problem receives a natural
solution. PACS codes: 03.65.-w, 03.65.Ca, 03.65.Fd, 03.65.Ta Keywords: quantum
oscillator, number and phase, uncertainty relations.


title: Quantum optical phenomena in semiconductor quantum dots

abstract:
  Quantum optical phenomena are explored in artificial atoms well known as
semiconductor quantum dots, in the presence of excitons and biexcitons. The
analytical results are obtained using the conventional time-dependent
perturbation technique. Numerical estimations are made for arealistic sample of
CdS quantum dots in a high-Q cavity. Quantum optical phenomena such as quantum
Rabi oscillations, photon statistics and collapse and revival of population
inversion in exciton and biexciton states are observed. In the presence of
biexcitons the collapse and revival phenomenon becomes faster due to the strong
coupling of biexciton with cavity field.


title: Investigation of phase-equivalent potentials by a halo transfer reaction

abstract:
  Using the supersymmetric quantum mechanics we investigate the wave
function-sensitive properties of the supersymmetric potentials which have
received a lot of attention in the literature recently. We show that a
superdeep potential and its phase-equivalent shallow-partner potential give
very similar "rms" values for the weakly bound systems such as the deuteron and
11Be nuclei. Although the corresponding eigenstates differ in the node-number,
our investigation on the 11Be(p,d)10Be single nucleon halo transfer reaction at
35 MeV show that also other physical quantities such as the cross section
angular distributions calculated using these wave functions reflect the nodal
structure rather weakly. This lends support to two nearly equivalent treatments
of the Pauli principle.


title: Local observables for entanglement witnesses

abstract:
  We present an explicit construction of entanglement witnesses for depolarized
states in arbitrary finite dimension. For infinite dimension we generalize the
construction to twin-beams perturbed by Gaussian noises in the phase and in the
amplitude of the field. We show that entanglement detection for all these
families of states requires only three local measurements. The explicit form of
the corresponding set of local observables (quorom) needed for entanglement
witness is derived.


title: Fast quantum computing with semiconductor quantum dots in a microcavity

abstract: The paper has been withdrawn by the authors


title: Measurement does not always aid state discrimination

abstract:
  We have investigated the problem of discriminating between nonorthogonal
quantum states with least probability of error. We have determined that the
best strategy for some sets of states is to make no measurement at all, and
simply to always assign the most commonly occurring state. Conditions which
describe such sets of states have been derived.


title: Quantum theory: kinematics, linearity and no-signaling condition

abstract:
  We show that the linearity of an evolution of Quantum Mechanics follows from
the definition of kinematics. The same result is obtained for an arbitrary
theory with the state space that includes mixtures of different preparations.
Next, we formulate the non-signaling theorem and show that the theorem poses no
additional restriction on Quantum Mechanics provided the kinematics is given.
We also discuss validity of the postulate for the case of more general
theories.


title: A priori probability that a qubit-qutrit pair is separable

abstract:
  We extend to arbitrarily coupled pairs of qubits (two-state quantum systems)
and qutrits (three-state quantum systems) our earlier study (quant-ph/0207181),
which was concerned with the simplest instance of entangled quantum systems,
pairs of qubits. As in that analysis -- again on the basis of numerical
(quasi-Monte Carlo) integration results, but now in a still higher-dimensional
space (35-d vs. 15-d) -- we examine a conjecture that the Bures/SD (statistical
distinguishability) probability that arbitrarily paired qubits and qutrits are
separable (unentangled) has a simple exact value, u/(v Pi^3)= >.00124706, where
u = 2^20 3^3 5 7 and v = 19 23 29 31 37 41 43 (the product of consecutive
primes). This is considerably less than the conjectured value of the Bures/SD
probability, 8/(11 Pi^2) = 0736881, in the qubit-qubit case. Both of these
conjectures, in turn, rely upon ones to the effect that the SD volumes of
separable states assume certain remarkable forms, involving "primorial"
numbers. We also estimate the SD area of the boundary of separable qubit-qutrit
states, and provide preliminary calculations of the Bures/SD probability of
separability in the general qubit-qubit-qubit and qutrit-qutrit cases.


title:
Non-classical behavior in multimode and disordered transverse structures
  in OPO. Use of the Q representation

abstract:
  We employ the Q representation to study the non-classical correlations that
are present from below to above-threshold in the degenerate optical parametric
oscillator. Our study shows that such correlations are present just above
threshold, in the regime in which stripe patterns are formed, but that they
also persist further above threshold in the presence of spatially disordered
structures.


title:
Scalable Architecture for Adiabatic Quantum Computing of NP-Hard
  Problems

abstract:
  We present a comprehensive review of past research into adiabatic quantum
computation and then propose a scalable architecture for an adiabatic quantum
computer that can treat NP-hard problems without requiring local coherent
operations. Instead, computation can be performed entirely by adiabatically
varying a magnetic field applied to all the qubits simultaneously. Local
(incoherent) operations are needed only for: (1) switching on or off certain
pairwise, nearest-neighbor inductive couplings in order to set the problem to
be solved and (2) measuring some subset of the qubits in order to obtain the
answer to the problem.


title:
Quantum Key Distribution with High Loss: Toward Global Secure
  Communication

abstract:
  We propose a decoy-state method to overcome the photon-number-splitting
attack for Bennett-Brassard 1984 quantum key distribution protocol in the
presence of high loss: A legitimate user intentionally and randomly replaces
signal pulses by multi-photon pulses (decoy-states). Then they check the loss
of the decoy-states. If the loss of the decoy-states is abnormally less than
that of signal pulses, the whole protocol is aborted. Otherwise, to continue
the protocol, they estimate loss of signal multi-photon pulses based on that of
decoy-states. This estimation can be done with an assumption that the two
losses have similar values, that we justify.


title: Test of Quantum Action for Inverse Square Potential

abstract:
  We present a numerical study of the quantum action previously introduced as a
parametrisation of Q.M. transition amplitudes. We address the questions: Is the
quantum action possibly an exact parametrisation in the whole range of
transition times ($0 < T < \infty$)? Is the presence of potential terms beyond
those occuring in the classical potential required? What is the error of the
parametrisation estimated from the numerical fit? How about convergence and
stability of the fitting method (dependence on grid points, resolution, initial
conditions, internal precision etc.)? Further we compare two methods of
numerical determination of the quantum action: (i) global fit of the Q.M.
transition amplitudes and (ii) flow equation. As model we consider the inverse
square potential, for which the Q.M. transition amplitudes are analytically
known. We find that the relative error of the parametrisation starts from zero
at T=0 increases to about $10^{-3}$ at $T=1/E_{gr}$ and then decreases to zero
when $T \to \infty$. Second, we observe stability of the quantum action under
variation of the control parameters. Finally, the flow equation method works
well in the regime of large $T$ giving stable results under variation of
initial data and consistent with the global fit method.


title: Eavesdropping on practical quantum cryptography

abstract:
  Practical implementations of quantum cryptography use attenuated laser pulses
as the signal source rather than single photons. The channels used to transmit
are also lossy. Here we give a simple derivation of two beam-splitting attacks
on quantum cryptographic systems using laser pulses, either coherent or mixed
states with any mean photon number. We also give a simple derivation of a
photon-number splitting attack, the most advanced, both in terms of performance
and technology required. We find bounds on the maximum disturbance for a given
mean photon number and observed channel transmission efficiency for which a
secret key can be distilled. We start by reviewing two incoherent attacks that
can be used on single photon quantum cryptographic systems. These results are
then adapted to systems that use laser pulses and lossy channels.


title: Robustness of entanglement for two qubit density matrix

abstract:
  By considering the decomposition of a generic two qubit density matrix
presented by Wootters [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)],
the robustness of entanglement for any mixed state of two qubit systems is
obtained algebraically. It is shown that the robustness of entanglement is
proportional to concurrence and in Bell decomposable density matrices it is
equal to the concurrence. We also give an analytic expression for two separable
states which wipe out all entanglement of these states. Since thus obtained
robustness is function of the norm of the vectors in the decomposition we give
an explicit parameterization for the decomposition.


title: Robust Entanglement in Atomic Systems via Lambda-Type Processes

abstract:
  It is shown that the system of two three-level atoms in $\Lambda$
configuration in a cavity can evolve to a long-lived maximum entangled state if
the Stokes photons vanish from the cavity by means of either leakage or
damping. The difference in evolution picture corresponding to the general model
and effective model with two-photon process in two-level system is discussed.


title: Superconducting Quantum Computing without Switches

abstract:
  This paper presents a very simple architecture for a large-scale
superconducting quantum computer. All of the SQUID qubits are fixed-coupled to
a single large superconducting loop.


title:
Relativistic-invariant quantum entanglement between the spins of moving
  bodies

abstract:
  The entanglement between spins of a pair of particles may change because the
spin and momentum become mixed when viewed by a moving observer [R.M. Gingrich
and C. Adami, Phys. Rev. Lett. 89, 270402 (2002)]. In this paper, it is shown
that, if the momenta are appropriately entangled, the entanglement between the
spins of the Bell states can remain maximal when viewed by any moving observer.
Further, we suggest a relativistic-invariant protocol for quantum
communication, with which the non-relativistic quantum information theory could
be invariantly applied to relativistic situations.


title:
Predicted Ultrafast Single Qubit Operations in Semiconductor Quantum
  Dots

abstract:
  Several recently proposed implementations of scalable quantum computation
rely on the ability to manipulate the spin polarization of individual electrons
in semiconductors. The most rapid single-spin-manipulation technique to date
relies on the generation of an effective magnetic field via a spin-sensitive
optical Stark effect. This approach has been used to split spin states in
colloidal CdSe quantum dots and to manipulate ensembles of spins in ZnMnSe
quantum wells with femtosecond optical pulses. Here we report that the process
will produce a coherent rotation of spin in quantum dots containing a single
electron. The calculated magnitude of the effective magnetic field depends on
the dot bandgap and the strain. We predict that in InAs/InP dots, for
reasonable experimental parameters, the magnitude of the rotation is sufficient
and the intrinsic error is low enough for them to serve as elements of a
quantum dot based quantum computer.


title: On the pseudo-Hermitian nondiagonalizable Hamiltonians

abstract:
  We consider a class of (possibly nondiagonalizable) pseudo-Hermitian
operators with discrete spectrum, showing that in no case (unless they are
diagonalizable and have a real spectrum) they are Hermitian with respect to a
semidefinite inner product, and that the pseudo-Hermiticity property is
equivalent to the existence of an antilinear involutory symmetry. Moreover, we
show that a typical degeneracy of the real eigenvalues (which reduces to the
well known Kramers degeneracy in the Hermitian case) occurs whenever a
fermionic (possibly nondiagonalizable) pseudo-Hermitian Hamiltonian admits an
antilinear symmetry like the time-reversal operator $T$. Some consequences and
applications are briefly discussed.


title: The cosmological origin of time-asymmetry

abstract:
  In this paper we address the problem of the arrow of time from a cosmological
point of view, rejecting the traditional entropic approach that defines the
future direction of time as the direction of the entropy increase: from our
perspective, the arrow of time has a global origin and it is an intrinsic,
geometrical feature of space-time. Time orientability and existence of a cosmic
time are necessary conditions for defining an arrow of time, which is
manifested globally as the time-asymmetry of the universe as a whole, and
locally as a time-asymmetric energy flux. We also consider arrows of time of
different origins (quantum, electromagnetic, thermodynamic, etc.) showing that
they can be non-conventionally defined only if the geometrical arrow is
previously defined.


title: The self-induced approach to decoherence in cosmology

abstract:
  In this paper we will present the \QTR{it}{self-induced approach} to
decoherence, which does not require the interaction between the system and the
environment: decoherence in closed quantum systems is possible. This fact has
relevant consequences in cosmology, where the aim is to explain the emergence
of classicality in the universe conceived as a closed (non-interacting) quantum
system. In particular, we will show that the self-induced approach may be used
for describing the evolution of a closed quantum universe, whose classical
behavior arises as a result of decoherence.


title:
Comment on ``Dynamics of open quantum systems initially entangled with
  environment: Beyond the Kraus representation'' [PRA 64, 062106 (2001)]

abstract:
  We correct a mistake in a result reported in [PRA 64, 062106 (2001)], where
it is rightfully argued that initial correlations between a system and its
environment may render the system reduced dynamics not completely positive. We
prove how not only these initial correlations but also the specific joint
dynamics does play a significant role in the question of the complete positivy
of the reduced dynamics.


title:
Comment on "Some implications of the quantum nature of laser fields for
  quantum computations"

abstract:
  A recent discussion of quantum limitations to the fidelity with which
superpositions of internal atomic energy levels can be generated by an applied,
quantized, laser pulse is shown to be based on unrealistic physical
assumptions. This discussion assumed the validity of Jaynes-Cummings dynamics
for an atom interacting with a laser field in free space, that is, when the
atom is not surrounded by a resonant cavity. If the laser field is a multimode
quantum coherent state, and the Rabi frequency is much greater than the
spontaneous decay rate, then the total atomic decoherence rate is on the order
of the spontaneous decay rate. With the use of a unitary transformation of the
field states due to Mollow, it can be shown that the atomic decoherence rate is
the same as if the laser field were treated classically, without any additional
contribution due to the quantum nature of the laser field.


title:
Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum
  Mechanics

abstract:
  In a recent paper it was shown that if a Hamiltonian H has an unbroken PT
symmetry, then it also possesses a hidden symmetry represented by the linear
operator C. The operator C commutes with both H and PT. The inner product with
respect to CPT is associated with a positive norm and the quantum theory built
on the associated Hilbert space is unitary. In this paper it is shown how to
construct the operator C for the non-Hermitian PT-symmetric Hamiltonian
$H={1\over2}p^2+{1\over2}x^2 +i\epsilon x^3$ using perturbative techniques. It
is also shown how to construct the operator C for
$H={1\over2}p^2+{1\over2}x^2-\epsilon x^4$ using nonperturbative methods.


title: Maximum speed of quantum gate operation

abstract:
  We consider a quantum gate, driven by a general time-dependent Hamiltonian,
that complements the state of a qubit and then adds to it an arbitrary phase
shift. It is shown that the minimum operation time of the gate is tau =
(h/4E)(1+2 theta/pi), where h is Planck's constant, E is the average over time
of the quantum-mechanical average energy, and theta is the phase shift modulo
pi.


title:
Bound State Wave Functions through the Quantum Hamilton - Jacobi
  Formalism

abstract:
  The bound state wave functions for a wide class of exactly solvable
potentials are found utilizing the quantum Hamilton-Jacobi formalism. It is
shown that, exploiting the singularity structure of the quantum momentum
function, until now used only for obtaining the bound state energies, one can
straightforwardly find both the eigenvalues and the corresponding
eigenfunctions. After demonstrating the working of this approach through a
number of solvable examples, we consider Hamiltonians, which exhibit broken and
unbroken phases of supersymmetry. The natural emergence of the eigenspectra and
the wave functions, in both the unbroken and the algebraically non-trivial
broken phase, demonstrates the utility of this formalism.


title:
Optimal asymmetric cloning machine on a great circle using no-signalling
  condition

abstract:
  Assuming the condition of no superluminal signalling, we got an upper bound
on the quality of all asymmetric $ 1\to 2$ cloning machines, acting on qubits
whose Bloch vectors lie on a great circle. Then we constructed an $ 1\to 2$
cloning machine, which asymmetrically clone all qubits corresponding to this
great circle, and this machine matches with that upper bound, and hence this is
optimal one.


title: Entanglement-assisted capacity of constrained quantum channel

abstract:
  In this paper we fill the gap in previous works by proving the formula for
entanglement-assisted capacity of quantum channel with additive constraint
(such as bosonic Gaussian channel). The main tools are the coding theorem for
classical-quantum constrained channels and a finite dimensional approximation
of the input density operators for entanglement-assisted capacity. The new
version contains improved formulation of sufficient conditions under which
suprema in the capacity formulas are attained.


title:
Impairment of consciousness in Alzheimer's disease: the amyloid
  water-filled nanotubes manifest quantum optical coherence interfering with
  the normal QBD?

abstract:
  Recent discovery by Perutz et al. of the physical structure of the amyloid
that accumulates in neurons in certain neurodegenerative diseases like
Alzheimer's disease or Huntington's disease, suggests novel mechanism of
consciousness impairment, different from the neuronal loss, which is the end
stage of the pathogenic process. Amyloid is shown to be water-filled nanotubes
made of polymerized pathologically-changed proteins. It is hypothesized that
the water inside the new-formed nanotubes can manifest optical coherent
laser-like excitations and superradiance similarly to the processes taking part
in the normal brain microtubules as shown by Jibu et al. The interfering with
the macroscopic quantum effects within the normal microtubules can lead to
impairment of conscious experience. Experimental data in favor of quantum
theory of consciousness can be obtained from the research of the amyloid
nanotubes.


title: Decoherence-Free Subspaces in Supersymmetric Oscillator Networks

abstract:
  Quantum superpositions can be used for parallel information processing, but
only if protected against decoherence. A two-particle four-state system may
have two-dimensional subspaces that are partially or completely
decoherence-free, e.g., the symmetric triplet state as an example of the
former, the anti-symmetric singlet state of the latter. By extension, a
multiparticle system that in the laboratory basis is plagued by decoherence may
in some other basis exhibit the symmetries that yield such decoherence-free
subspaces (DFS's). Fully-interacting many-fermion spin 1/2 networks may be
mathematically transformed to a more tractable many-to-one (or -to-some)
variant. This paper applies such a transformation to a hypothetical network of
boson-like operators and then argues that a fully-interacting particle
number-preserving network of bosons plus fermions with supersymmetric degrees
of freedom may be more plausibly exploited so as to contain DFS's. Physical
systems that in some basis are inherently anti-symmetric are already known to
be useful for quantum information processing. Supersymmetric systems may be
likewise.


title: Driving non-Gaussian to Gaussian states with linear optics

abstract:
  We introduce a protocol that maps finite-dimensional pure input states onto
approximately Gaussian states in an iterative procedure. This protocol can be
used to distill highly entangled bi-partite Gaussian states from a supply of
weakly entangled pure Gaussian states. The entire procedure requires only the
use of passive optical elements and photon detectors that solely distinguish
between the presence and absence of photons.


title: Quantum Time-Space Tradeoffs for Sorting

abstract:
  We investigate the complexity of sorting in the model of sequential quantum
circuits. While it is known that in general a quantum algorithm based on
comparisons alone cannot outperform classical sorting algorithms by more than a
constant factor in time complexity, this is wrong in a space bounded setting.
We observe that for all storage bounds n/\log n\ge S\ge \log^3 n, one can
devise a quantum algorithm that sorts n numbers (using comparisons only) in
time T=O(n^{3/2}\log^{3/2} n/\sqrt S). We then show the following lower bound
on the time-space tradeoff for sorting $n$ numbers from a polynomial size range
in a general sorting algorithm (not necessarily based on comparisons):
TS=\Omega(n^{3/2}). Hence for small values of S the upper bound is almost
tight. Classically the time-space tradeoff for sorting is TS=\Theta(n^2).


title: Cyclic networks of quantum gates

abstract:
  In this article initial steps in an analysis of cyclic networks of quantum
logic gates is given. Cyclic networks are those in which the qubit lines are
loops. Here we have studied one and two qubit systems plus two qubit cyclic
systems connected to another qubit on an acyclic line. The analysis includes
the group classification of networks and studies of the dynamics of the qubits
in the cyclic network and of the perturbation effects of an acyclic qubit
acting on a cyclic network. This is followed by a discussion of quantum
algorithms and quantum information processing with cyclic networks of quantum
gates, and a novel implementation of a cyclic network quantum memory. Quantum
sensors via cyclic networks are also discussed.


title: Casimir Forces between Nanoparticles and Substrates

abstract:
  We study the Casimir force between a nanoparticle and a substrate. We
consider the interaction of metal nanoparticles with different substrates
within the dipolar approximation. We study the force as a function of the
distance for gold and potassium spheres, which are over a substrate of titanium
dioxide, sapphire and a perfect conductor. We show that Casimir force is
important in systems at the nanometer scale. We study the force as a function
of the material properties, radii of the spheres, and the distance between the
sphere and the substrate.


title: Relativistic Einstein-Podolsky-Rosen correlation and Bell's inequality

abstract:
  We formulate the Einstein-Podolsky-Rosen (EPR) gedankenexperiment within the
framework of relativistic quantum theory to analyze a situation in which
measurements are performed by moving observers. We point out that under certain
conditions the perfect anti-correlation of an EPR pair of spins in the same
direction is deteriorated in the moving observers' frame due to the Wigner
rotation, and show that the degree of the violation of Bell's inequality prima
facie decreases with increasing the velocity of the observers if the directions
of the measurement are fixed. However, this does not imply a breakdown of
non-local correlation since the perfect anti-correlation is maintained in
appropriately chosen different directions. We must take account of this
relativistic effect in utilizing in moving frames the EPR correlation and the
violation of Bell's inequality for quantum communication.


title: Two-Step Enantio-selective Optical Switch

abstract:
  We present an optical "enantio-selective switch", that, in two steps, turns a
("racemic") mixture of left-handed and right-handed chiral molecules into the
enantiomerically pure state of interest. The optical switch is composed of an
"enantio-discriminator" and an "enantio-converter" acting in tandem. The method
is robust, insensitive to decay processes, and does not require molecular
preorientation. We demonstrate the method on the purification of a racemate of
(transiently chiral) D$_2$S$_2$ molecules, performed on the nanosecond
timescale.


title: Comparing EQP and MOD_{p^k}P using Polynomial Degree Lower Bounds

abstract:
  We show that an oracle A that contains either 1/4 or 3/4 of all strings of
length n can be used to separate EQP from the counting classes MOD_{p^k}P. Our
proof makes use of the degree of a representing polynomial over the finite
field of size p^k. We show a linear lower bound on the degree of this
polynomial.
  We also show an upper bound of O(n^{1/log_p m}) on the degree over the ring
of integers modulo m, whenever m is a squarefree composite with largest prime
factor p.


title: Quantum Mechanics interpreted in Quantum Real Numbers

abstract:
  The concept of number is fundamental to the formulation of any physical
theory. We give a heuristic motivation for the reformulation of Quantum
Mechanics in terms of non-standard real numbers called Quantum Real Numbers.
The standard axioms of quantum mechanics are re-interpreted. Our aim is to show
that, when formulated in the language of quantum real numbers, the laws of
quantum mechanics appear more natural, less counterintuitive than when they are
presented in terms of standard numbers.


title: From Fermat Principle to Wave equation

abstract:
  The Fermat principle indicates that light chooses the temporally shortest
path. The action for this "motion" is the observed time, and it has no Lorentz
invariance. In this paper we show how this action can be obtained from
relativistic action, and how the classical wave equation of light can be
obtained from this action.


title: Approaching the Heisenberg limit with two mode squeezed states

abstract:
  Two mode squeezed states can be used to achieve Heisenberg limit scaling in
interferometry: a phase shift of $\delta \phi \approx 2.76 / < N >$ can be
resolved. The proposed scheme relies on balanced homodyne detection and can be
implemented with current technology. The most important experimental
imperfections are studied and their impact quantified.


title:
Stabilization of Quantum Computer Calculation Basis by Qubit Encoding in
  Virtual Spin Representation

abstract:
  It is proposed to map the quantum information qubit not to individual spin
1/2 states, but to the collective spin states being eigenfunctions of the
Hamiltonian including spin-spin interactions, which may be not small. Such an
approach allows to introduce more stable calculation basis for quantum computer
based on the solid state NMR systems.