title: Efficient decomposition of quantum gates

abstract:
  Optimal implementation of quantum gates is crucial for designing a quantum
computer. We consider the matrix representation of an arbitrary multiqubit
gate. By ordering the basis vectors using the Gray code, we construct the
quantum circuit which is optimal in the sense of fully controlled single-qubit
gates and yet is equivalent with the multiqubit gate. In the second step of the
optimization, superfluous control bits are eliminated, which eventually results
in a smaller total number of the elementary gates. In our scheme the number of
controlled NOT gates is $O(4^n)$ which coincides with the theoretical lower
bound.


title: Parametric Resonance in a Vibrating Cavity

abstract:
  We present the study of parametric resonance in a one-dimensional cavity
based on the analysis of classical optical paths. The recursive formulas for
field energy are given. We separate the mechanism of particle production and
the resonance amplification of radiation. The production of photons is a purely
quantum effect described in terms of quantum anomalies in recursive formulas.
The resonance enhancement is a classical phenomenon of focusing and amplifying
beams of photons due to D\"{o}ppler effect.


title: Quantum Energy in a Vibrating Cavity

abstract:
  We discuss the quantized field inside a general one-dimensional cavity
system. We recognize the $SL(2,R)$ symmetry being the remainder of the
conformal group. The explanation of the lack of the resonance production for
the fundamental frequency is given and the asymptotic behavior of the cavity
system is properly described.


title: Structure of sufficient quantum coarse-grainings

abstract:
  Let H and K be Hilbert spaces and T be a coarse-graining from B(H) to B(K).
Assume that density matrices D_1 and D_2 acting on H are given. In the paper
the consequences of the existence of a coarse-graining S from B(K) to B(H)
satisfying ST(D_1)=D_1 and ST(D_2)=D_2 are given. (This condition means the
sufficiency of T for D_1 and D_2.) Sufficiency implies a particular
decomposition of the density matrices. This decomposition allows to deduce the
exact condition for equality in the strong subadditivity of the von Neumann
entropy.


title:
Observation of sub-Doppler absorption in the /Lambda-type three-level
  Doppler-broadened cesium system

abstract:
  Thanks to the atomic coherence in coupling laser driven atomic system,
sub-Doppler absorption has been observed in Doppler-broadened cesium vapor cell
via the /Lambda-type three-level scheme. The linewidth of the sub-Doppler
absorption peak become narrower while the frequency detuning of coupling laser
increases. The results are in agreement with the theoretical prediction by G.
Vemuri et al.[PRA,Vol.53(1996) p.2842].


title:
Faithful sharing of multipartite entanglement over noisy quantum
  channels

abstract:
  We present a protocol in which two or more parties can share multipartite
entanglement over noisy quantum channels. The protocol is based on the
entanglement purification presented by Shor and Preskill [Phys. Rev. Lett. 85,
441 (2000)] and the quantum teleportation via an isotropic state. We show that
a nearly perfect purification implies a nearly perfect sharing of multipartite
entanglement between two parties so that the protocol can assure a faithful
sharing of multipartite entanglement with Shor and Preskill's proof on the
entanglement purification.


title: The Casimir force between real mirrors at non zero temperature

abstract:
  The Casimir force between dissipative metallic mirrors at non zero
temperature has recently given rise to contradictory claims which have raised
doubts about the theoretical expression of the force. In order to contribute to
the resolution of this difficulty, we come back to the derivation of the force
from basic principles of the quantum theory of lossy optical cavities. We
obtain an expression which is valid for arbitrary mirrors, including
dissipative ones, characterized by frequency dependent reflection amplitudes.


title: The simplified Toffoli gate implementation by Margolus is optimal

abstract:
  Unitary operations are expressed in the quantum circuit model as a finite
sequence of elementary gates, such as controlled-not gates and single qubit
gates. We prove that the simplified Toffoli gate by Margolus, which coincides
with the Toffoli gate up to a single change of sign, cannot be realized with
less than three controlled-not gates. If the circuit is implemented with three
controlled-not gates, then at least four additional single qubit gates are
necessary. This proves that the implementation suggested by Margolus is
optimal.


title:
A feasible gate for scalable linear optics quantum computation using
  polarization optics

abstract:
  Knill, Laflamme, and Milburn (KLM) proved that it is possible to build a
scalable universal quantum computer using only linear-optics elements and
conditional dynamics [Nature (London) {\bf 409}, 46 (2001)\cite{Knill}].
However, the practical realization of the quantum logic gate for the scheme is
still technically difficult. A major difficulty is the requirement for
sub-wavelength level stabilization of the interlocking interferometers.
Following our recent experimental work[Phys. Rev. Lett.{\bf 92}, 017902
(2004)\cite{Sanaka2}], we describe a more feasible scheme to implement the gate
that greatly reduces the experimental stability requirements. The scheme uses
only polarizing beam splitters and half-wave plates.


title:
The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty
  Wave Bullet?

abstract:
  Several situations, in which an empty wave causes an observable effect, are
reviewed. They include an experiment showing ``surrealistic trajectories''
proposed by Englert et al. and protective measurement of the density of the
quantum state. Conditions for observable effects due to empty waves are
derived. The possibility (in spite of the existence of these examples) of
minimalistic interpretation of Bohmian Quantum Mechanics in which only Bohmian
positions supervene on our experience is discussed.


title: Remarks on Clifford codes

abstract:
  Clifford codes are a class of quantum error control codes that form a natural
generalization of stabilizer codes. These codes were introduced in 1996 by
Knill, but only a single Clifford code was known, which is not already a
stabilizer code. We derive a necessary and sufficient condition that allows to
decide when a Clifford code is a stabilizer code, and compile a table of all
true Clifford codes for error groups of small order.


title: Revivals of Coherence in Chaotic Atom-Optics Billiards

abstract:
  We investigate the coherence properties of thermal atoms confined in optical
dipole traps where the underlying classical dynamics is chaotic. A perturbative
expression derived for the coherence of the echo scheme of [Andersen et. al.,
Phys. Rev. Lett. 90, 023001 (2003)] shows it is a function of the survival
probability or fidelity of eigenstates of the motion of the atoms in the trap.
The echo coherence and the survival probability display "system specific"
features, even when the underlying classical dynamics is chaotic. In
particular, partial revivals in the echo signal and the survival probability
are found for a small shift of the potential. Next, a "semi-classical"
expression for the averaged echo signal is presented and used to calculate the
echo signal for atoms in a light sheet wedge billiard. Revivals in the echo
coherence are found in this system, indicating they may be a generic feature of
dipole traps.


title: A note on the classical lower bound for a quantum walk algorithm

abstract:
  A recent paper on quantum walks by Childs et al. [STOC'03] provides an
example of a black-box problem for which there is a quantum algorithm with
exponential speedup over the best classical randomized algorithm for the
problem, but where the quantum algorithm does not involve any use of the
quantum Fourier transform. They give an exponential lower bound for a classical
randomized algorithm solving the black-box graph traversal problem defined in
their paper. In this note we give an improved lower bound for this problem via
a straightforward and more complete analysis.


title: Constraints on relaxation rates for N-level quantum systems

abstract:
  We study the constraints imposed on the population and phase relaxation rates
by the physical requirement of completely positive evolution for open N-level
systems. The Lindblad operators that govern the evolution of the system are
expressed in terms of observable relaxation rates, explicit formulas for the
decoherence rates due to population relaxation are derived, and it is shown
that there are additional, non-trivial constraints on the pure dephasing rates
for N>2. Explicit experimentally testable inequality constraints for the
decoherence rates are derived for three and four-level systems, and the
implications of the results are discussed for generic ladder-, Lambda- and
V-systems, and transitions between degenerate energy levels.


title:
Conditional Production of Superpositions of Coherent States with
  Inefficient Photon Detection

abstract:
  It is shown that a linear superposition of two macroscopically
distinguishable optical coherent states can be generated using a single photon
source and simple all-optical operations. Weak squeezing on a single photon,
beam mixing with an auxiliary coherent state, and photon detecting with
imperfect threshold detectors are enough to generate a coherent state
superposition in a free propagating optical field with a large coherent
amplitude ($\alpha>2$) and high fidelity ($F>0.99$). In contrast to all
previous schemes to generate such a state, our scheme does not need photon
number resolving measurements nor Kerr-type nonlinear interactions.
Furthermore, it is robust to detection inefficiency and exhibits some
resilience to photon production inefficiency.


title:
Optical realization of optimal unambiguous discrimination for pure and
  mixed quantum states

abstract:
  Quantum mechanics forbids deterministic discrimination among non-orthogonal
states. Nonetheless, the capability to distinguish nonorthogonal states
unambiguously is an important primitive in quantum information processing. In
this work, we experimentally implement generalized measurements in an optical
system and demonstrate the first optimal unambiguous discrimination between
three nonorthogonal states, with a success rate of 55%, to be compared with the
25% maximum achievable using projective measurements. Furthermore we present
the first realization of unambiguous discrimination between a pure state and a
nonorthogonal mixed state.


title:
Optical tests of Bell's inequalities not resting upon the absurd fair
  sampling assumption

abstract:
  A simple local hidden-variables model is exhibited which reproduces the
results of all performed tests of Bell\'{}s inequalities involving optical
photon pairs. For the old atomic-cascade experiments, like Aspect\'{}s, the
model agrees with quantum mechanics even for ideal set-ups. For more recent
experiments, using parametric down-converted photons, the agreement occurs only
for actual experiments, involving low efficiency detectors. Arguments are given
against the fair sampling assumption, currently combined with the results of
the experiments in order to claim a contradiction with local realism. New tests
are proposed which are able to discriminate between quantum mechanics and a
restricted, but appealing, family of local hidden-variables models. Such tests
require detectors with efficiencies just above 20%.


title: Quantum Mechanics on discrete space and time

abstract:
  We propose the assumption of quantum mechanics on a discrete space and time,
which implies the modification of mathematical expressions for some postulates
of quantum mechanics. In particular we have a Hilbert space where the vectors
are complex functions of discrete variable. As a concrete example we develop a
discrete analog of the one-dimensional quantum harmonic oscillator, using the
dependence of the Wigner functions in terms of Kravchuk polynomials. In this
model the position operator has a discrete spectrum given by one index of the
Wigner functions, in the same way that the energy eigenvalues are given by the
other matricial index. Similar picture can be made for other models where the
differential equation and their solutions correspond to the continuous limit of
some difference operator and orthogonal polynomial of discrete variable.


title: Information Erasure and Recover in Quantum Memory

abstract:
  We show that information in quantum memory can be erased and recovered
perfectly if it is necessary. That the final states of environment are
completely determined by the initial states of the system allows that an easure
operation can be realized by a swap operation between system and an ancilla.
Therefore, the erased information can be recoverd. When there is an
irreversible process, e.g. an irreversible operation or a decoherence process,
in the erasure process, the information would be erased perpetually. We present
that quantum erasure will also give heat dissipation in environment. And a
classical limit of quantum erasure is given which coincides with Landauer's
erasure principle.


title: Endophysical information transfer in quantum processes

abstract:
  We give a mathematical criterion for the concept of information flow within
closed quantum systems described by quantum registers. We define the concepts
of separations and entanglements over quantum registers and use them with the
quantum zip properties of inner products over quantum registers to establish
the concept of partition change, which is fundamental to our criterion of
endophysical information exchange within such quantum systems.


title: Identifying entanglement using quantum "ghost" interference and imaging

abstract:
  We report a quantum interference and imaging experiment which quantitatively
demonstrates that Einstein-Podolsky-Rosen (EPR) type entangled two-photon
states exhibit both momentum-momentum and position-position correlations,
stronger than any classical correlation. The measurements show indeed that the
uncertainties in the sum of momenta and in the difference of positions of the
entangled two-photon satisfy both EPR inequalities D(k1+k2)<min(D(k1),D(k2))
and D(x1-x2)<min(D(x1),D(x2)). These two inequalities, together, represent a
non-classicality condition. Our measurements provide a direct way to
distinguish between quantum entanglement and classical correlation in
continuous variables for two-photons/two photons systems.


title: Bohmian Mechanics with Discrete Operators

abstract:
  A deterministic Bohmian mechanics for operators with continuous and discrete
spectra is presented. Randomness enters only through initial conditions.
Operators with discrete spectra are incorporated into Bohmian mechanics by
associating with each operator a continuous variable in which a finite range of
the continuous variable correspond to the same discrete eigenvalue. In this way
Bohmian mechanics can handle the creation and annihilation of particles.
Examples are given and generalizations are discussed.


title:
Maintenance of Coherence and Polarization Evolution in a Supersymmetric
  Multiphoton Model

abstract:
  The elimination of decoherence of two-state quantum systems interacting with
a thermal reservoir through an external controllable driving field is discussed
in the present paper. The restriction equation with which the external
controllable driving field should agree will be derived. Based on this, we
obtain the time-development equation of the off-diagonal elements of density
operator in the supersymmetric multiphoton two-state quantum systems, which is
helpful for studying the polarization evolution in this two-state quantum
model.


title:
Control the entanglement of two atoms in an optical cavity via white
  noise

abstract:
  Two two-level atoms within a leaky optical cavity is driven by two
independent external optical white noise fields. We investigate how
entanglement between two atoms arises in such a situation. The steady state
entanglement of two atoms is also investigated. A stochastic-resonance-like
behavior of entanglement is revealed. Finally, the Bell violation between atoms
is discussed.


title: Einstein-De Broglie relations on the lattice

abstract:
  Historically the starting point of wave mechanics is the Planck and
Einstein-de Broglie relations for the energy and momentum of a particle, where
the momentum is connected to the group velocity of the wave packet. We
translate the arguments given by de Broglie to the case of a wave defined on
the grid points of a space-time lattice and explore the physical consequences
such as integral period, wave length, discrete energy, momentum and rest mass.


title: Nonadiabatic effects of atomic motion inside a high Q optical cavity

abstract:
  We revisit the topic of atomic center of mass motion of a three level atom
Raman coupled strongly to an external laser field and the quantum field of a
high Q optical cavity. We focus on the motion related nonadiabatic effects of
the atomic internal dynamics and provide a quantitative answer to the validity
regime for the application of the motional insensitive dark state as recently
suggested in Ref. [Phys. Rev. A {\bf 67}, 032305 (2003)].


title: Universal Test for Quantum One-Way Permutations

abstract:
  The next bit test was introduced by Blum and Micali and proved by Yao to be a
universal test for cryptographic pseudorandom generators. On the other hand, no
universal test for the cryptographic one-wayness of functions (or permutations)
is known, though the existence of cryptographic pseudorandom generators is
equivalent to that of cryptographic one-way functions. In the quantum
computation model, Kashefi, Nishimura and Vedral gave a sufficient condition of
(cryptographic) quantum one-way permutations and conjectured that the condition
would be necessary. In this paper, we affirmatively settle their conjecture and
complete a necessary and sufficient for quantum one-way permutations. The
necessary and sufficient condition can be regarded as a universal test for
quantum one-way permutations, since the condition is described as a collection
of stepwise tests similar to the next bit test for pseudorandom generators.


title: Technique of quantum state transfer for a double Lambda atomic beam

abstract:
  The transfer technique of quantum states from light to collective atomic
excitations in a double $\Lambda$ type system is extended to matter waves in
this paper, as a novel scheme towards making a continuous atom laser. The
intensity of the output matter waves is found to be determined by the initial
relative phase of the two independent coherent probe lights, which may indicate
an interesting method for the measurement of initial relative phase of two
independent light sources.


title: Critical temperature for entanglement transition in Heisenberg models

abstract:
  We study thermal entanglement in some low-dimensional Heisenberg models. It
is found that in each model there is a critical temperature above which thermal
entanglement is absent.


title: Quantum-implemented selective reconstruction of high-resolution images

abstract:
  This paper proposes quantum image reconstruction. Input-triggered selection
of an image among many stored ones, and its reconstruction if the input is
occluded or noisy, has been simulated by a computer program implementable in a
real quantum-physical system. It is based on the Hopfield associative net; the
quantum-wave implementation bases on holography. The main limitations of the
classical Hopfield net are much reduced with the new, original --
quantum-optical -- implementation. Image resolution can be almost arbitrarily
increased.


title:
What's wrong with Einstein's 1927 hidden-variable interpretation of
  quantum mechanics?

abstract:
  Einstein's unpublished 1927 deterministic trajectory interpretation of
quantum mechanics is critically examined, in particular with regard to the
reason given by Einstein for rejecting his theory. It is shown that the aspect
Einstein found objectionable - the mutual dependence of the motions of
particles when the (many-body) wavefunction factorises - is a generic attribute
of his theory but that this feature may be removed by modifying Einstein's
method in either of two ways: using a suggestion of Grommer or, in a physically
important special case, using a simpler technique. It is emphasized though that
the presence or absence of the interdependence property does not determine the
acceptability of a trajectory theory. It is shown that there are other grounds
for rejecting Einstein's theory (and the two modified theories), to do with its
domain of applicability and compatibility with empirical predictions. That
Einstein's reason for rejection is not a priori grounds for discarding a
trajectory theory is demonstrated by reference to an alternative deterministic
trajectory theory that displays similar particle interdependence yet is
compatible with quantum predictions.


title:
Extracting quantum dynamics from genetic learning algorithms through
  principal control analysis

abstract:
  Genetic learning algorithms are widely used to control ultrafast optical
pulse shapes for photo-induced quantum control of atoms and molecules. An
unresolved issue is how to use the solutions found by these algorithms to learn
about the system's quantum dynamics. We propose a simple method based on
covariance analysis of the control space, which can reveal the degrees of
freedom in the effective control Hamiltonian. We have applied this technique to
stimulated Raman scattering in liquid methanol. A simple model of two-mode
stimulated Raman scattering is consistent with the results.


title: Quantum computing

abstract:
  This article gives an elementary introduction to quantum computing. It is a
draft for a book chapter of the "Handbook of Nature-Inspired and Innovative
Computing", Eds. A. Zomaya, G.J. Milburn, J. Dongarra, D. Bader, R. Brent, M.
Eshaghian-Wilner, F. Seredynski (Springer, Berlin Heidelberg New York, 2006).


title:
Scalable Trapped Ion Quantum Computation with a Probabilistic Ion-Photon
  Mapping

abstract:
  We propose a method for scaling trapped ions for large-scale quantum
computation and communication based on a probabilistic ion-photon mapping.
Deterministic quantum gates between remotely located trapped ions can be
achieved through detection of spontaneously-emitted photons, accompanied by the
local Coulomb interaction between neighboring ions. We discuss gate speeds and
tolerance to experimental noise for different probabilistic entanglement
schemes.


title: The information entropy of quantum mechanical states

abstract:
  It is well known that a Shannon based definition of information entropy leads
in the classical case to the Boltzmann entropy. It is tempting to regard the
Von Neumann entropy as the corresponding quantum mechanical definition. But the
latter is problematic from quantum information point of view. Consequently we
introduce a new definition of entropy that reflects the inherent uncertainty of
quantum mechanical states. We derive for it an explicit expression, and discuss
some of its general properties. We distinguish between the minimum uncertainty
entropy of pure states, and the excess statistical entropy of mixtures.


title: A CH-type Inequality For Real Experiments

abstract:
  We derive an efficient CH-type inequality. Quantum mechanics violates our
proposed inequality independent of the detection-efficiency problem.


title:
Multipartite Entanglement under Stochastic Local Operations and
  Classical Communication

abstract:
  Stochastic local operations and classical communication (SLOCC), also called
local filtering operations, are a convenient, useful set of quantum operations
in grasping essential properties of entanglement. We give a quick overview
about the characteristics of multipartite entanglement in terms of SLOCC,
illustrating the 2-qubit and the rest (2 x 2 x n) quantum system. This not only
includes celebrated results of 3-qubit pure states, but also has implications
to 2-qubit mixed states.


title: Qubit Field Theory

abstract:
  The canonical commutation relations of quantum field theory require all pairs
of observables located in spacelike-separated regions to commute. In the theory
as it is currently constituted, this implies that the information-carrying
capacity of a finite volume of space is infinite. Yet Bekenstein's bound gives
us strong reason to believe that it is finite. A class of quantum field
theories is presented in which observables localised in spacelike-separated
regions do not necessarily commute, but which nevertheless has no physical
pathologies.


title: Squeezed-light source for the superresolving microscopy

abstract:
  We propose a source of multimode squeezed light that can be used for the
superresolving microscopy beyond the standard quantum limit. This source is an
optical parametric amplifier with a properly chosen diaphragm on its output and
a Fourier lens. We demonstrate that such an arrangement produces squeezed
prolate spheroidal waves which are the eigen modes of the optical imaging
scheme used in microscopy. The degree of squeezing and the number of spatial
modes in illuminating light, necessary for the effective object field
reconstruction, are evaluated


title: Comments on multiplicativity of maximal p-norms when p = 2

abstract:
  We consider the maximal p-norm associated with a completely positive map and
the question of its multiplicativity under tensor products. We give a condition
under which this multiplicativity holds when p = 2, and we describe some maps
which satisfy our condition. This class includes maps for which
multiplicativity is known to fail for large p.
  Our work raises some questions of independent interest in matrix theory;
these are discussed in two appendices.


title:
Less (precision) is more (information): quantum information in fuzzy
  probability theory

abstract:
  A comparison of structural features of quantum and classical physical
theories, such as the information capacity of systems subject to these
theories, requires a common formal framework for the presentation of
corresponding concepts (such as states, observables, probability, entropy).
Such a framework is provided by the notion of statistical model developed in
the convexity approach to statistical physical theories. Here we use
statistical models to classify and survey all possible types of embedding and
extension of quantum probabilistic theories subject to certain reasonable
constraints. It will be shown that the so-called canonical classical extension
of quantum mechanics is essentially the only `good' representation of the
quantum statistical model in a classical framework. All quantum observables are
thus identified as fuzzy classical random variables.


title:
Creation of atomic coherent superpositions in manifolds of levels
  without multi-photon resonance

abstract:
  We propose a scheme for creating atomic coherent superpositions via
stimulated Raman adiabatic passage in a Lambda-type system where the final
state has twofold levels. In the employ of a control field, the presence of
double dark states leads to two arbitrary coherent superposition states with
equal amplitude but inverse relative phase without the condition of
multi-photon resonance. In particular, two orthogonal maximal coherent
superposition states are created when the control field is resonant with the
transition of the twofold levels. This scheme can also be extended to manifold
Lambda-type systems.


title: Phase Transitions in Generalised Spin-Boson (Dicke) Models

abstract:
  We consider a class of generalised single mode Dicke Hamiltonians with
arbitrary boson coupling in the pseudo-spin $x$-$z$ plane. We find exact
solutions in the thermodynamic, large-spin limit as a function of the coupling
angle, which allows us to continuously move between the simple dephasing and
the original Dicke Hamiltonians. Only in the latter case (orthogonal static and
fluctuating couplings), does the parity-symmetry induced quantum phase
transition occur.


title:
Time-dependent unitary perturbation theory for intense laser driven
  molecular orientation

abstract:
  We apply a time-dependent perturbation theory based on unitary
transformations combined with averaging techniques, on molecular orientation
dynamics by ultrashort pulses. We test the validity and the accuracy of this
approach on LiCl described within a rigid-rotor model and find that it is more
accurate than other approximations. Furthermore, it is shown that a noticeable
orientation can be achieved for experimentally standard short laser pulses of
zero time average. In this case, we determine the dynamically relevant
parameters by using the perturbative propagator, that is derived from this
scheme, and we investigate the temperature effects on the molecular orientation
dynamics.


title: Quantum wave packet revivals

abstract:
  The numerical prediction, theoretical analysis, and experimental verification
of the phenomenon of wave packet revivals in quantum systems has flourished
over the last decade and a half. Quantum revivals are characterized by
initially localized quantum states which have a short-term, quasi-classical
time evolution, which then can spread significantly over several orbits, only
to reform later in the form of a quantum revival in which the spreading
reverses itself, the wave packet relocalizes, and the semi-classical
periodicity is once again evident. Relocalization of the initial wave packet
into a number of smaller copies of the initial packet (`minipackets' or
`clones') is also possible, giving rise to fractional revivals. Systems
exhibiting such behavior are a fundamental realization of time-dependent
interference phenomena for bound states with quantized energies in quantum
mechanics and are therefore of wide interest in the physics and chemistry
communities.
  We review the theoretical machinery of quantum wave packet construction
leading to the existence of revivals and fractional revivals, in systems with
one (or more) quantum number(s), as well as discussing how information on the
classical period and revival time is encoded in the energy eigenvalue spectrum.
We discuss a number of one-dimensional model systems which exhibit revival
behavior, including the infinite well, the quantum bouncer, and others, as well
as several two-dimensional integrable quantum billiard systems. Finally, we
briefly review the experimental evidence for wave packet revivals in atomic,
molecular, and other systems, and related revival phenomena in condensed matter
and optical systems.


title: Control of trapped-ion quantum states with optical pulses

abstract:
  We present new results on the quantum control of systems with infinitely
large Hilbert spaces. A control-theoretic analysis of the control of trapped
ion quantum states via optical pulses is performed. We demonstrate how resonant
bichromatic fields can be applied in two contrasting ways -- one that makes the
system completely uncontrollable, and the other that makes the system
controllable. In some interesting cases, the Hilbert space of the
qubit-harmonic oscillator can be made finite, and the Schr\"{o}dinger equation
controllable via bichromatic resonant pulses. Extending this analysis to the
quantum states of two ions, a new scheme for producing entangled qubits is
discovered.


title: Quantum channel using photon number correlated twin beams

abstract:
  We report quantum communications channel using photon number correlated twin
beams. The twin beams are generated from a nondegenerate optical parametric
oscillator, and the photon number difference is used to encode the signal. The
bit error rate of our system will be 0.067 by using the twin beams comparing
with 0.217 by using the coherent state as the signal carrier.


title:
Quantum entanglement and Bell violation of two coupled cavity fields in
  dissipative environment

abstract:
  We study the quantum entanglement between two coupled cavities, in which one
is initially prepared in a mesoscopic superposition state and the other is in
the vacuum in dissipative environment and show how the entanglement between two
cavities can arise in the dissipative environment. The dynamic behavior of the
nonlocality for the system is also investigated.


title: On the classical limit of the hyperbolic quantum mechanics

abstract:
  We demonstrated that classical mechanics have, besides the well known quantum
deformation, another deformation -- so called hyperbolic quantum mechanics. The
classical Poisson bracket can be obtained as the limit $h\to 0$ not only of the
ordinary Moyal bracket, but also hyperbolic analogue of the Moyal bracket. Thus
there are two different deformations of classical phase-space: complex Hilbert
space and hyperbolic Hilbert space (module over a so called hyperbolic algebra
-- the two dimensional Clifford algebra). To prove the correspondence principle
we use the calculus over the hyperbolic algebra similar to functional
superanalysis of Vladimirov-Volovich. Ordinary (complex) and hyperbolic quantum
mechanics are characterized by two types of interference perturbation of the
classical formula of total probability: ordinary $\cos$-interference and
hyperbolic $\cosh$-interference.


title:
Conditional implementation of asymmetrical universal quantum cloning
  machine

abstract:
  We propose two feasible experimental implementations of an optimal asymmetric
1->2 quantum cloning of a polarization state of photon. Both implementations
are based on a partial and optimal reverse of recent conditional symmetrical
quantum cloning experiments. The reversion procedure is performed only by a
local measurement of one from the clones and ancilla followed by a local
operation on the other clone. The local measurement consists only of a single
unbalanced beam splitter followed in one output by a single photon detector and
the asymmetry of fidelities in the cloning is controlled by a reflectivity of
the beam splitter.


title: Bell states, mutually unbiased bases and the Mean King's problem

abstract:
  When the state of a quantum system belongs to a N-dimensional Hilbert space,
with N the power of a prime number, it is possible to associate to the system a
finite field (Galois field) with N elements. In this paper, we introduce
generalized Bell states that can be intrinsically expressed in terms of the
field operations.These Bell states are in one to one correspondence with the
N^2 elements of the generalised Pauli group or Heisenberg-Weyl group.
  This group consists of discrete displacement operators and provides a
discrete realisation of the Weyl function.Thanks to the properties of
generalised Bell states and of quadratic extensions of finite fields, we derive
a particular solution for the Mean King's problem. This solution is in turn
shown to be in one to one correspondence with a set of N^2 self-adjoint
operators that provides a discrete realisation of the Wigner
quasi-distribution.


title: Survival of quantum effects for observables after decoherence

abstract:
  When a quantum nonlinear system is linearly coupled to an infinite bath of
harmonic oscillators, quantum coherence of the system is lost on a decoherence
time-scale $\tau_D$. Nevertheless, quantum effects for observables may still
survive environment-induced decoherence, and be observed for times much larger
than the decoherence time-scale. In particular, we show that the Ehrenfest
time, which characterizes a departure of quantum dynamics for observables from
the corresponding classical dynamics, can be observed for a quasi-classical
nonlinear oscillator for times $\tau \gg\tau_D$. We discuss this observation in
relation to recent experiments on quantum nonlinear systems in the
quasi-classical region of parameters.


title: Quantum partial teleportation as optimal cloning at a distance

abstract:
  We propose a feasible scheme of conditional quantum partial teleportation of
a qubit as optimal asymmetric cloning at a distance. In this scheme, Alice
preserves one imperfect clone whereas other clone is teleported to Bob.
Fidelities of the clones can be simply controlled by an asymmetry in Bell-state
measurement. The optimality means that tightest inequality for the fidelities
in the asymmetric cloning is saturated. Further we design a conditional
teleportation as symmetric optimal N-> N+1 cloning from N Alice's replicas on
single distant clone. We shortly discussed two feasible experimental
implementations, first one for teleportation of polarization state of a photon
and second one, for teleportation of a time-bin qubit.


title: Quantum Cellular Automata Pseudo-Random Maps

abstract:
  Quantum computation based on quantum cellular automata (QCA) can greatly
reduce the control and precision necessary for experimental implementations of
quantum information processing. A QCA system consists of a few species of
qubits in which all qubits of a species evolve in parallel. We show that, in
spite of its inherent constraints, a QCA system can be used to study complex
quantum dynamics. To this aim, we demonstrate scalable operations on a QCA
system that fulfill statistical criteria of randomness and explore which
criteria of randomness can be fulfilled by operators from various QCA
architectures. Other means of realizing random operators with only a few
independent operators are also discussed.


title:
Quantum Watermarking by Frequency of Error when Observing Qubits in
  Dissimilar Bases

abstract:
  We present a so-called fuzzy watermarking scheme based on the relative
frequency of error in observing qubits in a dissimilar basis from the one in
which they were written. Then we discuss possible attacks on the system and
speculate on how to implement this watermarking scheme for particular kinds of
messages (images, formated text, etc.).


title:
Conditional implementation of a quantum phase gate with distant atoms
  trapped in different optical cavities

abstract:
  We propose a scheme for conditional implementation of a quantum phase gate by
using distant atoms trapped in different optical cavities. Instead of direct
interaction between atoms, the present scheme makes use of quantum interference
of polarized photons decaying from the optical cavities to conditionally create
the desired quantum phase gate between two distant atoms. The proposed scheme
only needs linear optical elements and a two-fold coincidence detection, and
are insensitive to the quantum noise. The scheme can be directly used to
prepare any quantum state of many distant atoms.


title:
Propagator Of A Particle In A Photonic And A Magnetic Field And
  Evolution Of A Coherent State

abstract:
  In the present paper we study the interaction of a photonic field with a
particle in a magnetic field. We use formalism similar to the Born-Oppenheimer
approximation of molecular physics and we eliminate the photonic field
variables by using a method related to the Berry phase to obtain an effective
Hamiltonian and then extract the propagator of the particle. As an initial
photonic state we assume a coherent one.


title: Geometric phase in optics and angular momentum of light

abstract:
  Physical mechanism for the geometric phase in terms of angular momentum
exchange is elucidated. It is argued that the geometric phase arising out of
the cyclic changes in the tranverse mode space of the Gaussian light beams is a
manifestation of the cycles in the momentum space of the light. Nonconservation
of angular momentum in the spontaneous parametric down-conversion for the
classical light beams is proposed to be related with the geometric phase.


title: Ionization of Rydberg atoms embedded in an ultracold plasma

abstract:
  We have studied the behavior of cold Rydberg atoms embedded in an ultracold
plasma. We demonstrate that even deeply bound Rydberg atoms are completely
ionized in such an environment, due to electron collisions. Using a fast pulse
extraction of the electrons from the plasma we found that the number of excess
positive charges, which is directly related to the electron temperature Te, is
not strongly affected by the ionization of the Rydberg atoms. Assuming a
Michie-King equilibrium distribution, in analogy with globular star cluster
dynamics, we estimate Te. Without concluding on heating or cooling of the
plasma by the Rydberg atoms, we discuss the range for changing the plasma
temperature by adding Rydberg atoms.


title:
If 1=2+3, then 1=2.3: Bell states, finite groups, and mutually unbiased
  bases, a unifying approach

abstract:
  We study the relationship between Bell states, finite groups and complete
sets of bases. We show how to obtain a set of N+1 bases in which Bell states
are invariant.
  They generalize the X, Y and Z qubit bases and are associated to groups of
unitary transformations that generalize the sigma operators of Pauli. When the
dimension N is a prime power, we derive (in agreement with well-known results)
a set of mutually unbiased bases. We show how they can be expressed in terms of
the (operations of the) associated finite field of N elements.


title: Planar Ion Trap Geometry for Microfabrication

abstract:
  We describe a novel high aspect ratio radiofrequency linear ion trap geometry
that is amenable to modern microfabrication techniques. The ion trap electrode
structure consists of a pair of stacked conducting cantilevers resulting in
confining fields that take the form of fringe fields from parallel plate
capacitors. The confining potentials are modeled both analytically and
numerically. This ion trap geometry may form the basis for large scale quantum
computers or parallel quadrupole mass spectrometers.
  PACS: 39.25.+k, 03.67.Lx, 07.75.+h, 07.10+Cm


title:
N-Partite Separability Inequalities Exponentially Stronger Than Local
  Reality inequalities

abstract:
  For an N-partite quantum system we show that separability implies
inequalities on Bell correlations which are stronger than the local reality
inequalities by a factor 2^{(N-1)/2}.


title:
Quantum interference and local field effects in a medium of V-type
  three-level atoms

abstract:
  We study the intrinsic optical bistability displayed by a small sample of
$V$-type three-level atoms induced by the near dipole-dipole interaction. The
use of the coherent state properties in the limit of the generalized
second-order Born approximation for BBGKY-hierarchy of equations for the
reduced density operators allows one to derive the operator describing the near
dipole-dipole interaction (local field correction) with interference terms
involving no additional assumptions. The dynamics of populations of the excited
states and the total spontaneous intensity are analysed as functions of the
external laser field strength allowing for the off-diagonal structure of the
local field and relaxation operators.


title: Cooperative quantum jumps for three dipole-interacting atoms

abstract:
  We investigate the effect of the dipole-dipole interaction on the quantum
jump statistics of three atoms. This is done for three-level systems in a V
configuration and in what may be called a D configuration. The transition rates
between the four different intensity periods are calculated in closed form.
Cooperative effects are shown to increase by a factor of 2 compared to two of
either three-level systems. This results in transition rates that are, for
distances of about one wavelength of the strong transition, up to 100% higher
than for independent systems. In addition the double and triple jump rates are
calculated from the transition rates. In this case cooperative effects of up to
170% for distances of about one wavelength and still up to 15% around 10
wavelengths are found. Nevertheless, for the parameters of an experiment with
Hg+ ions the effects are negligible, in agreement with the experimental data.
For three Ba+ ions this seems to indicate that the large cooperative effects
observed experimentally cannot be explained by the dipole-dipole interaction.


title:
Non-Markovian dynamics in a spin star system: Exact solution and
  approximation techniques

abstract:
  The reduced dynamics of a central spin coupled to a bath of N spin-1/2
particles arranged in a spin star configuration is investigated. The exact time
evolution of the reduced density operator is derived, and an analytical
solution is obtained in the limit of an infinite number of bath spins, where
the model shows complete relaxation and partial decoherence. It is demonstrated
that the dynamics of the central spin cannot be treated within the Born-Markov
approximation. The Nakajima-Zwanzig and the time-convolutionless projection
operator technique are applied to the spin star system. The performance of the
corresponding perturbation expansions of the non-Markovian equations of motion
is examined through a comparison with the exact solution.


title: In defense of the epistemic view of quantum states: a toy theory

abstract:
  We present a toy theory that is based on a simple principle: the number of
questions about the physical state of a system that are answered must always be
equal to the number that are unanswered in a state of maximal knowledge. A wide
variety of quantum phenomena are found to have analogues within this toy
theory. Such phenomena include: the noncommutativity of measurements,
interference, the multiplicity of convex decompositions of a mixed state, the
impossibility of discriminating nonorthogonal states, the impossibility of a
universal state inverter, the distinction between bi-partite and tri-partite
entanglement, the monogamy of pure entanglement, no cloning, no broadcasting,
remote steering, teleportation, dense coding, mutually unbiased bases, and many
others. The diversity and quality of these analogies is taken as evidence for
the view that quantum states are states of incomplete knowledge rather than
states of reality. A consideration of the phenomena that the toy theory fails
to reproduce, notably, violations of Bell inequalities and the existence of a
Kochen-Specker theorem, provides clues for how to proceed with this research
program.


title: Spectra of Quantized Walks and a $\sqrt{\delta\epsilon}$ rule

abstract:
  We introduce quantized bipartite walks, compute their spectra, generalize the
algorithms of Grover \cite{g} and Ambainis \cite{amb03} and interpret them as
quantum walks with memory. We compare the performance of walk based classical
and quantum algorithms and show that the latter run much quicker in general.
Let $P$ be a symmetric Markov chain with transition probabilities $P[i,j]$, $(i
,j\in [n])$. Some elements of the state space are marked. We are promised that
the set of marked elements has size either zero or at least $\epsilon n$. The
goal is to find out with great certainty which of the above two cases holds.
Our model is a black box that can answer certain yes/no questions and can
generate random elements picked from certain distributions. More specifically,
by request the black box can give us a uniformly distributed random element for
the cost of $\wp_{0}$. Also, when ``inserting'' an element $i$ into the black
box we can obtain a random element $j$, where $j$ is distributed according to
$P[i,j]$. The cost of the latter operation is $\wp_{1}$. Finally, we can use
the black box to test if an element $i$ is marked, and this costs us $\wp_{2}$.
If $\delta$ is the eigenvalue gap of $P$, there is a simple classical algorithm
with cost $O(\wp_{0} + (\wp_{1}+\wp_{2})/\delta\epsilon)$ that solves the above
promise problem. (The algorithm is efficient if $\wp_{0}$ is much larger than
$\wp_{1}+\wp_{2}$.) In contrast,we show that for the ``quantized'' version of
the algorithm it costs only $O(\wp_{0} +
(\wp_{1}+\wp_{2})/\sqrt{\delta\epsilon})$ to solve the problem. We refer to
this as the $\sqrt{\delta\epsilon}$ rule. Among the technical contributions we
give a formula for the spectrum of the product of two general reflections.


title: Teleportation of a two-particle entangled state via W class states

abstract:
  A scheme for teleporting an unknown two-particle entangled state via W class
states is proposed. In this scheme, the W class entangled states are considered
as quantum channels. It is shown that by means of optimal discrimination
between two nonorthogonal quantum states, probabilistic teleportation of the
two-particle entangled state can be achieved.


title:
Characterization and quantification of symmetric Gaussian state
  entanglement through a local classicality criterion

abstract:
  A necessary and sufficient condition for characterization and quantification
of entanglement of any bipartite Gaussian state belonging to a special symmetry
class is given in terms of classicality measures of one-party states. For
Gaussian states whose local covariance matrices have equal determinants it is
shown that separability of a two-party state and classicality of one party
state are completely equivalent to each other under a nonlocal operation,
allowing entanglement features to be understood in terms of any available
classicality measure.


title: On the P-representable subset of all bipartite Gaussian separable states

abstract:
  P-representability is a necessary and sufficient condition for separability
of bipartite Gaussian states only for the special subset of states whose
covariance matrix are $Sp(2,R)\otimes Sp(2,R)$ locally invariant. Although this
special class of states can be reached by a convenient $Sp(2,R)\otimes Sp(2,R)$
transformation over an arbitrary covariance matrix, it represents a loss of
generality, avoiding inference of many general aspects of separability of
bipartite Gaussian states.


title: Unconditionally Secure Quantum m-out-of-n Oblivious Transfer

abstract: This paper has been withdrawn.


title: Two-Qubits Entanglement Induced by a Faster Data Bus

abstract:
  We propose a theoretical protocol to create the entanglement of two qubits
via the Born-Oppenheimer (BO) approximation. In our scheme, each qubit is
coupled to a faster data bus whose frequency is much larger than the energy
spacing of the qubits and thus the BO approximation is valid. Then the
adiabatic separation of qubits from the data bus can induce an effective
potential to couple the two qubits, which can be utilized to create a quantum
logic gate. We also discuss the quantum decoherence caused by the adiabatic
entanglement between the two qubits and the external field.


title: A New Proof of The Strong Subadditivity Theorem

abstract:
  It is well known that the strong subadditivity theorem is hold for classical
system, but it is very difficult to prove that it is hold for quantum system.
The first proof of this theorem is due to Lieb by using the Lieb's theorem.
Here we use the conditions obtained in our previous work of matrix analysis
method to give a new proof of this famous theorem. This new proof is very
elementary, it only needs to carefully analyse the minimal value of a function.
This proof also shows that the conditions obtained in our previous work are
stronger than the strong subadditivity theorem.


title: Quantum and Classical Message Identification via Quantum Channels

abstract:
  We discuss concepts of message identification in the sense of Ahlswede and
Dueck via general quantum channels, extending investigations for classical
channels, initial work for classical-quantum (cq) channels and "quantum
fingerprinting".
  We show that the identification capacity of a discrete memoryless quantum
channel for classical information can be larger than that for transmission;
this is in contrast to all previously considered models, where it turns out to
equal the common randomness capacity (equals transmission capacity in our
case): in particular, for a noiseless qubit, we show the identification
capacity to be 2, while transmission and common randomness capacity are 1.
  Then we turn to a natural concept of identification of quantum messages (i.e.
a notion of "fingerprint" for quantum states). This is much closer to quantum
information transmission than its classical counterpart (for one thing, the
code length grows only exponentially, compared to double exponentially for
classical identification). Indeed, we show how the problem exhibits a nice
connection to visible quantum coding. Astonishingly, for the noiseless qubit
channel this capacity turns out to be 2: in other words, one can compress two
qubits into one and this is optimal. In general however, we conjecture quantum
identification capacity to be different from classical identification capacity.


title:
Frustration, interaction strength and ground-state entanglement in
  complex quantum systems

abstract:
  Entanglement in the ground state of a many-body quantum system may arise when
the local terms in the system Hamiltonian fail to commute with the interaction
terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy
between ground-state entanglement and the phenomenon of frustration in spin
systems. In particular, we prove that the amount of ground-state entanglement
is bounded above by a measure of the extent to which interactions frustrate the
local terms in the Hamiltonian. As a corollary, we show that the amount of
ground-state entanglement is bounded above by a ratio between parameters
characterizing the strength of interactions in the system, and the local energy
scale. Finally, we prove a qualitatively similar result for other energy
eigenstates of the system.


title: Is Quantum Mechanics An Island In Theoryspace?

abstract:
  This recreational paper investigates what happens if we change quantum
mechanics in several ways. The main results are as follows. First, if we
replace the 2-norm by some other p-norm, then there are no nontrivial
norm-preserving linear maps. Second, if we relax the demand that norm be
preserved, we end up with a theory that allows rapid solution of PP-complete
problems (as well as superluminal signalling). And third, if we restrict
amplitudes to be real, we run into a difficulty much simpler than the usual one
based on parameter-counting of mixed states.


title: Quantum Mechanics Unscrambled

abstract:
  Is quantum mechanics about 'states'? Or is it basically another kind of
probability theory? It is argued that the elementary formalism of quantum
mechanics operates as a well-justified alternative to 'classical'
instantiations of a probability calculus. Its providing a general framework for
prediction accounts for its distinctive traits, which one should be careful not
to mistake for reflections of any strange ontology. The suggestion is also made
that quantum theory unwittingly emerged, in Schroedinger's formulation, as a
'lossy' by-product of a quantum-mechanical variant of the Hamilton-Jacobi
equation. As it turns out, the effectiveness of quantum theory qua predictive
algorithm makes up for the computational impracticability of that master
equation.


title: PT symmetry of a conditionally exactly solvable potential

abstract:
  A conditionally exactly solvable potential, the supersymmetric partner of the
harmonic oscillator is investigated in the PT-symmetric setting. It is shown
that a number of properties characterizing shape-invariant and Natanzon-class
potentials generated by an imaginary coordinate shift $x-{\rm i}\epsilon$ also
hold for this potential outside the Natanzon class.


title:
General criterion for the entanglement of two indistinguishable
  particles

abstract:
  We relate the notion of entanglement for quantum systems composed of two
identical constituents to the impossibility of attributing a complete set of
properties to both particles. This implies definite constraints on the
mathematical form of the state vector associated with the whole system. We then
analyze separately the cases of fermion and boson systems, and we show how the
consideration of both the Slater-Schmidt number of the fermionic and bosonic
analog of the Schmidt decomposition of the global state vector and the von
Neumann entropy of the one-particle reduced density operators can supply us
with a consistent criterion for detecting entanglement. In particular, the
consideration of the von Neumann entropy is particularly useful in deciding
whether the correlations of the considered states are simply due to the
indistinguishability of the particles involved or are a genuine manifestation
of the entanglement. The treatment leads to a full clarification of the subtle
aspects of entanglement of two identical constituents which have been a source
of embarrassment and of serious misunderstandings in the recent literature.


title: Charge detection enables free-electron quantum computation

abstract:
  It is known that a quantum computer operating on electron-spin qubits with
single-electron Hamiltonians and assisted by single-spin measurements can be
simulated efficiently on a classical computer. We show that the exponential
speed-up of quantum algorithms is restored if single-charge measurements are
added. These enable the construction of a CNOT (controlled NOT) gate for free
fermions, using only beam splitters and spin rotations. The gate is nearly
deterministic if the charge detector counts the number of electrons in a mode,
and fully deterministic if it only measures the parity of that number.


title: Measuring polynomial functions of states

abstract:
  In this paper I show that any $m$th-degree polynomial function of the
elements of the density matrix $\rho$ can be determined by finding the
expectation value of an observable on $m$ copies of $\rho$, without performing
state tomography. Since a circuit exists which can approximate the measurement
of any observable, in principle one can find a circuit which will estimate any
such polynomial function by averaging over many runs. I construct some simple
examples and compare these results to existing procedures.


title: The Dirac Field in Real Domain

abstract:
  The Dirac field is analysed in real domain. A connection with the classical
field theory is shown and corresponding relation to the quantum physics.


title: On the Self-Interaction in Theory of Real Dirac Field

abstract:
  Reduction of the self-interaction in the theory of real Dirac field is
considered.


title: On the Quadratic Interaction Term in the Real Dirac Field Theory

abstract:
  Effects of the quadratic interaction term in the real Dirac field theory are
considered.


title: Quantum Computing in Arrays Coupled by 'Always On' Interactions

abstract:
  It has recently been shown that one can perform quantum computation in a
Heisenberg chain in which the interactions are 'always on', provided that one
can abruptly tune the Zeeman energies of the individual (pseudo-)spins. Here we
provide a more complete analysis of this scheme, including several
generalizations. We generalize the interaction to an anisotropic form
(incorporating the XY, or Forster, interaction as a limit), providing a proof
that a chain coupled in this fashion tends to an effective Ising chain in the
limit of far off-resonant spins. We derive the primitive two-qubit gate that
results from exploiting abrupt Zeeman tuning with such an interaction. We also
demonstrate, via numerical simulation, that the same basic scheme functions in
the case of smoothly shifted Zeeman energies. We conclude with some remarks
regarding generalisations to two- and three-dimensional arrays.


title: V\"axj\"o interpretation-2003: realism of contexts

abstract:
  We present a new variant of the V\"axj\"o interpretation: contextualistic
statistical realistic. Basic ideas of the V\"axj\"o interpretation-2001 are
essentially clarified. We also discuss applications to biology, psychology,
sociology, economy,...


title: A polynomial quantum query lower bound for the set equality problem

abstract:
  The set equality problem is to tell whether two sets $A$ and $B$ are equal or
disjoint under the promise that one of these is the case. This problem is
related to the Graph Isomorphism problem. It was an open problem to find any
$\omega(1)$ query lower bound when sets $A$ and $B$ are given by quantum
oracles. We will show that any error-bounded quantum query algorithm that
solves the set equality problem must evaluate oracles
$\Omega(\sqrt[5]{\frac{n}{\ln n}})$ times, where $n=|A|=|B|$.


title: Dynamical parameter estimation using realistic photodetection

abstract:
  We investigate the effect of imperfections in realistic detectors upon the
problem of quantum state and parameter estimation by continuous monitoring of
an open quantum system. Specifically, we have reexamined the system of a
two-level atom with an unknown Rabi frequency introduced by Gambetta and
Wiseman [Phys. Rev. A 64, 042105 (2001)]. We consider only direct
photodetection and use the realistic quantum trajectory theory reported by
Warszawski, Wiseman, and Mabuchi [Phys. Rev. A 65, 023802 (2002)]. The most
significant effect comes from a finite bandwidth, corresponding to an
uncertainty in the response time of the photodiode. Unless the bandwidth is
significantly greater than the Rabi frequency, the observer's ability to obtain
information about the unknown Rabi frequency, and about the state of the atom,
is severely compromised. This result has implications for quantum control in
the presence of unknown parameters for realistic detectors, and even for ideal
detectors, as it implies that most of the information in the measurement record
is contained in the precise timing of the detections.


title: Simulating causal collapse models

abstract:
  We present simulations of causal dynamical collapse models of field theories
on a 1+1 null lattice. We use our simulations to compare and contrast two
possible interpretations of the models, one in which the field values are real
and the other in which the state vector is real. We suggest that a procedure of
coarse graining and renormalising the fundamental field can overcome its
noisiness and argue that this coarse grained renormalised field will show
interesting structure if the state vector does on the coarse grained scale.


title: Quantum Networking

abstract:
  We first give a brief overview over quantum computing, quantum key
distribution (QKD), a practical architecture that integrates (QKD) in current
internet security architectures, and aspects of network security. We introduce
the concept of quantum contracts inspired from game theory. Finally, we
introduce the basic architecture of the quantum internet and present some
protocols.


title: Some Integrable Quantum Systems on the Lattice

abstract:
  The Weyl relations, the harmonic oscillator, the hydrogen atom, the Dirac
equation on the lattice are presented with the help of the difference equations
and the orthogonal polynomials of discrete variable. This area of research is
attracting more interest due to the lattice field theories and the hypothesis
of a finite space.


title: N-Partner Secure Direct Communication Based on Quantum Nonlocality

abstract:
  A multipartner secure direct communication protocol is presented, using
quantum nonlocality. Security of this protocol is based on `High fidelity
implies low entropy'. When the entanglement was successfully distributed,
anyone of the multipartner can send message secretly by using local operation
and reliable public channel. Since message transfered only by using local
operation and public channel after entanglement successfully distributed, so
this protocol can protect the communication against
destroying-travel-qubit-type attack.


title:
Local field effects and multimode stimulated light scattering in a
  two-level medium

abstract:
  Scattering of a short (much shorter then the spontaneous lifetime) laser
pulse has been considered in a dense resonant medium subject to local field
effects. The system was studied in the limit of Hartree-Fock approximation for
Bogolubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations for reduced
density operators. A closed set of equations for atomic and field density
operators was derived to describe stimulated scattering of radiation.
Numerically as well as theoretically the capability of multicomponent spectrum
with maximums multiple to Rabi frequency has been demonstrated. Relative line
intensities in the spectrum were found in the limit of low density.


title:
Improved storage of coherent and squeezed states in imperfect ring
  cavity

abstract:
  We propose a method of an improving quality of a ring cavity which is
imperfect due to non-unit mirror reflectivity. The method is based on using
squeezed states of light pulses illuminating the mirror and gradual homodyne
detection of a radiation escaping from the cavity followed by single
displacement and single squeezing operation performed on the released state. We
discuss contribution of this method in process of storing unknown coherent and
known squeezed state and generation of squeezing in the optical ring cavities.


title: Three and Four-Body Interactions in Spin-Based Quantum Computers

abstract:
  In the effort to design and to construct a quantum computer, several leading
proposals make use of spin-based qubits. These designs generally assume that
spins undergo pairwise interactions. We point out that, when several spins are
engaged mutually in pairwise interactions, the quantitative strengths of the
interactions can change and qualitatively new terms can arise in the
Hamiltonian, including four-body interactions. In parameter regimes of
experimental interest, these coherent effects are large enough to interfere
with computation, and may require new error correction or avoidance techniques.


title: Remarks on the Schrodinger equation

abstract:
  Various origins of linear and nonlinear Schrodinger equations are discussed
in connection with diffusion, hydrodynamics, and fractal structure. The
treatment is mainly expository, emphasizing the quantum potential, with a few
new observations.


title:
The quantum query complexity of the hidden subgroup problem is
  polynomial

abstract:
  We present a quantum algorithm which identifies with certainty a hidden
subgroup of an arbitrary finite group G in only a polynomial (in log |G|)
number of calls to the oracle. This is exponentially better than the best
classical algorithm. However our quantum algorithm requires exponential time,
as in the classical case. Our algorithm utilizes a new technique for
constructing error-free algorithms for non-decision problems on quantum
computers.


title: Pulse-driven quantum dynamics beyond the impulsive regime

abstract:
  We review various unitary time-dependent perturbation theories and compare
them formally and numerically. We show that the Kolmogorov-Arnold-Moser
technique performs better owing to both the superexponential character of
correction terms and the possibility to optimize the accuracy of a given level
of approximation which is explored in details here. As an illustration, we
consider a two-level system driven by short pulses beyond the sudden limit.


title: Time Reversal and Exceptional Points

abstract:
  Eigenvectors of decaying quantum systems are studied at exceptional points of
the Hamiltonian. Special attention is paid to the properties of the system
under time reversal symmetry breaking. At the exceptional point the chiral
character of the system -- found for time reversal symmetry -- generically
persists. It is, however, no longer circular but rather elliptic.


title: Gravitational self-localization in quantum measurement

abstract:
  Within Newton-Schr\"odinger quantum mechanics which allows gravitational
self-interaction, it is shown that a no-split no-collapse measurement scenario
is possible. A macroscopic pointer moves at low acceleration, controlled by the
Ehrenfest-averaged force acting on it. That makes classicality self-sustaining,
resolves Everett's paradox, and outlines a way to spontaneous emergence of
quantum randomness. Numerical estimates indicate that enhanced short-range
gravitational forces are needed for the scenario to work. The scheme fails to
explain quantum nonlocality, including two-detector anticorrelations, which
points towards the need of a nonlocal modification of the Newton-Schr\"odinger
coupling scheme.


title:
Continuous vs. discrete models for the quantum harmonic oscillator and
  the hydrogen atom

abstract:
  The Kravchuk and Meixner polynomials of discrete variable are introduced for
the discrete models of the harmonic oscillator and hydrogen atom. Starting from
Rodrigues formula we construct raising and lowering operators, commutation and
anticommutation relations. The physical properties of discrete models are
figured out through the equivalence with the continuous models obtained by
limit process.


title:
Two photon absorption and coherent control with broadband down-converted
  light

abstract:
  We experimentally demonstrate two-photon absorption (TPA) with broadband
down-converted light (squeezed vacuum). Although incoherent and exhibiting the
statistics of a thermal noise, broadband down-converted light can induce TPA
with the same sharp temporal behavior as femtosecond pulses, while exhibiting
the high spectral resolution of the narrowband pump laser. Using pulse-shaping
methods, we coherently control TPA in Rubidium, demonstrating spectral and
temporal resolutions that are 3-5 orders of magnitude below the actual
bandwidth and temporal duration of the light itself. Such properties can be
exploited in various applications such as spread-spectrum optical
communications, tomography and nonlinear microscopy.


title:
Optical conductivity of small adiabatic polarons with a long-range
  electron-phonon interaction

abstract:
  The hopping of an electron, interacting with many ions of a lattice via the
long-range (Fr\"{o}hlich) electron-phonon interaction and optical absorption
are studied at zero temperature. Ions are assumed to be isotropic
three-dimensional oscillators. The optical conductivity and a renormalized mass
of small adiabatic Fr\"{o}hlich polarons is calculated and compared with those
of small adiabatic Holstein polarons.


title: Braiding Operators are Universal Quantum Gates

abstract:
  This paper explores of the role of unitary braiding operators in quantum
computing. We show that a single specific solution R (the Bell basis change
matrix) of the Yang-Baxter Equation is a universal gate for quantum computing,
in the presence of local unitary transformations. We show that this same R
generates a new non-trivial invariant of braids, knots, and links. Other
solutions of the Yang-Baxter Equation are also shown to be universal for
quantum computation. The paper discusses these results in the context of
comparing quantum and topological points of view. In particular, we discuss
quantum computation of link invariants, the relationship between quantum
entanglement and topological entanglement, teleportation, and the structure of
braiding in a topological quantum field theory.


title: Quantum query complexity of some graph problems

abstract:
  Quantum algorithms for graph problems are considered, both in the adjacency
matrix model and in an adjacency list-like array model. We give almost tight
lower and upper bounds for the bounded error quantum query complexity of
Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source
Shortest Paths. For example we show that the query complexity of Minimum
Spanning Tree is in Theta(n^{3/2}) in the matrix model and in Theta(sqrt{nm})
in the array model, while the complexity of Connectivity is also in
Theta(n^{3/2}) in the matrix model, but in Theta(n) in the array model. The
upper bounds utilize search procedures for finding minima of functions under
various conditions.


title: Darboux transformations of the Jaynes-Cummings Hamiltonian

abstract:
  A detailed analysis of matrix Darboux transformations under the condition
that the derivative of the superpotential be self-adjoint is given. As a
onsequence, a class of the symmetries associated to Schr\"odinger matrix
Hamiltonians is characterized. The applications are oriented towards the
Jaynes-Cummings eigenvalue problem, so that exactly solvable $2\times 2$ matrix
Hamiltonians of the Jaynes-Cummings type are obtained. It is also established
that the Jaynes-Cummings Hamiltonian is a quadratic function of a Dirac-type
Hamiltonian.


title:
Darboux transformations of coherent states of the time-dependent
  singular oscillator

abstract:
  Darboux transformation of both Barut-Girardello and Perelomov coherent states
for the time-dependent singular oscillator is studied. In both cases the
measure that realizes the resolution of the identity operator in terms of
coherent states is found and corresponding holomorphic representation is
constructed. For the particular case of a free particle moving with a fixed
value of the angular momentum equal to two it is shown that Barut-Giriardello
coherent states are more localized at the initial time moment while the
Perelomov coherent states are more stable with respect to time evolution. It is
also illustrated that Darboux transformation may keep unchanged this different
time behavior.


title: Dissipative Quantum Control

abstract:
  Nature, in the form of dissipation, inevitably intervenes in our efforts to
control a quantum system. In this talk we show that although we cannot, in
general, compensate for dissipation by coherent control of the system, such
effects are not always counterproductive; for example, the transformation from
a thermal (mixed) state to a cold condensed (pure state) can only be achieved
by non-unitary effects such as population and phase relaxation.


title:
On Peres' statement "opposite momenta lead to opposite directions",
  decaying systems and optical imaging

abstract:
  We re-examine Peres' statement ``opposite momenta lead to opposite
directions''. It will be shown that Peres' statement is only valid in the large
distance or large time limit. In the short distance or short time limit an
additional deviation from perfect alignment occurs due to the uncertainty of
the location of the source. This error contribution plays a major role in
Popper's orginal experimental proposal. Peres' statement applies rather to the
phenomenon of optical imaging, which was regarded by him as a verification of
his statement. This is because this experiment can in a certain sense be seen
as occurring in the large distance limit. We will also reconsider both
experiments from the viewpoint of Bohmian mechanics. In Bohmian mechanics
particles with exactly opposite momenta will move in opposite directions. In
addition it will prove particularly usefull to use Bohmian mechanics because
the Bohmian trajectories coincide with the conceptual trajectories drawn by
Pittman et al. In this way Bohmian mechanics provides a theoretical basis for
these conceptual trajectories.


title:
Frames of Reference and the Intrinsic Directional Information of a
  Particle With Spin

abstract:
  "Information is physical", and here we consider the physical directional
information of a particle with spin. We ask whether, in the presence of a
classical frame of reference, such a particle contains any intrinsic
directional information, ie. information above that which can be transmitted by
a classical bit. We show that when sending a large number of spins, the answer
is asymptotically "no". For finite numbers of spins, N, we do not know the
answer. We also show that any frame of reference which we can consider to be
classical must use some resource which is exponentially large in N. This gives
a quantitative meaning to the idea that classical objects are big.


title: Complex collective states in a one-dimensional two-atom system

abstract:
  We consider a pair of identical two-level atoms interacting with a scalar
field in one dimension, separated by a distance $x_{21}$. We restrict our
attention to states where one atom is excited and the other is in the ground
state, in symmetric or anti-symmetric combinations. We obtain exact collective
decaying states, belonging to a complex spectral representation of the
Hamiltonian. The imaginary parts of the eigenvalues give the decay rates, and
the real parts give the average energy of the collective states. In one
dimension there is strong interference between the fields emitted by the atoms,
leading to long-range cooperative effects. The decay rates and the energy
oscillate with the distance $x_{21}$. Depending on $x_{21}$, the decay rates
will either decrease, vanish or increase as compared with the one-atom decay
rate. We have sub- and super-radiance at periodic intervals. Our model may be
used to study two-cavity electron wave-guides. The vanishing of the collective
decay rates then suggests the possibility of obtaining stable configurations,
where an electron is trapped inside the two cavities.


title: Lorentz Group in Ray Optics

abstract:
  It has been almost one hundred years since Einstein formulated his special
theory of relativity in 1905. He showed that the basic space-time symmetry is
dictated by the Lorentz group. It is shown that this group of Lorentz
transformations is not only applicable to special relativity, but also
constitutes the scientific language for optical sciences. It is noted that
coherent and squeezed states of light are representations of the Lorentz group.
The Lorentz group is also the basic underlying language for classical ray
optics, including polarization optics, interferometers, the Poincare\'e sphere,
one-lens optics, multi-lens optics, laser cavities, as well multilayer optics.


title: Quantum logic gates using Stark shifted Raman transitions in a cavity

abstract:
  We present a scheme to realise the basic two-quibit logic gates such as
quantum phase gate and controlle-NOT gate using a detuned optical cavity
interacting with a three-level Raman system. We discuss the role of Stark
shifts which are as important as the terms leading to two-photon transition.
The operation of the proposed logic gates involves metastable states of the
atom and hence is not affected by spontaneous emission. These ideas can be
extended to produce multiparticle entanglement.


title: Measured Quantum Fourier Transform of 1024 Qubits on Fiber Optics

abstract:
  Quantum Fourier transform (QFT) is a key function to realize quantum
computers. A QFT followed by measurement was demonstrated on a simple circuit
based on fiber-optics. The QFT was shown to be robust against imperfections in
the rotation gate. Error probability was estimated to be 0.01 per qubit, which
corresponded to error-free operation on 100 qubits. The error probability can
be further reduced by taking the majority of the accumulated results. The
reduction of error probability resulted in a successful QFT demonstration on
1024 qubits.


title:
Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy
  Threshold for a Toric Quantum Memory

abstract:
  We study the phase structure of the random-plaquette Z_2 lattice gauge model
in three dimensions. In this model, the "gauge coupling" for each plaquette is
a quenched random variable that takes the value \beta with the probability 1-p
and -\beta with the probability p. This model is relevant for the recently
proposed quantum memory of toric code. The parameter p is the concentration of
the plaquettes with "wrong-sign" couplings -\beta, and interpreted as the error
probability per qubit in quantum code. In the gauge system with p=0, i.e., with
the uniform gauge couplings \beta, it is known that there exists a second-order
phase transition at a certain critical "temperature", T(\equiv \beta^{-1}) =
T_c =1.31, which separates an ordered(Higgs) phase at T<T_c and a
disordered(confinement) phase at T>T_c. As p increases, the critical
temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects
with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The
value p_c is just the accuracy threshold for a fault-tolerant quantum memory
and associated quantum computations. By the Monte-Carlo simulations, we
calculate the specific heat and the expectation values of the Wilson loop to
obtain the phase-transition line T_c(p) numerically. The accuracy threshold is
estimated as p_c \simeq 0.033.


title: Effective quantum spin systems with ion traps

abstract:
  We show that the physical system consisting of trapped ions interacting with
lasers may undergo a rich variety of quantum phase transitions. By changing the
laser intensities and polarizations the dynamics of the internal states of the
ions can be controlled, in such a way that an Ising or Heisenberg-like
interaction is induced between effective spins. Our scheme allows us to build
an analogue quantum simulator of spin systems with trapped ions, and observe
and analyze quantum phase transitions with unprecedent opportunities for the
measurement and manipulation of spins.


title:
Strength functions, entropies and duality in weakly to strongly
  interacting fermionic systems

abstract:
  We revisit statistical wavefunction properties of finite systems of
interacting fermions in the light of strength functions and their participation
ratio and information entropy. For weakly interacting fermions in a mean-field
with random two-body interactions of increasing strength $\lambda$, the
strength functions $F_k(E)$ are well known to change, in the regime where level
fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We
propose an ansatz for the function describing this transition which we use to
investigate the participation ratio $\xi_2$ and the information entropy $S^{\rm
info}$ during this crossover, thereby extending the known behavior valid in the
Gaussian domain into much of the Breit-Wigner domain. Our method also allows us
to derive the scaling law for the duality point $\lambda = \lambda_d$, where
$F_k(E)$, $\xi_2$ and $S^{\rm info}$ in both the weak ($\lambda=0$) and strong
mixing ($\lambda = \infty$) basis coincide as $\lambda_d \sim 1/\sqrt{m}$,
where $m$ is the number of fermions. As an application, the ansatz function for
strength functions is used in describing the Breit-Wigner to Gaussian
transition seen in neutral atoms CeI to SmI with valence electrons changing
from 4 to 8.


title: Poincare group operators with 4-vector position

abstract:
  We present a new set of massless Poincar\'e group operators Hermitian with
respect to the $ 1 / r $ inner product space, which have quasi-plane wave
energy-momentum eigenfunctions having velocity $ c $ along their axis of
propagation. These are constructed by means of a unitary transformation from a
known set of massless Poincar\'e group operators of helicity $ s = 0, \pm {1
\over 2}, \pm 1 ... $ The position vector $ {\bf r} $ is the space part of a
null 4-vector.


title: Possibilities for a Causal Interpretation for Quantum Mechanics

abstract:
  The basic physical problems that necessitated the emergence of quantum
physics are summarized, along with the elements of wave mechanics and its
traditional statistical interpretation. Alternative interpretations to the
statistical one, such as the hydrodynamical and optical interpretations,
nonlinear waves and nonlinear electrodynamics, and the conception of spacetime
as an ordered medium are reviewed.


title:
Three-spin interactions in optical lattices and criticality in cluster
  Hamiltonians

abstract:
  We demonstrate that in a triangular configuration of an optical lattice of
two atomic species a variety of novel spin-1/2 Hamiltonians can be generated.
They include effective three-spin interactions resulting from the possibility
of atoms tunneling along two different paths. This motivates the study of
ground state properties of various three-spin Hamiltonians in terms of their
two-point and n-point correlations as well as the localizable entanglement. We
present a Hamiltonian with a finite energy gap above its unique ground state
for which the localizable entanglement length diverges for a wide interval of
applied external fields, while at the same time the classical correlation
length remains finite.


title: Suppression of Spin Projection Noise in Broadband Atomic Magnetometry

abstract:
  Our 2005 Physical Review Letter entitled "Suppression of Spin-Projection
Noise in Broadband Atomic Magnetometry" (volume 94, 203002) relied heavily in
its claims of experimental quantum-limited performance on the results of a
prior publication from our group [1]. In subsequent work we have determined
that the results of [1] were incorrect and must therefore retract this Physical
Review Letter as well. The authors would like to emphasize that the broadband
magnetometry approach taken in our work remains valid, as described in the
theoretical paper [2], but we have lost confidence in the calibration
procedures employed at the time to establish sensitivity relative to the
spin-projection noise level.
  [1] JM Geremia, John K. Stockton and Hideo Mabuchi, "Real-Time Quantum
Feedback Control of Atomic Spin-Squeezing," Science 304, 270, (2004).
  [2] John K. Stockton, JM Geremia, Andrew C. Doherty and Hideo Mabuchi,
"Robust quantum parameter estimation: Coherent magnetometry with feedback,"
Phys. Rev. A 69, 032109, (2004).


title: Linear Positivity and Virtual Probability

abstract:
  We investigate the quantum theory of closed systems based on the linear
positivity decoherence condition of Goldstein and Page. A quantum theory of
closed systems requires two elements; 1) a condition specifying which sets of
histories may be assigned probabilities that are consistent with the rules of
probability theory, and 2) a rule for those probabilities. The linear
positivity condition of Goldstein and Page is the weakest of the general
conditions proposed so far. Its general properties relating to exact
probability sum rules, time-neutrality, and conservation laws are explored. Its
inconsistency with the usual notion of independent subsystems in quantum
mechanics is reviewed. Its relation to the stronger condition of medium
decoherence necessary for classicality is discussed. The linear positivity of
histories in a number of simple model systems is investigated with the aim of
exhibiting linearly positive sets of histories that are not decoherent. The
utility of extending the notion of probability to include values outside the
range of 0 to 1 is described. Alternatives with such virtual probabilities
cannot be measured or recorded, but can be used in the intermediate steps of
calculating real probabilities. Virtual probabilities give a simple and general
way of formulating quantum theory.


title:
One-Photon and Two-Photon Double-Slit Interferences in Spontaneous and
  Stimulated Parametric Down-Conversions

abstract:
  We theoretically discuss one-photon and two-photon double-slit interferences
for spontaneous and stimulated parametric down-conversions. We show that the
two-photon sub-wavelength interference can exist in a general spontaneous
parametric down-conversion (SPDC) for both type I and type II crystals. We
propose an alternative way to observe sub-wavelength interference by a
joint-intensity measurement which occurs for only type I crystal in a higher
gain of SPDC. When a signal beam injects into the crystal, it may create two
interference patterns by two stimulated down-converted beams, showing no
sub-wavelength interference effect.


title: A stochastic limit approach to the SAT problem

abstract:
  We propose a new approach to solve an NP complete problem by means of
stochastic limit.


title: Steady state of atoms in a resonant field with elliptical polarization

abstract:
  We present a complete set of analytical and invariant expressions for the
steady-state density matrix of atoms in a resonant radiation field with
arbitrary intensity and polarization. The field drives the closed dipole
transition with arbitrary values of the angular momenta $J_{g}$ and $J_{e}$ of
the ground and excited state. The steady-state density matrix is expressed in
terms of spherical harmonics of a complex direction given by the field
polarization vector. The generalization to the case of broad-band radiation is
given. We indicate various applications of these results.


title:
Proposed direct test of a certain type of noncontextuality in quantum
  mechanics

abstract:
  The noncontextuality of quantum mechanics can be directly tested by measuring
two entangled particles with more than two outcomes per particle. The two
associated contexts are "interlinked" by common observables.


title: Noncontextuality in multipartite entanglement

abstract:
  We discuss several multiport interferometric preparation and measurement
configurations and show that they are noncontextual. Generalizations to the n
particle case are discussed.


title:
Instrumental processes, entropies, information in quantum continual
  measurements

abstract:
  In this paper we will give a short presentation of the quantum Levy-Khinchin
formula and of the formulation of quantum continual measurements based on
stochastic differential equations, matters which we had the pleasure to work on
in collaboration with Prof. Holevo. Then we will begin the study of various
entropies and relative entropies, which seem to be promising quantities for
measuring the information content of the continual measurement under
consideration and for analysing its asymptotic behaviour.


title:
Quantum effects in the evolution of vortices in the electromagnetic
  field

abstract:
  We analyze the influence of electron-positron pairs creation on the motion of
vortex lines in electromagnetic field. In our approach the electric and
magnetic fields satisfy nonlinear equations derived from the Euler-Heisenberg
effective Lagrangian. We show that these nonlinearities may change the
evolution of vortices.


title:
Long Range Interactions in Quantum Many Body Problem in
  One-Dimension:Ground State

abstract:
  We investigate the ground state properties of a family of $N$-body systems in
1-dimension, trapped in a polynomial potential and having long range 2-body
interaction in addition to the inverse square potential studied in the
Calogero-Sutherland model (CSM). We show that for such a Hamiltonian, the
ground state energy is similar to that of free fermions in a harmonic well with
a displacement that depends on the number of particles and depth of the well.
We obtain the ground state wave function and using random matrix results, study
the particle density and pair correlation function (PCF). We observe that the
particles are arranged in bands. Due to the presence of long range interaction,
the PCF shows a departure from the CSM.


title: Towards the understanding of Decoherence on Ion Traps

abstract:
  Two mechanisms of decoherence in ion traps are studied, specially related to
the experiment [Kielpinski et al., Science 291 (2001) 1013]. Statistical
hypothesis are made about the unknown variables and the expected behaviour of
the visibility of the best experimental pattern is calculated for each
mechanism. Data from the experiment are analyzed and show to be insufficient to
distinguish between them. We suggest improvements which can do this with slight
modifications in the present facilities.


title: Simplifying Schmidt number witnesses via higher-dimensional embeddings

abstract:
  We apply the generalised concept of witness operators to arbitrary convex
sets, and review the criteria for the optimisation of these general witnesses.
We then define an embedding of state vectors and operators into a
higher-dimensional Hilbert space. This embedding leads to a connection between
any Schmidt number witness in the original Hilbert space and a witness for
Schmidt number two (i.e. the most general entanglement witness) in the
appropriate enlarged Hilbert space. Using this relation we arrive at a
conceptually simple method for the construction of Schmidt number witnesses in
bipartite systems.


title: On duality between quantum maps and quantum states

abstract:
  We investigate the space of quantum operations, as well as the larger space
of maps which are positive, but not completely positive. A constructive
criterion for decomposability is presented. A certain class of unistochastic
operations, determined by unitary matrices of extended dimensionality, is
defined and analyzed. Using the concept of the dynamical matrix and the
Jamiolkowski isomorphism we explore the relation between the set of quantum
operations (dynamics) and the set of density matrices acting on an extended
Hilbert space (kinematics). An analogous relation is established between the
classical maps and an extended space of the discrete probability distributions.


title: Are N=1 and N=2 supersymmetric quantum mechanics equivalent?

abstract:
  After recalling different formulations of the definition of supersymmetric
quantum mechanics given in the literature, we discuss the relationships between
them in order to provide an answer to the question raised in the title.


title: Quantum entanglement, interaction, and the classical limit

abstract:
  Two or more quantum systems are said to be in an entangled or
non-factorisable state if their joint (supposedly pure) wave-function is not
expressible as a product of individual wave functions but is instead a
superposition of product states. It is only when the systems are in a
factorisable state that they can be considered to be separated (in the sense of
Bell). We show that whenever two quantum systems interact with each other, it
is impossible that all factorisable states remain factorisable during the
interaction unless the full Hamiltonian does not couple these systems so to say
unless they do not really interact. We also present certain conditions under
which particular factorisable states remain factorisable although they
represent a bipartite system whose components mutually interact. We identify
certain quasi-classical regimes that satisfy these conditions and show that
they correspond to classical, pre-quantum, paradigms associated to the concept
of particle.


title: Hardy's nonlocality for generalized n-particle GHZ states

abstract:
  In this paper we extend Hardy's nonlocality proof for two spin-1/2 particles
[PRL 71 (1993) 1665] to the case of n spin-1/2 particles configured in the
generalized GHZ state. We show that, for all n \geq 3, any entangled GHZ state
violates the Bell inequality associated with the Hardy experiment. This feature
is important since it has been shown [PRL 88 (2002) 210402] that, for all n
odd, there are entangled GHZ states that do not violate any standard n-particle
correlation Bell inequality.


title: Introduction to Quantum Cellular Automata

abstract: We provide an introduction to Quantum Cellular Automata.


title: Quantum Artificial Intelligence

abstract:
  This report introduces researchers in AI to some of the concepts in quantum
heurisitics and quantum AI.


title: A two species trap for chromium and rubidium atoms

abstract:
  We realize a combined trap for bosonic chromium 52Cr and rubidium 87Rb atoms.
First experiments focus on exploring a suitable loading scheme for the combined
trap and on studies of new trap loss mechanisms originating from simultaneous
trapping of two species. By comparing the trap loss from the 87Rb
magneto-optical trap (MOT) in absence and presence of magnetically trapped
ground state 52Cr atoms we determine the scattering cross section of
sigma_{inelRbCr}=(5.0+-4.0)*10^{-18}m^2 for light induced inelastic collisions
between the two species. Studying the trap loss from the Rb magneto-optical
trap induced by the Cr cooling-laser light, the photoionization cross section
of the excited 5P_{3/2} state at an ionizing wavelength of 426nm is measured to
be sigma_{p}=(1.1+-0.3)*10^{-21}m^2.


title: One-parameter groups and combinatorial physics

abstract:
  In this communication, we consider the normal ordering of sums of elements of
the form (a*^r a a*^s), where a* and a are boson creation and annihilation
operators. We discuss the integration of the associated one-parameter groups
and their combinatorial by-products. In particular, we show how these groups
can be realized as groups of substitutions with prefunctions.


title: Quantum computing in neural networks

abstract:
  According to the statistical interpretation of quantum theory, quantum
computers form a distinguished class of probabilistic machines (PMs) by
encoding n qubits in 2n pbits (random binary variables). This raises the
possibility of a large-scale quantum computing using PMs, especially with
neural networks which have the innate capability for probabilistic information
processing. Restricting ourselves to a particular model, we construct and
numerically examine the performance of neural circuits implementing universal
quantum gates. A discussion on the physiological plausibility of proposed
coding scheme is also provided.


title: Entanglement criterion for pure $M\otimes N$ bipartite quantum states

abstract:
  We propose a entanglement measure for pure $M \otimes N$ bipartite quantum
states. We obtain the measure by generalizing the equivalent measure for a $2
\otimes 2$ system, via a $2 \otimes 3$ system, to the general bipartite case.
The measure emphasizes the role Bell states have, both for forming the measure,
and for experimentally measuring the entanglement. The form of the measure is
similar to generalized concurrence. In the case of $2 \otimes 3$ systems, we
prove that our measure, that is directly measurable, equals the concurrence. It
is also shown that in order to measure the entanglement, it is sufficient to
measure the projections of the state onto a maximum of $M(M-1)N(N-1)/2$ Bell
states.


title: Entanglement measure for general pure multipartite quantum states

abstract:
  We propose an explicit formula for an entanglement measure of pure
multipartite quantum states, then study a general pure tripartite state in
detail, and at end we give some simple but illustrative examples on four-qubits
and m-qubits states.


title: Stability of atomic clocks based on entangled atoms

abstract:
  We analyze the effect of realistic noise sources for an atomic clock
consisting of a local oscillator that is actively locked to a spin-squeezed
(entangled) ensemble of $N$ atoms. We show that the use of entangled states can
lead to an improvement of the long-term stability of the clock when the
measurement is limited by decoherence associated with instability of the local
oscillator combined with fluctuations in the atomic ensemble's Bloch vector.
Atomic states with a moderate degree of entanglement yield the maximal clock
stability, resulting in an improvement that scales as $N^{1/6}$ compared to the
atomic shot noise level.


title: Probability representation entropy for spin-state tomogram

abstract:
  Probability representation entropy (tomographic entropy) of arbitrary quantum
state is introduced. Using the properties of spin tomogram to be standard
probability distribution function the tomographic entropy notion is discussed.
Relation of the tomographic entropy to Shannon entropy and von Neumann entropy
is elucidated.