title: Exclusion of correlation in the theorem of Bell

abstract:
  Several fatal defects in recent defenses of Bell's theorem are identified. It
is shown again that ``proofs'' of the existence of non-locality are not valid
because they inadvertently exclude all correlation. A fully classical
simulation of EPR correlations, based on using Malus' Law for both photocurrent
generation and for the ``coincidence circuitry,'' is described.


title: Information theoretic aspects in ponderomotive systems

abstract:
  We show the possibility to entangle radiation modes through a simple
reflection on a moving mirror. The model of an optical cavity having a movable
end mirror, and supporting different modes is employed. The mechanical motion
of the mirror mediates information between the modes leading to an effective
mode-mode interaction. We characterize the modes' entanglement on the basis of
recent separability criteria. The effect of the thermal noise associate to the
mirror's motion is accounted for. Then, we evaluate the performances of such
{\it ponderomotive entanglement} in possible applications like teleportation
and telecloning.


title: Storing and releasing light in a gas of moving atoms

abstract:
  We propose a scheme of storing and releasing pulses or cw beams of light in a
moving atomic medium illuminated by two stationary and spatially separated
control lasers. The method is based on electromagnetically induced transparency
(EIT) but in contrast to previous schemes, storage and retrieval of the probe
pulse can be achieved at different locations and without switching off the
control laser.


title: No limit on the energy extracted from a Dirac quantum state

abstract:
  When a Dirac quantum state interacts with an applied electric field the
energy of the quantum state changes. It is generally assumed that there is a
maximum limit on the amount of energy that can be extracted from a Dirac
quantum state, due to its interaction with an electric field. In this article
it is shown that this assumption is not correct and that, for a properly
applied electric field, an arbitrarily large amount of energy can be extracted
from the quantum state.


title: Role of many-body entanglement in decoherence processes

abstract:
  A pure state decoheres into a mixed state as it entangles with an
environment. When an entangled two-mode system is embedded in a thermal
environment, however, each mode may not be entangled with its environment by
their simple linear interaction. We consider an exactly solvable model to study
the dynamics of a total system, which is composed of an entangled two-mode
system and a thermal environment, and also an array of infinite beam splitters.
It is shown that many-body entanglement of the system and the environment plays
a crucial role in the process of disentangling the system.


title:
Sub-wavelength resolution of optical fields probed by single trapped
  ions: Interference, phase modulation, and which-way information

abstract:
  Taking recent experiments as examples, we discuss the conditions for
sub-wavelength probing of optical field structures by single trapped atoms. We
calculate the achievable resolution, highlighting its connection to the fringe
visibility in an interference experiment. We show that seemingly different
physical pictures, such as spatial averaging, phase modulation, and which-way
information, describe the situation equally and lead to identical results. The
connection to Bohr's moving slit experiment is pointed out.


title: Quasi-deterministic generation of entangled atoms in a cavity

abstract:
  We present a scheme to generate a maximally entangled state of two
three-level atoms in a cavity. The success or failure of the generation of the
desired entangled state can be determined by detecting the polarization of the
photon leaking out of the cavity. With the use of an automatic feedback, the
success probability of the scheme can be made to approach unity.


title:
Ultrafast geometric manipulation of electron spin and detection of the
  geometric phase via Faraday rotation spectroscopy

abstract:
  Time-resolved Faraday rotation spectroscopy is currently exploited as a
powerful technique to probe spin dynamics in semiconductors. We propose here an
all-optical approach to geometrically manipulate electron spin and to detect
the geometric phase by this type of extremely sensitive experiment. The global
nature of the geometric phase can make the quantum manipulation more stable,
which may find interesting application in quantum devices.


title:
Control of Decoherence: Dynamical Decoupling versus Quantum Zeno Effect
  - a case study for trapped ions

abstract:
  The control of thermal decoherence via dynamical decoupling and via the
quantum Zeno effect (Zeno control) is investigated for a model of trapped ion,
where the dynamics of two low lying hyperfine states undergoes decoherence due
to the thermal interaction with an excited state. Dynamical decoupling is a
procedure that consists in periodically driving the excited state, while the
Zeno control consists in frequently measuring it. When the control frequency is
high enough, decoherence is shown to be suppressed. Otherwise, both controls
may accelerate decoherence.


title: Integrable Lattice Systems and Markov Processes

abstract:
  Lattice systems with certain Lie algebraic or quantum Lie algebraic
symmetries are constructed. These symmetric models give rise to series of
integrable systems. As examples the $A_n$-symmetric chain models and the
SU(2)-invariant ladder models are investigated. It is shown that corresponding
to these $A_n$-symmetric chain models and SU(2)-invariant ladder models there
are exactly solvable stationary discrete-time (resp. continuous-time) Markov
chains with transition matrices (resp. intensity matrices) having spectra which
coincide with the ones of the corresponding integrable models.


title: Quantum And Classical Dynamics Of Atoms In A Magneto-optical Lattice

abstract:
  The transport of ultra-cold atoms in magneto-optical potentials provides a
clean setting in which to investigate the distinct predictions of classical
versus quantum dynamics for a system with coupled degrees of freedom. In this
system, entanglement at the quantum level and chaos at the classical level
arise from the coupling between the atomic spin and its center-of- mass motion.
Experiments, performed deep in the quantum regime, correspond to dynamic
quantum tunneling. This nonclassical behavior is contrasted with the
predictions for an initial phase space distribution produced in the experiment,
but undergoing classical Hamiltonian flow. We study conditions under which the
trapped atoms can be made to exhibit classical dynamics through the process of
continuous measurement, which localizes the probability distribution to phase
space trajectories, consistent with the uncertainty principle and quantum
back-action noise. This method allows us to analytically and numerically
identify the quantum-classical boundary.


title:
Experimental demonstration of tripartite entanglement and controlled
  dense coding for continuous variables

abstract:
  A tripartite entangled state of bright optical field is experimentally
produced using an Einstein-Podolsky-Rosen entangled state for continuous
variables and linear optics. The controlled dense coding among a sender, a
receiver and a controller is demonstrated by exploiting the tripartite
entanglement. The obtained three-mode position correlation and relative
momentum correlation between the sender and the receiver and thus the
improvements of the measured signal to noise ratios of amplitude and phase
signals with respect to the shot noise limit are 3.28dB and 3.18dB
respectively. If the mean photon number $\bar{n}$ equals 11 the channel
capacity can be controllably inverted between 2.91 and 3.14. When $\bar{n}$ is
larger than 1.0 and 10.52 the channel capacities of the controlled dense coding
exceed the ideal single channel capacities of coherent and squeezed state light
communication.


title:
A dressing of zero-range potentials and electron-molecule scattering
  problem at low energies

abstract:
  A dressing of a nonspherical potential, which includes $n$ zero range
potentials, is considered. The dressing technique is used to improve ZRP model.
Concepts of the partial waves and partial phases for non-spherical potential
are used in order to perform Darboux transformation. The problem of scattering
on the regular $\hbox{X}_n$ and $\hbox{YX}_n$ structures is studied. The
possibilities of dressed ZRP are illustrated by model calculation of the
low-energy electron-Silane ($\hbox{SiH}_4$) scattering. The results are
discussed. Key words: multiple scattering, silane, zero range potential.


title:
Experimental detection of entanglement via witness operators and local
  measurements

abstract:
  In this paper we address the problem of detection of entanglement using only
few local measurements when some knowledge about the state is given. The idea
is based on an optimized decomposition of witness operators into local
operators. We discuss two possible ways of optimizing this local decomposition.
We present several analytical results and estimates for optimized detection
strategies for NPT states of 2x2 and NxM systems, entangled states in 3 qubit
systems, and bound entangled states in 3x3 and 2x4 systems.


title: Semiclassical wave packet tunneling in real-time

abstract:
  Quantum mechanical real-time tunneling through general scattering potentials
is studied in the semiclassical limit. It is shown that the exact path integral
of the real-time propagator is dominated in the long time sector by
quasi-stationary fluctuations associated with caustics. This leads to an
extended semiclassical propagation scheme for wave packet dynamics which
accurately describes deep tunneling through static and, for the first time,
driven barrier potentials.


title:
Entanglement generation and Hamiltonian simulation in
  Continuous-Variable Systems

abstract:
  Several recent experiments have demonstrated the promise of atomic ensembles
for quantum teleportation and quantum memory. In these cases the collective
internal state of the atoms is well described by continuous variables $X_1,
P_1$ and the interaction with the optical field ($X_2, P_2$) by a quadratic
Hamiltonian $X_1X_2$. We show how this interaction can be used optimally to
create entanglement and squeezing. We derive conditions for the efficient
simulation of quadratic Hamiltonians and the engineering of all Gaussian
operations and states.


title: Separability criterion for separate quantum systems

abstract:
  Entanglement, or quantum inseparability, is a crucial resource in quantum
information applications, and therefore the experimental generation of
separated yet entangled systems is of paramount importance. Experimental
demonstrations of inseparability with light are not uncommon, but such
demonstrations in physically well-separated massive systems, such as distinct
gases of atoms, are new and present significant challenges and opportunities.
Rigorous theoretical criteria are needed for demonstrating that given data are
sufficient to confirm entanglement. Such criteria for experimental data have
been derived for the case of continuous-variable systems obeying the
Heisenberg-Weyl (position- momentum) commutator. To address the question of
experimental verification more generally, we develop a sufficiency criterion
for arbitrary states of two arbitrary systems. When applied to the recent study
by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 - 403 (2001)] of spin-state
entanglement of two separate, macroscopic samples of atoms, our new criterion
confirms the presence of spin entanglement.


title:
Generation of Entangled N-Photon States in a Two-Mode Jaynes-Cummings
  Model

abstract:
  We describe a mathematical solution for the generation of entangled N-photon
states in two field modes. A simple and compact solution is presented for a
two-mode Jaynes-Cummings model by combining the two field modes in a way that
only one of the two resulting quasi-modes enters in the interaction term. The
formalism developed is then applied to calculate various generation
probabilities analytically. We show that entanglement, starting from an initial
field and an atom in one defined state may be obtained in a single step. We
also show that entanglement may be built up in the case of an empty cavity and
excited atoms whose final states are detected, as well as in the case when the
final states of the initially excited atoms are not detected.


title:
Local distinguishability of quantum states and the distillation of
  entanglement

abstract:
  This paper tries to probe the relation between the local distinguishability
of orthogonal quantum states and the distillation of entanglement. An new
interpretation for the distillation of entanglement and the distinguishability
of orthogonal quantum states in terms of information is given, respectively. By
constraining our discussion on a special protocol we give a necessary and
sufficient condition for the local distinguishability of the orthogonal pure
states, and gain the maximal yield of the distillable entanglement. It is shown
that the information entropy, the locally distinguishability of quantum states
and the distillation of entanglement are closely related.


title:
On Hamilton-Jacobi theory: its geometry and relation to pilot-wave
  theory

abstract:
  This paper gives a technically elementary treatment of some aspects of
Hamilton-Jacobi theory, especially in relation to the calculus of variations.
The second half of the paper describes the application to geometric optics, the
optico-mechanical analogy and the transition to quantum mechanics. Finally, I
report recent work of Holland providing a Hamiltonian formulation of the
pilot-wave theory.


title: A Continuous Variable Shor Algorithm

abstract:
  In this paper, we use the methods found in quant-ph/0201095 to create a
continuous variable analogue of Shor's quantum factoring algorithm. By this we
mean a quantum hidden subgroup algorithm that finds the period P of a function
F:R-->R from the reals R to the reals R, where F belongs to a very general
class of functions, called the class of admissible functions.
  One objective in creating this continuous variable quantum algorithm was to
make the structure of Shor's factoring algorithm more mathematically
transparent, and thereby give some insight into the inner workings of Shor's
original algorithm. This continuous quantum algorithm also gives some insight
into the inner workings of Hallgren's Pell's equation algorithm. Two key
questions remain unanswered. Is this quantum algorithm more efficient than its
classical continuous variable counterpart? Is this quantum algorithm or some
approximation of it implementable?


title:
Quantum diffraction and interference of spatially correlated photon
  pairs generated by spontaneous parametric down-conversion

abstract:
  We demonstrate one- and two-photon diffraction and interference experiments
utilizing parametric down-converted photon pairs (biphotons) and a transmission
grating. With two-photon detection, the biphoton exhibits a
diffraction-interference pattern equivalent to that of an effective single
particle that is associated with half the wavelength of the constituent
photons. With one-photon detection, however no diffraction-interference pattern
is observed. We show that these phenomena originate from the spatial quantum
correlation between the down-converted photons.


title:
Existence of superposition solutions for pulse propagation in nonlinear
  resonant media

abstract:
  Existence of self-similar, superposed pulse-train solutions of the nonlinear,
coupled Maxwell-Schr\"odinger equations, with the frequencies controlled by the
oscillator strengths of the transitions, is established. Some of these
excitations are specific to the resonant media, with energy levels in the
configurations of $\Lambda$ and $N$ and arise because of the interference
effects of cnoidal waves, as evidenced from some recently discovered identities
involving the Jacobian elliptic functions. Interestingly, these excitations
also admit a dual interpretation as single pulse-trains, with widely different
amplitudes, which can lead to substantially different field intensities and
population densities in different atomic levels.


title:
Effects of nonlocality in time of interactions of an atom with its
  surroundings on the broadening of spectral lines of atoms

abstract:
  We investigate effects of nonlocality in time of the interaction of an atom
with its surroundings on the spectral line broadening. We show that these
effects can be very significant: In some cases nonlocality in time of this
interaction can give rise to a spectral line splitting.


title: The Hess-Philipp Model is Non-local

abstract:
  Hess and Philipp have constructed what, they claim, is a local hidden
variables model reproducing the empirical predictions of quantum mechanics. In
this paper explicit expressions for the conditional probabilities for the
outcomes of the measurements at the two detectors are calculated. These
expressions provide a conclusive demonstration of the falsity of the authors'
claim. The authors give two different accounts of their model. The published
version omits a crucial detail. As a result it disagrees with quantum
mechanics. It also violates signal locality. The unpublished version agrees
with quantum mechanics. However, it violates the condition of parameter
independence, as Myrvold has previously shown.


title: Quantum inference of states and processes

abstract:
  The maximum-likelihood principle unifies inference of quantum states and
processes from experimental noisy data. Particularly, a generic quantum process
may be estimated simultaneously with unknown quantum probe states provided that
measurements on probe and transformed probe states are available. Drawbacks of
various approximate treatments are considered.


title:
Experimental investigation of pulsed entangled photons and photonic
  quantum channels

abstract:
  The development of key devices and systems in quantum information technology,
such as entangled particle sources, quantum gates and quantum cryptographic
systems, requires a reliable and well-established method for characterizing how
well the devices or systems work. We report our recent work on experimental
characterization of pulsed entangled photonic states and photonic quantum
channels, using the methods of state and process tomography. By using state
tomography, we could reliably evaluate the states generated from a two-photon
source under development and develop a highly entangled pulsed photon source.
We are also devoted to characterization of single-qubit and two-qubit photonic
quantum channels. Characterization of typical single-qubit decoherence channels
has been demonstrated using process tomography. Characterization of two-qubit
channels, such as classically correlated channels and quantum mechanically
correlated channels is under investigation. These characterization techniques
for quantum states and quantum processes will be useful for developing photonic
quantum devices and for improving their performances.


title:
The information-theoretical viewpoint on the physical complexity of
  classical and quantum objects and their dynamical evolution

abstract:
  Charles Bennett's measure of physical complexity for classical objects,
namely logical-depth, is used in order to prove that a chaotic classical
dynamical system is not physical complex. The natural measure of physical
complexity for quantum objects, quantum logical-depth, is then introduced in
order to prove that a chaotic quantum dynamical system is not physical complex
too.


title: Conditional Density Matrix: Systems and Subsystems in Quantum Mechanics

abstract:
  A new quantum mechanical notion -- Conditional Density Matrix -- is discussed
and is applied to describe some physical processes. This notion is a natural
generalization of von Neumann density matrix for such processes as divisions of
quantum systems into subsystems and reunifications of subsystems into new joint
systems. Conditional Density Matrix assigns a quantum state to a subsystem of a
composite system under condition that another part of the composite system is
in some pure state.


title: The "Chaotic Ball" model,local realism and the Bell test loopholes

abstract:
  It has long been known that the "detection loophole", present when detector
efficiencies are below a critical figure, could open the way for alternative
"local realist" explanations for the violation of Bell tests. It has in recent
years become common to assume the loophole can be ignored, regardless of which
version of the Bell test is employed. A simple model is presented that
illustrates that this may not be justified. Two of the versions -- the standard
test of form -2 <= S <= 2 and the currently-popular "visibility" test -- are at
grave risk of bias. Statements implying that experimental evidence "refutes
local realism" or shows that the quantum world really is "weird" should be
reviewed. The detection loophole is on its own unlikely to account for more
than one or two test violations, but when taken in conjunction with other
loopholes (briefly discussed) it is seen that the experiments refute only a
narrow class of "local hidden variable" models, applicable to idealised
situations, not to the real world. The full class of local realist models
provides straightforward explanations not only for the publicised Bell-test
violations but also for some lesser-known "anomalies".


title:
Born--Infeld theory of electroweak and gravitational fields: Possible
  correction to Newton and Coulomb laws

abstract:
  In this note one suggests a possibility of direct observation of the
$\theta$-parameter, introduced in the Born--Infeld theory of electroweak and
gravitational fields, developed in quant-ph/0202024. Namely, one may treat
$\theta$ as a universal constant, responsible for correction to the Coulomb and
Newton laws, allowing direct interaction between electrical charges and masses.


title:
On the interpretation of quantum theory - from Copenhagen to the present
  day

abstract:
  A central feature in the Copenhagen interpretation is the use of classical
concepts from the outset. Modern developments show, however, that the emergence
of classical properties can be understood within the framework of quantum
theory itself, through the process of decoherence. This fact becomes most
crucial for the interpretability of quantum cosmology - the application of
quantum theory to the Universe as a whole. I briefly review these developments
and emphasize the importance of an unbiased attitude on the interpretational
side for future progress in physics.


title: Family of analytic entanglement monotones

abstract:
  We derive a family of entanglement monotones, one member of which turns out
to be the negativity. Two others are shown to be lower bounds on the
I-concurrence, and on the I-tangle, respectively [P. Rungta and C. M. Caves, to
appear in Phys. Rev. A]. We compare these bounds with the I-concurrence and
I-tangle on the isotropic states, and on rank-two density operators resulting
from a Tavis-Cummings interaction. Our results provide a global structure
relating several different entanglement measures. Additionally, they possess
analytic forms which are easily evaluated in the most general cases.


title: Quantum Computing of Quantum Chaos in the Kicked Rotator Model

abstract:
  We investigate a quantum algorithm which simulates efficiently the quantum
kicked rotator model, a system which displays rich physical properties, and
enables to study problems of quantum chaos, atomic physics and localization of
electrons in solids. The effects of errors in gate operations are tested on
this algorithm in numerical simulations with up to 20 qubits. In this way
various physical quantities are investigated. Some of them, such as second
moment of probability distribution and tunneling transitions through invariant
curves are shown to be particularly sensitive to errors. However,
investigations of the fidelity and Wigner and Husimi distributions show that
these physical quantities are robust in presence of imperfections. This implies
that the algorithm can simulate the dynamics of quantum chaos in presence of a
moderate amount of noise.


title: Characterizing the entanglement of bipartite quantum systems

abstract:
  We derive a separability criterion for bipartite quantum systems which
generalizes the already known criteria. It is based on observables having
generic commutation relations. We then discuss in detail the relation among
these criteria.


title: Entangling power and operator entanglement in qudit systems

abstract:
  We establish the entangling power of a unitary operator on a general
finite-dimensional bipartite quantum system with and without ancillas, and give
relations between the entangling power based on the von Neumann entropy and the
entangling power based on the linear entropy. Significantly, we demonstrate
that the entangling power of a general controlled unitary operator acting on
two equal-dimensional qudits is proportional to the corresponding operator
entanglement if linear entropy is adopted as the quantity representing the
degree of entanglement. We discuss the entangling power and operator
entanglement of three representative quantum gates on qudits: the SUM, double
SUM, and SWAP gates.


title: Quantum Computing with an 'Always On' Heisenberg Interaction

abstract:
  Many promising ideas for quantum computing demand the experimental ability to
directly switch 'on' and 'off' a physical coupling between the component
qubits. This is typically the key difficulty in implementation, and precludes
quantum computation in generic solid state systems, where interactions between
the constituents are 'always on'. Here we show that quantum computation is
possible in strongly coupled (Heisenberg) systems even when the interaction
cannot be controlled. The modest ability of 'tuning' the transition energies of
individual qubits proves to be sufficient, with a suitable encoding of the
logical qubits, to generate universal quantum gates. Furthermore, by tuning the
qubits collectively we provide a scheme with exceptional experimental
simplicity: computations are controlled via a single 'switch' of only six
settings. Our schemes are applicable to a wide range of physical
implementations, from excitons and spins in quantum dots through to bulk
magnets.


title:
The Possibilities of the Quantum Memory Realization for Short Pulses of
  Light in the Photon Echo Technique

abstract:
  The possibilities of recording, storage and reconstruction of short single
photon wave packets in the photon echo technique are analyzed. The influence of
the photon field and medium parameters on the quality and precision of the
photon quantum state reconstruction is theoretically studied.


title:
Coherent processing of a light pulse stored in a medium of four-level
  atoms

abstract:
  It is demonstrated that the properties of light stored in a four-level atomic
system can be modified by an additional control interaction present during the
storage stage. By choosing the pulse area of this interaction one can in
particular continuously switch between two channels into which light is
released.


title: A conditional quantum phase gate between two 3-state atoms

abstract:
  We propose a scheme for conditional quantum logic between two 3-state atoms
that share a quantum data-bus such as a single mode optical field in cavity QED
systems, or a collective vibrational state of trapped ions. Making use of
quantum interference, our scheme achieves successful conditional phase
evolution without any real transitions of atomic internal states or populating
the quantum data-bus. In addition, it only requires common addressing of the
two atoms by external laser fields.


title: Quantum Walks driven by many coins

abstract:
  Quantum random walks have been much studied recently, largely due to their
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum random walk on the line: the use of
multiple quantum ``coins'' in order to diminish the effects of interference
between paths. We find solutions to this system in terms of the single coin
random walk, and compare the asymptotic limit of these solutions to numerical
simulations. We find exact analytical expressions for the time-dependence of
the first two moments, and show that in the long time limit the ``quantum
mechanical'' behavior of the one-coin walk persists. We further show that this
is generic for a very broad class of possible walks, and that this behavior
disappears only in the limit of a new coin for every step of the walk.


title:
Reversible entanglement in a Kerr-like interaction Hamiltonian: an
  integrable model

abstract:
  An exactly soluble non-linear interaction Hamiltonian is proposed to study
fundamental properties of the entanglement dynamics for a coupled non-linear
oscillators. The time-evolved state is obtained analytically for initial
products of two coherent and two number states and relevant informations are
extracted from the dynamics of various quantities like subsystem linear and Von
Neumann entropies, quadrature mean values, variances and Q-functions. We
determined the re-coherence time scales and found among the interaction terms
present in the Hamiltonian the one responsible for the entanglement in both
cases. We identify the existence of two regimens for the entanglement dynamics
in the case of initially coherent states: the short time, phase spread regimen
where the entropy rises monotonically and the self-interference regimen where
the entropy oscillates and re-coherence phenomenon can be observed. We also
found that the break time from the first regimen to the second one becomes
longer, as well as the re-coherence and reversibility times, as the Planck's
constant becomes much smaller than a typical action in phase space.


title:
Mean of continuous variables observable {\it via} measurement on single
  qubit

abstract:
  It is shown that mean value of any observable with bounded spectrum can be
uniquely determined from binary statistics of the measurement performed on {\it
single} qubit ancilla coupled to a given system. The observable structure is
fully encoded in the corresponding POVM. The method is generalised to the case
of distant labs paradigm and discussed in the context of entanglement detection
with few local measurements. The results are also discussed in the context of
quantum programming.


title:
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert
  Space

abstract:
  Classical mechanics is formulated in complex Hilbert space with the
introduction of a commutative product of operators, an antisymmetric bracket,
and a quasidensity operator. These are analogues of the star product, the Moyal
bracket, and the Wigner function in the phase space formulation of quantum
mechanics. Classical mechanics can now be viewed as a deformation of quantum
mechanics. The forms of semiquantum approximations to classical mechanics are
indicated.


title: Semiconductor-cavity QED in high-Q regimes: Detuning effect

abstract:
  The non-resonant interaction between the high-density excitons in a quantum
well and a single mode cavity field is investigated. An analytical expression
for the physical spectrum of the excitons is obtained. The spectral properties
of the excitons, which are initially prepared in the number states or the
superposed states of the two different number states by the resonant
femtosecond pulse pumping experiment, are studied. Numerical study of the
physical spectrum is carried out and a discussion of the detuning effect is
presented.


title:
N-Level System Interacting with Single Radiation Mode and Multi Cat
  States of Schrodinger in the Strong Coupling Regime

abstract:
  In this paper we consider some (generalized) models which deal with n--level
atom interacting with a single radiation mode and study a general structure of
Rabi floppings of these generalized ones in the strong coupling regime.
  To solve these models we introduce multi cat states of Schr{\" o}dinger in
our terminology and extend the result in (quant--ph/0203135) which Rabi
frequencies are given by matrix elements of generalized coherent operators
(quant--ph/0202081) under the rotating--wave approximation. Our work is a full
generalization of Frasca (quant--ph/0111134) and Fujii (quant--ph/0203135).
  In last we make a brief comment on an application to Quantum Computation on
the space of qudits.


title: The Rigged Hilbert Space of the Free Hamiltonian

abstract:
  We explicitly construct the Rigged Hilbert Space (RHS) of the free
Hamiltonian $H_0$. The construction of the RHS of $H_0$ provides yet another
opportunity to see that when continuous spectrum is present, the solutions of
the Schrodinger equation lie in a RHS rather than just in a Hilbert space.


title: A note on separability criteria for multipartite state

abstract:
  The recent proposed realignment separability criterion for mixed is analyzed.
We identify the essential part of this criterion is a swap operator followed by
a partial transposition. Then we analyze the separability criterion of
permutation indices of the density matrix for multipartite state which is a
generalization of the realignment criterion. We give a method to solve the
equivalence problem of the separability criterion of permutation indices of the
density matrix. For tripartite state, we show the non-trivial separability
criteria are either partial transposition criterion or realignment criterion.


title: Additivity of entanglement of formation for some special cases

abstract:
  The proof of additivity of entanglement of formation for some special cases
is given. The strong concavity of von Neumann entropy due to strong
subadditivity of von Neumann entropy is presented. Some general relations
concerning about the entanglement of formation are proposed.


title: Entangled Photons from Small Quantum Dots

abstract:
  We discuss level schemes of small quantum-dot turnstiles and their
applicability in the production of entanglement in two-photon emission. Due to
the large energy splitting of the single-electron levels, only one single
electron level and one single hole level can be made resonant with the levels
in the conduction band and valence band. This results in a model with nine
distinct levels, which are split by the Coulomb interactions. We show that the
optical selection rules are different for flat and tall cylindrically symmetric
dots, and how this affects the quality of the entanglement generated in the
decay of the biexciton state. The effect of charge carrier tunneling and of a
resonant cavity is included in the model.


title: Bound Modes in Dielectric Microcavities

abstract:
  We demonstrate how exactly bound cavity modes can be realized in dielectric
structures other than 3d photonic crystals. For a microcavity consisting of
crossed anisotropic layers, we derive the cavity resonance frequencies, and
spontaneous emission rates. For a dielectric structure with dissipative loss
and central layer with gain, the beta factor of direct spontaneous emission
into a cavity mode and the laser threshold is calculated.


title: Upper Bounds for the Number of Quantum Clones under Decoherence

abstract:
  Universal quantum cloning machines (UQCMs), sometimes called quantum cloners,
generate many outputs with identical density matrices, with as close a
resemblance to the input state as is allowed by the basic principles of quantum
mechanics. Any experimental realization of a quantum cloner has to cope with
the effects of decoherence which terminate the coherent evolution demanded by a
UQCM. We examine how many clones can be generated within a decoherence time. We
compare the time that a quantum cloner implemented with trapped ions requires
to produce $M$ copies from $N$ identical pure state inputs and the decoherence
time during which the probability of spontaneous emission becomes
non-negligible. We find a method to construct an $N\to M$ cloning circuit, and
estimate the number of elementary logic gates required. It turns out that our
circuit is highly vulnerable to spontaneous emission as the number of gates in
the circuit is exponential with respect to the number of qubits involved.


title: Casimir effect and vacuum energy

abstract:
  Vacuum fluctuations have observable consequences, like the Casimir force
appearing between two mirrors in vacuum. This force is now measured with good
accuracy and agreement with theory. We discuss the meaning and consequences of
these statements by emphasizing their relation with the problem of vacuum
energy, one of the main unsolved problems at the interface between
gravitational and quantum theory.


title: The Casimir force and the quantum theory of lossy optical cavities

abstract:
  We present a new derivation of the Casimir force between two parallel plane
mirrors at zero temperature. The two mirrors and the cavity they enclose are
treated as quantum optical networks. They are in general lossy and
characterized by frequency dependent reflection amplitudes. The additional
fluctuations accompanying losses are deduced from expressions of the optical
theorem. A general proof is given for the theorem relating the spectral density
inside the cavity to the reflection amplitudes seen by the inner fields. This
density determines the vacuum radiation pressure and, therefore, the Casimir
force. The force is obtained as an integral over the real frequencies,
including the contribution of evanescent waves besides that of ordinary waves,
and, then, as an integral over imaginary frequencies. The demonstration relies
only on general properties obeyed by real mirrors which also enforce general
constraints for the variation of the Casimir force.


title:
Geometric phase shift in quantum computation using superconducting
  nanocircuits: nonadiabatic effects

abstract:
  The nonadiabatic geometric quantum computation may be achieved using coupled
low-capacitance Josephson juctions. We show that the nonadiabtic effects as
well as the adiabatic condition are very important for these systems. Moreover,
we find that it may be hard to detect the adiabatic Berry's phase in this kind
of superconducting nanocircuits; but the nonadiabatic phase may be measurable
with current techniques. Our results may provide useful information for the
implementation of geometric quantum computation.


title: Quantum Pattern Recognition

abstract:
  I review and expand the model of quantum associative memory that I have
recently proposed. In this model binary patterns of n bits are stored in the
quantum superposition of the appropriate subset of the computational basis of n
qbits. Information can be retrieved by performing an input-dependent rotation
of the memory quantum state within this subset and measuring the resulting
state. The amplitudes of this rotated memory state are peaked on those stored
patterns which are closest in Hamming distance to the input, resulting in a
high probability of measuring a memory pattern very similar to it. The accuracy
of pattern recall can be tuned by adjusting a parameter playing the role of an
effective temperature. This model solves the well-known capacity shortage
problem of classical associative memories, providing an exponential improvement
in capacity. The price to pay is the probabilistic nature of information
retrieval, a feature that, however, this model shares with our own brain.

categories: quant-ph cond-mat.dis-nn cs.IR nlin.AO q-bio.NC


title:
Generating Fock states and two-Fock states superposition from circular
  states, in a trapped ion

abstract:
  We propose three schemes to engineer 2^M and M+1 circular states for the
motion of the center of mass of a trapped ion, $M$ being the number of laser
pulses. Since the ion is subjected to several laser pulses, we analyze the
necessary duration of each one for generating the circular states, and from
these, the Fock states and superposition of two-Fock states. We also calculate
the probability for obtaining the required states.


title: quantum interference in bosonic and fermionic matter-wave amplification

abstract:
  We investigate the quantum interference effects in two types of matter-wave
mixing experiments: one with initial matter waves prepared in independent Fock
states (type I) and the other with each individual particle prepared in a same
coherent superposition of states (type II). In the type I experiment, a
symmetric wavefunction of bosons leads to constructive quantum interference and
shows final state stimulation, while an anti-symmetric wavefunction of fermions
results in destructive quantum interference and inhibited matter wave mixing.
In the type II experiment, a coherent superposition state leads to constructive
quantum interference and enhanced matter wave mixing for both bosons and
fermions, independent of their quantum statistics.


title:
Distinguishing two-qubit states using local measurements and restricted
  classical communication

abstract:
  The problem of unambiguous state discrimination consists of determining which
of a set of known quantum states a particular system is in. One is allowed to
fail, but not to make a mistake. The optimal procedure is the one with the
lowest failure probability. This procedure has been extended to bipartite
states where the two parties, Alice and Bob, are allowed to manipulate their
particles locally and communicate classically in order to determine which of
two possible two-particle states they have been given. The failure probability
of this local procedure has been shown to be the same as if the particles were
together in the same location. Here we examine the effect of restricting the
classical communication between the parties, either allowing none or
eliminating the possibility that one party's measurement depends on the result
of the other party's. These issues are studied for two-qubit states, and
optimal procedures are found. In some cases the restrictions cause increases in
the failure probability, but in other cases they do not. Applications of these
procedures, in particular to secret sharing, are discussed.


title: Quantum random walks with decoherent coins

abstract:
  The quantum random walk has been much studied recently, largely due to its
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum walk on the line: the presence of
decoherence in the quantum ``coin'' which drives the walk. We find exact
analytical expressions for the time dependence of the first two moments of
position, and show that in the long-time limit the variance grows linearly with
time, unlike the unitary walk. We compare this to the results of direct
numerical simulation, and see how the form of the position distribution changes
from the unitary to the usual classical result as we increase the strength of
the decoherence.


title: Quantum Statistics and Entanglement Problems

abstract:
  Interpretations of quantum measurement theory have been plagued by two
questions, one concerning the role of observer consciousness and the other the
entanglement phenomenon arising from the superposition of quantum states. We
emphasize here the remarkable role of quantum statistics in describing the
entanglement problem correctly and discuss the relationship to issues arising
from current discussions of intelligent observers in entangled, decohering
quantum worlds.


title:
The quantum mechanical geometric phase of a particle in a resonant
  vibrating cavity

abstract:
  We study the general-setting quantum geometric phase acquired by a particle
in a vibrating cavity. Solving the two-level theory with the rotating-wave
approximation and the SU(2) method, we obtain analytic formulae that give
excellent descriptions of the geometric phase, energy, and wavefunction of the
resonating system. In particular, we observe a sudden $\pi$-jump in the
geometric phase when the system is in resonance. We found similar behaviors in
the geometric phase of a spin-1/2 particle in a rotating magnetic field, for
which we developed a geometrical model to help visualize its evolution.


title:
Fixed point theorem for simple quantum strategies in quantum market
  games

abstract:
  A simple but nontrivial class of the quantum strategies in buying-selling
games is presented. The player moves are a rational buying and an unconditional
selling. The possibility of gaining extremal profits in such the games is
considered. The entangled merchants hypothesis is proposed.


title: Classical and Quantum Problems for Quanputers

abstract:
  Quantum computers are considered as a part of the family of the reversible,
lineary-extended, dynamical systems (Quanputers). For classical problems an
operational reformulation is given. A universal algorithm for the solving of
classical and quantum problems on quanputers is formulated.


title: Quantum coherence, correlated noise and Parrondo games

abstract:
  We discuss the effect of correlated noise on the robustness of quantum
coherent phenomena. First we consider a simple, toy model to illustrate the
effect of such correlations on the decoherence process. Then we show how
decoherence rates can be suppressed using a Parrondo-like effect. Finally, we
report the results of many-body calculations in which an
experimentally-measurable quantum coherence phenomenon is significantly
enhanced by non-Markovian dynamics arising from the noise source.


title: Quantum information processing: The case of vanishing interaction energy

abstract:
  We investigate the rate of operation of quantum "black boxes" ("oracles") and
point out the possibility of performing an operation by a quantum "oracle"
whose average energy equals zero. This counterintuitive result not only
presents a generalization of the recent results of Margolus and Levitin, but
might also sharpen the conceptual distinction between the "classical" and the
"quantum" information.


title: A 2 rebit gate universal for quantum computing

abstract:
  We show, within the circuit model, how any quantum computation can be
efficiently performed using states with only real amplitudes (a result known
within the Quantum Turing Machine model). This allows us to identify a 2-qubit
(in fact 2-rebit) gate which is universal for quantum computing, although it
cannot be used to perform arbitrary unitary transformations.


title: Continuous Variables (2,3) Threshold Quantum Secret Sharing Schemes

abstract:
  We present two experimental schemes to perform continuous variable (2,3)
threshold quantum secret sharing on the quadratures amplitudes of bright light
beams. Both schemes require a pair of entangled light beams. The first scheme
utilizes two phase sensitive optical amplifiers, whilst the second uses an
electro-optic feedforward loop for the reconstruction of the secret. We examine
the efficacy of quantum secret sharing in terms of fidelity, as well as the
signal transfer coefficients and the conditional variances of the reconstructed
output state. We show that both schemes in the ideal case yield perfect secret
reconstruction.


title: Quasi-spin wave quantum memories with dynamic symmetry

abstract:
  For the two-mode exciton system formed by the quasi-spin wave collective
excitation of many $\Lambda$ atoms fixed at the lattice sites of a crystal, we
discover a dynamic symmetry depicted by the semi-direct product algebra
$SU(2)\bar{\otimes} h_2 $ in the large $N$ limit with low excitations. With the
help of the spectral generating algebra method, we obtain a larger class of
exact zero-eigenvalue states adiabatically interpolating between the initial
state of photon-type and the final state of quasi-spin wave exciton-type. The
conditions for the adiabatic passage of dark states are shown to be valid, even
with the presence of the level degeneracy. These theoretical results can lead
to propose new protocol of implementing quantum memory robust against quantum
decoherence.


title: Measurement and Physical Content of Quantum Information

abstract:
  Basic quantum information measures involved in the information analysis of
quantum systems are considered. It is shown that the main quantum information
measurement methods depend on whether the corresponding quantum events are
compatible or incompatible. For purely quantum channels, the coherent and
compatible information measures, which are qualitatively different, can be
distinguished. A general information scheme is proposed for a quantum-physical
experiment. In this scheme, informational optimization of an experimental setup
is formulated as a mathematical problem.


title:
Physical Interpretation of the Mathematical Consequence of Lorentz'
  Transformations

abstract:
  A physical interpretation of the mathematical consequence of Lorentz
transformation within spatial relativity theory is presented as a result of my
new physical model of existent fluctuating vacuum (FlcVcm). It is assumed that
the FlcVcm is considered as a molecular dielectric, which consists from neutral
dynamides, streamlined in a close-packed crystalline lattice. Every dynamide is
a neutral pair, consistent by two massless opposite point-like elementary
electric charges (ElmElcChrgs): electrino (-) and positrino (+). In a frozen
equilibrium position two contrary pont-like ElmElcChrgs within every one
dynamide are very closely installed one to another and therefore the aggregate
polarization of every dynamide and its electric field also have zero values.
The aggregate electric field of every dynamide polarizes nearest neighbors
dynamides in an account of which nearest dynamides interact between them-self,
because of which their elementary excitations, phonons and photons, have a wave
character and behaviors. We suppose that the photon is an polarization result
of the phonon within the fluctuating vacuum considered as an ideal dielectric
and therefore the photon could be considered as an elementary collective
excitation of the FlcVcm in the form of a solitary needle cylindrical harmonic
oscillation. Hence the light, which is a packet of the photons, must move
within FlcVcm with constant velocity and Dopler effect must be observed in both
cases, for the light and sound. Then all mathematical results of Lorentz
transformation could be considered as results of a demand of an independence of
the observation results from the reactive velocity of the observation frame.


title: Non-Cooperative Quantum Game Theory

abstract:
  The physical world obeys the rules of quantum, as opposed to classical,
physics. Since the playing of any particular game requires physical resources,
the question arises as to how Game Theory itself would change if it were
extended into the quantum domain. Here we provide a general formalism for {\em
quantum} games, and illustrate the explicit application of this new formalism
to a quantized version of the well-known prisoner's dilemma game.


title:
From a Mechanical Lagrangian to the Schr\"odinger Equation. A Modified
  Version of the Quantum Newton's Law

abstract:
  In the one-dimensional stationary case, we construct a mechanical Lagrangian
describing the quantum motion of a non-relativistic spinless system. This
Lagrangian is written as a difference between a function $T$, which represents
the quantum generalization of the kinetic energy and which depends on the
coordinate $x$ and the temporal derivatives of $x$ up the third order, and the
classical potential $V(x)$. The Hamiltonian is then constructed and the
corresponding canonical equations are deduced. The function $T$ is first
assumed arbitrary. The development of $T$ in a power series together with the
dimensional analysis allow us to fix univocally the series coefficients by
requiring that the well-known quantum stationary Hamilton-Jacobi equation be
reproduced. As a consequence of this approach, we formulate the law of the
quantum motion representing a new version of the quantum Newton's law. We also
analytically establish the famous Bohm's relation % $\mu \dot{x} = \partial S_0
/\partial x $ % outside of the framework of the hydrodynamical approach and
show that the well-known quantum potential, although it is a part of the
kinetic term, it plays really a role of an additional potential as assumed by
Bohm.


title:
Information Security and Quantum Mechanics: Security of Quantum
  Protocols

abstract:
  The problem of security of quantum key protocols is examined. In addition to
the distribution of classical keys, the problem of encrypting quantum data and
the structure of the operators which perform quantum encryption is studied. It
is found that unitary bases are central to both encryption of quantum
information, as well as the generation of states used in generalized quantum
key distribution (which are called mutually unbiased bases). A one-to-one
correspondence between certain unitary bases and mutually unbiased bases is
found. Finally, a new protocol for making anonymous classical broadcasts is
given along with a security proof. An experimental procedure to implement this
protocol is also given. In order to prove these new results, some new bounds
for accessible information of quantum sources are obtained.


title:
Complex Probabilities on R^N as Real Probabilities on C^N and an
  Application to Path Integrals

abstract:
  We establish a necessary and sufficient condition for averages over complex
valued weight functions on R^N to be represented as statistical averages over
real, non-negative probability weights on C^N. Using this result, we show that
many path-integrals for time-ordered expectation values of bosonic degrees of
freedom in real-valued time can be expressed as statistical averages over
ensembles of paths with complex-valued coordinates, and then speculate on
possible consequences of this result for the relation between quantum and
classical mechanics.


title: Universal quantum information compression and degrees of prior knowledge

abstract:
  We describe a universal information compression scheme that compresses any
pure quantum i.i.d. source asymptotically to its von Neumann entropy, with no
prior knowledge of the structure of the source. We introduce a diagonalisation
procedure that enables any classical compression algorithm to be utilised in a
quantum context. Our scheme is then based on the corresponding quantum
translation of the classical Lempel-Ziv algorithm. Our methods lead to a
conceptually simple way of estimating the entropy of a source in terms of the
measurement of an associated length parameter while maintaining high fidelity
for long blocks. As a by-product we also estimate the eigenbasis of the source.
Since our scheme is based on the Lempel-Ziv method, it can be applied also to
target sequences that are not i.i.d.


title: Quantum limits to dynamical evolution

abstract:
  We establish the minimum time it takes for an initial state of mean energy E
and energy spread DE to move from its initial configuration by a predetermined
amount. Distances in Hilbert space are estimated by the fidelity between the
initial and final state. In this context, we also show that entanglement is
necessary to achieve the ultimate evolution speed when the energy resources are
distributed among all subsystems.


title: Nonlinear Reformulation of Heisenberg's Dynamics

abstract:
  A structural similarity between Classical Mechanics (CM) and Quantum
Mechanics (QM) was revealed by P.A.M. Dirac in terms of Lie Algebras: while in
CM the dynamics is determined by the Lie algebra of Poisson brackets on the
manifold of scalar fields for classical position/momentum observables q/p, d/dt
q={q,H}, d/dt p={p,H}, QM evolves (in Heisenberg's picture) according to the
formally similar Lie algebra of commutator brackets of the corresponding
operators Q/P: d/dt Q=i/h [Q,H], d/dt P=i/h [P,H] where QP-PQ=ih. A further
common framework for comparing CM and QM is the category of symplectic
manifolds. Other than previous authors, this paper considers phase space of
Heisenberg's picture, i.e., the manifold of pairs of operator observables (Q,P)
satisfying commutation relation. On a sufficiently high algebraic level of
abstraction -- which we believe to be of interest on its own -- it turns out
that this approach leads to a truly NON-linear yet Hamiltonian reformulation of
QM evolution.


title: Decoherence in a Two-Particle Model

abstract:
  We consider a simple one dimensional quantum system consisting of a heavy and
a light particle interacting via a point interaction. The initial state is
chosen to be a product state, with the heavy particle described by a coherent
superposition of two spatially separated wave packets with opposite momentum
and the light particle localized in the region between the two wave packets. We
characterize the asymptotic dynamics of the system in the limit of small mass
ratio, with an explicit control of the error. We derive the corresponding
reduced density matrix for the heavy particle and explicitly compute the
(partial) decoherence effect for the heavy particle induced by the presence of
the light one for a particular set up of the parameters.


title:
Physics of a microsystem starting from non-equilibrium quantum
  statistical mechanics

abstract:
  In this paper we address the problem to give a concrete support to the idea,
originally stemming from Niels Bohr, that quantum mechanics must be rooted
inside the physics of macroscopic systems. It is shown that, starting from the
formalism of the non-equilibrium statistical operator, which is now a
consolidated part of quantum statistical mechanics, particular correlations
between two isolated systems can be singled out and interpreted as
microsystems. In this way also a new framework is established in which
questions of decoherence can be naturally addressed.


title: Formulation of a Family of Sure-Success Quantum Search Algorithms

abstract:
  In this work, we consider a family of sure-success quantum algorithms, which
is grouped into even and odd members for solving a generalized Grover search
problem. We prove the matching conditions for both groups and give the
corresponding formulae for evaluating the iterations or oracle calls required
in the search computation. We also present how to adjust the phase angles in
the generalized Grover operator to ensure the sure-success if minimal oracle
calls are demanded in the search.


title: Quantum cellular automata quantum computing with endohedral fullerenes

abstract:
  We present a scheme to perform universal quantum computation using global
addressing techniques as applied to a physical system of endohedrally doped
fullerenes. The system consists of an ABAB linear array of Group V endohedrally
doped fullerenes. Each molecule spin site consists of a nuclear spin coupled
via a Hyperfine interaction to an electron spin. The electron spin of each
molecule is in a quartet ground state $S=3/2$. Neighboring molecular electron
spins are coupled via a magnetic dipole interaction. We find that an
all-electron construction of a quantum cellular automata is frustrated due to
the degeneracy of the electronic transitions. However, we can construct a
quantum celluar automata quantum computing architecture using these molecules
by encoding the quantum information on the nuclear spins while using the
electron spins as a local bus. We deduce the NMR and ESR pulses required to
execute the basic cellular automata operation and obtain a rough figure of
merit for the the number of gate operations per decoherence time. We find that
this figure of merit compares well with other physical quantum computer
proposals. We argue that the proposed architecture meets well the first four
DiVincenzo criteria and we outline various routes towards meeting the fifth
criteria: qubit readout.


title:
On the Question of Interference in Radiation Produced by Relativistic
  Channeled Particles

abstract:
  Two approaches used in the description of the channeling radiation emitted
from relativistic positrons are compared with each other.
  In the first (traditional) case, the probability of the process is
proportional to a sum of absolute squares of the amplitudes of the transition
between two states with definite transverse energy levels of the positrons
traversing single crystals. In the second case, we begin with calculation of
the sum of amplitudes for transition between states with different transverse
energy levels for corresponding radiation frequency, and then the sum is
squared. One must keep in mind that the latter approach can be used only in the
case when positrons move in a nearly harmonic planar potential with equidistant
transverse energy levels. It is shown that the calculation based on the second
approach can give rise to a peak structure in the spectrum when the number of
transverse energy levels is much greater than one.


title: Quantum Computation and Many Worlds

abstract:
  An Everett (`Many Worlds') interpretation of quantum mechanics due to
Saunders and Zurek is presented in detail. This is used to give a physical
description of the process of a quantum computation. Objections to such an
understanding are discussed.


title: Estimating the post-measurement state

abstract:
  We study generalized measurements (POVM measurements) on a single d-level
quantum system which is in a completely unknown pure state, and derive the best
estimate of the post-measurement state. The mean post-measuremement estimation
fidelity of a generalized measurement is obtained and related to the operation
fidelity of the device. This illustrates how the information gain about the
post-measurement state and the corresponding state disturbance are mutually
dependent. The connection between the best estimates of the pre- and
post-measurement state is established and interpreted. For pure generalized
measurements the two states coincide.


title: Why there is no impossibility theorem on Secure Quantum Bit Commitment

abstract:
  The impossibility proof on unconditionally secure quantum bit commitment is
critically reviewed. Different ways of obtaining secure protocols are
indicated.


title: Two Arrows of Time in Nonlocal Particle Dynamics

abstract:
  Considering what the world would be like if backwards causation were possible
is usually mind-bending. Here I discuss something that is easier to study: a
toy model that incorporates a very restricted sort of backwards causation. It
defines particle world lines by means of a kind of differential delay equation
with negative delay. The model presumably prohibits signalling to the past and
superluminal signalling, but allows nonlocality while being fully covariant.
And that is what constitutes the model's value: it is an explicit example of
the possibility of Lorentz invariant nonlocality. That is surprising in so far
as many authors thought that nonlocality, in particular nonlocal laws for
particle world lines, must conflict with relativity. The development of this
model was inspired by the search for a fully covariant version of Bohmian
mechanics.


title:
Physical Model of the Fluctuating Vacuum and Photon as its Elementary
  Excitation

abstract:
  A physical model of the fluctuating vacuum (FlcVcm) and the photon as an
elementary collective excitation in a solitary needle cylindrical form are
offered. We assume that the FlcVcm is consistent by neutral dynamides, which
are streamlined in a close-packed crystalline lattice. Every dynamide is a
neutral pair, consistent by massless opposite point-like elementary electric
charges (ElmElcChrgs): electrino (-) and positrino (+). In an equilibrium
position two contrary Pnt-Lk ElmElcChrgs within every one dynamide are very
closely installed one to another and therefore its aggregate polarization and
its ElcFld also have zero values. However the absence of a mass in a rest of an
electrino and positrino makes possible they to display an infinitesimal
inertness of their own QntElcMgnFlds and a big mobility, what permits them to
be found a bigger time in an unequilibrium distorted position. The aggregate
ElcFld of dynamide reminds us that it could be considered as the QntElcFld of
an electric quasi-dipole because both massless electrino and positrino have the
same inertness. The aggregate ElcFld of every dynamide polarizes nearest
neighbour dynamides in an account of which they interact between them-self, on
account of which their photons display a wave character and behaviour. In order
to obtain a clear physical evidence and true physical explanation of an
emission and absorption of RlPhtns, I use Fermi method for the determination of
the time dependence of expansion coefficients of wave function of SchEl in a
hybrid state, using the solution of the Schrodinger quadratic differential wave
equation in partial derivatives with the potentials of Coulomb and of Lorentz
friction force.


title:
Correlation of energy and free energy for the thermal Casimir force
  between real metals

abstract:
  The energy of fluctuating electromagnetic field is investigated for the
thermal Casimir force acting between parallel plates made of real metal. It is
proved that for nondissipative media with temperature independent dielectric
permittivity the energy at nonzero temperature comprises of the (renormalized)
energies of the zero-point and thermal photons. In this manner photons can be
considered as collective elementary excitations of the matter of plates and
electromagnetic field. If the dielectric permittivity depends on temperature
the energy contains additional terms proportional to the derivatives of
dielectric permittivity with respect to temperature, and the quasiparticle
interpretation of the fluctuating field is not possible. The correlation
between energy and free energy is considered. Previous calculations of the
Casimir energy in the framework of the Lifshitz formula at zero temperature and
optical tabulated data supplemented by the Drude model at room temperature are
analysed. It is demonstrated that this quantity is not a good approximation
either for the free energy or the energy. A physical interpretation of this
hybrid quantity is suggested. The contradictory results in the recent
literature on whether the zero-frequency term of the Lifshitz formula for the
perpendicular polarized modes has any effective contribution to the physical
quantities are discussed. Four main approaches to the resolution of this
problem are specified. The precise expressions for entropy of the fluctuating
field between plates made of real metal are obtained, which helps to decide
between the different approaches. The conclusion is that the Lifshitz formula
supplemented by the plasma model and the surface impedance approach are best
suited to describe the thermal Casimir force between real metals.


title:
Exploiting quantum parallelism of entanglement for a complete
  experimental quantum characterization of a single qubit device

abstract:
  We present the first full experimental quantum tomographic characterization
of a single-qubit device achieved with a single entangled input state. The
entangled input state plays the role of all possible input states in quantum
parallel on the tested device. The method can be trivially extended to any
n-qubits device by just replicating the whole experimental setup n times.


title: Language is Physical

abstract:
  Some aspects of the physical nature of language are discussed. In particular,
physical models of language must exist that are efficiently implementable. The
existence requirement is essential because without physical models no
communication or thinking would be possible. Efficient implementability for
creating and reading language expressions is discussed and illustrated with a
quantum mechanical model. The reason for interest in language is that language
expressions can have meaning, either as an informal language or as a formal
language associated with a mathematical or physical theory. It is noted that
any universally applicable physical theory, or coherent theory of physics and
mathematics together, includes in its domain physical models of expressons for
both the informal language used to discuss the theory and expressions of the
theory itself. It follows that there must be formulas in the formal theory that
express some of their own physical properties. Inclusion of intelligent system
in the theory domain means that the theory, e.g., quantum mechanics, must
describe in some sense its own validation. Maps of language expressions into
physical states are discussed as are conditions under which such a map is a
Godel map. The possibility that language is also mathematical is very briefly
discussed.


title: Quantum Markov Channels for Qubits

abstract:
  We examine stochastic maps in the context of quantum optics. Making use of
the master equation, the damping basis, and the Bloch picture we calculate a
non-unital, completely positive, trace-preserving map with unequal damping
eigenvalues. This results in what we call the squeezed vacuum channel. A
geometrical picture of the effect of stochastic noise on the set of pure state
qubit density operators is provided. Finally, we study the capacity of the
squeezed vacuum channel to transmit quantum information and to distribute EPR
states.


title: An Arbitrary Two-qubit Computation In 23 Elementary Gates

abstract:
  Quantum circuits currently constitute a dominant model for quantum
computation. Our work addresses the problem of constructing quantum circuits to
implement an arbitrary given quantum computation, in the special case of two
qubits. We pursue circuits without ancilla qubits and as small a number of
elementary quantum gates as possible. Our lower bound for worst-case optimal
two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2
CNOTs. To this end, we constructively prove a worst-case upper bound of 23
elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions.
Our analysis shows that synthesis algorithms suggested in previous work,
although more general, entail much larger quantum circuits than ours in the
special case of two qubits. One such algorithm has a worst case of 61 gates of
which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie
theory as well as the polar and spectral (symmetric Shur) matrix decompositions
from numerical analysis and operator theory. They are related to the canonical
decomposition of a two-qubit gate with respect to the ``magic basis'' of
phase-shifted Bell states, published previously. We further extend this
decomposition in terms of elementary gates for quantum computation.


title: Decoherence Correction by the Zeno Effect and Non-Holonomic Control

abstract:
  We show that multidimensional Zeno effect combined with non-holonomic control
allows to efficiently protect quantum systems from decoherence by a method
similar to classical coding. Contrary to the conventional approach, our method
is applicable to arbitrary error-inducing Hamiltonians and general quantum
systems. We also propose algorithms of finding encoding that approaches the
Hamming upper bound along with methods of practical realizations of the
encodings. Two new codes protecting 2 information qubits out of 7 and 4
information qubits out of 9 against a single error with arbitrarily small
probability of failure are constructed as an example.


title: Implementation of dense coding using the generalized Grover's algorithm

abstract:
  Dense coding has been implemented using the generalized Grover's algorithm
and its inverse operation. Exploiting the superpositions of two
Einstein-Podolsky-Rosen (EPR) states, messages that are possible to be
transmitted increase. Our scheme is demonstrated using nuclear magnetic
resonance (NMR). Experimental results show a good agreement between theory and
experiment.


title: Odd numbers of photons and teleportation

abstract:
  Several teleportation protocols, namely those using entangled coherent
states, entangled squeezed states, and the single-photon EPR state, are all
shown to be particular instances of a more general scheme that relies on the
detection of an odd number of photons.


title: Extracting Classical Correlations from a Bipartite Quantum System

abstract:
  In this paper we discuss the problem of splitting the total correlations for
a bipartite quantum state described by the Von Neumann mutual information into
classical and quantum parts. We propose a measure of the classical correlations
as the difference between the Von Neumann mutual information and the relative
entropy of entanglement. We compare this measure with different measures
proposed in the literature.


title:
Restriction on relaxation times derived from the Lindblad-type master
  equations for 2-level systems

abstract:
  We discuss a restriction on relaxation times derived from the Lindblad-type
master equations for 2-level systems and show that none of the inverse
relaxation times can be greater than the sum of the others. The relation is
experimentally proved or disproved and can be considered to be a measure for or
against the applicability of the Lindblad-type master equations and therefore
of the so-called completely positive condition.


title: Complex Optical Potentials and Pseudo-Hermitian Hamiltonians

abstract:
  Recently some authors have broadened the scope of canonical quantum mechanics
by replacing the conventional Hermiticity condition on the Hamiltonian by a
weaker requirement through the introduction of the notion of
pseudo-Hermiticity. In the present study we investigate eigenvalues,
transmission and reflection from complex optical potentials enjoying the
property of pseudo-Hermiticity.


title: States of light via reducible quantization

abstract:
  Multi-photon and coherent states of light are formulated in terms of a
reducible representation of canonical commutation relations. Standard
properties of such states are recovered as certain limiting cases. The new
formalism leads to field operators and not operator-valued distributions. The
example of radiation fields produced by a classical current shows an automatic
regularization of the infrared divergence.


title: Collapse helps to probe the structure of particles

abstract:
  We present a possible method to probe the inner structure of particles based
on one kind of promising dynamical collapse theory. It is shown that the
present decay data of KL meson indicates that quarks have no inner structure.


title: The Impossibility of Pseudo-Telepathy Without Quantum Entanglement

abstract:
  Imagine that Alice and Bob, unable to communicate, are both given a 16-bit
string such that the strings are either equal, or they differ in exactly 8
positions. Both parties are then supposed to output a 4-bit string in such a
way that these short strings are equal if and only if the original longer
strings given to them were equal as well. It is known that this task can be
fulfilled without failure and without communication if Alice and Bob share 4
maximally entangled quantum bits. We show that, on the other hand, they CANNOT
win the same game with certainty if they only share classical bits, even if it
is an unlimited number. This means that for fulfilling this particular
distributed task, quantum entanglement can completely replace communication.
This phenomenon has been called pseudo-telepathy. The results of this paper
complete the analysis of the first proposed game of this type between two
players.


title: Quantum mechanics and EPR paradox

abstract:
  The orthodox quantum mechanics has been commonly regarded as being supported
decisively by the polarization EPR experiments, in which Bell's inequalities
have been violated. The given conclusion has been based, however, on several
mistakes that have not been yet commonly known and sufficiently analyzed. The
whole problem will be newly discussed and a corresponding solution will be
proposed.


title:
State-Insensitive Cooling and Trapping of Single Atoms in an Optical
  Cavity

abstract:
  Single Cesium atoms are cooled and trapped inside a small optical cavity by
way of a novel far-off-resonance dipole-force trap (FORT), with observed
lifetimes of 2 to 3 seconds. Trapped atoms are observed continuously via
transmission of a strongly coupled probe beam, with individual events lasting ~
1 s. The loss of successive atoms from the trap N = 3 -> 2 -> 1 -> 0 is thereby
monitored in real time. Trapping, cooling, and interactions with strong
coupling are enabled by the FORT potential, for which the center-of-mass motion
is only weakly dependent on the atom's internal state.


title: Efficient Quantum Circuits for Non-Qubit Quantum Error-Correcting Codes

abstract:
  We present two methods for the construction of quantum circuits for quantum
error-correcting codes (QECC). The underlying quantum systems are tensor
products of subsystems (qudits) of equal dimension which is a prime power. For
a QECC encoding k qudits into n qudits, the resulting quantum circuit has
O(n(n-k)) gates. The running time of the classical algorithm to compute the
quantum circuit is O(n(n-k)^2).


title:
Unitary reduction of the Liouville equation relative to a two-level atom
  coupled to a bimodal lossy cavity

abstract:
  The Liouville equation of a two-level atom coupled to a degenerate bimodal
lossy cavity is unitarily and exactly reduced to two uncoupled Liouville
equations. The first one describes a dissipative Jaynes-Cummings model and the
other one a damped harmonic oscillator. Advantages related to the reduction
method are discussed.


title:
Improvement of Laser Cooling of Ions in a Penning Trap by use of the
  Axialisation Technique

abstract:
  We report a study of the axialisation and laser cooling of single ions and
small clouds of ions in a Penning trap. A weak radiofrequency signal applied to
a segmented ring electrode couples the magnetron motion to the cyclotron
motion, which results in improved laser cooling of the magnetron motion. This
allows us to approach the trapping conditions of a Paul trap, but without any
micromotion. Using an ICCD camera we show that the motion of a single ion can
be confined to dimensions of the order of 10 $\mu$m. We have measured increased
magnetron cooling rates using an rf-photon correlation technique. For certain
laser cooling conditions, the magnetron motion of the centre of mass of the
cloud grows and stabilises at a large value. This results in the ions orbiting
the centre of the trap together in a small cloud, as confirmed by photon-photon
correlation measurements.


title: Phase space localization of antisymmetric functions

abstract:
  Upper and lower bounds are written down for the minimum information entropy
in phase space of an antisymmetric wave function in any number of dimensions.
Similar bounds are given when the wave function is restricted to belong to any
of the proper subspaces of the Fourier transform operator.


title: Quasi exactly solvable operators and Lie superalgebras

abstract:
  Linear operators preserving the direct sum of polynomial rings P(m)\oplus
P(n) are constructed. In the case |m-n|=1 they correspond to atypical
representations of the superalgebra osp(2,2). For |m-n|=2 the generic, finite
dimensional representations of the superalgebra q(2) are recovered. An example
of a Hamiltonian possessing such a hidden algebra is analyzed.


title: Towards Characterizing the Non-Locality of Entangled Quantum States

abstract:
  The behavior of entangled quantum systems can generally not be explained as
being determined by shared classical randomness. In the first part of this
paper, we propose a simple game for n players demonstrating this non-local
property of quantum mechanics: While, on the one hand, it is immediately clear
that classical players will lose the game with substantial probability, it can,
on the other hand, always be won by players sharing an entangled quantum state.
The simplicity of the classical analysis of our game contrasts the often quite
involved analysis of previously proposed examples of this type.
  In the second part, aiming at a quantitative characterization of the
non-locality of n-partite quantum states, we consider a general class of
n-player games, where the amount of communication between certain (randomly
chosen) groups of players is measured. Comparing the classical communication
needed for both classical players and quantum players (initially sharing a
given quantum state) to win such a game, a new type of separation results is
obtained. In particular, we show that in order to simulate two separated qubits
of an n-partite GHZ state at least (roughly) log(log(n)) bits of information
are required.


title: Entangled graphs: Bipartite entanglement in multi-qubit systems

abstract:
  Quantum entanglement in multipartite systems cannot be shared freely. In
order to illuminate basic rules of entanglement sharing between qubits we
introduce a concept of an entangled structure (graph) such that each qubit of a
multipartite system is associated with a point (vertex) while a bi-partite
entanglement between two specific qubits is represented by a connection (edge)
between these points. We prove that any such entangled structure can be
associated with a pure state of a multi-qubit system. Moreover, we show that a
pure state corresponding to a given entangled structure is a superposition of
vectors from a subspace of the $2^N$-dimensional Hilbert space, whose dimension
grows linearly with the number of entangled pairs.


title: Quantum Physics and Classical Physics - in the Light of Quantum Logic

abstract:
  In contrast to the Copenhagen interpretation we consider quantum mechanics as
universally valid and query whether classical physics is really intuitive and
plausible. - We discuss these problems within the quantum logic approach to
quantum mechanics where the classical ontology is relaxed by reducing
metaphysical hypotheses. On the basis of this weak ontology a formal logic of
quantum physics can be established which is given by an orthomodular lattice.
By means of the Soler condition and Piron's result one obtains the classical
Hilbert spaces. - However, this approach is not fully convincing. There is no
plausible justification of Soler's law and the quantum ontology is partly too
weak and partly too strong. We propose to replace this ontology by an ontology
of unsharp properties and conclude that quantum mechanics is more intuitive
than classical mechanics and that classical mechanics is not the macroscopic
limit of quantum mechanics.


title:
Reply to the Comment on `Deterministic Single-Photon Source for
  Distributed Quantum Networking'

abstract:
  Reply to the comment of H. J. Kimble [quant-ph/0210032] on the experiment
realizing a "deterministic single-photon source for distributed quantum
networking" by Kuhn, Hennrich, and Rempe [Phys. Rev. Lett. 89, 067901 (2002),
quant-ph/0204147].


title:
Family of Zeilinger-Horne-Greenberger "W" states lead to stronger
  nonclassicality than family of Greenberger-Horne-Zeilinger "GHZ" states

abstract:
  The N-qubit states of the W class, for N>10, lead to more robust (against
noise admixture) violations of local realism, than the GHZ states. These
violations are most pronounced for correlations for a pair of qubits,
conditioned on specific measurement results for the remaining (N-2) qubits. The
considerations provide us with a qualitative difference between the W state and
GHZ state in the situation when they are separately sent via depolarizing
channels. For sufficiently high amount of noise in the depolarizing channel,
the GHZ states cannot produce a distillable state between two qubits, whereas
the W states can still produce a distillable state in a similar situation.


title: Quantum mechanics and irreversible time flow

abstract:
  Time flow has been embodied in time-dependent Schroedinger equation
representing one of the foundations of quantum mechanics. Pauli's criticism
(1933) has, however, indicated that the assumptions concerning representation
Hilbert space have led to some contradictions. Many authors have tried to solve
this discrepancy practically without any actual success. The reason may be seen
in that two different problems have been mixed: the problem of Pauli (being
more general and more important) and non-unitarity of exponential phase
operator of linear harmonic oscillator introduced by Dirac, as demonstrated in
1964. The problem will be discussed in a broad historical context and a
solution based on extension of representation Hilbert space will be shown.


title:
The Klein-Gordon Equation of Generalized Hulthen Potential in Complex
  Quantum Mechanics

abstract:
  We have investigated the reality of exact bound states of complex and/or
PT-symmetric non-Hermitian exponential-type generalized Hulthen potential. The
Klein-Gordon equation has been solved by using the Nikiforov-Uvarov method
which is based on solving the second-order linear differential equations by
reduction to a generalized equation of hypergeometric type. In many cases of
interest, negative and positive energy states have been discussed for different
types of complex potentials.


title:
Three-dimensional harmonic oscillator and time evolution in quantum
  mechanics

abstract:
  The problem of defining time (or phase) operator for three-dimensional
harmonic oscillator has been analyzed. A new formula for this operator has been
derived. The results have been used to demonstrate a possibility of
representing quantum-mechanical time evolution in the framework of an extended
Hilbert space structure. Physical interpretation of the extended structure has
been discussed shortly, too.


title: Dissipative "Groups" and the Bloch Ball

abstract:
  We show that a quantum control procedure on a two-level system including
dissipation gives rise to a semi-group corresponding to the Lie algebra
semi-direct sum gl(3,R)+R^3. The physical evolution may be modelled by the
action of this semi-group on a 3-vector as it moves inside the Bloch sphere, in
the Bloch ball.


title: Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited

abstract:
  We derive explicit formulas for the normal ordering of powers of arbitrary
monomials of boson operators. These formulas lead to generalisations of
conventional Bell and Stirling numbers and to appropriate generalisations of
the Dobinski relations. These new combinatorial numbers are shown to be
coherent state matrix elements of powers of the monomials in question. It is
further demonstrated that such Bell-type numbers, when considered as power
moments, give rise to positive measures on the positive half-axis, which in
many cases can be written in terms of known functions.


title: Quantum Zero-Error Algorithms Cannot be Composed

abstract:
  We exhibit two black-box problems, both of which have an efficient quantum
algorithm with zero-error, yet whose composition does not have an efficient
quantum algorithm with zero-error. This shows that quantum zero-error
algorithms cannot be composed. In oracle terms, we give a relativized world
where ZQP^{ZQP}\=ZQP, while classically we always have ZPP^{ZPP}=ZPP.


title:
Efficient implementations of the Quantum Fourier Transform: an
  experimental perspective

abstract:
  The Quantum Fourier transform (QFT) is a key ingredient in most quantum
algorithms. We have compared various spin-based quantum computing schemes to
implement the QFT from the point of view of their actual time-costs and the
accuracy of the implementation. We focus here on an interesting decomposition
of the QFT as a product of the non-selective Hadamard transformation followed
by multiqubit gates corresponding to square- and higher-roots of controlled-NOT
gates. This decomposition requires only O(n) operations and is thus linear in
the number of qubits $n$. The schemes were implemented on a two-qubit NMR
quantum information processor and the resultant density matrices reconstructed
using standard quantum state tomography techniques. Their experimental
fidelities have been measured and compared.


title: Correlations for a new Bell's inequality experiment

abstract:
  Proofs of Bell's theorem and the data analysis used to show its violation
have commonly assumed a spatially stationary underlying process. However, it
has been shown recently that the appropriate Bell's inequality holds
identically for cross correlations of three or four lists of + or - 1's,
independently of statistical assumptions. When data consistent with its
derivation are analyzed without imposition of the stationarity assumption, the
resulting correlations satisfy the Bell inequality.


title: Continuous loading of cold atoms into a Ioffe-Pritchard magnetic trap

abstract:
  We present a robust continuous optical loading scheme for a Ioffe-Pritchard
(IP) type magnetic trap. Atoms are cooled and trapped in a modified
magneto-optical trap (MOT) consisting of a conventional 2D-MOT in radial
direction and an axial molasses. The radial magnetic field gradient needed for
the operation of the 2D-MOT is provided by the IP trap. A small axial curvature
and offset field provide magnetic confinement and suppress spin-flip losses in
the center of the magnetic trap without altering the performance of the 2D-MOT.
Continuous loading of atoms into the IP trap is provided by radiative leakage
from the MOT to a metastable level which is magnetically trapped and decoupled
from the MOT light. We are able to accumulate 30 times more atoms in the
magnetic trap than in the MOT. The absolute number of $2\times 10^8$~atoms is
limited by inelastic collisions. A model based on rate equations shows good
agreement with our data. Our scheme can also be applied to other atoms with
similar level structure like alkaline earth metals.


title: Noncommutative probability in classical systems

abstract:
  Two examples of the situation when the classical observables should be
described by a noncommutative probability space are investigated. Possible
experimental approach to find quantum-like correlations for classical
disordered systems is discussed. The interpretation of noncommutative
probability in experiments with classical systems as a result of context
(complex of experimental physical conditions) dependence of probability is
considered.


title:
Invariance of Stationary and Ergodic Properties of a Quantum Source
  under Memoryless Transformations

abstract:
  We prove that the stationarity and the ergodicity of a quantum source are
preserved by any trace-preserving completely positive linear map of the tensor
product form ${\cal E}^{\otimes m}$, where a copy of ${\cal E}$ acts locally on
each spin lattice site. We also establish ergodicity criteria for so called
classically-correlated quantum sources.


title: Quantum Chaos and Quantum-Classical Correspondence

abstract:
  The quantum dynamics of a classically chaotic model are studied in the
approach to the macroscopic limit. The quantum predictions are compared and
contrasted with the classical predictions of both Newtonian and Liouville
mechanics. The time-domain scaling of the optimal quantum-classical
correspondence is analyzed in detail in the case of both classical theories. In
both cases the correspondence for observable quantities is shown to break down
on a time-scale that increases very slowly (logarithmically) with increasing
system size. In the case of quantum-Liouville correspondence such a short
time-scale does not imply a breakdown of correspondence since the largest
quantum-Liouville differences reached on this time-scale decrease rapidly (as
an inverse power) with increasing system size. Therefore the statistical
properties of chaotic dynamics are, as expected, well described by quantum
theory in the macroscopic limit. In contrast, the largest quantum-Newtonian
differences reached on the log time-scale actually increase in proportion to
the system size. Since the invariance properties of the Hamiltonian impose
functional constraints on the time-varying chaotic coordinates, it is possible
to show, moreover, that if the quantum predictions are believed to describe the
coordinates of individual chaotic systems, then they also predict macroscopic
violations of any kinematic or dynamic constants of the motion. These results
for chaotic systems indicate that a valid description of the time-varying
properties of individual macroscopic bodies is not available within the
standard interpretive framework of quantum theory.


title: Continuous Quantum Measurement and the Quantum to Classical Transition

abstract:
  While ultimately they are described by quantum mechanics, macroscopic
mechanical systems are nevertheless observed to follow the trajectories
predicted by classical mechanics. Hence, in the regime defining macroscopic
physics, the trajectories of the correct classical motion must emerge from
quantum mechanics, a process referred to as the quantum to classical
transition. Extending previous work [Bhattacharya, Habib, and Jacobs, Phys.
Rev. Lett. {\bf 85}, 4852 (2000)], here we elucidate this transition in some
detail, showing that once the measurement processes which affect all
macroscopic systems are taken into account, quantum mechanics indeed predicts
the emergence of classical motion. We derive inequalities that describe the
parameter regime in which classical motion is obtained, and provide numerical
examples. We also demonstrate two further important properties of the classical
limit. First, that multiple observers all agree on the motion of an object, and
second, that classical statistical inference may be used to correctly track the
classical motion.


title:
Environment - Assisted Invariance, Causality, and Probabilities in
  Quantum Physics

abstract:
  I introduce environment - assisted invariance -- a symmetry related to
causality that is exhibited by correlated quantum states -- and describe how it
can be used to understand the nature of ignorance and, hence, the origin of
probabilities in quantum physics.


title: Quantum Computations with Optical Waveguide Modes

abstract:
  A fully optical method to perform any quantum computation with optical
waveguide modes is proposed by supplying the prescriptions for a universal set
of quantum gates. The proposal for quantum computation is based on implementing
a quantum bit with two normal modes of multi-mode waveguides. The proposed
universal set of gates has the potential of being more compact and easily
realized than other optical implementations, since it is based on planar
lightwave circuit technology and can be constructed by using Mach-Zehnder
interferometer configurations having semiconductor optical amplifiers with very
high refractive nonlinearity in their arms.


title: Quantisation on general spaces

abstract:
  Quantisation on spaces with properties of curvature, multiple connectedness
and non orientablility is obtained.
  The geodesic length spectrum for the Laplacian operator is extended to solve
the Schroedinger operator. Homotopy fundamental group representations are used
to obtain a direct sum of Hilbert spaces, with a Holonomy method for the non
simply connected manifolds.The covering spaces of isometric and hence
isospectral manifolds are used to obtain the representation of states on
orientable and non orientable spaces. Problems of deformations of the operators
and the domains are discussed.Possible applications of the geometric and
topological effects in physics are mentioned.


title:
Exact Solutions of the Time Dependent Schroedinger Equation in One Space
  Dimension

abstract:
  A closed expression for the harmonic oscillator wave function after the
passage of a linear signal with arbitrary time dependence is derived.
Transition probabilities are simple to express in terms of Laguerre
polynomials. Spontaneous transitions are neglected. The exact result is of some
interest for the physics of short laser pulses, since it may serve as an
accuracy test for numerical methods.


title: Quantum and Classical Phase Space: Separability and Entanglement

abstract:
  The formalism of classical and quantum mechanics on phase space leads to
symplectic and Heisenberg group representations, respectively. The Wigner
functions give a representation of the quantum system using classical
variables. The correspondence between the classical and the quantum criterion
of separability for the system is obtained in terms of these functions.
  Entanglement is generic and separability is special. Some applications are
discussed in commonly occuring examples and possibly in exotic systems.


title:
Constructive control of quantum systems using factorization of unitary
  operators

abstract:
  We demonstrate how structured decompositions of unitary operators can be
employed to derive control schemes for finite-level quantum systems that
require only sequences of simple control pulses such as square wave pulses with
finite rise and decay times or Gaussian wavepackets. To illustrate the
technique it is applied to find control schemes to achieve population transfers
for pure-state systems, complete inversions of the ensemble populations for
mixed-state systems, create arbitrary superposition states and optimize the
ensemble average of dynamic observables.


title: Cooling atomic motion with quantum interference

abstract:
  We theoretically investigate the quantum dynamics of the center of mass of
trapped atoms, whose internal degrees of freedom are driven in a
$\Lambda$-shaped configuration with the lasers tuned at two-photon resonance.
In the Lamb-Dicke regime, when the motional wave packet is well localized over
the laser wavelenght, transient coherent population trapping occurs, cancelling
transitions at the laser frequency. In this limit the motion can be efficiently
cooled to the ground state of the trapping potential. We derive an equation for
the center-of-mass motion by adiabatically eliminating the internal degrees of
freedom. This treatment provides the theoretical background of the scheme
presented in [G. Morigi {\it et al}, Phys. Rev. Lett. {\bf 85}, 4458 (2000)]
and implemented in [C.F. Roos {\it et al}, Phys. Rev. Lett. {\bf 85}, 5547
(2000)]. We discuss the physical mechanisms determining the dynamics and
identify new parameters regimes, where cooling is efficient. We discuss
implementations of the scheme to cases where the trapping potential is not
harmonic.


title: Reconstructing the vibrational state of a trapped ion

abstract:
  A new approach for reconstructing the vibrational quantum state of a trapped
ion is proposed. The method rests upon the current ability of manipulating the
trapped ion state and on the possibility of effectively measuring the scalar
product of the two vibrational cofactors of a vibronic entangled state. The
experimental feasibility of the method is briefly discussed.


title: Sheaf Cohomology and Geometrical Approach to EPR Non-locality

abstract:
  A consistent geometrical approach to EPR non-locality as well as other
non-local effects in QM like the Aharanov-Bohm effect, Berry phase, Gauge
theories within Yang-Mills theory etc. is possible within the framework of
sheaf cohomology. This sheds new light on our understanding on non-local
correlations in QM, and provides a fundamental mathematical approach to
fundamental problems in physics.