title: Quantum mechanics as the objective local theory

abstract:
  In the work it is shown that the principles "the objective local theory" and
corollaries of the standard quantum mechanics are not in such antagonistic
inconsistency as it is usually supposed. In the framework of algebraic
approach, the postulates are formulated which allow constructing the updated
mathematical scheme of quantum mechanics. This scheme incorporates the standard
mathematical apparatus of quantum mechanics. Simultaneously, in it there is a
mathematical object, which adequately describes individual experiment.


title: Phase-covariant quantum cloning of qudits

abstract:
  We study the phase-covariant quantum cloning machine for qudits, i.e. the
input states in d-level quantum system have complex coefficients with arbitrary
phase but constant module. A cloning unitary transformation is proposed. After
optimizing the fidelity between input state and single qudit reduced density
opertor of output state, we obtain the optimal fidelity for 1 to 2
phase-covariant quantum cloning of qudits and the corresponding cloning
transformation.


title: Selection of Squeezed States via Decoherence

abstract:
  In the framework of Lindblad theory for open quantum systems, we calculate
the entropy of a damped quantum harmonic oscillator which is initially in a
quasi-free state. The maximally predictable states are identified as those
states producing the minimum entropy increase after a long enough time. In
general, the states with a squeezing parameter depending on the environment's
diffusion coefficients and friction constant are singled out, but if the
friction constant is much smaller than the oscillator's frequency, coherent
states
  (or thermalized coherent states) are obtained as the preferred classical
states.


title: Authentication of Quantum Messages

abstract:
  Authentication is a well-studied area of classical cryptography: a sender S
and a receiver R sharing a classical private key want to exchange a classical
message with the guarantee that the message has not been modified by any third
party with control of the communication line. In this paper we define and
investigate the authentication of messages composed of quantum states. Assuming
S and R have access to an insecure quantum channel and share a private,
classical random key, we provide a non-interactive scheme that enables S both
to encrypt and to authenticate (with unconditional security) an m qubit message
by encoding it into m+s qubits, where the failure probability decreases
exponentially in the security parameter s. The classical private key is 2m+O(s)
bits. To achieve this, we give a highly efficient protocol for testing the
purity of shared EPR pairs. We also show that any scheme to authenticate
quantum messages must also encrypt them. (In contrast, one can authenticate a
classical message while leaving it publicly readable.) This has two important
consequences: On one hand, it allows us to give a lower bound of 2m key bits
for authenticating m qubits, which makes our protocol asymptotically optimal.
On the other hand, we use it to show that digitally signing quantum states is
impossible, even with only computational security.


title:
Quantum information processing and quantum logic: toward mutual
  illumination

abstract:
  Quantum information and computation may serve as a source of useful axioms
and ideas for the quantum logic/quantum structures project of characterizing
and classifying types of physical theories, including quantum mechanics and
classical mechanics. The axiomatic approach of quantum structures may help
isolate what aspects of quantum mechanics are responsible for what aspects of
its greater-than-classical information processing power, and whether more
general physical theories may escape some common limitations of classical and
quantum theories. Also, by by helping us understand how existing quantum
algorithms work, quantum structures analyses may suggest new quantum protocols
exploiting general features of quantum mechanics. I stress the importance, for
these matters, of understanding open and closed-system dynamics, and the
structure of composite systems in general frameworks for operational theories,
such as effect algebras, convex sets, and related structures.


title: A Zoology of Bell inequalities resistant to detector inefficiency

abstract:
  We derive both numerically and analytically Bell inequalities and quantum
measurements that present enhanced resistance to detector inefficiency. In
particular we describe several Bell inequalities which appear to be optimal
with respect to inefficient detectors for small dimensionality d=2,3,4 and 2 or
more measurement settings at each side. We also generalize the family of Bell
inequalities described in Collins et all (Phys. Rev. Lett. 88, 040404) to take
into account the inefficiency of detectors. In addition we consider the
possibility for pairs of entangled particles to be produced with probability
less than one. We show that when the pair production probability is small, one
must in general use different Bell inequalities than when the pair production
probability is high.


title:
Nonlocality of Hardy type in experiments using independent particle
  sources

abstract:
  By applying Hardy's argument, we demonstrate the violation of local realism
in a gedanken experiment using independent and separated particle sources.


title: Quantum processes on phase space

abstract:
  Quantum theory predicts probabilities as well as relative phases between
different alternatives of the system. A unified description of both
probabilities and phases comes through a generalisation of the notion of a
density matrix for histories; this object is the decoherence functional of the
consistent histories approach. If we take phases as well as probabilities as
primitive elements of our theory, we abandon Kolmogorov probability and can
describe quantum theory in terms of fundamental commutative observables,
without being obstructed by Bell's and related theorems. Generalising the
theory of stochastic processes, we develop the description of relative phases
and probabilities for paths on the classical phase space. This description
provides a theory of quantum processes. We identify a number of basic
postulates and study its corresponding properties. We strongly emphasise the
notion of conditioning and are able to write ``quantum differential equations''
as analogous to stochastic differential equations. These can be interpreted as
referring to individual systems. We, then, show the sense in which quantum
theory is equivalent to a quantum process on phase space (using coherent
states). Conversely, starting from quantum processes on phase space we recover
standard quantum theory on Hilbert space from the requirement that the process
satisfies (the Markov property together with time reversibility. The
statistical predictions of our theory are identical to the ones of standard
quantum theory, but the ``logic'' of events is Boolean; events are not
represented by projectors any more. We discuss some implication of this fact
for the interpretation of quantum theory, emphasising that it makes plausible
the existence of realist theories for individual quantum systems.


title:
Adaptive Quantum Computation, Constant Depth Quantum Circuits and
  Arthur-Merlin Games

abstract:
  We present evidence that there exist quantum computations that can be carried
out in constant depth, using 2-qubit gates, that cannot be simulated
classically with high accuracy. We prove that if one can simulate these
circuits classically efficiently then the complexity class BQP is contained in
AM.


title: IR control of atoms laser instability

abstract:
  In this paper we show how to control the quantum laser atoms instability
using IR radiation. The control can be achieved by controlling the scattering
length constant via the infrared coupling constant. This method is applied in
the scheme of a continuous CW laser and involves three occupation levels in the
condensed atoms.This atoms in Lambda configuration the description of which is
given by a Reformed Gross-Pitaevskii equation (RGPE), together with a rate
equation.The system is taken to a nonconservative complex Ginzburg Landau
equation (CGLE) description from where we use the Benjamin-Feir stability
criterium.This method allows us a theoretical construction of any atom laser
even for negative interaction constant as is the case of $^{7}Li$.


title: A switchable controlled-NOT gate in a spin-chain NMR quantum computer

abstract:
  A method of switching a controlled-NOT gate in a solid-stae NMR quantum
computer is presented. Qubits of I=1/2 nuclear spins are placed periodically
along a quantum spin chain (1-D antiferromagnet) having a singlet ground state
with a finite spin gap to the lowest excited state caused by some quantum
effect. Irradiation of a microwave tuned to the spin gap energy excites a
packet of triplet magnons at a specific part of the chain where control and
target qubits are involved. The packet switches on the Suhl-Nakamura
interaction between the qubits, which serves as a controlled NOT gate. The
qubit initialization is achieved by a qubit initializer consisting of
semiconducting sheets attached to the spin chain, where spin polarizations
created by the optical pumping method in the semiconductors are transferred to
the spin chain. The scheme allows us to separate the initialization process
from the computation, so that one can optimize the computation part without
being restricted by the initialization scheme, which provides us with a wide
selection of materials for a quantum computer.


title: Quantum time-of-flight measurements: kick clock versus continuous clock

abstract:
  The measurement of time durations or instants of ocurrence of events has been
frequently modelled ``operationally'' by coupling the system of interest to a
``clock''. According to several of these models the operational approach is
limited at low energies because the perturbation of the clock does not allow to
reproduce accurately the corresponding ideal time quantity, defined for the
system in isolation. We show that, for a time-of-flight measurement model that
can be set to measure dwell or arrival times, these limitations may be overcome
by extending the range of energies where the clock works properly using pulsed
couplings rather than continuous ones.


title: Comparing Quantum Entanglement and Topological Entanglement

abstract:
  This paper discusses relationships between topological entanglement and
quantum entanglement. Specifically, we propose that for this comparison it is
fundamental to view topological entanglements such as braids as "entanglement
operators" and to associate to them unitary operators that are capable of
creating quantum entanglement.


title:
A Tight Bound for Probability of Error for Quantum Counting Based
  Multiuser Detection

abstract:
  Future wired and wireless communication systems will employ pure or combined
Code Division Multiple Access (CDMA) technique, such as in the European 3G
mobile UMTS or Power Line Telecommunication system, but also several 4G
proposal includes e.g. multi carrier (MC) CDMA. Former examinations carried out
the drawbacks of single user detectors (SUD), which are widely employed in
narrowband IS-95 CDMA systems, and forced to develop suitable multiuser
detection schemes to increase the efficiency against interference. However, at
this moment there are only suboptimal solutions available because of the rather
high complexity of optimal detectors. One of the possible receiver technologies
can be the quantum assisted computing devices which allows high level
parallelism in computation. The first commercial devices are estimated for the
next years, which meets the advert of 3G and 4G systems. In this paper we
analyze the error probability and give tight bounds in a static and dynamically
changing environment for a novel quantum computation based Quantum Multiuser
detection (QMUD) algorithm, employing quantum counting algorithm, which
provides optimal solution.


title: Fredkin Gates for Finite-valued Reversible and Conservative Logics

abstract:
  The basic principles and results of Conservative Logic introduced by Fredkin
and Toffoli on the basis of a seminal paper of Landauer are extended to
d-valued logics, with a special attention to three-valued logics. Different
approaches to d-valued logics are examined in order to determine some possible
universal sets of logic primitives. In particular, we consider the typical
connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As
a result, some possible three-valued and d-valued universal gates are described
which realize a functionally complete set of fundamental connectives.


title:
Tailoring Single and Multiphoton Probabilities of a Single Photon
  On-Demand Source

abstract:
  As typically implemented, single photon sources cannot be made to produce
single photons with high probability, while simultaneously suppressing the
probability of yielding two or more photons. Because of this, single photon
sources cannot really produce single photons on demand. We describe a
multiplexed system that allows the probabilities of producing one and more
photons to be adjusted independently, enabling a much better approximation of a
source of single photons on demand.


title: State Vectors and Physical States

abstract:
  Causality and the relativity of simultaneity seem at odds with the apparently
sudden, acausal state-vector changes ("collapses") characteristic of quantum
phenomena. The problem of how physical phenomena can be causally determined,
have the probabilities predicted by quantum theory, and be consistent with
special relativity appears to be solved by the assumption, essentially the same
as one first used by Aharonov, Bergmann, and Lebowitz to address a different
problem, that the "initial" and "final" state vectors of a phenomenon or
observation, along with certain other state vectors, all represent the system's
state at all times. Each member of such an aggregate of state vectors is
postulated to represent a different aspect of a physical state rather than a
state, so that most of the state vectors in effect constitute a set of nonlocal
hidden variables. Various implications of this assumption are illustrated
through several physical situations. Among the results is a somewhat surprising
resolution of a paradox in a three-spin Greenberger-Horne-Zeilinger experiment
(a "three-particle EPR" experiment), which involves a logical consequence that
differs from familiar ideas of quantum physics that has no practical
experimental consequence, and the prediction of new experimental phenomena
related to the Zou-Wang-Mandel superposed-idler system. The potential value of
the concepts described as heuristics for new predictions and for developing
physical intuition by clarifying the interrelation and coherence of physical
principles that would otherwise seem contradictory is briefly discussed.


title:
Quantum and Classical Noise in Practical Quantum Cryptography Systems
  based on polarization-entangled photons

abstract:
  Quantum-cryptography key distribution (QCKD) experiments have been recently
reported using polarization-entangled photons. However, in any practical
realization, quantum systems suffer from either unwanted or induced
interactions with the environment and the quantum measurement system, showing
up as quantum and, ultimately, statistical noise. In this paper, we investigate
how ideal polarization entanglement in spontaneous parametric downconversion
(SPDC) suffers quantum noise in its practical implementation as a secure
quantum system, yielding errors in the transmitted bit sequence. Because all
SPDC-based QCKD schemes rely on the measurement of coincidence to assert the
bit transmission between the two parties, we bundle up the overall quantum and
statistical noise in an exhaustive model to calculate the accidental
coincidences. This model predicts the quantum-bit error rate and the sifted key
and allows comparisons between different security criteria of the hitherto
proposed QCKD protocols, resulting in an objective assessment of performances
and advantages of different systems.


title: The Harmonic Oscillator in the Plane and the Jordan-Schwinger Algebras

abstract:
  The direct and indirect Lagrangian representations of the planar harmonic
oscillator have been discussed. The reduction of these Lagrangians in their
basic forms characterising either chiral, or pseudo - chiral oscillators have
been given. A Hamiltonian analysis, showing its equivalence with the Lagrangian
formalism has also been provided. Finally, we show that the chiral and pseudo -
chiral modes act as dynamical structures behind the Jordan - Schwinger
realizations of the SU(2) and SU(1,1) algebras. Also, the SU(1,1) construction
found here is different from the standard Jordan - Schwinger form.


title: Femtosecond Time-Bin Entangled Qubits for Quantum Communication

abstract:
  We create pairs of non-degenerate time-bin entangled photons at telecom
wavelengths with ultra-short pump pulses. Entanglement is shown by performing
  Bell kind tests of the Franson type with visibilities of up to 91%. As
time-bin entanglement can easily be protected from decoherence as encountered
in optical fibers, this experiment opens the road for complex quantum
communication protocols over long distances. We also investigate the creation
of more than one photon pair in a laser pulse and present a simple tool to
quantify the probability of such events to happen.


title: On Integrability of Many-Body Problems with Point Interactions

abstract:
  A study of the integrability of one-dimensional quantum mechanical many-body
systems with general point interactions and boundary conditions describing the
interactions which can be independent or dependent on the spin states of the
particles is presented. The corresponding Bethe ansatz solutions, bound states
and scattering matrices are explicitly given. Hamilton operators corresponding
to special spin dependent boundary conditions are discussed.


title: Phases of quantum states in completely positive non-unitary evolution

abstract:
  We define an operational notion of phases in interferometry for a quantum
system undergoing a completely positive non-unitary evolution. This definition
is based on the concepts of quantum measurement theory. The suitable
generalization of the Pancharatnan connection allows us to determine the
dynamical and geometrical parts of the total phase between two states linked by
a completely positive map. These results reduce to the knonw expressions of
total, dynamical and geometrical phases for pure and mixed states evolving
unitarily.


title: Schrodinger's cat and the problem of two cultures

abstract:
  A mathematical model of the interaction mechanism for the
intuitive-imaginative and heuristic-logical thinking responsible for the rift
in the intellectual activity into two cultures has been suggested. The said
model proceeds from the assumption that human thinking is based on the
principles of the many-channel quantum-mechanical logic of the "both ... and"
type surpassing the rigid confines of the "either ... or" type classical logic.
The aggregate product of the person equally endowed in the said two-cultural
space has been calculated. The interferential part of the latter achieves its
maximum at the extreme values of such parameters as the inter-state exchange
frequency and the difference of the states phases.


title: Quantum sensitive dependence

abstract:
  Wave functions of bounded quantum systems with time-independent potentials,
being almost periodic functions, cannot have time asymptotics as in classical
chaos. However, bounded quantum systems with time-dependent interactions, as
used in quantum control, may have continuous spectrum and the rate of growth of
observables is an issue of both theoretical and practical concern. Rates of
growth in quantum mechanics are discussed by constructing quantities with the
same physical meaning as those involved in the classical Lyapunov exponent. A
generalized notion of quantum sensitive dependence is introduced and the
mathematical structure of the operator matrix elements that correspond to
different types of growth is characterized.


title: Experimental Quantum Cloning of Single Photons

abstract:
  Although perfect copying of unknown quantum systems is forbidden by the laws
of quantum mechanics, approximate cloning is possible. A natural way of
realizing quantum cloning of photons is by stimulated emission. In this context
the fundamental quantum limit to the quality of the clones is imposed by the
unavoidable presence of spontaneous emission. In our experiment a single input
photon stimulates the emission of additional photons from a source based on
parametric down-conversion. This leads to the production of quantum clones with
near optimal fidelity. We also demonstrate universality of the copying
procedure by showing that the same fidelity is achieved for arbitrary input
states.


title: Single qubit estimation from repeated unsharp measurements

abstract:
  When estimating an unknown single pure qubit state, the optimum fidelity is
2/3. As it is well known, the value 2/3 can be achieved in one step, by a
single ideal measurement of the polarization along a random direction. I
analyze the opposite strategy which is the long sequence of unsharp
polarization measurements. The evolution of the qubit under the influence of
repeated measurements is quite complicated in the general case. Fortunately, in
a certain limit of very unsharp measurements the qubit will obey simple
stochastic evolution equations known for long under the name of time-continuous
measurement theory. I discuss how the outcomes of the very unsharp measurements
will asymptotically contribute to our knowledge of the original qubit. It is
reassuring that the fidelity will achieve the optimum 2/3 for long enough
sequences of the unsharp measurements.


title:
Nonclassicality and information exchange in deterministic entanglement
  formation

abstract:
  We discuss the role of nonclassicality of quantum states as a necessary
resource in deterministic generation of multipartite entangled states. In
particular for three bilinearly coupled modes of the electromagnetic field,
tuning of the coupling constants between the parties allows the total system to
evolve into both Bell and GHZ states only when one of the parties is initially
prepared in a nonclassical state. A superposition resource is then converted
into an entanglement resource.


title: Adiabatic Theory of Nonlinear Evolution of Quantum States

abstract:
  We present a general theory for adiabatic evolution of quantum states as
governed by the nonlinear Schrodinger equation, and provide examples of
applications with a nonlinear tunneling model for Bose-Einstein condensates.
Our theory not only spells out conditions for adiabatic evolution of
eigenstates, but also characterizes the motion of non-eigenstates which cannot
be obtained from the former in the absence of the superposition principle. We
find that in the adiabatic evolution of non-eigenstates, the Aharonov-Anandan
phases play the role of classical canonical actions.


title:
Revealing non-classical behaviours in the oscillatory motion of a
  trapped ion

abstract:
  The possibility of revealing non-classical behaviours in the dynamics of a
trapped ion via measurements of the mean value of suitable operators is
reported. In particular we focus on the manifestation known as `` Parity
Effect\rq\rq which may be observed \emph{directly measuring} the expectation
value of an appropriate correlation operator. The experimental feasibility of
our proposal is discussed.


title: The intensity correlation function of "blinking" quantum systems

abstract:
  Explicit expressions are determined for the photon correlation function of
``blinking'' quantum systems, i.e. systems with different types of fluorescent
periods. These expressions can be used for a fit to experimental data and for
obtaining system parameters therefrom. For two dipole-dipole interacting $V$
systems the dependence on the dipole coupling constant is explicitly given and
shown to be particularly pronounced if the strong driving is reduced. We
propose to use this for an experimental verification of the dipole-dipole
interaction.


title:
Information-disturbance tradeoff in quantum measurement on the uniform
  ensemble and on the mutually unbiased bases

abstract:
  I consider the tradeoff between the information gained about an initially
unknown quantum state, and the disturbance caused to that state by the
measurement process. I show that for any distribution of initial states, the
information-disturbance frontier is convex, and disturbance is nondecreasing
with information gain. I consider the most general model of quantum
measurements, and all post-measurement dynamics compatible with a given
measurement. For the uniform initial distribution over states, I show that the
least-disturbing way of making any measurement is with conditional dynamics
satisfying a generalization of the projection postulate, the ``square-root
dynamics.'' Thus, procedures for achieving a point on the
information-disturbance frontier may be assumed to involve such conditional
dynamics. Also, the information-disturbance frontier for the uniform ensemble
may be achieved with ``isotropic'' (unitarily covariant) dynamics. This results
in a significant simplification of the optimization problem for calculating the
tradeoff in this case, giving hope for a closed-form solution. I also show that
the discrete ensembles uniform on the d(d+1) vectors of a certain set of d+1
``mutually unbiased'' or conjugate bases in d dimensions form spherical
2-designs in CP_{d-1} when d is a power of an odd prime. This implies that many
of the results of the paper apply also to these discrete ensembles.


title: Empirical Determination of Bang-Bang Operations

abstract:
  Strong and fast "bang-bang" (BB) pulses have been recently proposed as a
means for reducing decoherence in a quantum system. So far theoretical analysis
of the BB technique relied on model Hamiltonians. Here we introduce a method
for empirically determining the set of required BB pulses, that relies on
quantum process tomography. In this manner an experimenter may tailor his or
her BB pulses to the quantum system at hand, without having to assume a model
Hamiltonian.


title:
Bell Inequalities in Phase Space and their Violation in Quantum
  Mechanics

abstract:
  We derive ``Bell inequalities'' in four dimensional phase space and prove the
following ``three marginal theorem'' for phase space densities
$\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing
conjecture : ``there exist quantum states for which more than three of the
quantum probability distributions for $(q_1,q_2)$, $(p_1,p_2)$, $(q_1,p_2)$ and
$(p_1,q_2)$ cannot be reproduced as marginals of a positive
$\rho(\overrightarrow{q},\overrightarrow{p})$''. We also construct the most
general positive $\rho(\overrightarrow{q},\overrightarrow{p})$ which reproduces
any three of the above quantum probability densities for arbitrary quantum
states. This is crucial for the construction of a maximally realistic quantum
theory.


title:
Steep optical wave group velocity reduction and storage of light without
  electromagnetically induced transparency

abstract:
  We report experimental investigationd of optical pulse group velocity
reduction and probe pulse regeneration using a Raman scheme. The new scheme
which does not rely on the on-one-photon resonance electromagnetically induced
transparency (EIT), has many advantages over the conventional method which
critically relys on the transparency window created by an EIT process. We
demonstrate significant reduction of group velocity, less probe field loss,
reduced probe pulse distortion, and high probe pulse regeneration efficiency.


title: Quantum mechanics in finite dimensional Hilbert space

abstract:
  The quantum mechanical formalism for position and momentum of a particle in a
one dimensional cyclic lattice is constructively developed. Some mathematical
features characteristic of the finite dimensional Hilbert space are compared
with the infinite dimensional case. The construction of an unbiased basis for
state determination is discussed.


title: Generalization of geometric phase to completely positive maps

abstract:
  We generalize the notion of relative phase to completely positive maps with
known unitary representation, based on interferometry. Parallel transport
conditions that define the geometric phase for such maps are introduced. The
interference effect is embodied in a set of interference patterns defined by
flipping the environment state in one of the two paths. We show for the qubit
that this structure gives rise to interesting additional information about the
geometry of the evolution defined by the CP map.


title:
Contextualizing Concepts using a Mathematical Generalization of the
  Quantum Formalism

abstract:
  We outline the rationale and preliminary results of using the State Context
Property (SCOP) formalism, originally developed as a generalization of quantum
mechanics, to describe the contextual manner in which concepts are evoked,
used, and combined to generate meaning. The quantum formalism was developed to
cope with problems arising in the description of (1) the measurement process,
and (2) the generation of new states with new properties when particles become
entangled. Similar problems arising with concepts motivated the formal
treatment introduced here. Concepts are viewed not as fixed representations,
but entities existing in states of potentiality that require interaction with a
context--a stimulus or another concept--to 'collapse' to an instantiated form
(e.g. exemplar, prototype, or other possibly imaginary instance). The stimulus
situation plays the role of the measurement in physics, acting as context that
induces a change of the cognitive state from superposition state to collapsed
state. The collapsed state is more likely to consist of a conjunction of
concepts for associative than analytic thought because more stimulus or concept
properties take part in the collapse. We provide two contextual measures of
conceptual distance--one using collapse probabilities and the other weighted
properties--and show how they can be applied to conjunctions using the pet fish
problem


title:
The Linearity of Quantum Mechanics at Stake: The Description of
  Separated Quantum Entities

abstract:
  We consider the situation of a physical entity that is the compound entity
consisting of two 'separated' quantum entities. In earlier work it has been
proven by one of the authors that such a physical entity cannot be described by
standard quantum mechanics. More precisely, it was shown that two of the axioms
of traditional quantum axiomatics are at the origin of the impossibility for
standard quantum mechanics to describe this type of compound entity. One of
these axioms is equivalent with the superposition principle, which means that
separated quantum entities put the linearity of quantum mechanics at stake. We
analyze the conceptual steps that are involved in this proof, and expose the
necessary material of quantum axiomatics to be able to understand the argument


title: Connectedness Applied to Closure Spaces and State Property Systems

abstract:
  In earlier work a description of a physical entity is given by means of a
state property system and it is proven that any state property system is
equivalent to a closure space. In the present paper we investigate the
relations between classical properties and connectedness for closure spaces.
The main result is a decomposition theorem, which allows us to split a state
property system into a number of 'pure nonclassical state property systems' and
a 'totally classical state property system'


title: Being and Change: Foundations of a Realistic Operational Formalism

abstract:
  The aim of this article is to represent the general description of an entity
by means of its states, contexts and properties. The entity that we want to
describe does not necessarily have to be a physical entity, but can also be an
entity of a more abstract nature, for example a concept, or a cultural
artifact, or the mind of a person, etc..., which means that we aim at very
general description. The effect that a context has on the state of the entity
plays a fundamental role, which means that our approach is intrinsically
contextual. The approach is inspired by the mathematical formalisms that have
been developed in axiomatic quantum mechanics, where a specific type of quantum
contextuality is modelled. However, because in general states also influence
context -- which is not the case in quantum mechanics -- we need a more general
setting than the one used there. Our focus on context as a fundamental concept
makes it possible to unify `dynamical change' and `change under influence of
measurement', which makes our approach also more general and more powerful than
the traditional quantum axiomatic approaches. For this reason an experiment (or
measurement) is introduced as a specific kind of context. Mathematically we
introduce a state context property system as the structure to describe an
entity by means of its states, contexts and properties. We also strive from the
start to a categorical setting and derive the morphisms between state context
property systems from a merological covariance principle. We introduce the
category SCOP with as elements the state context property systems and as
morphisms the ones that we derived from this merological covariance principle.
We introduce property completeness and state completeness and study the
operational foundation of the formalism


title: Reality and Probability: Introducing a New Type of Probability Calculus

abstract:
  We consider a conception of reality that is the following: An object is
'real' if we know that if we would try to test whether this object is present,
this test would give us the answer 'yes' with certainty. If we consider a
conception of reality where probability plays a fundamental role it can be
shown that standard probability theory is not well suited to substitute
'certainty' by means of 'probability equal to 1'. The analysis of this problem
leads us to propose a new type of probability theory that is a generalization
of standard probability theory. This new type of probability is a function to
the set of all subsets of the interval [0, 1] instead of to the interval [0, 1]
itself, and hence its evaluation happens by means of a subset instead of a
number. This subset corresponds to the different limits of sequences of
relative frequency that can arise when an intrinsic lack of knowledge about the
context and how it influences the state of the physical entity under study in
the process of experimentation is taken into account. The new probability
theory makes it possible to define probability on the whole set of experiments
within the Geneva-Brussels approach to quantum mechanics, which was not
possible with standard probability theory. We introduce the structure of a
'state experiment probability system' and derive the state property system as a
special case of this structure. The category SEP of state experiment
probability systems and their morphisms is linked with the category SP of state
property systems and their morphisms


title:
Linearity and Compound Physical Systems: The Case of Two Separated Spin
  1/2 Entities

abstract:
  We illustrate some problems that are related to the existence of an
underlying linear structure at the level of the property lattice associated
with a physical system, for the particular case of two explicitly separated
spin 1/2 objects that are considered, and mathematically described, as one
compound system. It is shown that the separated product of the property
lattices corresponding with the two spin 1/2 objects does not have an
underlying linear structure, although the property lattices associated with the
subobjects in isolation manifestly do. This is related at a fundamental level
to the fact that separated products do not behave well with respect to the
covering law (and orthomodularity) of elementary lattice theory. In addition,
we discuss the orthogonality relation associated with the separated product in
general and consider the related problem of the behavior of the corresponding
Sasaki projections as partial state space mappings


title:
Determination of quantum instrument parameters for a Stern-Gerlach
  non-ideal device

abstract:
  The paper identifies and determines some parameters with experimental
relevance, which could describe the influence of the non-ideality for the
measurement of the intrinsic spin of an atom, using a real Stern-Gerlach
device.


title: Metrics Fluctuational Theory

abstract:
  It is supposed the alternative to Quantum Mechanics Axiomatic. Fluctuational
Theory save the Mathematics of Quantum Mechanic without change, naming this
Mathematics as Method of Indirect Computation.
  Fluctuational Theory is delete the axiomatic of Quantum Mechanics and
replaces it by the assumption of Gravitational Noise. This assumption is
connects the Method of Indirect Computation to the Classical Physics.
  Physical fluctuations of classical gravitational fields are mathematically
expressed through geometric fluctuations of metrics of Riemann Space.
  Metrics Fluctuational Theory and Quantum Mechanic is describe the classical
experiment of electrons interference by two different way.


title: Entanglement concentration of continuous variable quantum states

abstract:
  We propose two probabilistic entanglement concentration schemes for a single
copy of two-mode squeezed vacuum state. The first scheme is based on the
off-resonant interaction of a Rydberg atom with the cavity field while the
second setup involves the cross Kerr interaction, auxiliary mode prepared in a
strong coherent state and a homodyne detection. We show that the
continuous-variable entanglement concentration allows us to improve the
fidelity of teleportation of coherent states.


title: Exact solutions of time-dependent three-generator systems

abstract:
  There exist a number of typical and interesting systems or models which
possess three-generator Lie-algebraic structure in atomic physics, quantum
optics, nuclear physics and laser physics. The well-known fact that all simple
3-generator algebras are either isomorphic to the algebra $sl(2,C)$ or to one
of its real forms enables us to treat these time-dependent quantum systems in a
unified way. By making use of the Lewis-Riesenfeld invariant theory and the
invariant-related unitary transformation formulation, the present paper obtains
exact solutions of the time-dependent Schr\"{o}dinger equations governing
various three-generator quantum systems. For some quantum systems whose
time-dependent Hamiltonians have no quasialgebraic structures, we show that the
exact solutions can also be obtained by working in a sub-Hilbert-space
corresponding to a particular eigenvalue of the conserved generator (i.e., the
time-independent invariant that commutes with the time-dependent Hamiltonian).
The topological property of geometric phase factors in time-dependent systems
is briefly discussed.


title:
Entangled photons, nonlocality and Bell inequalities in the
  undergraduate laboratory

abstract:
  We use polarization-entangled photon pairs to demonstrate quantum nonlocality
in an experiment suitable for advanced undergraduates. The photons are produced
by spontaneous parametric downconversion using a violet diode laser and two
nonlinear crystals. The polarization state of the photons is tunable. Using an
entangled state analogous to that described in the Einstein-Podolsky-Rosen
``paradox,'' we demonstrate strong polarization correlations of the entanged
photons. Bell's idea of a hidden variable theory is presented by way of an
example and compared to the quantum prediction. A test of the Clauser, Horne,
Shimony and Holt version of the Bell inequality finds $S = 2.307 \pm 0.035$, in
clear contradiciton of hidden variable theories. The experiments described can
be performed in an afternoon.


title: Entangled photon apparatus for the undergraduate laboratory

abstract:
  We present detailed instructions for constructing and operating an apparatus
to produce and detect polarization-entangled photons. The source operates by
type-I spontaneous parametric downconversion in a two-crystal geometry. Photons
are detected in coincidence by single-photon counting modules and show strong
angular and polarization correlations. We observe more than 100 entangled
photon pairs per second. A test of a Bell inequality can be performed in an
afternoon.


title: Decoherence in quantum open systems revisited

abstract:
  The following statements belonging to the folklore of the theory of
environmental decoherence are shown to be incorrect: 1) linear coupling to
harmonic oscillator bath is a universal model of decoherence, 2) chaotic
environments are more efficient decoherers.


title: Scalable solid-state quantum processor using subradiant two-atom states

abstract:
  We propose a realization of a scalable, high-performance quantum processor
whose qubits are represented by the ground and subradiant states of effective
dimers formed by pairs of two-level systems coupled by resonant dipole-dipole
interaction. The dimers are implanted in low-temperature solid host material at
controllable nanoscale separations. The two-qubit entanglement either relies on
the coherent excitation exchange between the dimers or is mediated by external
laser fields.


title: Multi-object searching algorithm using subgrouped oracles

abstract:
  We present in this work, if a set of well organized suboracles is available,
an algorithm for multiobject search with certainty in an unsorted database of
$N$ items. Depending on the number of the objects, the technique of phase
tunning is included in the algorithm. If one single object is to be searched,
this algorithm performs a factor of two improvement over the best algorithm for
a classical sorted database. While if the number of the objects is larger than
one, the algorithm requires slightly less than $\log_{4}N$ queries, but no
classical counterpart exists since the resulting state is a superposition of
the marked states.


title: Scheme for preparation of mulipartite entanglement of atomic ensembles

abstract:
  We describe an experimental scheme of preparing multipartite W class of
maximally entangled states between many atomic ensembles. The scheme is based
on laser manipulation of atomic ensembles and single-photon detection, and well
fits the status of the current experimental technology. In addition, we show
one of the applications of the kind of W class states, teleporting an entangled
state of atomic ensembles with unknown coefficients to more than one distant
parties, either one of which equally likely receives the transmitted state.


title:
Interpretation of the Five Dimensional Quantum Propagation of a Spinless
  Massless Particle

abstract:
  We consider a five dimensional (5D) space-time with a space-like fifth
dimension. We implement a quantum formalism by path integrals, and postulate
that all the physical information on a 5D massless particle propagation is
provided by the statistics over null paths in this 5D space-time. If the 5D
metric is independent of the fifth coordinate, then the propagation problem can
be reduced to four dimensions by foliation along the fifth coordinate, and we
obtain a formulation of 4D Quantum Mechanics. If the 5D metric is independent
of time, we foliate along the time coordinate, and obtain a formulation of 4D
Statistical Mechanics. If the 5D metric is independent of both time and the
fifth coordinate, then Quantum and Statistical Mechanics are pictures of the
same 5D reality. We also discuss the foliation of a proper space dimension, the
Klein-Gordon equation, and a 5D Special Relativity, completing our
interpretation of the 5D geometry.


title: Designing Optimal Quantum Detectors Via Semidefinite Programming

abstract:
  We consider the problem of designing an optimal quantum detector to minimize
the probability of a detection error when distinguishing between a collection
of quantum states, represented by a set of density operators. We show that the
design of the optimal detector can be formulated as a semidefinite programming
problem. Based on this formulation, we derive a set of necessary and sufficient
conditions for an optimal quantum measurement. We then show that the optimal
measurement can be found by solving a standard (convex) semidefinite program
followed by the solution of a set of linear equations or, at worst, a standard
linear programming problem. By exploiting the many well-known algorithms for
solving semidefinite programs, which are guaranteed to converge to the global
optimum, the optimal measurement can be computed very efficiently in polynomial
time.
  Using the semidefinite programming formulation, we also show that the rank of
each optimal measurement operator is no larger than the rank of the
corresponding density operator. In particular, if the quantum state ensemble is
a pure-state ensemble consisting of (not necessarily independent) rank-one
density operators, then we show that the optimal measurement is a pure-state
measurement consisting of rank-one measurement operators.


title: Quantum Entanglement of Moving Bodies

abstract:
  We study the properties of quantum information and quantum entanglement in
moving frames. We show that the entanglement between the spins and the momenta
of two particles can be interchanged under a Lorentz transformation, so that a
pair of particles that is entangled in spin but not momentum in one reference
frame, may, in another frame, be entangled in momentum at the expense of
spin-entanglement. Similarly, entanglement between momenta may be transferred
to spin under a Lorentz transformation. While spin and momentum entanglement
each is not Lorentz invariant, the joint entanglement of the wave function is.


title:
Synthesizing NMR analogues of Einstein-Podolsky-Rosen states using
  generalized Grover's algorithm

abstract:
  By designing a proper unitary operator U, we synthesize NMR analogues of
Einstein-Podolsky-Rosen states (pseudo-EPR states) using generalized Grover's
algorithm on a nuclear magnetic resonance (NMR) quantum computer. Experiments
also demonstrate generalized Grover's algorithm for the case in which there are
multiple marked states.


title:
Relations for classical communication capacity and entanglement
  capability of two-qubit operations

abstract:
  Bipartite operations underpin both classical communication and entanglement
generation. Using a superposition of classical messages, we show that the
capacity of a two-qubit operation for error-free entanglement-assisted
bidirectional classical communication can not exceed twice the entanglement
capability. In addition we show that any bipartite two-qubit operation can
increase the communication that may be performed using an ensemble by twice the
entanglement capability.


title: Time-Reversed EPR and the Choice of Histories in Quantum Mechanics

abstract:
  When a single photon is split by a beam splitter, its two `halves' can
entangle two distant atoms into an EPR pair. We discuss a time-reversed
analogue of this experiment where two distant sources cooperate so as to emit a
single photon. The two `half photons,' having interacted with two atoms, can
entangle these atoms into an EPR pair once they are detected as a single
photon. Entanglement occurs by creating indistinguishabilility between the two
mutually exclusive histories of the photon. This indistinguishabilility can be
created either at the end of the two histories (by `erasing' the single
photon's path) or at their beginning (by `erasing' the two atoms' positions).


title:
Two qubits of a W state violate Bell's inequality beyond Cirel'son's
  bound

abstract:
  It is shown that the correlations between two qubits selected from a trio
prepared in a W state violate the Clauser-Horne-Shimony-Holt inequality more
than the correlations between two qubits in any quantum state. Such a violation
beyond Cirel'son's bound is smaller than the one achieved by two qubits
selected from a trio in a Greenberger-Horne-Zeilinger state [A. Cabello, Phys.
Rev. Lett. 88, 060403 (2002)]. However, it has the advantage that all local
observers can know from their own measurements whether their qubits belongs or
not to the selected pair.


title: Focusing of atoms with strongly confined light potentials

abstract:
  Focusing of atoms with light potentials is studied. In particular, we
consider strongly confined, cylindrical symmetric potential, and demonstrate
their applications in both red and blue-detuned focusing of atoms. We also
study the influence of aberrations, and find that a resolution of 1 nm should
in principle be possible.


title:
Bell Inequalities in Four Dimensional Phase Space and the Three Marginal
  Theorem

abstract:
  We address the classical and quantum marginal problems, namely the question
of simultaneous realizability through a common probability density in phase
space of a given set of compatible probability distributions. We consider only
distributions authorized by quantum mechanics, i.e. those corresponding to
complete commuting sets of observables. For four-dimensional phase space with
position variables qi and momentum variables pj, we establish the two following
points: i) given four compatible probabilities for (q1,q2), (q1,p2), (p1,q2)
and (p1,p2), there does not always exist a positive phase space density
rho({qi},{pj}) reproducing them as marginals; this settles a long standing
conjecture; it is achieved by first deriving Bell-like inequalities in phase
space which have their own theoretical and experimental interest. ii) given
instead at most three compatible probabilities, there always exist an
associated phase space density rho({qi},{pj}); the solution is not unique and
its general form is worked out. These two points constitute our ``three
marginal theorem''.


title: Energy spectra of two electrons in a circular quantum dot

abstract:
  The electron interaction energy of two interacting electrons in a circular
quantum dot (with hard wall confinement) is investigated in the framework of
the semi-classical Wentzel-Kramers-Brillouin (WKB) approximation. The two
electrons are assumed to be in an infinitely deep well of radius $r_0$, in a
simple configuration with one electron fixed at the origin. The corresponding
Schrodinger equation, with hard wall boundary conditions, is also solved
exactly by numerical integration. It is observed that the agreement between the
two energy values is quite good, suggesting that the WKB approximation works
well for such a confined quantum system as well. This may provide motivation to
extend this to more realistic confined potentials.


title: Relativistic corrections to the Ekert test for eavesdropping

abstract:
  A degree of violation of the Bell inequality depends on momenta of massive
particles with respect to a laboratory if spin plays a role af a "yes--no"
observable. For ultra-relativistic particles the standard Ekert test has to
take into accont this velocity dependent suppression of the degree of violation
of the inequality. Otherwise Alice and Bob may "discover" a nonexisting
eavesdropper.


title: Invitation to quantum dynamical semigroups

abstract:
  The theory of quantum dynamical semigroups within the mathematically rigorous
framework of completely positive dynamical maps is reviewed. First, the
axiomatic approach which deals with phenomenological constructions and general
mathematical structures is discussed. Then basic derivation schemes of the
constructive approach including singular coupling, weak coupling and low
density limits are presented in their higly simplified versions. Two-level
system coupled to a heat bath, damped harmonic oscillator, models of
decoherence, quantum Brownian particle and Bloch-Boltzmann equations are used
as illustrations of the general theory. Physical and mathematical limitations
of the quantum open system theory, the validity of Markovian approximation and
alternative approaches are discussed also.


title: Outline for a formal general theory of physical measurements

abstract: The paper gives the main lines of a general theory for physical measurements.


title: Spontaneous emission suppression on arbitrary atomic transitions

abstract:
  We propose a very simple scheme to slow down the usual exponential decay of
upper state population in an atomic two level system considerably. The scheme
makes use of an additional intense field with frequency lower than the total
decay width of the atomic transition. This allows for additional decay channels
with the exchange of one or more low-frequency photons during an atomic
transition. The various channels may then interfere with each other. The
intensity and the frequency of the low-frequency field are shown to act as two
different control parameters modifying the duration and the amount of the
population trapping. An extension of the scheme to include transitions to more
than one lower state is straightforward.


title: Security of quantum cryptography using balanced homodyne detection

abstract:
  In this paper we investigate the security of a quantum cryptographic scheme
which utilizes balanced homodyne detection and weak coherent pulse (WCP). The
performance of the system is mainly characterized by the intensity of the WCP
and postselected threshold. Two of the simplest intercept/resend eavesdropping
attacks are analyzed. The secure key gain for a given loss is also discussed in
terms of the pulse intensity and threshold.


title:
Dipole-Dipole Coupling in the Presence of Dispersing and Absorbing
  Bodies

abstract:
  An effective Hamiltonian and equations of motion for treating both the
resonant dipole-dipole interaction between two-level atoms and the resonant
atom-field interaction are derived, which can suitably be used for studying the
influence of arbitrary dispersing and absorbing material surroundings on these
interactions. It is shown that the dipole-dipole interaction and the atom-field
interaction, respectively, are closely related to the real part and the
imaginary part of the (classical) Green tensor. The theory is applied to the
study of the transient behavior of two atoms that initially share a single
excitation, with special emphasis on the role of the two competing processes of
virtual and real photon exchange in the energy transfer between the atoms. To
illustrate the powerfulness of the theory, specific results for the case of the
atoms being near a dispersing and absorbing microsphere are presented. In
particular, the regimes of weak and strong atom-field coupling are addressed.


title: Experimental Quantum Computation with Nuclear Spins in Liquid Solution

abstract:
  We have taken significant steps towards the realization of a practical
quantum computer: using nuclear spins and magnetic resonance techniques at room
temperature, we provided proof of principle of quantum computing in a series of
experiments which culminated in the implementation of the simplest instance of
Shor's quantum algorithm for prime factorization (15=3x5), using a seven-spin
molecule. This algorithm achieves an exponential advantage over the best known
classical factoring algorithms and its implementation represents a milestone in
the experimental exploration of quantum computation. These remarkable successes
have been made possible by the synthesis of suitable molecules and the
development of many novel techniques for initialization, coherent control and
readout of the state of multiple coupled nuclear spins. Furthermore, we devised
and implemented a model to simulate both unitary and decoherence processes in
these systems, in order to study and quantify the impact of various
technological as well as fundamental sources of errors. In summary, this work
has given us a much needed practical appreciation of what it takes to build a
quantum computer. While liquid NMR quantum computing has well-understood
scaling limitations, many of the techniques that originated from this research
may find use in other, perhaps more scalable quantum computer implementations.


title:
Eliminating nonlinear phase mismatch in resonantly enhanced 4-wave
  mixing

abstract:
  Resonantly enhanced four wave mixing in double-Lambda systems is limited by
ac-Stark induced nonlinear phase shifts. With counter-propagating pump fields
the intensity-phase coupling has minimal impact on the dynamics, but it is of
critical importance for co-propagation. The nonlinear phase terms lead to an
increase of the conversion length linearly proportional to the inverse seed
intensity, while without nonlinear phase-mismatch the scaling is only
logarithmic. We here show that the ac-Stark contributions can be eliminated
while retaining the four-wave mixing contribution by choosing a suitable five
level system with appropriate detunings.


title: Comment on "How the No-Cloning Theorem Got its Name"

abstract:
  A review by A. Peres [quant-ph/0205076] appears recently. It is difficult to
add something to such kind of fundamental themes, but here is briefly presented
some ideas about challenges of the no-cloning theorem and imaginary
modifications of quantum mechanics, that could make precise cloning possible.


title: High efficiency photon counting using stopped light

abstract:
  Single-photon detection and photon counting play a central role in a large
number of quantum communication and computation protocols. While the efficiency
of state-of-the-art photo-detectors is well below the desired limits, quantum
state measurements in trapped ions can be carried out with efficiencies
approaching 100%. Here, we propose a method that can in principle achieve ideal
photon counting, by combining the techniques of photonic quantum memory and
ion-trap fluorescence detection: after mapping the quantum state of a
propagating light pulse onto metastable collective excitations of a trapped
cold atomic gas, it is possible to monitor the resonance fluorescence induced
by an additional laser field that only couples to the metastable excited state.
Even with a photon collection/detection efficiency as low as 10%, it is
possible to achieve photon counting with efficiency approaching 100%.


title: The role of entanglement in dynamical evolution

abstract:
  Entanglement or entanglement generating interactions permit to achieve the
maximum allowed speed in the dynamical evolution of a composite system, when
the energy resources are distributed among subsystems. The cases of
pre-existing entanglement and of entanglement-building interactions are
separately addressed. The role of classical correlations is also discussed.


title: Relationship between the wave function and space

abstract:
  We criticize the current standard interpretation of quantum mechanics, review
its paradoxes with attention to non-locality, and conclude that a
reconsideration of it must be made. We underline the incompatibility of the
conceptions ascribed to space of field, and stage in modern theories, with
differing roles for coordinates. We hence trace the non-locality difficulty to
the identification of the basis space of the wave function and physical space.
An interpretation of the wave function in which space loses its stage use at
the local level, and its physical (field) meaning is assigned to the wave
function, can solve this difficulty. An application of this proposal implies a
field-equation extension based on a unified description of bosons and fermions
able to provide new information on the standard model.


title: How Powerful is Adiabatic Quantum Computation?

abstract:
  We analyze the computational power and limitations of the recently proposed
'quantum adiabatic evolution algorithm'.


title: Aharanov Anandan Phase for the Quasi Exactly Solvable Bose Systems

abstract:
  An extended notion of quasi-exactly solvable potential model is used here to
treat quasi exactly solvable (QES) Bose systems. We report an analytic
expression for the Ahoronov Anandan non-adiabatic geometric phase for the QES
Bose system in general. The generalized expression is then used to study some
particular cases of physical interest and we observe that the geometric phase
can be tuned.


title: SU(N) Coherent States

abstract:
  We generalize Schwinger boson representation of SU(2) algebra to SU(N) and
define coherent states of SU(N) using $2(2^{N-1}-1)$ bosonic harmonic
oscillator creation and annihilation operators. We give an explicit
construction of all (N-1) Casimirs of SU(N) in terms of these creation and
annihilation operators. The SU(N) coherent states belonging to any irreducible
representations of SU(N) are labelled by the eigenvalues of the Casimir
operators and are characterized by (N-1) complex orthonormal vectors describing
the SU(N) manifold. The coherent states provide a resolution of identity,
satisfy the continuity property, and possess a variety of group theoretic
properties.


title: Uncertainty In Quantum Computation

abstract:
  We examine the effect of previous history on starting a computation on a
quantum computer. Specifically, we assume that the quantum register has some
unknown state on it, and it is required that this state be cleared and replaced
by a specific superposition state without any phase uncertainty, as needed by
quantum algorithms. We show that, in general, this task is computationally
impossible.


title: Conditional quantum logic using two atomic qubits

abstract:
  In this paper we propose and analyze a feasible scheme where the detection of
a single scattered photon from two trapped atoms or ions performs a conditional
unitary operation on two qubits. As examples we consider the preparation of all
four Bell states, the reverse operation that is a Bell measurement, and a CNOT
gate. We study the effect of atomic motion and multiple scattering, by
evaluating Bell inequalities violations, and by calculating the CNOT gate
fidelity.


title: Separability of mixed quantum states: linear contractions approach

abstract:
  Recently, a new and powerful separability criterion was introduced in [O.
Rudolph, quant-ph/0202121] and [Chen {\it et al.}, quant-ph/0205017]. Composing
the main idea behind the above criterion and the necessary and sufficient
condition in terms of positive maps, we provide a characterization of separable
states by means of linear contractions. The latter need not be positive maps.
We extend the idea to multipartite systems, and find that, somewhat
suprisingly, partial realigment (unlike partial transposition) can detect
genuinely triparite entanglement. We also show that for multipartite system any
permutation of indices of density matrix leads to separability criterion.


title:
On a subject of diverse improvisations: The uncertainty relations on a
  circle

abstract:
  The disputed question of uncertainty relations (UR) on a circle is regarded
as a particular element of a more general problem which refers to the quantum
description of angular observables $L_z$ and $\phi$. The improvised $L_z-\phi$
UR are found to be affected by unsourmontable shortcomings. Also in
contradiction with a largely accepted belief it is proved that the usual
procedures of quantum mechanics are accurately applicable for the $L_z-\phi$
pair. The applicability regards both the known circular motions and the less
known non-circular rotational motions. The presented facts contribute as
arguments to the following indubitable conclusions: (i) the traditional
interpretation of UR must be denied as an incorrect doctrine, (ii) for a
natural physical consideration of the the $L_z-\phi$ pair the results from the
usual quantum mechanics are sufficient while the improvised $L_z-\phi$ UR must
be rejected as senseless formulas and (iii) the descriptions of quantum
measurements have to be done in a framework which is distinct and additional in
respect with the usual quantum mechanics.


title: A possible new approach of quantum measurements

abstract:
  It is proposed a possible new approach of quantum measurements (QMS),
disconnected of the traditional interpretation of uncertainty relations and
independent of any appeal to the strange idea of collapse (reduction) of wave
functions. The new approach regards QMS as a statistical samplings (but not as
simple detection acts) and their description as a distinct task, independent of
actual procedures of quantum mechanics. A QMS is described by means of
transformations of probability density and probability current, from intrinsic
into recorded readings. The quantum observables appear as random variables,
described by usual operators and valuable through probabilistic numerical
parameters (mean values, correlations and standard deviations). The values of
the respective parameters are not the same in the two mentioned readings. Then
the measurement uncertainties (errors) are described by means of the changes in
the alluded values. The new QMS approach is illustrated through an
one-dimensional example.


title: Classical and Quantum Oscillators of Sextic and Octic Anharmonicities

abstract:
  Classical oscillators of sextic and octic anharmonicities are solved
analytically up to the linear power of \lambda (Anharmonic Constant) by using
Taylor series method. These solutions exhibit the presence of secular terms
which are summed up for all orders. The frequency shifts of the oscillators for
small anharmonic constants are obtained. It is found that the calculated shifts
agree nicely with the available results to-date. The solutions for classical
anharmonic oscillators are used to obtain the solutions corresponding to
quantum anharmonic oscillators by imposing fundamental commutation relations
between position and momentum operators.


title: Coherent states, entanglement, and geometric invariant theory

abstract:
  The main objective of the paper is to unveil an adequate mathematics hidden
behind entanglement, that is Geometric Invariant Theory. More specifically
relation between these two subjects can be described by the following theses.
  (i) Total variance of completely entangled state is maximal. (ii) This
distinguishes the state as a minimal vector in its orbit under action of
complexified dynamic group.
  (iii) An ultimate aim of Geometric Invariant Theory is a description of
complex orbits and their minimal vectors. It suggests that noncompletely
entangled states are just GIT semistable vectors.


title:
The interplay of supersymmetry and PT symmetry in quantum mechanics: a
  case study for the Scarf II potential

abstract:
  Motivated by the duality of normalizable states and the presence of the
quasi-parity quantum number q=+/-1 in PT symmetric (non-Hermitian) quantum
mechanical potential models, the relation of PT symmetry and supersymmetry
(SUSY) is studied. As an illustrative example the PT invariant version of the
Scarf II potential is presented, and it is shown that the "bosonic" Hamiltonian
has two different "fermionic" SUSY partner Hamiltonians (potentials) generated
from the ground-state solutions with q=1 and q=-1. It is shown that the
"fermionic" potentials cease to be PT invariant when the PT symmetry of the
"bosonic" potential is spontaneously broken. A modified PT symmetry inspired
SUSY construction is also discussed, in which the SUSY charge operators contain
the antilinear operator T. It is shown that in this scheme the "fermionic"
Hamitonians are just the complex conjugate of the original "fermionic"
Hamiltonians, and thus possess the same energy eigenvalues.


title: Survival of the Fittest and Zero Sum Games

abstract:
  Competition for available resources is natural amongst coexisting species,
and the fittest contenders dominate over the rest in evolution. The dynamics of
this selection is studied using a simple linear model. It has similarities to
features of quantum computation, in particular conservation laws leading to
destructive interference. Compared to an altruistic scenario, competition
introduces instability and eliminates the weaker species in a finite time.


title: Ladder proof of nonlocality for two spin-half particles revisited

abstract:
  In this paper we extend the ladder proof of nonlocality without inequalities
for two spin-half particles given by Boschi et al [PRL 79, 2755 (1997)] to the
case in which the measurement settings of the apparatus measuring one of the
particles are different from the measurement settings of the apparatus
measuring the other particle. It is shown that, in any case, the proportion of
particle pairs for which the contradiction with local realism goes through is
maximized when the measurement settings are the same for each apparatus. Also
we write down a Bell inequality for the experiment in question which is
violated by quantum mechanics by an amount which is twice as much as the amount
by which quantum mechanics violates the Bell inequality considered in the above
paper by Boschi et al.


title: The Dirac Equation in Classical Statistical Mechanics

abstract:
  The Dirac equation, usually obtained by `quantizing' a classical stochastic
model is here obtained directly within classical statistical mechanics. The
special underlying space-time geometry of the random walk replaces the missing
analytic continuation, making the model `self-quantizing'. This provides a new
context for the Dirac equation, distinct from its usual context in relativistic
quantum mechanics.


title:
Experimental demonstration of continuous variable polarization
  entanglement

abstract:
  We report the experimental transformation of quadrature entanglement between
two optical beams into continuous variable polarization entanglement. We extend
the inseparability criterion proposed by Duan, et al. [Duan00] to polarization
states and use it to quantify the entanglement between the three Stokes
operators of the beams. We propose an extension to this scheme utilizing two
quadrature entangled pairs for which all three Stokes operators between a pair
of beams are entangled.


title: Enhancement of thermal entanglement in two-qubit XY models

abstract:
  We analyze conditions leading to enhancement of thermal entanglement in
two-qubit XY models. The effect of including cross-product terms, besides the
standard XY exchange interactions, in the presence of an external magnetic
field, is investigated. We show that entanglement can be yield at elevated
temperatures by tuning the orientation of the external magnetic field. The
details of the intrinsic exchange interactions determine the optimal
orientation.


title:
The Innsbruck quantum teleportation experimental scheme can be modified
  to the unconditional one

abstract:
  We show that the Innsbruck quantum teleportation experiment(Bouwmeester D et
al, Nature 390, 575(1997)) can be modified by using the polarized beam
splitter. In this modified scheme, Bob does not have to do any meassurement and
an unknown state from Victor can be verified to be teleported to Bob from Alice
by the currently exisiting technology, i.e., by using the normal photon
detectors which do not distinguish one photon and two photons.


title: Time scale of forerunners in quantum tunneling

abstract:
  The forerunners preceding the main tunneling signal of the wave created by a
source with a sharp onset or by a quantum shutter, have been generally
associated with over-the-barrier (non-tunneling) components. We demonstrate
that, while this association is true for distances which are larger than the
penetration lenght, for smaller distances the forerunner is dominated by
under-the-barrier components. We find that its characteristic arrival time is
inversely proportional to the difference between the barrier energy and the
incidence energy, a tunneling time scale different from both the phase time and
the B\"uttiker-Landauer (BL) time.


title: Entanglement and Properties

abstract:
  Various topics concerning the entanglement of composite quantum systems are
considered with particular emphasis concerning the strict relations of such a
problem with the one of attributing objective properties to the constituents.
In particular we will focus our attention to composite quantum systems composed
of identical constituents, with the purpose of dealing with subtle issues,
which have never been adequately discussed in the literature, originating from
the true indistinguishability of the subsystems involved.


title:
Covariant Effective Action for Quantum Particle with
  Coordinate-Dependent Mass

abstract:
  Using a covariant background field method we calculate the one-loop quantum
effective action for a particle with coordinate-dependent mass moving slowly
through a one-dimensional configuration space. The procedure can easily be
extended to any desired loop order.


title:
Tractability of Approximation for Weighted Korobov Spaces on Classical
  and Quantum Computers

abstract:
  The paper studies quantum complexity, tractability, and strong tractability
for high dimensional multivariate approximation. We study a space of functions
important in many applications. A function space is weighted if certain
variables are more important than others; the weights show the relative
importance of the variables. In an unweighted space all variables are equally
important and multivariate approximation is intractable. We want to study when
the complexity of multivariate approximation is independent of the number of
variables and depends polynomially on 1/E. The main conclusions are:
Multivariate approximation on a quantum computer can be solved roughly
(1/E)^(1+r) times faster than on a classical computer using randomization.
Here, r is a positive parameter that depends on the weights and may be large.
This means that the speed-up of quantum over classical computers may be much
larger than quadratic. Multivariate approximation on a quantum computer is
exponentially faster than on a classical computer with a worst case assurance
even if the sum of weights is infinite but a certain power of them is finite.
We have designed a quantum algorithm with error at most E that uses about
d+log(1/E) qubits. Hence, we have only linear dependence on the dimension d and
logarithmic dependence on 1/E. Therefore, for some applications the number of
qubits is quite modest.


title:
Two-photon linewidth of light "stopping" via electromagnetically induced
  transparency

abstract:
  We analyze the two-photon linewidth of the recently proposed adiabatic
transfer technique for ``stopping'' of light using electromagnetically induced
transparency (EIT). We shown that a successful and reliable transfer of
excitation from light to atoms and back can be achieved if the spectrum of the
input probe pulse lies within the initial transparency window of EIT, and if
the two-photon detuning $\delta$ is less than the collective coupling strength
(collective vacuum Rabi-frequency) $g\sqrt{N}$ divided by $\sqrt{\gamma T}$,
with $\gamma$ being the radiative decay rate, $N$ the effective number of atoms
in the sample, and $T$ the pulse duration. Hence in an optically thick medium
light ``storage'' and retrieval is possible with high fidelity even for systems
with rather large two-photon detuning or inhomogeneous broadening.


title:
Universal Fault-Tolerant Quantum Computation in the Presence of
  Spontaneous Emission and Collective Dephasing

abstract:
  A universal and fault tolerant scheme for quantum computation is proposed
which utilizes a class of error correcting codes that is based on the detection
of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme
is compatible with a number of promising solid-state and quantum-optical
proposals for quantum computer implementations, such as quantum dots in
cavities, electrons on helium, and trapped ions.


title: The Spirit and the Letter of Copenhagen: A Response to Andrei Khrennikov

abstract:
  The present communication addresses (by way of a response to Andrei
Khrennikov's recent argument), the epistemology of quantum mechanics and Bohr's
interpretation of quantum mechanics as complementarity.


title: Understanding Quantum Superarrivals using the Bohmian model

abstract:
  We investigate the orgin of ``quantum superarrivals'' in the reflection and
transmission probabilities of a Gaussian wave packet for a rectangular
potential barrier while it is perturbed by either reducing or increasing its
height. There exists a finite time interval during which the probability of
reflection is {\it larger} (superarrivals) while the barrier is {\it lowered}
compared to the unperturbed case. Similarly, during a certain interval of time,
the probability of transmission while the barrier is {\it raised} {\it exceeds}
that for free propagation. We compute {\it particle trajectories} using the
Bohmian model of quantum mechanics in order to understand {\it how} this
phenomenon of superarrivals occurs.


title: Quantum Plain and Carry Look-Ahead Adders

abstract:
  In this paper, two quantum networks for the addition operation are presented.
One is the Modified Quantum Plain (MQP) adder, and the other is the Quantum
Carry Look-Ahead (QCLA) adder. The MQP adder is obtained by modifying the
Conventional Quantum Plain (CQP) adder. The QCLA adder is an extension of
conventional digital Carry Look-Ahead adder. Compared with the CQP adder, two
main advantages are as follows: First, the proposed MQP and QCLA adders have
less number of elementary gates than the CQP adder. Secondly, the number of
processing stages of the MQP and QCLA adder are less than ones of the CQP
adder. As a result, the throughput time for computing the sum of two numbers on
the quantum computer can be improved.


title: The classical limit for a class of quantum baker's maps

abstract:
  We show that the class of quantum baker's maps defined by Schack and Caves
have the proper classical limit provided the number of momentum bits approaches
infinity. This is done by deriving a semi-classical approximation to the
coherent-state propagator.


title:
Nonclassical Total Probability Formula and Quantum Interference of
  Probabilities

abstract:
  Interpretation of the nonclassical total probability formula arising in some
quantum experiments is provided based on stochastic models described by means
of a sequence of random vectors changing in the measurement procedures.


title:
Better detection of Multipartite Bound Entanglement with Three-Setting
  Bell Inequalities

abstract:
  It was shown in Phys. Rev. Lett., 87, 230402 (2001) that N (N >= 4) qubits
described by a certain one parameter family F of bound entangled states violate
Mermin-Klyshko inequality for N >= 8. In this paper we prove that the states
from the family F violate Bell inequalities derived in Phys. Rev. A, 56, R1682
(1997), in which each observer measures three non-commuting sets of orthogonal
projectors, for N >=7. We also derive a simple one parameter family of
entanglement witnesses that detect entanglement for all the states belonging to
F. It is possible that these new entanglement witnesses could be generated by
some Bell inequalities.


title:
PT symmetry breaking and explicit expressions for the pseudo-norm in the
  Scarf II potential

abstract:
  Closed expressions are derived for the pseudo-norm, norm and orthogonality
relations for arbitrary bound states of the PT symmetric and the Hermitian
Scarf II potential for the first time. The pseudo-norm is found to have
indefinite sign in general. Some aspects of the spontaneous breakdown of PT
symmetry are analysed.


title:
Manipulating the shape of electronic non-dispersive wave-packets in the
  hydrogen atom: numerical tests in realistic experimental conditions

abstract:
  We show that combination of a linearly polarized resonant microwave field and
a parallel static electric field may be used to create a non-dispersive
electronic wavepacket in Rydberg atoms. The static electric field allows for
manipulation of the shape of the elliptical trajectory the wavepacket is
propagating on. Exact quantum numerical calculations for realistic experimental
parameters show that the wavepacket evolving on a linear orbit can be very
easily prepared in a laboratory either by a direct optical excitation or by
preparing an atom in an extremal Stark state and then slowly switching on the
microwave field. The latter scheme seems to be very resistant to experimental
imperfections. Once the wavepacket on the linear orbit is excited, the static
field may be used to manipulate the shape of the orbit.


title:
Critique of an Experiment Regarding Quantum States in a Gravitational
  Field and Possible Geometrical Explanations

abstract:
  We discuss an experiment conducted by Nesvizhevsky et al. As it is the first
experiment claimed to have observed gravitational quantum states, it is
imperative to investigate all alternative explanations of the result. In a
student project course in applied quantum mechanics, we consider the
possibility of quantummechanical effects arising from the geometry of the
experimental setup, due to the "cavity" formed. We try to reproduce the
experimental result using geometrical arguments only. Due to the influence of
several unknown parameters our result is still inconclusive.


title: Kochen-Specker Theorem for Finite Precision Spin One Measurements

abstract:
  Unsharp spin 1 observables arise from the fact that a residual uncertainty
about the actual orientation of the measurement device remains. If the
uncertainty is below a certain level, and if the distribution of measurement
errors is covariant under rotations, a Kochen-Specker theorem for the unsharp
spin observables follows: There are finite sets of directions such that not all
the unsharp spin observables in these directions can consistently be assigned
approximate truth-values in a non-contextual way.


title: Geometric phases for wave packets in a uniform magnetic field

abstract:
  A wave packet of a charged particle always make cyclic circular motion in a
uniform magnetic field, just like a classical particle. The nonadiabatic
geometric phase for an arbitrary wave packet can be expressed in terms of the
mean value of a number operator. For a large class of wave packets, the
geometric phase is proportional to the magnetic flux encircled by the orbit of
the wave packet. For more general wave packets, however, the geometric phase
contains an extra term.


title:
Experimentally realizable characterizations of continuous variable
  Gaussian states

abstract:
  Measures of entanglement, fidelity and purity are basic yardsticks in quantum
information processing. We propose how to implement these measures using linear
devices and homodyne detectors for continuous variable Gaussian states. In
particular, the test of entanglement becomes simple with some prior knowledge
which is relevant to current experiments.


title: Spatial antibunching of photons with parametric down-conversion

abstract:
  The theoretical framework behind a recent experiment by Nogueira et. al.
[Phys. Rev. Lett. 86}, 4009 (2001)] of spatial antibunching in a two-photon
state generated by collinear type II parametric down-conversion and a
birefringent double-slit is presented. The fourth-order quantum correlation
function is evaluated and shown to violate the classical Schwarz-type
inequality, ensuring that the field does not have a classical analog. We expect
these results to be useful in the rapidly growing fields of quantum imaging and
quantum information.


title: Experimental observation of spatial antibunching of photons

abstract:
  We report an interference experiment that shows transverse spatial
antibunching of photons. Using collinear parametric down-conversion in a
Young-type fourth-order interference setup we show interference patterns that
violate the classical Schwarz inequality and should not exist at all in a
classical description.


title:
Producing the {\it a priori} pure entangled states by type II prametric
  downconversion

abstract:
  We propose a scheme to produce the pure entangled states through type II
downconversion. In the scheme, the vacuum states are excluded and the a prori
pure entangled states are produced and verified without destroying the state
itself. This can help to carry out the many unditional experiments related to
quantum entanglement.


title: Entanglement of individual photon and atomic ensembles

abstract:
  Here we present an experimentally feasible scheme to entangle flying qubit
(individual photon with polarization modes) and stationary qubit (atomic
ensembles with long-lived collective excitations). This entanglement integrate
two different species can act as a critical element for the coherent transform
of quantum information between flying and stationary qubits. The entanglement
degree can be also adjusted expediently with linear optics. Furthermore, the
present scheme can be modified to generate this entanglement in a way
event-ready with the employment of a pair of entangled photons. Then successful
preparation can be unambiguously heralded by coincident between two
single-photon detectors. Its application for individal photons quantum memory
is also analyzed. The physical requirements of all those preparation and
applications processing are moderate, and well fit the present technique.


title: Does Excess Quantum Noise Exist in Spontaneous Processes?

abstract:
  We investigate the role of excess quantum noise in type-II degenerate
parametric down conversion in a cavity with non-orthogonal polarization
eigenmodes. Since only two modes are involved we are able to derive an
analytical expression for the twin-photon generation rate measured outside the
cavity as a function of the degree of mode nonorthogonality. Contrary to recent
claims we conclude that there is no evidence of excess quantum noise for a
parametric amplifier working so far below threshold that spontaneous processes
dominate.


title: Stability properties of |Psi|^2 in Bohmian dynamics

abstract:
  According to Bohmian dynamics, the particles of a quantum system move along
trajectories, following a velocity field determined by the wave-function
Psi(x,t). We show that for simple one-dimensional systems any initial
probability distribution of a statistical ensemble approaches asymptotically
|Psi(x,t)}|^2 if the system is subject to a random noise of arbitrarily small
intensity.


title: Local Detection of Entanglement

abstract:
  We construct an explicit model where it can be established if a two mode pure
Gaussian system is entangled or not by acting only on one of the parts that
constitute the system. Measuring the dispersion in momentum and the time
evolution of the dispersion in position of one particle we can tell if
entanglement is present as well as the degree of entanglement of the system.


title: Equations of motion in odd-dimensional spaces and T-, C-invariance

abstract:
  The properties of the equation of Dirac type in three-dimensional and
five-dimensional Minkowski space-time with respect to time reflection (in sense
of Pauli and Wigner) as well as to the operation of charge conjugation are
investigated. P-, T-, C-invariance of Dirac equation for the cases of four
components (in three-dimentional space) and eight components (in
five-dimensional space) is established. Within the framework of the Poincare
group a relativistic equation is suggested wich describes the movement of a
particle with non-fixed (indefinite) mass in external electromagnetic field.


title: Logical Inconsistencies in Proofs of the Theorem of Bell

abstract:
  We discuss a class of proofs of Bell-type inequalities that are based on
tables of potential outcomes. These proofs state in essence: if one can only
imagine (or write down in a table) the potential outcome of a hidden parameter
model for EPR experiments then a contradiction to experiment and quantum
mechanics follows. We show that these proofs do not contain hidden variables
that relate to time or, if they do, lead to logical contradictions that render
them invalid.


title:
On representations of the inhomogeneous de Sitter group and equations in
  five-dimensional Minkowski space

abstract:
  This paper is a continuation and elaboration of our brief notice
quant-ph/0206057 (Nucl. Phys. B, 1968, 7, 79) where some approach to the
variable-mass problem was proposed. Here we have found a definite realization
of irreducible representations of the inhomogeneous group P(1,n), the group of
translations and rotations in (1+n)-dimensional Minkowski space, in two classes
(when P_0^2-P_k^2>0 and P_0^2-P_k^2<0). All P(1,n)-invariant equations of the
Schrodinger-Foldy type are written down. Some equations of physical
interpretation of the quantal scheme based on the inhomogeneous de Sitter group
P(1,4) are discussed. The analysis of the Dirac and Kemmer-Duffin type
equations in the P(1,4) scheme is carried out. A concrete realization of
representations of the algebra P(1,4) connected with this equations, is
obtained. The transformations of the Foldy-Wouthuysen type for this equations
are found. It is shown that in the P(1,4) scheme of the Kemmer-Duffin type
equation describes a fermion multiplet like the nucleon-antinucleon.


title:
On representations of the inhomogeneous de Sitter group and on equations
  of the Schrodinger-Foldy type

abstract:
  This paper is a continuation and elaboration of our work quant-ph/0206057
(Nucl. Phys. B, 1968, 7, 79) where some approach to the variable-mass problem
were proposed. Here we have found a concret realization of irreducible
representations of the inhomogeneous group P(1,n) - the group of translations
and rotations in (1+n)-dimensional Minkowski space in two classes (when
P_0^2-P_k^2>0 and P_0^2-P_k^2<0). All the P(1,n)-invariant equations of the
Schrodinger-Foldy type are written down. Some questions of a physical
interpretation of the quantum, mechanical scheme based on the inhomogeneous de
Sitter group P(1,n) are discussed.


title:
Atomic vapor-based high efficiency optical detectors with photon number
  resolution

abstract:
  We propose a novel approach to the important fundamental problem of detecting
weak optical fields at the few photon level. The ability to detect with high
efficiency (>99%), and to distinguish the number of photons in a given time
interval is a very challenging technical problem with enormous potential
pay-offs in quantum communications and information processing. Our proposal
diverges from standard solid-state photo-detector technology by employing an
atomic vapor as the active medium, prepared in a specific quantum state using
laser radiation. The absorption of a photon will be aided by a dressing laser,
and the presence or absence of an excited atom will be detected using the
``cycling transition'' approach perfected for ion traps. By first incorporating
an appropriate upconversion scheme, our method can be applied to a wide variety
of optical wavelengths.


title: Phase space localization of a scalar charged particle

abstract:
  The thesis is devoted to the phase space representation of relativistic
quantum mechanics. For a class of observables with matrix-valued Weyl symbols
proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is
proposed. The evolution equations are found to coincide with their counterparts
in relativistic quantum mechanics with non-local Hamiltonian. The difference
between the theories is connected with peculiarities of the constraints on the
initial conditions. Effective increase in coherence between eigenstates of the
Hamiltonian is found. Relativistic coherent states that take into account a
non-trivial charge structure of the position and momentum operators and satisfy
the charge superselection rule are considered. On this basis, the entangled
coherent states are developed.


title: Hydrodynamic Models of Quantum Mechanics

abstract: This paper has been withdrawn by the author.


title: Non-locality of Quantum Mechanics and the Locality of General Relativity

abstract:
  The conflict between the locality of general relativity, reflected in its
space-time description, and the non-locality of quantum mechanics, contained in
its Hilbert space description, is discussed. Gauge covariant non-local
observables that depend on gauge fields and gravity as well as the wave
function are used in order to try to understand and minimize this conflict
within the frame-work of these two theories. Applications are made to the
Aharonov-Bohm effect and its generalizations to non Abelian gauge fields and
gravity.


title: Quantum random walks in one dimension

abstract:
  This letter treats the quantum random walk on the line determined by a 2
times 2 unitary matrix U. A combinatorial expression for the mth moment of the
quantum random walk is presented by using 4 matrices, P, Q, R and S given by U.
The dependence of the mth moment on U and initial qubit state phi is clarified.
A new type of limit theorems for the quantum walk is given. Furthermore
necessary and sufficient conditions for symmetry of distribution for the
quantum walk is presented. Our results show that the behavior of quantum random
walk is striking different from that of the classical ramdom walk.


title:
Cornelius Lanczos -- Discoveries in the Quantum and General Relativity
  Theories

abstract:
  Two of Lanczos' seminal contributions in physics that are not generally known
about in the physics community are discussed and commented in relation to more
recent investigations: First, his integral formulation of the Schroedinger
equation that he published just before Schroedinger himself published his
differential equation formulation of quantum mechanics, and, second, his
solution to the problem of equations of motion of material particles in the
theory of general relativity.


title:
Pseudo-Hermiticity, weak pseudo-Hermiticity and eta-orthogonality
  condition

abstract:
  We discuss certain features of pseudo-Hermiticity and weak pseudo-Hermiticity
conditions and point out that, contrary to a recent claim, there is no
inconsistency if the correct orthogonality condition is used for the class of
pseudo-Hermitian, PT-symmetric Hamiltonians of the type $H_{\beta} = [p + {\rm
i} \beta \nu(x)]^2/2m + V(x)$.


title: A relativistically invariant mass operator

abstract:
  In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given
(discrete) mass spectrum of elementary or hypothetical particles, it was
possible to construct a non-trivial algebra G containing a Poincare algebra P
as a subalgebra so that the mass operator, defined throughout the space where
one of the irreducible representations G is given, is self-conjugate and its
spectrum coincides with the given mass spectrum. Such an algebra was
constructed in explicit form for the nonrelativistic case, i.e., the generators
were written for the algebra. However, the problem of how to assign the algebra
G constructively and determine an explicit form of the mass operator in the
relativistic case has remained unsolved. In the present work we present a
solution of this problem, construct continuum analogs of the classical algebras
U(N) and Sp(2N), and show that the problem of including the Poincare algebra
can be formulated in the language of wave function equations.


title: On a possible approach to the variable-mass problem

abstract:
  The mass operator M is introduced as an independent dynamical variable which
is taken as the translation generator P_4 of the inhomogenous De Sitter group.
The classification of representations of the algebra P(1,4) of this group is
performed and the corresponding P(1,4) invariant equations for variable-mass
particles are written out. In this way we have succeeded, in particular, in
uniting the ``external'' and ``internal'' (SU_2) symmetries in a non-trivial
fashion.


title:
The Adaptive Classical Capacity of a Quantum Channel, or Information
  Capacities of Three Symmetric Pure States in Three Dimensions

abstract:
  We investigate the capacity of three symmetric quantum states in three real
dimensions to carry classical information. Several such capacities have already
been defined, depending on what operations are allowed in the sending and
receiving protocols. These include the C_{1,1} capacity, which is the capacity
achievable if separate measurements must be used for each of the received
states, and the C_{1,infinity} capacity, which is the capacity achievable if
joint measurements are allowed on the tensor product of all the received
states. We discover a new classical information capacity of quantum channels,
the adaptive capacity C_{1,A}, which lies strictly between the C_{1,1} and the
C_{1,infinity} capacities. The adaptive capacity requires each of the signals
to be measured by a separate apparatus, but allows the quantum states of these
signals to be measured in stages, with the first stage partially reducing their
quantum states, and where measurements in subsequent stages which further
reduce the quantum states may depend on the results of a classical computation
taking as input the outcomes of the first round of measurements.


title: Adiabatic Quantum Computing for Random Satisfiability Problems

abstract:
  The discrete formulation of adiabatic quantum computing is compared with
other search methods, classical and quantum, for random satisfiability (SAT)
problems. With the number of steps growing only as the cube of the number of
variables, the adiabatic method gives solution probabilities close to 1 for
problem sizes feasible to evaluate via simulation on current computers.
However, for these sizes the minimum energy gaps of most instances are fairly
large, so the good performance scaling seen for small problems may not reflect
asymptotic behavior where costs are dominated by tiny gaps. Moreover, the
resulting search costs are much higher than for other methods. Variants of the
quantum algorithm that do not match the adiabatic limit give lower costs, on
average, and slower growth than the conventional GSAT heuristic method.


title: Does particle decay cause wave function collapse: An experimental test

abstract:
  We describe an experimental test of whether particle decay causes wave
function collapse. The test uses interference between two well separated, but
coherent, sources of vector mesons. The short-lived mesons decay before their
wave functions can overlap, so any interference must involve identical final
states. Unlike previous tests of nonlocality, the interference involves
continuous variables, momentum and position. Interference can only occur if the
wave function retains amplitudes for all possible decays. The interference can
be studied through the transverse momentum spectrum of the reconstructed
mesons.