title: Fidelity trade-off for finite ensembles of identically prepared qubits

abstract:
  We calculate the trade-off between the quality of estimating the quantum
state of an ensemble of identically prepared qubits and the minimum level of
disturbance that has to be introduced by this procedure in quantum mechanics.
The trade-off is quantified using two mean fidelities: the operation fidelity
which characterizes the average resemblance of the final qubit state to the
initial one, and the estimation fidelity describing the quality of the obtained
estimate. We analyze properties of quantum operations saturating the
achievability bound for the operation fidelity versus the estimation fidelity,
which allows us to reduce substantially the complexity of the problem of
finding the trade-off curve. The reduced optimization problem has the form of
an eigenvalue problem for a set of tridiagonal matrices, and it can be easily
solved using standard numerical tools.


title:
On a Lie algebraic approach of quasi-exactly solvable potentials with
  two known eigenstates

abstract:
  We compare two recent approaches of quasi-exactly solvable Schr\" odinger
equations, the first one being related to finite-dimensional representations of
$sl(2,R)$ while the second one is based on supersymmetric developments. Our
results are then illustrated on the Razavy potential, the sextic oscillator and
a scalar field model.


title: Noise and Order in Cavity Quantum Electrodynamics

abstract:
  In this paper we investigate the various aspects of noise and order in the
micromaser system. In particular, we study the effect of adding fluctuations to
the atom cavity transit time or to the atom-photon frequency detuning. By
including such noise-producing mechanisms we study the probability and the
joint probability for excited atoms to leave the cavity. The influence of such
fluctuations on the phase structure of the micromaser as well as on the
long-time atom correlation length is also discussed. We also derive the
asymptotic form of micromaser observables.


title: Multipartite entangled coherent states

abstract:
  We propose a scheme for generating multipartite entangled coherent states via
entanglement swapping, with an example of a physical realization in ion traps.
Bipartite entanglement of these multipartite states is quantified by the
concurrence. We also use the $N$--tangle to compute multipartite entanglement
for certain systems. Finally we establish that these results for entanglement
can be applied to more general multipartite entangled nonorthogonal states.


title: Mutually unbiased binary observable sets on N qubits

abstract:
  The Pauli operators (tensor products of Pauli matrices) provide a complete
basis of operators on the Hilbert space of N qubits. We prove that the set of
4^N-1 Pauli operators may be partitioned into 2^N+1 distinct subsets, each
consisting of 2^N-1 internally commuting observables. Furthermore, each such
partitioning defines a unique choice of 2^N+1 mutually unbiased basis sets in
the N-qubit Hilbert space. Examples for 2 and 3 qubit systems are discussed
with emphasis on the nature and amount of entanglement that occurs within these
basis sets.


title: Local realism for K0-K0bar pairs

abstract:
  In this talk we discuss the predictions of local realistic theories for the
evolution of a K0-K0bar quantum entangled pair created in the decay of the
phi-meson. It is shown, in agreement with Bell's theorem, that the most general
local hidden-variable model fails in reproducing the whole set of
quantum-mechanical observables. We achieve this conclusion by employing two
different approaches. In the first approach, the local realistic observables
are deduced from the most general premises concerning locality and realism, and
Bell-like inequalities are not employed. The other approach makes use of Bell's
inequalities. Under particular conditions for the detection times, within the
first approach the discrepancy between quantum mechanics and local realism for
the asymmetry parameter turns out to be not less than 20%. A similar
incompatibility can be made evident by means of a Bell-type test, by employing
a Clauser-Horne-Shimony-Holt's inequality written in terms of properly
normalized observables. Because of its relatively low experimental accuracy,
the data obtained by the CPLEAR collaboration do not yet allow a decisive test
of local realism. Such a test, both with and without the use of Bell's
inequalities, should be feasible in the future at the Frascati Phi-factory.


title: Continuous variable teleportation of single photon states

abstract:
  The properties of continuous variable teleportation of single photon states
are investigated. The output state is different from the input state due to the
non-maximal entanglement in the EPR beams. The photon statistics of the
teleportation output are determined and the correlation between the field
information beta obtained in the teleportation process and the change in photon
number is discussed. The results of the output photon statistics are applied to
the transmission of a qbit encoded in the polarization of a single photon.


title: Intrinsic decoherence in atomic diffraction by standing light wave

abstract:
  We study the effects of time uncertainty in the interaction of atoms with a
standing light wave. We discuss its physical origin and the possibility to
observe intrinsic decoherence effects by measuring the atomic momentum
distribution.


title:
Quantum Key Distribution between N partners: optimal eavesdropping and
  Bell's inequalities

abstract:
  Quantum secret-sharing protocols involving N partners (NQSS) are key
distribution protocols in which Alice encodes her key into $N-1$ qubits, in
such a way that all the other partners must cooperate in order to retrieve the
key. On these protocols, several eavesdropping scenarios are possible: some
partners may want to reconstruct the key without the help of the other ones,
and consequently collaborate with an Eve that eavesdrops on the other partners'
channels. For each of these scenarios, we give the optimal individual attack
that the Eve can perform. In case of such an optimal attack, the authorized
partners have a higher information on the key than the unauthorized ones if and
only if they can violate a Bell's inequality.


title: QED derived from the two-body interaction (1) Mapping to M-space

abstract:
  We have shown in a previous paper that the Dirac bispinor can vary like a
four-vector and that Quantum Electrodynamics (QED) can be reproduced with this
form of behaviour.(1) Here, in part I of this paper, we show that QED with the
same transformational behaviour also holds in an alternative space we call
M-space. We use the four-vector behaviour to model the two-body interaction in
M and show that this has similar physical properties to the usual model which
it predicts. In part (2) of this paper(4) we use M-space to show that QED can
be reduced to two simple rules for a two-body interaction.


title: QED derived from the two-body interaction (2) The derivation

abstract:
  We have shown in a previous paper that the Dirac bispinor can vary like a
four-vector and that Quantum Electrodynamics (QED) can be reproduced with this
form of behaviour.(2) We have also shown in part I (3) of this paper, that QED
with the same transformational behaviour also holds in a second space which we
called M-space. Here we use M-space to show that QED can be reduced to two
simple rules for a two-body interaction.


title:
Kronecker product/Direct product/Tensor product in Quantum Information
  theory

abstract:
  The properties and applications of kronecker product in quantum theory is
studied thoroughly. The use of kronecker product in quantum information theory
to get the exact spin Hamiltonian is given. The proof of non-commutativity of
matrices, when kronecker product is used between them is given. It is shown
that the non-commutative matrices after kronecker product are similar or they
are similar matrices.


title:
The dissipative dynamics of the field of two-photon Jaynes-Cummings
  model with Stark shift in dispersive approximation

abstract:
  We present the dissipative dynamics of the field of two-photon
Jaynes-Cummings model (JCM) with Stark shift in dispersive approximation and
investigate the influence of dissipation on entanglement. We show the coherence
properties of the field can be affected by the dissipative cavity when
nonlinear two-photon process is involved.


title: Quantum Zeno tomography

abstract:
  We show that the resolution "per absorbed particle" of standard absorption
tomography can be outperformed by a simple interferometric setup, provided that
the different levels of "gray" in the sample are not uniformly distributed. The
technique hinges upon the quantum Zeno effect and has been tested in numerical
simulations. The scheme we propose could be implemented in experiments with
UV-light, neutrons or X-rays.


title: Slow light propagation in trapped atomic quantum gases

abstract:
  We study semi-classical slow light propagation in trapped two level atomic
quantum gases. The temperature dependent behaviors of both group velocity and
transmissions are compared for low temperature Bose, Fermi, and Boltzman gases
within the local density approximation for their spatial density profile.


title: Quantum computation by quantum-like systems

abstract:
  Using a quantumlike description for light propagation in nonhomogeneous
optical fibers, quantum information processing can be implemented by optical
means. Quantum-like bits (qulbits) are associated to light modes in the optical
fiber and quantum gates to segments of the fiber providing an unitary
transformation of the mode structure along a space direction. Simulation of
nonlinear quantum effects is also discussed.


title: Finite-precision measurement does not nullify the Kochen-Specker theorem

abstract:
  It is proven that any hidden variable theory of the type proposed by Meyer
[Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755
(1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101
(2000)] leads to experimentally testable predictions that are in contradiction
with those of quantum mechanics. Therefore, it is argued that the existence of
dense Kochen-Specker-colorable sets must not be interpreted as a nullification
of the physical impact of the Kochen-Specker theorem once the finite precision
of real measurements is taken into account.


title: Perturbation Theory for Quantum Computation with Large Number of Qubits

abstract:
  We describe a new and consistent perturbation theory for solid-state quantum
computation with many qubits. The errors in the implementation of simple
quantum logic operations caused by non-resonant transitions are estimated. We
verify our perturbation approach using exact numerical solution for relatively
small (L=10) number of qubits. A preferred range of parameters is found in
which the errors in processing quantum information are small. Our results are
needed for experimental testing of scalable solid-state quantum computers.


title:
Universal Elementary Constituents of Potential Transformations Shifting
  Waves (Qualitative Theory)

abstract:
  It is shown that the potential perturbation that shifts a chosen standing
wave in space is a block of potential barrier and well for every wave bump
between neighbouring knots. The algorithms shifting the range of the primary
localization of a chosen bound state in a potential well of finite width are as
well applicable to the scattering functions if states of the continuous
spectrum are considered as bound states normalized to unity but distributed on
an infinite interval with vanishing density. The potential perturbations of the
same type on the half-axis concentrate the scattering wave at the origin, thus
creating a bound state embedded into the continuous spectrum (zero width
resonance). It is an improved version of paper: Annalen der Physik, 6 (1997)
136.


title: Semicausal operations are semilocalizable

abstract:
  We prove a conjecture by DiVincenzo, which in the terminology of Preskill et
al. [quant-ph/0102043] states that ``semicausal operations are
semilocalizable''. That is, we show that any operation on the combined system
of Alice and Bob, which does not allow Bob to send messages to Alice, can be
represented as an operation by Alice, transmitting a quantum particle to Bob,
and a local operation by Bob. The proof is based on the uniqueness of the
Stinespring representation for a completely positive map. We sketch some of the
problems in transferring these concepts to the context of relativistic quantum
field theory.


title: Nonclassical radiation from diamond nanocrystals

abstract:
  The quantum properties of the fluorescence light emitted by diamond
nanocrystals containing a single nitrogen-vacancy (NV) colored center is
investigated. We have observed photon antibunching with very low background
light. This system is therefore a very good candidate for the production of
single photon on demand. In addition, we have measured larger NV center
lifetime in nanocrystals than in the bulk, in good agreement with a simple
quantum electrodynamical model.


title: Comment on `Quantum-Anti-Zeno Paradox'

abstract:
  One can reduce the involved derivation of Balachandran and Roy of their
`anti-Zeno' effect [Phys.Rev.Lett. 84, 4019 (2000)] to the derivation of
standard Zeno effect. The mechanism of what the authors call `anti-Zeno' effect
is a dynamic version of Zeno effect.


title:
Efficient Scheme for Initializing a Quantum Register with an Arbitrary
  Superposed State

abstract:
  Preparation of a quantum register is an important step in quantum computation
and quantum information processing. It is straightforward to build a simple
quantum state such as $|i_1 i_2 ... i_n\ket$ with $i_j$ being either 0 or 1,
but is a non-trivial task to construct an {\it arbitrary} superposed quantum
state. In this Paper, we present a scheme that can most generally initialize a
quantum register with an arbitrary superposition of basis states.
Implementation of this scheme requires $O(Nn^2)$ standard 1- and 2-bit gate
operations, {\it without introducing additional quantum bits}. Application of
the scheme in some special cases is discussed.


title: Multi-directional higher-order amplitude squeezing

abstract:
  Fan-even K-quantum nonlinear coherent states are introduced and higher-order
amplitude squeezing is investigated in such states. It is shown that for a
given K the lowest order in which an amplitude component can be squeezed is 2K
and the squeezing appears simultaneously in K directions separated successively
in phase by \pi/K.


title: Experimental Tests for Stochastic Reduction Models

abstract:
  Stochastic models for quantum state reduction give rise to statistical laws
that are in many respects in agreement with those of standard quantum
measurement theory. Here we construct a counterexample involving a Hamiltonian
with degenerate eigenvalues such that the statistical predictions of stochastic
reduction models differ from the predictions of quantum measurement theory. An
idealised experiment is proposed whereby the validity of these predictions can
be put to the test.


title: The Structure of the Multiverse

abstract: The structure of the multiverse is determined by information flow.


title:
Simple Pulses for Universal Quantum Computation with a Heisenberg ABAB
  Chain

abstract:
  Recently Levy has shown that quantum computation can be performed using an
ABAB.. chain of spin-1/2 systems with nearest-neighbor Heisenberg interactions.
Levy notes that all necessary elementary computational `gates' can be achieved
by using spin-resonance techniques involving modulating the spin-spin
interaction strength at high frequency. Here we note that, as an alternative to
that approach, it is possible to perform the elementary gates with simple,
non-oscillatory pulses.


title:
Observation of the Quantum Zeno and Anti-Zeno effects in an unstable
  system

abstract:
  We report the first observation of the Quantum Zeno and Anti-Zeno effects in
an unstable system. Cold sodium atoms are trapped in a far-detuned standing
wave of light that is accelerated for a controlled duration. For a large
acceleration the atoms can escape the trapping potential via tunneling.
Initially the number of trapped atoms shows strong non-exponential decay
features, evolving into the characteristic exponential decay behavior. We
repeatedly measure the number of atoms remaining trapped during the initial
period of non-exponential decay. Depending on the frequency of measurements we
observe a decay that is suppressed or enhanced as compared to the unperturbed
system.


title: The Quantum State of an Ideal Propagating Laser Field

abstract:
  We give a quantum information-theoretic description of an ideal propagating
CW laser field and reinterpret typical quantum-optical experiments in light of
this. In particular we show that contrary to recent claims [T. Rudolph and B.
C. Sanders, Phys. Rev. Lett. 87, 077903 (2001)], a conventional laser can be
used for quantum teleportation with continuous variables and for generating
continuous-variable entanglement. Optical coherence is not required, but phase
coherence is. We also show that coherent states play a priveleged role in the
description of laser light.


title: A Systematic Algorithm for Quantum Boolean Circuits Construction

abstract:
  To build a general-purpose quantum computer, it is crucial for the quantum
devices to implement classical boolean logic. A straightforward realization of
quantum boolean logic is to use auxiliary qubits as intermediate storage. This
inefficient implementation causes a large number of auxiliary qubits to be
used. In this paper, we have derived a systematic way of realizing any general
m-to-n bit combinational boolean logic using elementary quantum gates. Our
approach transforms the m-to-n bit classical mapping into a t-bit unitary
quantum operation with minimum number of auxiliary qubits, then a variation of
Toffoli gate is used as the basic building block to construct the unitary
operation. Finally, each of these building blocks can be decomposed into
one-bit rotation and two-bit control-U gates. The efficiency of the network is
taken into consideration by formulating it as a constrained set partitioning
problem.


title: Second order quantum decoherence in the boson system

abstract:
  The second order quantum decoherence (SOQDC)is proposed as a novel
description for the loss of quantum coherence only reflected by second order
quantum correlations. By calculating the two-time correlation function, the
phenomenon of SOQDC is studied in details for a simple model, a two boson
system interacting with a reservoir composed of one or many bosons. The second
order quantum decoherence effects can be observed in the sketched cavity QED
experiment.


title: A Practical Scheme for Entanglement Concentration

abstract:
  We present a realistic purification scheme for pure non-maximally entangled
states. In the scheme, Alice and Bob at two distant parties first start with
two shared but less entangled photon pairs to produce a conditional four-photon
GHZ state, then perform a 45-degree polarization measurement onto one of the
two photons at each party such that the remaining two photons are projected
onto a maximally entangled state.


title: Effects of twin-beam squashed light on a three-level atom

abstract:
  An electro-optical feedback loop can make in-loop light (squashed light)
which produces a photocurrent with noise below the standard quantum limit (such
as squeezed light). We investigate the effect of squashed light interacting
with a three-level atom in the cascade configuration and compare it to the
effects produced by squeezed light and classical noise. It turns out that one
master equation can be formulated for all three types of light and that this
unified formalism can also be applied to the evolution of a two-level atom. We
show that squashed light does not mimic all aspects of squeezed light, and in
particular, it does not produce the characteristic linear intensity dependence
of the population of the upper-most level of the cascade three-level atom.
Nevertheless, it has nonclassical transient effects in the de-excitation.


title: Ion-trap quantum logic using long-wavelength radiation

abstract:
  A quantum information processor is proposed that combines experimental
techniques and technology successfully demonstrated either in nuclear magnetic
resonance experiments or with trapped ions. An additional inhomogenenous
magnetic field applied to an ion trap i) shifts individual ionic resonances
(qubits), making them distinguishable by frequency, and, ii) mediates the
coupling between internal and external degrees of freedom of trapped ions. This
scheme permits one to individually address and coherently manipulate ions
confined in an electrodynamic trap using radiation in the radiofrequency or
microwave regime.


title: Magnetic Dipoles and Quantum Coherence in Muscle Contraction

abstract:
  An actin filament contacting myosin molecules as a functional unit of muscle
contraction induces magnetic dipoles along the filament when ATP molecules to
be hydrolyzed are available there. The induced magnetic dipoles are coherent
over the entire filament, though they are fluctuating altogether as constantly
being subject to the ambient thermal agitations.


title:
Moller operators and Lippmann-Schwinger equations for step-like
  potentials

abstract:
  The Moller operators and the asociated Lippman-Schwinger equations obtained
from different partitionings of the Hamiltonian for a step-like potential
barrier are worked out, compared and related.


title:
Conditional generation of sub-Poissonian light from two-mode squeezed
  vacuum via balanced homodyne detection on idler mode

abstract:
  A simple scheme for conditional generation of nonclassical light with
sub-Poissonian photon-number statistics is proposed. The method utilizes
entanglement of signal and idler modes in two-mode squeezed vacuum state
generated in optical parametric amplifier. A quadrature component of the idler
mode is measured in balanced homodyne detector and only those experimental runs
where the absolute value of the measured quadrature is higher than certain
threshold are accepted. If the threshold is large enough then the conditional
output state of signal mode exhibits reduction of photon-number fluctuations
below the coherent-state level.


title: Comments on discrete time in quantum mechanics

abstract:
  The possibility that time can be regarded as a discrete parameter is
re-examined. We study the dynamics of the free particle and find in some cases
superluminal propagation.


title: Generalized quantum measurement

abstract:
  We overcome one of Bell's objections to `quantum measurement' by generalizing
the definition to include systems outside the laboratory. According to this
definition a {\sl generalized quantum measurement} takes place when the value
of a classical variable is influenced significantly by an earlier state of a
quantum system. A generalized quantum measurement can then take place in
equilibrium systems, provided the classical motion is chaotic. This paper deals
with this classical aspect of quantum measurement, assuming that the Heisenberg
cut between the quantum dynamics and the classical dynamics is made at a very
small scale. For simplicity, a gas with collisions is modelled by an `Arnold
gas'.


title: Experimental Four-photon Entanglement and High-fidelity Teleportation

abstract:
  We experimentally demonstrate observation of highly pure four-photon GHZ
entanglement produced by parametric down-conversion and a projective
measurement. At the same time this also demonstrates teleportation of
entanglement with very high purity. Not only does the achieved high visibility
enable various novel tests of quantum nonlocality, it also opens the
possibility to experimentally investigate various quantum computation and
communication schemes with linear optics. Our technique can in principle be
used to produce entanglement of arbitrarily high order or, equivalently,
teleportation and entanglement swapping over multiple stages.


title: Solving Random Satisfiability Problems with Quantum Computers

abstract:
  Quantum computer algorithms can exploit the structure of random
satisfiability problems. This paper extends a previous empirical evaluation of
such an algorithm and gives an approximate asymptotic analysis accounting for
both the average and variation of amplitudes among search states with the same
costs. The analysis predicts good performance, on average, for a variety of
problems including those near a phase transition associated with a high
concentration of hard cases. Based on empirical evaluation for small problems,
modifying the algorithm in light of this analysis improves its performance. The
algorithm improves on both GSAT, a commonly used conventional heuristic, and
quantum algorithms ignoring problem structure.


title: Controversy about quantum time decay

abstract:
  In the recent physics literature there have appeared contradictory statements
concerning the behaviour of scattering solutions of the 3-dimensional
Schroedinger equation at large times. We clarify the situation and point out
that the issue was rigorously resolved in the mathematics literature.


title: Separability Criterion for all bipartite Gaussian States

abstract:
  We provide a necessary and sufficient condition for separability of Gaussian
states of bipartite systems of arbitrarily many modes. The condition provides
an operational criterion since it can be checked by simple computation.
Moreover, it allows us to find a pure product-state decomposition of any given
separable Gaussian state. Our criterion is independent of the one based on
partial transposition, and is strictly stronger.


title:
A Hamiltonian for the description of a non-relativistic spin-1/2 free
  particle

abstract:
  We propose a Hamiltonian for a nonrelativistic spin 1/2 \QTR{it}{free}
particle (e.g. an electron) and find that it contains information of its
internal degrees of freedom in the rest coordinate system. We comment on the
dynamical symmetry associated with the electron \QTR{it}{Zitterbewegung}.


title:
Emergence of classicality in non relativistic quantum mechanics through
  gravitational self-interaction

abstract:
  An explicit dynamical model for non relativistic quantum mechanics with an
effective gravitational interaction is proposed, which, as being well defined,
allows in principle for the evaluation of every physical quantity. Its non
unitary dynamics results from a unitary one in a space with twice as many
degrees of freedom as the ordinary ones. It exhibits a threshold for the
emergence of classical behavior for bodies of ordinary density on rather long
times or instantaneously, respectively at around 10^11 or 10^20 proton masses.


title: Quantum Formulas: a Lower Bound and Simulation

abstract:
  We show that Nechiporuk's method for proving lower bounds for Boolean
formulas can be extended to the quantum case. This leads to an $\Omega(n^2 /
\log^2 n)$ lower bound for quantum formulas computing an explicit function. The
only known previous explicit lower bound for quantum formulas states that the
majority function does not have a linear-size quantum formula. We also show
that quantum formulas can be simulated by Boolean circuits of almost the same
size.


title:
Entanglement Concentration of Individual Photon Pairs via Linear Optical
  Logic

abstract:
  We propose a scheme for concentrating nonmaximally pure and mixed
polarization-entangled state of individual photon pairs. The scheme uses only
simple linear optical elements and may be feasible within current optical
technology.


title:
Stochastic Noise as a Source of Decoherence in a Solid State Quantum
  Computer

abstract:
  We examine a stochastic noise process that has a decohering effect on the
average evolution of qubits in the quantum register of the solid state quantum
computer proposed by Kane. We consider the effects of this process on the
single qubit operations necessary to perform quantum logical gates and derive
an expression for the fidelity of these gates in this system. We then calculate
an upper bound on the level of this stochastic noise tolerable in a workable
quantum computer.


title: Spontaneous Decay in the Presence of Absorbing Media

abstract:
  After giving a summary of the basic-theoretical concept of quantization of
the electromagnetic field in the presence of dispersing and absorbing
(macroscopic) bodies, their effect on spontaneous decay of an excited atom is
studied. Various configurations such as bulk material, planar half space media,
spherical cavities, and microspheres are considered. In particular, the
influence of material absorption on the local-field correction, the decay rate,
the line shift, and the emission pattern are examined. Further, the interplay
between radiative losses and losses due to material absorption is analyzed.
Finally, the possibility of generating entangled states of two atoms coupled by
a microsphere-assisted field is discussed.


title: Nearly ideal binary communication in squeezed channels

abstract:
  We analyze the effect of squeezing the channel in binary communication based
on Gaussian states. We show that for coding on pure states, squeezing increases
the detection probability at fixed size of the strategy, actually saturating
the optimal bound already for moderate signal energy. Using Neyman-Pearson
lemma for fuzzy hypothesis testing we are able to analyze also the case of
mixed states, and to find the optimal amount of squeezing that can be
effectively employed. It results that optimally squeezed channels are robust
against signal-mixing, and largely improve the strategy power by comparison
with coherent ones.


title:
The trumping relation and the structure of the bipartite entangled
  states

abstract:
  The majorization relation has been shown to be useful in classifying which
transformations of jointly held quantum states are possible using local
operations and classical communication. In some cases, a direct transformation
between two states is not possible, but it becomes possible in the presence of
another state (known as a catalyst); this situation is described mathematically
by the trumping relation, an extension of majorization. The structure of the
trumping relation is not nearly as well understood as that of majorization. We
give an introduction to this subject and derive some new results. Most notably,
we show that the dimension of the required catalyst is in general unbounded;
there is no integer $k$ such that it suffices to consider catalysts of
dimension $k$ or less in determining which states can be catalyzed into a given
state. We also show that almost all bipartite entangled states are potentially
useful as catalysts.


title: Anomalous doublets of states in a PT symmetric quantum model

abstract:
  We complexify one of the Natanzon's exactly solvable potentials in PT
symmetric manner and discover that it supports the pairs of bound states with
the same number of nodal zeros. This could indicate that the Sturm Liouville
oscillation theorem does not admit an immediate generalization.


title: Dynamic disquantization of Dirac equation

abstract:
  Classical model S_dc of Dirac particle S_D is constructed. S_D is the dynamic
system described by the Dirac equation. Its classical analog S_dc is described
by a system of ordinary differential equations, containing the quantum constant
h as a parameter. Dynamic equations for S_dc are determined by the Dirac
equation uniquely. Both dynamic systems S_D and S_dc appear to be
nonrelativistic. One succeeded in transforming nonrelativistic dynamic system
S_dc into relativistic one S_dcr. The dynamic system S_dcr appears to be a
two-particle structure (special case of a relativistic rotator). It explains
freely such properties of S_D as spin and magnetic moment, which are strange
for pointlike structure. The rigidity function f_r(a), describing rotational
part of total mass as a function of the radius $a$ of rotator, has been
calculated for S_dcr. For investigation of S_D and construction of S_dc one
uses new dynamic methods: dynamic quantization and dynamic disquantization.
These relativistic pure dynamic procedures do not use principles of quantum
mechanics (QM). They generalize and replace conventional quantization and
transition to classical approximation. Totality of these methods forms the
model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle
and effective, than conventional methods of QM. MCQP relates to conventional
QM, much as the statistical physics relates to thermodynamics.


title: Efficient Implementation and the Product State Representation of Numbers

abstract:
  The relation between the requirement of efficient implementability and the
product state representation of numbers is examined. Numbers are defined to be
any model of the axioms of number theory or arithmetic. Efficient
implementability (EI) means that the basic arithmetic operations are physically
implementable and the space-time and thermodynamic resources needed to carry
out the implementations are polynomial in the range of numbers considered.
Different models of numbers are described to show the independence of both EI
and the product state representation from the axioms. The relation between EI
and the product state representation is examined. It is seen that the condition
of a product state representation does not imply EI. Arguments used to refute
the converse implication, EI implies a product state representation, seem
reasonable; but they are not conclusive. Thus this implication remains an open
question.


title:
Revisiting Hardy's Paradox: Counterfactual Statements, Real
  Measurements, Entanglement and Weak Values

abstract:
  Classical-realistic analysis of entangled systems have lead to retrodiction
paradoxes, which ordinarily have been dismissed on the grounds of
counter-factuality. Instead, we claim that such paradoxes point to a deeper
logical structure inherent to quantum mechanics, which is naturally described
in the language of weak values, and which is accessible experimentally via weak
measurements. Using as an illustration, a gedanken-experiment due to
Hardy\cite{hardy}, we show that there is in fact an exact numerical coincidence
between a) a pair of classically contradictory assertions about the locations
of an electron and a positron, and b) the results of weak measurements of their
location. The internal consistency of these results is due to the novel way by
which quantum mechanics "resolves" the paradox: first, by allowing for two
distinguishable manifestations of how the electron and positron can be at the
same location: either as single particles or as a pair; and secondly, by
allowing these properties to take either sign. In particular, we discuss the
experimental meaning of a {\em negative} number of electron-positron pairs.


title: A Quantum-Mechanical Explanation of the Collapse of the Wave Function

abstract:
  The quantum field of a single particle is expressed as the sum of the
particle's ordinary wave function and the vacuum fluctuations. An exact
quantum-field calculation shows that the squared amplitude of this field sums,
at any time, to a delta function representing a discrete corpuscle at one point
and zero everywhere else. The peak of the delta function is located at the
point where the vacuum fluctuations interfere constructively with the ordinary
wave function. Similarly, the collapsed wave function after a measurement of an
observable is determined by interference between the initial wave function and
vacuum fluctuations.


title:
Observation of Image Transfer and Phase Conjugation in Stimulated
  Down-Conversion

abstract:
  We observe experimentally the transfer of angular spectrum and image
formation in the process of stimulated parametric down-conversion. Images and
interference patterns can be transferred either from the pump or the auxiliary
laser beams to the stimulated down-converted one. The stimulated field
propagates as the complex conjugate of the auxiliary laser. The phase
conjugation is observed through intensity pattern measurements.


title: Are all noisy quantum states obtained from pure ones?

abstract:
  We ask what type of mixed quantum states can arise when a number of separated
parties start by sharing a pure quantum state and then this pure state becomes
contaminated by noise. We show that not all mixed states arise in this way.
This is even the case if the separated parties actively try to degrade their
initial pure state by arbitrary local actions and classical communication.


title: Mechanical interpretation of the Klein-Gordon equation

abstract:
  The substratum for physics can be seen microscopically as an ideal fluid
pierced in all directions by the straight vortex filaments. Small disturbances
of an isolated filament are considered. The Klein-Gordon equation without mass
corresponds to elastic stretching of the filament. The wave function has the
meaning of the curve's position vector. The mass part of the Klein-Gordon
equation describes the rotation of the helical curve about the screw axis due
to the hydrodynamic self-induction of the bent vortex filament.


title: Hidden Variables, Statistical Mechanics and the Early Universe

abstract:
  It is argued that our universe happens to be in a state of statistical
equilibrium at the hidden-variable level, such that nonlocality is masked by
quantum noise. To account for this 'quantum equilibrium', we outline a
subquantum statistical mechanics in configuration space, and an H-theorem
analogous to the classical coarse-graining H-theorem. Foundational issues in
statistical mechanics are addressed, and an alternative explanation based on
'typicality' is criticised. An estimate is given for the relaxation timescale,
and an illustrative numerical simulation is provided. Assuming the universe
began in quantum non-equilibrium, we sketch a scenario in which relaxation is
suppressed at very early times by the rapid expansion of space, raising the
possibility that deviations from quantum theory could survive to the present
day for relic cosmological particles that decoupled sufficiently early. It is
concluded that quantum noise is a remnant of the big bang and, like the
microwave background, should be probed experimentally. Possible tests with
relic particles are briefly discussed.


title:
Optimally Conclusive Discrimination of Non-orthogonal Entangled States
  Locally

abstract:
  We consider one copy of a quantum system prepared with equal prior
probability in one of two non-orthogonal entangled states of multipartite
distributed among separated parties. We demonstrate that these two states can
be optimally distinguished in the sense of conclusive discrimination by local
operations and classical communications(LOCC) alone. And this proves strictly
the conjecture that Virmani et.al. [8] confirmed numerically and analytically.
Generally, the optimal protocol requires local POVM operations which are
explicitly constructed. The result manifests that the distinguishable
information is obtained only and completely at the last operation and all prior
ones give no information about that state.


title: Continuous-variable and hybrid quantum gates

abstract:
  We provide several schemes to construct the continuous-variable SWAP gate and
present a Hermitian generalized many-body continuous controlled^n-NOT gate. We
introduce and study the hybrid controlled-NOT gate and controlled-SWAP gate,
and physical realizations of them are discussed in trapped-ion systems. These
continuous-variable and hybrid quantum gates may be used in the corresponding
continuous-variable and hybrid quantum computations.


title: Entanglement of Orbital Angular Momentum States of Photons

abstract:
  So far experimental confirmation of entanglement has been restricted to
qubits, i.e. two-state quantum systems including recent realization of three-
and four-qubit entanglements. Yet, an ever increasing body of theoretical work
calls for entanglement in quantum system of higher dimensions. Here we report
the first realization of multi-dimensional entanglement exploiting the orbital
angular momentum of photons, which are states of the electromagnetic field with
phase singularities (doughnut modes). The properties of such states could be of
importance for the efforts in the field of quantum computation and quantum
communication. For example, quantum cryptography with higher alphabets could
enable one to increase the information flux through the communication channels.


title: Supersymmetric Dynamical Invariants

abstract:
  We address the problem of identifying the (nonstationary) quantum systems
that admit supersymmetric dynamical invariants. In particular, we give a
general expression for the bosonic and fermionic partner Hamiltonians. Due to
the supersymmetric nature of the dynamical invariant the solutions of the
time-dependent Schr\"odinger equation for the partner Hamiltonians can be
easily mapped to one another. We use this observation to obtain a class of
exactly solvable time-dependent Schr\"odinger equations. As applications of our
method, we construct classes of exactly solvable time-dependent generalized
harmonic oscillators and spin Hamiltonians.


title: Distillability Criterion for all Bipartite Gaussian States

abstract:
  We prove that all inseparable Gaussian states of two modes can be distilled
into maximally entangled pure states by local operations. Using this result we
show that a bipartite Gaussian state of arbitrarily many modes can be distilled
if and only if its partial transpose is not positive.


title:
Quantum Fluctuations of Light: A Modern Perspective on Wave/Particle
  Duality

abstract:
  We review studies of the fluctuations of light made accessible by the
invention of the laser and the strong interactions realized in cavity QED
experiments. Photon antibunching advocating the discrete (particles), is
contrasted with amplitude squeezing which speaks of the continuous (waves). The
tension between particles and waves is demonstrated by a recent experiment
which combines the measurement strategies used to observe these nonclassical
behaviors of light [Phys. Rev. Lett. 85, 3149 (2000)].


title:
Quantum Diffusion of H/Ni(111) through the Monte Carlo Wave Function
  Formalism

abstract:
  We consider a quantum system coupled to a dissipative background with many
degrees of freedom using the Monte Carlo Wave Function method. Instead of
dealing with a density matrix which can be very high-dimensional, the method
consists of integrating a stochastic Schrodinger equation with a non-hermitian
damping term in the evolution operator, and with random quantum jumps. The
method is applied to the diffusion of hydrogen on the Ni(111) surface below 100
K. We show that the recent experimental diffusion data for this system can be
understood through an interband activation process, followed by quantum
tunnelling.


title: Attacks on Symmetric Quantum Coin-Tossing Protocols

abstract:
  We suggest an attack on a symmetric non-ideal quantum coin-tossing protocol
suggested by Mayers Salvail and Chiba-Kohno. The analysis of the attack shows
that the protocol is insecure.


title:
An analysis of a two-atom double-slit experiment based on
  environment-induced measurements

abstract:
  To investigate the effect of a classical environment on a quantum mechanical
system we consider two two-level atoms in a free radiation field in the
presence of a screen. By assuming that the screen causes continuous ideal
measurements on the free radiation field we derive a quantum jump description
for the state of the atoms. Our results are consistent with the master
equations for dipole interacting atoms, but give more insight in the time
evolution of a single system. To illustrate this we derive a necessary and
sufficient criterion for interference in a two-atom double-slit experiment and
analyse bunching in the statistics of photons emitted in a certain direction.


title: Space of State Vectors in PT Symmetrical Quantum Mechanics

abstract:
  Space of states of PT symmetrical quantum mechanics is examined. Requirement
that eigenstates with different eigenvalues must be orthogonal leads to the
conclusion that eigenfunctions belong to the space with an indefinite metric.
The self consistent expressions for the probability amplitude and average value
of operator are suggested. Further specification of space of state vectors
yield the superselection rule, redefining notion of the superposition
principle. The expression for the probability current density, satisfying
equation of continuity and vanishing for the bound state, is proposed.


title: Time Interval Operators

abstract:
  In this work we will advance farther along a line previously developed
concerning our proposal of a time interval operator, on finite dimensional
spaces. The time interval operator is Hermitian, and its eigenvalues are time
values with a precise and interesting role on the dynamics. With the help of
the Discrete Phase Space Formalism (DPSF) previously developed, we show that
the time interval operator is the complementary pair of the Hamiltonian. From
that, a simple system is proposed as a quantum clock. The only restriction is
that our results do not apply to all possible Hamiltonians.


title: Comments on the Aharonov-Casher effect

abstract:
  We study the basic requirements for neutron confinement in the framework of
some 3-D Aharonov-Casher configurations.


title: Law of Excluded Quantum Gambling Strategies

abstract:
  We introduce and analyze a quantum analogue of the Law of Excluded Gambling
Strategies of Classical Decision Theory by the definition of different kind of
quantum casinos. The necessity of keeping into account entaglement (by the way
we give a staightforward generalization of Schmidt's entanglement measure)
forces us to adopt the general algebraic language of Quantum Probability Theory
whose essential points are reviewed. The Mathematica code of two packages
simulating, respectively, classical and quantum gambling is included. The deep
link existing between the censorship of winning quantum gambling strategies and
the central notion of Quantum Algorithmic Information Theory, namely quantum
algorithmic randomness (by the way we introduce and discard the naive
noncommutative generalization of the original Kolmogorov definition), is
analyzed


title: The hidden cost of quantum teleportation and remote state preparation

abstract:
  The amount of information transferred during standard quantum teleportation
or remote state preparation is equal to the preparation information of the
transmitted state, rather than the classical communication required by
respective protocol. This is shown by noting that the information required to
specify the operation that verifies the transmitted state is identical to the
preparation information, at the given level of precision m (in bits). Depending
on the resolution of the projective Hilbert space, the preparation information
can be made arbitrarily precise and hence indefinitely larger than the
classical communication cost. Therefore, the classical communication is
insufficient to account for the transfer of preparation information, which is
then attributed to the Einstein-Podolsky-Rosen channel. Some fundamental
repercussions for relativistic quantum information processing are briefly
discussed.


title: A Quantum Search Algorithm for a Specified Number of Targets

abstract:
  The quantum search algorithm of Chen and Diao, which finds with certainty a
single target item in an unsorted database, is modified so as to be capable of
searching for an arbitrary specified number of target items. If the number of
targets, nu_0, is a power of four, the new algorithm will with certainty find
one of the targets in a database of n items using
(1/2)(3(N/nu_0)^{log_base_4(3)}-1) \approx (1/2)(3(N/nu_0)^{0.7925}-1) oracle
calls, where N is the smallest power of four greater than or equal to n. If
nu_0 is not a power of four, the algorithm will, with a probability of at least
one-half, find one of the targets using no more than
(1/2)(9(N/nu)^{log_base_4(3)}-1) calls, where nu is the smallest power of four
greater than or equal to nu_0.


title: Thermodynamics of Coherent States and Black Hole Entropy

abstract:
  Entropy and temperature of a system in a coherent state are naturally defined
on a base of a density matrix of the system. As an example, entropy and
temperature are evaluated for coherent states of a harmonic oscillator and
quantum field described by the Klein--Gordon--Fock equation with a source term.
It is shown, in particular, that the temperature of the coherent oscillator in
a ground state coincides with the effective temperature of a harmonic
oscillator being in contact with a heat bath (Bloch formula) when the bath
temperature tends to zero. The Bekenstein--Hawking entropy of a black hole can
also be interpreted as an entropy of coherent states of a physical vacuum in
the vicinity of a horizon surface.


title:
An ultra-sensitive pulsed balanced homodyne detector: Application to
  time-domain quantum measurements

abstract:
  A pulsed balanced homodyne detector has been developed for precise
measurements of electric field quadratures of pulsed optical quantum states. A
high level of common mode suppression (> 85 dB) and low electronic noise (730
electrons per pulse) provide a signal to noise ratio of 14 dB for the
measurement of the quantum noise of individual pulses. Measurements at
repetition rates up to 1 MHz are possible. As a test, quantum tomography of the
coherent state is performed and the Wigner function and the density matrix are
reconstructed with a 99.5% fidelity. The detection system can also be used for
ultrasensitive balanced detection in cw mode, e.g. for weak absorption
measurements.


title: Programming physical realizations of quantum computers

abstract:
  We study effects of the physical realization of quantum computers on their
logical operation. Through simulation of physical models of quantum computer
hardware, we analyze the difficulties that are encountered in programming
physical realizations of quantum computers. Examples of logically identical
implementations of the controlled-NOT operation and Grover's database search
algorithm are used to demonstrate that the results of a quantum computation are
unstable with respect to the physical realization of the quantum computer. We
discuss the origin of these instabilities and discuss possibilities to overcome
this, for practical purposes, fundamental limitation of quantum computers.


title:
Delocalization border and onset of chaos in a model of quantum
  computation

abstract:
  We study the properties of spectra and eigenfunctions for a chain of $1/2-
$spins (qubits) in an external time-dependent magnetic field, and under the
conditions of non-selective excitation (when the amplitude of the magnetic
field is large). This model is known as a possible candidate for experimental
realization of quantum computation. We present the theory for finding
delocalization transition and show that for the interaction between nearest
qubits, the transition is very different from that to quantum chaos. We explain
this phenomena by showing that in the considered region of parameters our model
is close to an integrable one. According to a general opinion, the threshold
for the onset of quantum chaos due to the interqubit interaction decreases with
an increase of the number of qubits. Contrary to this expectation, for a
magnetic field with constant gradient we have found that chaos border does not
depend on the number of qubits. We give analytical estimates which explain this
effect, together with numerical data supporting our analysis. Random models
with long-range interactions are studied as well. In particular, we show that
in this case the delocalization and quantum chaos borders coincide.


title: Experimental realization of quantum games on a quantum computer

abstract:
  We generalize the quantum Prisoner's Dilemma to the case where the players
share a non maximally entangled states. We show that the game exhibits an
intriguing structure as a function of the amount of entanglement with two
thresholds which separate a classical region, an intermediate region and a
fully quantum region. Furthermore this quantum game is experimentally realized
on our nuclear magnetic resonance quantum computer.


title: Unknown Quantum States: The Quantum de Finetti Representation

abstract:
  We present an elementary proof of the quantum de Finetti representation
theorem, a quantum analogue of de Finetti's classical theorem on exchangeable
probability assignments. This contrasts with the original proof of Hudson and
Moody [Z. Wahrschein. verw. Geb. 33, 343 (1976)], which relies on advanced
mathematics and does not share the same potential for generalization. The
classical de Finetti theorem provides an operational definition of the concept
of an unknown probability in Bayesian probability theory, where probabilities
are taken to be degrees of belief instead of objective states of nature. The
quantum de Finetti theorem, in a closely analogous fashion, deals with
exchangeable density-operator assignments and provides an operational
definition of the concept of an ``unknown quantum state'' in quantum-state
tomography. This result is especially important for information-based
interpretations of quantum mechanics, where quantum states, like probabilities,
are taken to be states of knowledge rather than states of nature. We further
demonstrate that the theorem fails for real Hilbert spaces and discuss the
significance of this point.


title: Enhanced Autocompensating Quantum Cryptography System

abstract:
  We have improved the hardware and software of our autocompensating system for
quantum key distribution by replacing bulk optical components at the end
stations with fiber-optic equivalents and implementing software that
synchronizes end-station activities, communicates basis choices, corrects
errors and performs privacy amplification over a local area network. The all
fiber-optic arrangement provides stable, efficient and high-contrast routing of
the photons. The low bit error rate leads to high error correction efficiency
and minimizes data sacrifice during privacy amplification. Characterization
measurements made on a number of commercial avalanche photodiodes are presented
that highlight the need for improved devices tailored specifically for quantum
information applications. A scheme for frequency shifting the photons returning
from Alice's station to allow them to be distinguished from backscattered noise
photons is also described.
  OCIS codes: 030.5260, 060.0060, 060.2360, 230.2240, 270.5570.


title:
Quantum information processing for a coherent superposition state via a
  mixed entangled coherent channel

abstract:
  An entangled two-mode coherent state is studied within the framework of
$2\times 2$ dimensional Hilbert space. An entanglement concentration scheme
based on joint Bell-state measurements is worked out. When the entangled
coherent state is embedded in vacuum environment, its entanglement is degraded
but not totally lost. It is found that the larger the initial coherent
amplitude, the faster entanglement decreases. We investigate a scheme to
teleport a coherent superposition state while considering a mixed quantum
channel. We find that the decohered entangled coherent state may be useless for
quantum teleportation as it gives the optimal fidelity of teleportation less
than the classical limit 2/3.


title: Quantum mechanics gives stability to a Nash equilibrium

abstract:
  We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game
from the point of view of evolutionary stability. In its classical version the
game has a mixed Nash equilibrium (NE) not stable against mutants. We find a
quantized version of the RSP game for which the classical mixed NE becomes
stable.


title:
Reply to Comment on ``Proposal for the Measurement of Bell-Type
  Correlations from Continuous Variables''

abstract:
  Recently K. Banaszek, I. A. Walmsley, K. Wodkiewicz (quant-ph/0012097)
commented on our Proposal for the Measurement of Bell-Type Correlations from
Continuous Variables [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys.
Rev. Lett. 85, 2035 (2000)]. Their comment is based on a blatant misreading and
misunderstanding of our letter and as such is simply wrong.


title: Uniqueness of a convex sum of products of projectors

abstract:
  Relative to a given factoring of the Hilbert space, the decomposition of an
operator into a convex sum of products over sets of distinct 1-projectors, one
set linearly independent, is unique.


title: Rigid rotor in phase space

abstract:
  Angular momentum is important concept in physics, and its phase space
properties are important in various applications. In this work phase space
analysis of the angular momentum is made from its classical definition, and by
imposing uncertainty principle its quantum properties are obtained. It is shown
that kinetic energy operator is derived, but it has different interpretation of
its parts than in the standard treatment. Rigid rotor is discussed and it is
shown what is its phase space representation. True rigid rotor is defined and
also its phase space properties are discussed.


title:
Distillability via protocols respecting the positivity of partial
  transpose

abstract:
  We show that all quantum states that do not have a positive partial transpose
are distillable via channels, which preserve the positivity of the partial
transpose. The question whether NPT bound entanglement exist is therefore
closely related to the connection between the set of separable superoperators
and PPT-preserving maps.


title:
Generation of two-mode nonclassical motional states and a Fredkin gate
  operation in a two-dimensional ion trap

abstract:
  We present an efficient scheme to generate two-mode SU(2) macroscopic quantum
superposition (Schr\"odinger cat) states, entangled number states and entangled
coherent states for the vibrational motion of an ion trapped in a
two-dimensional harmonic potential well. We also show that the same scheme can
be used to realize a Fredkin gate operation.


title: Total Teleportation of an Entangled State

abstract:
  We present a setup for a direct, total teleportation of a single-particle
entangled state. Our scheme consists of a parametric down-conversion source,
which emits a pair of entangled photons, and a dual Bell measurement system
with two beam splitters and two pairs of detectors. An entangled state shared
by a pair of beams can be directly transferred to another pair of beams with a
50% probability of success. By a straightforward generalization of the scheme,
total teleportation of a multi-particle entangled state can also be performed.


title: Separable approximation for mixed states of composite quantum systems

abstract:
  We describe a purely algebraic method for finding the best separable
approximation to a mixed state of a composite 2x2 quantum system, consisting of
a decomposition of the state into a linear combination of a mixed separable
part and a pure entangled one. We prove that, in a generic case, the weight of
the pure part in the decomposition equals the concurrence of the state.


title:
Engineering arbitrary motional ionic state through realistic
  intensity-fluctuating laser pulses

abstract:
  We present a reliable scheme for engineering arbitrary motional ionic states
through an adaptation of the projection synthesis technique for trapped-ion
phenomena. Starting from a prepared coherent motional state, the Wigner
function of the desired state is thus sculpted from a Gaussian distribution.
The engineering process has also been developed to take into account the errors
arising from intensity fluctuations in the exciting-laser pulses required for
manipulating the electronic and vibrational states of the trapped ion. To this
end, a recently developed phenomenological-operator approach that allows for
the influence of noise will be applied. This approach furnishes a
straightforward technique to estimate the fidelity of the prepared state in the
presence of errors, precluding the usual extensive ab initio calculations. The
results obtained here by the phenomenological approach, to account for the
effects of noise in our engineering scheme, can be directly applied to any
other process involving trapped-ion phenomena.


title: Lower bounds in the quantum cell probe model

abstract:
  We introduce a new model for studying quantum data structure problems -- the
"quantum cell probe model". We prove a lower bound for the static predecessor
problem in the address-only version of this model where we allow quantum
parallelism only over the `address lines' of the queries. The address-only
quantum cell probe model subsumes the classical cell probe model, and many
quantum query algorithms like Grover's algorithm fall into this framework. Our
lower bound improves the previous known lower bound for the predecessor problem
in the classical cell probe model with randomised query schemes, and matches
the classical deterministic upper bound of Beame and Fich. Beame and Fich have
also proved a matching lower bound for the predecessor problem, but only in the
classical deterministic setting. Our lower bound has the advantage that it
holds for the more general quantum model, and also, its proof is substantially
simpler than that of Beame and Fich. We prove our lower bound by obtaining a
round elimination lemma for quantum communication complexity. A similar lemma
was proved by Miltersen, Nisan, Safra and Wigderson for classical communication
complexity, but it was not strong enough to prove a lower bound matching the
upper bound of Beame and Fich. Our quantum round elimination lemma also allows
us to prove rounds versus communication tradeoffs for some quantum
communication complexity problems like the "greater-than" problem. We also
study the "static membership" problem in the quantum cell probe model.
Generalising a result of Yao, we show that if the storage scheme is implicit,
that is it can only store members of the subset and `pointers', then any
quantum query scheme must make $\Omega(\log n)$ probes.


title: Entanglement in a two-identical-particle system

abstract:
  The definition of entanglement in identical-particle system is introduced.
The separability criterion in two-identical particle system is given. The
physical meaning of the definition is analysed. Applications to two-boson and
two-fermion systems are made. It is found new entanglement and correlation
phenomena in identical-boson systems exist, and they may have applications in
the field of quantum information.


title:
General Schemes for multi-particle d-dimensional Cat-like State
  Teleportation

abstract:
  Two kinds of $M$-particle d-dimensional cat-like state teleportation
protocols are present. In the first protocol, the teleportation is achieved by
d-dimensional Bell-basis measurements, while in the second protocol it is
realized by d-dimensional GHZ-basis measurement. It is also shown that the
second protocol has a simple mathematical formulation that is identical to
Bennett et al's original teleportation protocol for an unknown state of a
single particle.


title:
The breakdown flash of Silicon Avalance Photodiodes - backdoor for
  eavesdropper attacks?

abstract:
  Silicon avalanche photodiodes are the most sensitive photodetectors in the
visible to near infrared region. However, when they are used for single photon
detection in a Geiger mode, they are known to emit light on the controlled
breakdown used to detect a photoelectron. This fluorescence light might have
serious impacts on experimental applications like quantum cryptography or
single-particle spectroscopy. We characterized the fluorescence behaviour of
silicon avalanche photodiodes in the experimentally simple passive quenching
configuration and discuss implications for their use in quantum cryptography
systems.


title: A Continuous Transition Between Quantum and Classical Mechanics (I)

abstract:
  In spite of its popularity, it has not been possible to vindicate the
conventional wisdom that classical mechanics is a limiting case of quantum
mechanics. The purpose of the present paper is to offer an alternative
formulation of classical mechanics which provides a continuous transition to
quantum mechanics via environment-induced decoherence.


title: A Continous Transition Between Quantum and Classical Mechanics (II)

abstract:
  Examples are worked out using a new equation proposed in the previous paper
to show that it has new physical predictions for mesoscopic systems.


title: Geometric Phase in SU(N) Interferometry

abstract:
  An interferometric scheme to study Abelian geometric phase shift over the
manifold SU(N)/SU(N-1) is presented.


title:
Singlet states and the estimation of eigenstates and eigenvalues of an
  unknown Controlled-U gate

abstract:
  We consider several problems that involve finding the eigenvalues and
generating the eigenstates of unknown unitary gates. We first examine
Controlled-U gates that act on qubits, and assume that we know the eigenvalues.
It is then shown how to use singlet states to produce qubits in the eigenstates
of the gate. We then remove the assumption that we know the eigenvalues and
show how to both find the eigenvalues and produce qubits in the eigenstates.
Finally, we look at the case where the unitary operator acts on qutrits and has
eigenvalues of 1 and -1, where the eigenvalue 1 is doubly degenerate. The
eigenstates are unknown. We are able to use a singlet state to produce a qutrit
in the eigenstate corresponding to the -1 eigenvalue.


title: Biased EPR entanglement and its application to teleportation

abstract:
  We consider pure continuous variable entanglement with non-equal correlations
between orthogonal quadratures. We introduce a simple protocol which equates
these correlations and in the process transforms the entanglement onto a state
with the minimum allowed number of photons. As an example we show that our
protocol transforms, through unitary local operations, a single squeezed beam
split on a beam splitter into the same entanglement that is produced when two
squeezed beams are mixed orthogonally. We demonstrate that this technique can
in principle facilitate perfect teleportation utilising only one squeezed beam.


title:
Weak Quantum Theory: Complementarity and Entanglement in Physics and
  Beyond

abstract:
  The concepts of complementarity and entanglement are considered with respect
to their significance in and beyond physics. A formally generalized, weak
version of quantum theory, more general than ordinary quantum theory of
material systems, is outlined and tentatively applied to some examples.


title: Lowest threshold visibility for testing local realistic theories

abstract:
  Analytical and numerical arguments are presented in case of a pair of
two-state systems in a singlet state that the threshold visibility for testing
Bell's theorem on the entire range of measurement settings is 33.3%. It is also
shown that no lower treshold exists.


title: Relational modal interpretation for relativistic quantum field theories

abstract:
  The relational version of the modal interpretation offers both a consistent
quantum ontology and solution for quantum paradoxes within the framework of
nonrelativistic quantum mechanics. In the present paper this approach is
generalized for the case of relativistic quantum field theories. Physical
systems are defined as Hilbert spaces. The concept of the reduced density
matrix is also generalized so that its trace may become smaller than one,
expressing the possibility of annihilation. Superselection rules are shown to
follow if the whole Universe has a definite electric charge, barionic number
and leptonic number.


title: Quantum origin of classical properties within the modal interpretations

abstract:
  An example is presented when decoherence and quantum interference gives rise
to narrow eigenstates (in coordinate representation) for the reduced density
matrix of macroscopic quantum systems. On the basis of modal interpretations
this means the emergence of classical properties.


title: Discrete path integral for spin-1/2 in the Grassmannian representation

abstract:
  A variation to the usual formulation of Grassmann representation path
integrals is presented. Time-indexed anticommuting partners are introduced for
each Grassmann coherent state variable and a general method for handling the
effect of these introduced Grassmann partners is also developed. These
Grassmann partners carry the nilpotency and anticommutivity of the Grassmann
coherent state variables into the propagator and allow the propagator to be
written as a path integral. Two examples are introduced in which this variation
is shown to yield exact results. In particular, exact results are
demonstratated for a spin-1/2 in a time-dependent magnetic field, and for a
spin-boson system. The stationary path approximation is then shown to be exact
for each example.


title: Quantum Entanglement in Fermionic Lattices

abstract:
  The Fock space of a system of indistinguishable particles is isomorphic (in a
non-unique way) to the state-space of a composite i.e., many-modes, quantum
system. One can then discuss quantum entanglement for fermionic as well as
bosonic systems. We exemplify the use of this notion -central in quantum
information - by studying some e.g., Hubbard,lattice fermionic models relevant
to condensed matter physics.


title: Two-Photon Interferometry for High-Resolution Imaging

abstract:
  We discuss advantages of using non-classical states of light for two aspects
of optical imaging: creating of miniature images on photosensitive substrates,
which constitutes the foundation for optical lithography, and imaging of micro
objects. In both cases, the classical resolution limit given by the Rayleigh
criterion is approximately a half of the optical wavelength. It has been shown,
however, that by using multi-photon quantum states of the light field, and
multi-photon sensitive material or detector, this limit can be surpassed. We
give a rigorous quantum mechanical treatment of this problem, address some
particularly widespread misconceptions and discuss the requirements for turning
the research on quantum imaging into a practical technology.


title: Sensitivity optimization in quantum parameter estimation

abstract:
  We present a general framework for sensitivity optimization in quantum
parameter estimation schemes based on continuous (indirect) observation of a
dynamical system. As an illustrative example, we analyze the canonical scenario
of monitoring the position of a free mass or harmonic oscillator to detect weak
classical forces. We show that our framework allows the consideration of
sensitivity scheduling as well as estimation strategies for non-stationary
signals, leading us to propose corresponding generalizations of the Standard
Quantum Limit for force detection.


title: Quantum Computing with Globally Controlled Exchange-type Interactions

abstract:
  If the interaction between qubits in a quantum computer has a non-diagonal
form (e.g. the Heisenberg interaction), then one must be able to "switch it
off" in order to prevent uncontrolled propagation of states. Therefore, such QC
schemes typically demand local control of the interaction strength between each
pair of neighboring qubits. Here we demonstrate that this degree of control is
not necessary: it suffices to switch the interaction collectively - something
that can in principle be achieved by global fields rather than with local
manipulations. This observation may offer a significant simplification for
various solid state, optical lattice and NMR implementations.


title: Interaction of 3-level atom with radiation

abstract:
  The interaction of 3-level system with a quantum field in a non-equilibrium
state is considered. We describe a class of states of the quantum field for
wich a stationary state drives the system to inverse populated state. We find
that the quotient of the population of the energy levels in the simplest case
is described by the double Einstein formula which involves products of two
Einstein emission/absorption relations. Emission and absorption of radiation by
3-level atom in non-equlibrium stationary state is described.


title: Stimulated emission with a non-equilibrium state of radiation

abstract:
  The stimulated emission from an atom interacting with radiation in
non-equilibrium state is considered. The stochastic limit, applied to the
non-relativistic Hamiltonian describing the interaction, shows that the state
of atoms, driven by some non-equilibrium state of the field approaches a
stationary state which can continuously emit photon, unlike the case with an
equilibrium state.


title:
Generation and manipulation of squeezed states of light in optical
  networks for quantum communication and computation

abstract:
  We analyze a fiber-optic component which could find multiple uses in novel
information-processing systems utilizing squeezed states of light. Our approach
is based on the phenomenon of photon-number squeezing of soliton noise after
the soliton has propagated through a nonlinear optical fiber. Applications of
this component in optical networks for quantum computation and quantum
cryptography are discussed.


title: Dielectric black hole analogues

abstract:
  Alternative to the sonic black hole analogues we discuss a different scenario
for modeling the Schwarzschild geometry in a laboratory - the dielectric black
hole. The dielectric analogue of the horizon occurs if the velocity of the
medium with a finite permittivity exceeds the speed of light in that medium.
The relevance for experimental tests of the Hawking effect and possible
implications are addressed. PACS: 04.70.Dy, 04.62.+v, 04.80.-y, 42.50.Gy.


title:
Robust and Fragile Entanglement of Three Qubits: Relation to Permutation
  Symmetry

abstract:
  Entanglement properties of a basic set of eight entangled three particle pure
states possessing certain permutation symmetries are studied. They fall into
four sets of two entangled states, differing in their patterns of robustness to
entanglement when one of the states is lost. These features are related to the
permutation symmetries of the spin states of the three particles and their
corresponding marginal two-particle states. It is interesting to note that the
eight entangled three-qubit states discussed here are eigenstates of a
three-spin Heisenberg Hamiltonian.


title:
How a Quantum Theory Based on Generalized Coherent States Resolves the
  EPR and Measurement Problems

abstract:
  It is shown that the quantum theory can be formulated on homogeneous spaces
of generalized coherent states in a manner that accounts for interference,
entanglement, and the linearity of dynamics without using the superposition
principle. The coherent state labels, which are essentially instructions for
preparing states, make it unnecessary to identify properties with projectors in
Hilbert space. This eliminates the so called "eigenvalue-eigenstate" link, and
the theory thereby escapes the measurement problem. What the theory allows us
to predict is the distribution in the outcomes of tests of relations between
coherent states. It is shown that quantum non-determinism can be attributed to
a hidden variable (noise) in the space of relations without violating the no-go
theorems (e.g. Kochen-Specker). It is shown that the coherent state vacuum is
distorted when entangled states are generated. The non-locality of the vacuum
permits this distortion to be felt everywhere without the transmission of a
signal and thereby accounts for EPR correlations in a manifestly covariant way.


title: n+1 dimensional Dirac equation and the Klein paradox

abstract:
  The purpose of this comment is to clarify two points related to the Dirac
equation. First, the Lorentz structure of the potential and its connection with
the Klein paradox. Second, the connection between the number of space
dimensions and the number of spinor components.


title:
Propagation of Raman-matched laser pulses through a Bose-Einstein
  condensate

abstract:
  We investigate the role of non-uniform spatial density profiles of trapped
atomic Bose-Einstein condensates in the propagation of Raman-matched laser
pulses under conditions for electromagnetically induced transparency (EIT). We
find that the sharp edged axial density profile of an interacting condensate
(due to a balance between external trap and repulsive atomic interaction) is
advantageous for obtaining ultra slow averaged group velocities. Our results
are in good quantitative agreement with a recent experiment report [Nature {\bf
397}, 594 (1999)].


title: Probabilities, Tensors and Qubits

abstract:
  In the paper is discussed complete probabilistic description of quantum
systems with application to multiqubit quantum computations. In simplest case
it is a set of probabilities of transitions to some fixed set of states. The
probabilities in the set may be represented linearly via coefficients of
density matrix and it is very similar with description using mixed states, but
also may give some alternative view on specific properties of quantum circuits
due to possibility of direct comparison with classical statistical paradigm.


title:
Non-adiabatically detecting the geometric phase of the macroscopic
  quantum state with symmetric SQUID

abstract:
  We give a simple way to detect the geometric phase shift and the conditional
geometric phase shift with Josephson junction system. Comparing with the
previous work(Falcl G, Fazio R, Palma G.M., Siewert J and Verdal V, {\it
Nature} {\bf 407}, 355(2000)), our scheme has two advantages. We use the
non-adiabatic operation, thus the detection is less affected by the
decoherence. Also, we take the time evolution on zero dynamic phase loop, we
need not take any extra operation to cancel the dynamic phase.


title: Conditional evolution in single-atom cavity QED

abstract:
  We consider a typical setup of cavity QED consisting of a two-level atom
interacting strongly with a single resonant electromagnetic field mode inside a
cavity. The cavity is resonantly driven and the output undergoes continuous
homodyne measurements. We derive an explicit expression for the state of the
system conditional on a discrete photocount record. This expression takes a
particularly simple form if the system is initially in the steady state. As a
byproduct, we derive a general formula for the steady state that had been
conjectured before in the strong driving limit.


title:
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of
  an NP-Complete Problem

abstract:
  A quantum system will stay near its instantaneous ground state if the
Hamiltonian that governs its evolution varies slowly enough. This quantum
adiabatic behavior is the basis of a new class of algorithms for quantum
computing. We test one such algorithm by applying it to randomly generated,
hard, instances of an NP-complete problem. For the small examples that we can
simulate, the quantum adiabatic algorithm works well, and provides evidence
that quantum computers (if large ones can be built) may be able to outperform
ordinary computers on hard sets of instances of NP-complete problems.


title: Creating massive entanglement of Bose condensed atoms

abstract:
  We propose a direct, coherent coupling scheme that can create massively
entangled states of Bose-Einstein condensed atoms. Our idea is based on an
effective interaction between two atoms from coherent Raman processes through a
(two atom) molecular intermediate state. We compare our scheme with other
recent proposals for generation of massive entanglement of Bose condensed
atoms.


title: An NMR Analog of the Quantum Disentanglement Eraser

abstract:
  We report the implementation of a three-spin quantum disentanglement eraser
on a liquid-state NMR quantum information processor. A key feature of this
experiment was its use of pulsed magnetic field gradients to mimic projective
measurements. This ability is an important step towards the development of an
experimentally controllable system which can simulate any quantum dynamics,
both coherent and decoherent.


title: Time Evolution of tunneling and decoherence: soluble model

abstract:
  Decoherence effects associated to the damping of a tunneling two-level system
are shown to dominate the tunneling probability at short times in strong
coupling regimes in the context of a soluble model. A general decomposition of
tunneling rates in dissipative and unitary parts is implemented. Master
equation treatments fail to describe the model system correctly when more than
a single relaxation time is involved.


title: Bell's theorem without inequalities and only two distant observers

abstract:
  A proof of Bell's theorem without inequalities and involving only two
observers is given by suitably extending a proof of the Bell-Kochen-Specker
theorem due to Mermin. This proof is generalized to obtain an inequality-free
proof of Bell's theorem for a set of n Bell states (with n odd) shared between
two distant observers. A generalized CHSH inequality is formulated for n Bell
states shared symmetrically between two observers and it is shown that quantum
mechanics violates this inequality by an amount that grows exponentially with
increasing n.


title: Superfluidity in the stochastic limit

abstract:
  In the present paper we outline the stochastic limit approach to
superfluidity. The Hamiltonian describing the interaction between the Bose
condensate and the normal phase is introduced. Sufficient in the stochastic
limit condition of superfluidity is proposed. Existence of superfluidity in the
stochastic limit of this system is proved and the non-linear (quadratic)
equation of motion describing the superfluid liquid is obtained.


title:
Nonadditive measure and quantum entanglement in a class of mixed states
  of N^n-system

abstract:
  Through the generalization of Khinchin's classical axiomatic foundation, a
basis is developed for nonadditive information theory. The classical
nonadditive conditional entropy indexed by the positive parameter q is
introduced and then translated into quantum information. This quantity is
nonnegative for classically correlated states but can take negative values for
entangled mixed states. This property is used to study quantum entanglement in
the parametrized Werner-Popescu-like state of an N^n-system, that is, an
n-partite N-level system. It is shown how the strongest limitation on validity
of local realism (i.e., separability of the state) can be obtained in a novel
manner.


title: Finite Energy Sum Rules in Potential Scattering

abstract:
  We study scattering theory identities previously obtained as consistency
conditions in the context of one-loop quantum field theory calculations. We
prove the identities using Jost function techniques and study applications.


title: Quantum Walks on the Hypercube

abstract:
  Recently, it has been shown that one-dimensional quantum walks can mix more
quickly than classical random walks, suggesting that quantum Monte Carlo
algorithms can outperform their classical counterparts. We study two quantum
walks on the n-dimensional hypercube, one in discrete time and one in
continuous time. In both cases we show that the quantum walk mixes in (\pi/4)n
steps, faster than the O(n log n) steps required by the classical walk. In the
continuous-time case, the probability distribution is {\em exactly} uniform at
this time. More importantly, these walks expose several subtleties in the
definition of mixing time for quantum walks. Even though the continuous-time
walk has an O(n) instantaneous mixing time at which it is precisely uniform, it
never approaches the uniform distribution when the stopping time is chosen
randomly as in [AharonovAKV2001]. Our analysis treats interference between
terms of different phase more carefully than is necessary for the walk on the
cycle; previous general bounds predict an exponential, rather than linear,
mixing time for the hypercube.


title: Mermin's pentagram and Bell's theorem

abstract:
  It is shown how a proof of the Bell-Kochen-Specker (BKS) theorem given by
Kernaghan and Peres can be experimentally realized using a scheme of
measurements derived from a related proof of the same theorem by Mermin. It is
also pointed out that if this BKS experiment is carried out independently by
two distant observers who repeatedly make measurements on a specially
correlated state of six qubits, it provides an inequality-free demonstration of
Bell's theorem as well.


title:
Violation of multi-particle Bell inequalities for low and high flux
  parametric amplification using both vacuum and entangled input states

abstract:
  We show how polarisation measurements on the output fields generated by
parametric down conversion will reveal a violation of multi-particle Bell
inequalities, in the regime of both low and high output intensity. In this case
each spatially separated system, upon which a measurement is performed, is
comprised of more than one particle. In view of the formal analogy with spin
systems, the proposal provides an opportunity to test the predictions of
quantum mechanics for spatially separated higher spin states. Here the quantum
behaviour possible even where measurements are performed on systems of large
quantum (particle) number may be demonstrated. Our proposal applies to both
vacuum-state signal and idler inputs, and also to the quantum-injected
parametric amplifier as studied by De Martini et al. The effect of detector
inefficiencies is included.


title: Sundays in a Quantum Engineer's Life

abstract:
  I am a Quantum Engineer, but on Sundays I have principles, John Bell opened
his "underground colloquium" in March 1983, words which I will never forget!
What! John Bell, the great John Bell, presented himself as an engineer!?! one
of those people who make things work without even understanding how they
function?!? whereas I thought of John Bell as one of the greatest theoretician.


title: Why Genetic Information Processing could have a Quantum Basis

abstract:
  Living organisms are not just random collections of organic molecules. There
is continuous information processing going on in the apparent bouncing around
of molecules of life. Optimisation criteria in this information processing can
be searched for using the laws of physics. Quantum dynamics can explain why
living organisms have 4 nucleotide bases and 20 amino acids, as optimal
solutions of the molecular assembly process. Experiments should be able to tell
whether evolution indeed took advantage of quantum dynamics or not.


title: Of Some Theoretical Significance: Implications of Casimir Effects

abstract:
  In his autobiography Casimir barely mentioned the Casimir effect, but
remarked that it is "of some theortical significance." We will describe some
aspects of Casimir effects that appear to be of particular significance now,
more than half a century after Casimir's famous paper.


title: Ponderomotive entangling of atomic motions

abstract:
  We propose the use of ponderomotive forces to entangle the motions of
different atoms. Two situations are analyzed: one where the atoms belong to the
same optical cavity and interact with the same radiation field mode; the other
where each atom is placed in own optical cavity and the output field of one
cavity enters the other.


title: The Quantum Zeno Effect - Evolution of an Atom Impeded by Measurement

abstract:
  The evolution of a quantum system is supposed to be impeded by measurement of
an involved observable. This effect has been proven indistinguishable from the
effect of dephasing the system's wave function, except in an individual quantum
system. The coherent dynamics, on an optical E2 line, of a single trapped ion
driven by light of negligible phase drift has been alternated with
interrogations of the internal ion state. Retardation of the ion's nutation,
equivalent to the quantum Zeno effect, is demonstrated in the statistics of
sequences of probe-light scattering ''on'' and ''off'' detections, the latter
representing back-action-free measurement.


title: Quantum Period Query Proves NP in BQP

abstract:
  Withdrawn by the authors. Since the elements within each period of function
hA are not distinct, period finding cannot operate properly. Thanks to all for
the comments and sorry for the inconvenience.


title: Effect of noise on geometric logic gates for quantum computation

abstract:
  We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a
tool for quantum computation and show how it could be implemented with
superconducting charge qubits. While it may circumvent many of the drawbacks
related to the adiabatic (Berry) version of geometric gates, we show that the
effect of fluctuations of the control parameters on non-adiabatic phase gates
is more severe than for the standard dynamic gates. Similarly, fluctuations
also affect to a greater extent quantum gates that use the Berry phase instead
of the dynamic phase.


title:
Geometry of mixed states and degeneracy structure of geometric phases
  for multi-level quantum systems. A unitary group approach

abstract:
  We analyze the geometric aspects of unitary evolution of general states for a
multilevel quantum system by exploiting the structure of coadjoint orbits in
the unitary group Lie algebra. Using the same method in the case of SU(3) we
study the effect of degeneracies on geometric phases for three-level systems.
This is shown to lead to a highly nontrivial generalization of the result for
two-level systems in which degeneracy results in a "monopole" structure in
parameter space. The rich structures that arise are related to the geometry of
adjoint orbits in SU(3). The limiting case of a two-level degeneracy in a
three-level system is shown to lead to the known monopole structure.


title:
A Clarification on the Detection of Aharanov-Anandan's phase and fault
  tolerate computation with symmetric SQUID

abstract:
  We point out that our scheme in manuscript quant-ph/0104127 is misunderstood
by Alexander Blais and Andre-Marie S. Tremblay in their recent e-print
quant-ph/0105006.


title: Quantum Boltzmann statistics in interacting systems

abstract:
  Collective operators that describe interaction of generic quantum system with
discrete spectrum with a quantum field are investigated. These operators,
considered as operators in the entangled Fock space (space generated by action
of collective creations on the vacuum) in the stochastic limit satisfy a
particular kind of Quantum Boltzmann (or free) commutational relations. This
clarifies a general phenomenon of arising of Quantum Boltzmann relations in
interacting systems.


title: Klein Paradox for Optical Scattering from Excited Targets

abstract:
  The well known Klein paradox for the relativistic Dirac wave equation
consists in the computation of possible ``negative probabilities'' induced by
certain potentials in some regimes of energy. The paradox may be resolved
employing the notion of electron-positron pair production in which the number
of electrons present in a process can increase. The Klein paradox also exists
in Maxwell's equations viewed as the wave equation for photons. In a medium
containing ``inverted energy populations'' of excited atoms, e.g. in a LASER
medium, one may again compute possible ``negative probabilities''. The
resolution of the electromagnetic Klein paradox is that when the atoms decay,
the final state may contain more photons then were contained the initial state.
The optical theorem total cross section for scattering photons from excited
state atoms may then be computed as negative within a frequency band with
matter induced amplification.


title: Space Rotation Invariance

abstract:
  The space rotation invariance hypothesis is examined. The basic space-time
properties and the physical object description from this point of view are
considered. An $\omega$-invariance as an approximation of the space rotation
invariance hypothesis is introduced. It is shown that on frames of the
$\omega$-invariance it is possible to describe the ``wave'' properties of
elementary particles and to get the basic quantum mechanics equations, such as
Schr\"odinger and Klein-Gordon-Fock equations. The correlation between the
space rotation objects and models of the elementary particles, quarks and even
nuclei is found. The problems of metrics and gravitation from the space
rotation invariance point of view are discussed. The introduced hypothesis may
be a foundation of the theory of the Unification.


title: On the Equivalence Principle of Quantum Mechanics

abstract:
  A recent concept in theoretical physics, motivated in string duality and
M-theory, is the notion that not all quantum theories arise from quantising a
classical system. Also, a given quantum model may possess more than just one
classical limit. In view of these developments, we analyse some general
properties that quantum mechanics must satisfy, if it is not to be formulated
as a quantisation of a given classical mechanics. Instead, our approach to
quantum mechanics is modelled on a statement that is close in spirit to the
equivalence principle of general relativity, thus bearing a strong resemblance
with the equivalence principle of quantum mechanics formulated by
Faraggi-Matone.


title: The running of the Universe and the quantum structure of time

abstract:
  Some principles underpinning the running of the Universe are discussed. The
most important, the machine principle, states that the Universe is a fully
autonomous, self-organizing and self-testing quantum automaton. Continuous
space and time, consciousness and the semi-classical observers of quantum
mechanics are all emergent phenomena not operating at the fundamental level of
the machine Universe. Quantum processes define the present, the interface
between the future and the past, giving a time ordering to the running of the
Universe which is non-integrable except on emergent scales. A diagrammatic
approach is used to discuss the quantum topology of the EPR paradox, particle
decays and scattering processes. A toy model of a self-referential universe is
given.


title:
Remarkable relations for the expectation values of simultaneous action
  of the kinetic and potential energy operators on Schrodinger wavefunctions

abstract: Witdrawn. Error in Eq.(14).


title: Inequivalent classes of interference experiments with non-abelian anyons

abstract:
  We present a theoretical analysis of inequivalent classes of interference
experiments with non-abelian anyons using an idealized Mach-Zender type
interferometer. Because of the non-abelian nature of the braid group action one
has to distinguish the different possibilities in which the experiment can be
repeated, which lead to different interference patterns. We show that each
setup will, after repeated measurement, lead to a situation where the
two-particle (or multi-particle) state gets locked into an eigenstate of some
well defined operator. Also the probability to end up in such an eigenstate is
calculated. Some representative examples are worked out in detail.


title:
Unambiguous Discrimination Between Linearly Dependent States with
  Multiple Copies

abstract:
  A set of quantum states can be unambiguously discriminated if and only if
they are linearly independent. However, for a linearly dependent set, if C
copies of the state are available, then the resulting C particle states may
form a linearly independent set, and be amenable to unambiguous discrimination.
We obtain necessary and sufficient conditions for the possibility of
unambiguous discrimination between N states given that C copies are available
and that the single copies span a D dimensional space. These conditions are
found to be identical for qubits. We then examine in detail the linearly
dependent trine ensemble. The set of C>1 copies of each state is a set of
linearly independent lifted trine states. The maximum unambiguous
discrimination probability is evaluated for all C>1 with equal a priori
probabilities.


title: The Uniqueness Theorem for Entanglement Measures

abstract:
  We explore and develop the mathematics of the theory of entanglement
measures. After a careful review and analysis of definitions, of preliminary
results, and of connections between conditions on entanglement measures, we
prove a sharpened version of a uniqueness theorem which gives necessary and
sufficient conditions for an entanglement measure to coincide with the reduced
von Neumann entropy on pure states. We also prove several versions of a theorem
on extreme entanglement measures in the case of mixed states. We analyse
properties of the asymptotic regularization of entanglement measures proving,
for example, convexity for the entanglement cost and for the regularized
relative entropy of entanglement.


title: Robust control in the quantum domain

abstract:
  Recent progress in quantum physics has made it possible to perform
experiments in which individual quantum systems are monitored and manipulated
in real time. The advent of such new technical capabilities provides strong
motivation for the development of theoretical and experimental methodologies
for quantum feedback control. The availability of such methods would enable
radically new approaches to experimental physics in the quantum realm.
Likewise, the investigation of quantum feedback control will introduce crucial
new considerations to control theory, such as the uniquely quantum phenomena of
entanglement and measurement back-action. The extension of established analysis
techniques from control theory into the quantum domain may also provide new
insight into the dynamics of complex quantum systems. We anticipate that the
successful formulation of an input-output approach to the analysis and
reduction of large quantum systems could have very general applications in
non-equilibrium quantum statistical mechanics and in the nascent field of
quantum information theory.


title:
Partial recovery of entanglement in bipartite entanglement
  transformations

abstract:
  Any deterministic bipartite entanglement transformation involving finite
copies of pure states and carried out using local operations and classical
communication (LOCC) results in a net loss of entanglement. We show that for
almost all such transformations, partial recovery of lost entanglement is
achievable by using $2 \times 2$ auxiliary entangled states, no matter how
large the dimensions of the parent states are. For the rest of the special
cases of deterministic LOCC transformations, we show that the dimension of the
auxiliary entangled state depends on the presence of equalities in the
majorization relations of the parent states. We show that genuine recovery is
still possible using auxiliary states in dimensions less than that of the
parent states for all patterns of majorization relations except only one
special case.