title: Limitation of computational resource as physical principle

abstract:
  Limitation of computational resources is considered as a universal principle
that for simulation is as fundamental as physical laws are. It claims that all
experimentally verifiable implications of physical laws can be simulated by the
effective classical algorithms. It is demonstrated through a completely
deterministic approach proposed for the simulation of biopolymers assembly. A
state of molecule during its assembly is described in terms of the reduced
density matrix permitting only limited tunneling. An assembly is treated as a
sequence of elementary scatterings of simple molecules from the environment on
the point of assembly. A decoherence is treated as a forced measurement of
quantum state resulted from the shortage of computational resource. All results
of measurements are determined by a choice from the limited number of special
options of the nonphysical nature which stay unchanged till the completion of
assembly; we do not use the random numbers generators. Observations of equal
states during the assembly always give the same result. We treat a scenario of
assembly as an establishing of the initial states for elementary scatterings.
The different scenarios are compared according to the distributions of the
assembly results.


title:
Macroscopic Quantum Resonance of Coupled Flux Qubits; A Quantum
  Computation Scheme

abstract:
  We show that a superconducting circuit containing two loops, when treated
with Macroscopic Quantum Coherence (MQC) theory, constitutes a complete two-bit
quantum computer. The manipulation of the system is easily implemented with
alternating magnetic fields. A \textit{universal} set of quantum gates is
deemed available by means of all unitary single bit operations and a
controlled-not (\textsc{cnot}) sequence. We use multi-dimensional MQC theory
and time-dependent first order perturbation theory to analyze the model. Our
calculations show that a two qubit arrangement, each having a diameter of
200nm, operating in the flux regime can be operated with a static magnetic
field of $\sim 0.1$T, and an alternating dynamic magnetic field of amplitude
$\sim 1$ Gauss and frequency $\sim 10$Hz. The operational time $\tau_{op}$ is
estimated to be $\sim 10$ns.


title: Dressed Qubits

abstract:
  Inherent gate errors can arise in quantum computation when the actual system
Hamiltonian or Hilbert space deviates from the desired one. Two important
examples we address are spin-coupled quantum dots in the presence of spin-orbit
perturbations to the Heisenberg exchange interaction, and off-resonant
transitions of a qubit embedded in a multilevel Hilbert space. We propose a
``dressed qubit'' transformation for dealing with such inherent errors. Unlike
quantum error correction, the dressed qubits method does not require additional
operations or encoding redundancy, is insenstitive to error magnitude, and
imposes no new experimental constraints.


title:
Two-particle localization and antiresonance in disordered spin and qubit
  chains

abstract:
  We show that, in a system with defects, two-particle states may experience
destructive quantum interference, or antiresonance. It prevents an excitation
localized on a defect from decaying even where the decay is allowed by energy
conservation. The system studied is a qubit chain or an equivalent spin chain
with an anisotropic ($XXZ$) exchange coupling in a magnetic field. The chain
has a defect with an excess on-site energy. It corresponds to a qubit with the
level spacing different from other qubits. We show that, because of the
interaction between excitations, a single defect may lead to multiple localized
states. The energy spectra and localization lengths are found for
two-excitation states. The localization of excitations facilitates the
operation of a quantum computer. Analytical results for strongly anisotropic
coupling are confirmed by numerical studies.


title:
Quantum Algorithms for Lowest Weight Paths and Spanning Trees in
  Complete Graphs

abstract:
  Quantum algorithms for several problems in graph theory are considered.
Classical algorithms for finding the lowest weight path between two points in a
graph and for finding a minimal weight spanning tree involve searching over
some space. Modification of classical algorithms due to Dijkstra and Prim
allows quantum search to replace classical search and leads to more efficient
algorithms. In the case of highly asymmetric complete bipartite graphs, simply
replacing classical search with quantum search leads to a faster quantum
algorithm. A fast quantum algorithm for computing the diameter of a complete
graph is also given.


title: Unification of Dynamical Decoupling and the Quantum Zeno Effect

abstract:
  We unify the quantum Zeno effect (QZE) and the "bang-bang" (BB) decoupling
method for suppressing decoherence in open quantum systems: in both cases
strong coupling to an external system or apparatus induces a dynamical
superselection rule that partitions the open system's Hilbert space into
quantum Zeno subspaces. Our unification makes use of von Neumann's ergodic
theorem and avoids making any of the symmetry assumptions usually made in
discussions of BB. Thus we are able to generalize BB to arbitrary fast and
strong pulse sequences, requiring no symmetry, and to show the existence of two
alternatives to pulsed BB: continuous decoupling, and pulsed measurements. Our
unified treatment enables us to derive limits on the efficacy of the BB method:
we explicitly show that the inverse QZE implies that BB can in some cases
accelerate, rather than inhibit, decoherence.


title: Tunneling dynamics in relativistic and nonrelativistic wave equations

abstract:
  We obtain the solution of a relativistic wave equation and compare it with
the solution of the Schroedinger equation for a source with a sharp onset and
excitation frequencies below cut-off. A scaling of position and time reduces to
a single case all the (below cut-off) nonrelativistic solutions, but no such
simplification holds for the relativistic equation, so that qualitatively
different ``shallow'' and ``deep'' tunneling regimes may be identified
relativistically. The nonrelativistic forerunner at a position beyond the
penetration length of the asymptotic stationary wave does not tunnel;
nevertheless, it arrives at the traversal (semiclassical or
B\"uttiker-Landauer) time "tau". The corresponding relativistic forerunner is
more complex: it oscillates due to the interference between two saddle point
contributions, and may be characterized by two times for the arrival of the
maxima of lower and upper envelops. There is in addition an earlier
relativistic forerunner, right after the causal front, which does tunnel.
Within the penetration length, tunneling is more robust for the precursors of
the relativistic equation.


title: Effect of atomic transfer on the decay of a Bose-Einstein condensate

abstract:
  We present a model describing the decay of a Bose-Einstein condensate, which
assumes the system to remain in thermal equilibrium during the decay. We show
that under this assumption transfer of atoms occurs from the condensate to the
thermal cloud enhancing the condensate decay rate.


title: Nonseparability and squeezing of continuous polarization variables

abstract:
  The impact of the operator-valued commutator on nonclassical properties of
continuous polarization variables is discussed. The definition of polarization
squeezing is clarified to exclude those squeezed states which do not contain
any new physics beyond quadrature squeezing. We present a consistent derivation
of the general nonseparability criterion for the continuous variables with the
operator-valued commutator, and apply it to the polarization variables.


title:
Polarization Correlations of 1S0 Proton Pairs as Tests of Bell and
  Wigner Inequalities

abstract:
  In an experiment designed to overcome the loophole of observer dependent
reality and satisfying the counterfactuality condition, we measured
polarization correlations of 1S0 proton pairs produced in 12C(d,2He) and
1H(d,He) reactions in one setting. The results of these measurements are used
to test the Bell and Wigner inequalties against the predictions of quantum
mechanics.


title:
Generation of entangled ancilla states for use in linear optics quantum
  computing

abstract:
  We describe several different methods for generating the entangled ancilla
states that are required for linear optics quantum computing. We show that
post-selection can be used in combination with linear optical elements to
generate the entangled ancilla, but with an exponentially-small efficiency.
Alternatively, the ancilla can be efficiently generated using solid-state
devices consisting of quantum wells coupled with tunnel junctions. Finally, we
consider the possibility of using encoded ancilla in order to reduce the
effects of decoherence and measurement errors.


title:
A lower bound for bounded round quantum communication complexity of set
  disjointness

abstract:
  We consider the class of functions whose value depends only on the
intersection of the input X_1,X_2, ..., X_t; that is, for each F in this class
there is an f_F: 2^{[n]} \to {0,1}, such that F(X_1,X_2, ..., X_t) = f_F(X_1
\cap X_2 \cap ... \cap X_t). We show that the t-party k-round communication
complexity of F is Omega(s_m(f_F)/(k^2)), where s_m(f_F) stands for the
`monotone sensitivity of f_F' and is defined by s_m(f_F) \defeq max_{S\subseteq
[n]} |{i: f_F(S \cup {i}) \neq f_F(S)|. For two-party quantum communication
protocols for the set disjointness problem, this implies that the two parties
must exchange Omega(n/k^2) qubits. For k=1, our lower bound matches the
Omega(n) lower bound observed by Buhrman and de Wolf (based on a result of
Nayak, and for 2 <= k <= n^{1/4}, improves the lower bound of Omega(sqrt{n})
shown by Razborov. (For protocols with no restrictions on the number of rounds,
we can conclude that the two parties must exchange Omega(n^{1/3}) qubits. This,
however, falls short of the optimal Omega(sqrt{n}) lower bound shown by
Razborov.)


title:
Directly Observing Momentum Transfer in Twin-Slit "Which-Way"
  Experiments

abstract:
  Is the destruction of interference by a which-way measurement due to a random
momentum transfer $\wp\agt\hbar/s$, with $s$ the slit separation? The
weak-valued probability distribution $P_{\rm wv}(\wp)$, which is {\em directly
observable}, provides a subtle answer. $P_{\rm wv}(\wp)$ cannot have support on
the interval $[-\hbar/s,\hbar/s]$. Nevertheless, its moments can be identically
zero.


title: Entanglement constrained by superselection rules

abstract:
  Bipartite entanglement may be reduced if there are restrictions on allowed
local operations. We introduce the concept of a generalized superselection rule
(SSR) to describe such restrictions, and quantify the entanglement constrained
by it. We show that ensemble quantum information processing, where elements in
the ensemble are not individually addressable, is subject to the SSR associated
with the symmetric group (the group of permutations of elements). We prove that
even for an ensemble comprising many pairs of qubits, each pair described by a
pure Bell state, the entanglement per element constrained by this SSR goes to
zero for a large number of elements.


title: Some Bipartite States do not Arise from Channels

abstract:
  It is well-known that the action of a quantum channel on a state can be
represented, using an auxiliary space, as the partial trace of an associated
bipartite state. Recently, it was observed that for the bipartite state
associated with the optimal average input of the channel, the entanglement of
formation is simply the entropy of the reduced density matrix minus the Holevo
capacity. It is natural to ask if every bipartite state can be associated with
some channel in this way. We show that the answer is negative.


title: Quantum and Classical Coherent States

abstract:
  p-Mechanics is a consistent physical theory which describes both quantum and
classical mechanics simultaneously. We continue the development of p-mechanics
by introducing the concept of states. The set of coherent states we introduce
allow us to evaluate classical observables at any point of phase space
simultaneously to evaluating quantum probability amplitudes. The example of the
forced harmonic oscilator is used to demonstrate these concepts.


title: Unitary relation for the time-dependent SU(1,1) systems

abstract:
  The system whose Hamiltonian is a linear combination of the generators of
SU(1,1) group with time-dependent coefficients is studied. It is shown that
there is a unitary relation between the system and a system whose Hamiltonian
is simply proportional to the generator of the compact subgroup of the SU(1,1).
The unitary relation is described by the classical solutions of a
time-dependent (harmonic) oscillator. Making use of the relation, the wave
functions satisfying the Schr\"{o}dinger equation are given for a general
unitary representation in terms of the matrix elements of a finite group
transformation (Bargmann function). The wave functions of the harmonic
oscillator with an inverse-square potential is studied in detail, and it is
shown that, through an integral, the model provides a way of deriving the
Bargmann function for the representation of positive discrete series of the
SU(1,1).


title: Synchronized pulse control of decoherence

abstract:
  We present a new strategy for multipulse control over decoherence. When a
two-level system interacts with a reservoir characterized by a specific
frequency, we find that the decoherence is effectively suppressed by
synchronizing the pulse-train application with the dynamical motion of the
reservoir.


title: Bounds for entanglement of formation of two mode squeezed thermal states

abstract:
  The upper and lower bounds of entanglement of formation are given for two
mode squeezed thermal state. The bounds are compared with other entanglement
measure or bounds. The entanglement distillation and the relative entropy of
entanglement of infinitive squeezed state are obtained at the postulation of
hashing inequality.


title: Coherent States with SU(N) Charges

abstract:
  We define coherent states carrying SU(N) charges by exploiting generalized
Schwinger boson representation of SU(N) Lie algebra. These coherent states are
defined on $2 (2^{N - 1} - 1)$ complex planes. They satisfy continuity property
and provide resolution of identity. We also exploit this technique to construct
the corresponding non-linear SU(N) coherent states.


title: Post-measurement Nonlocal Gates

abstract:
  Several proposed quantum computer models include measurement processes, in
order to implement nonlocal gates and create necessary entanglement resources
during the computation. We introduce a scheme in which the measurements can be
delayed for two- and three-qubit nonlocal gates. We also discuss implementing
arbitrary nonlocal gates when measurements are included during the process.


title:
Invariant Operators vs Heisenberg Operators for Time-Dependent
  Generalized Oscillators

abstract:
  We investigate the relation between the invariant operators satisfying the
quantum Liouville-von Neumann and the Heisenberg operators satisfying the
Heisenberg equation. For time-dependent generalized oscillators we find the
invariant operators, known as the Ermakov-Lewis invariants, in terms of a
complex classical solution, from which the evolution operator is derived, and
obtain the Heisenberg position and momentum operators. Physical quantities such
as correlation functions are calculated using both the invariant operators and
Heisenberg operators.


title: Multimode cat-state entanglement and network teleportation

abstract:
  Schemes for generation and protocols for network teleportation of multimode
entangled cat-states are proposed. Explicit expressions for probability of
successful teleportation are derived for both symmetric and asymmetric
networks.


title:
Two-photon interference of multimode two-photon pairs with an unbalanced
  interferometer

abstract:
  Two-photon interference of multimode two-photon pairs produced by an optical
parametric oscillator has been observed for the first time with an unbalanced
interferometer. The time correlation between the multimode two photons has a
multi-peaked structure. This property of the multimode two-photon state induces
two-photon interference depending on delay time. The nonclassicality of this
interference is also discussed.


title: Dissipation-assisted quantum computation in atom-cavity systems

abstract:
  The principal obstacle to quantum information processing with many qubits is
decoherence. One source of decoherence is spontaneous emission which causes
loss of energy and information. Inability to control system parameters with
high precision is another possible source of error. Strategies aimed at
overcoming one kind of error typically increase sensitivity to others. As a
solution we propose quantum computing with dissipation-assisted quantum gates.
These can be run relatively fast while achieving fidelities close to one. The
success rate of each gate operation can, at least in principle, be arbitrary
close to one.


title:
The van der Waals energy of atomic systems near absorbing and dispersing
  bodies

abstract:
  Within the frame of macroscopic quantum electrodynamics in causal media, the
van der Waals interaction between an atomic system and an arbitrary arrangement
of dispersing and absorbing dielectric bodies including metals is studied. It
is shown that the minimal-coupling scheme and the multipolar-coupling scheme
lead to essentially the same formula for the van der Waals potential. As an
application, the vdW potential of an atom in the presence of a sphere is
derived. Closed expressions for the long-distance (retardation) and
short-distance (non-retardation) limits are given, and the effect of material
absorption is discussed.


title: New derivation of quantum equations from classical stochastic arguments

abstract:
  In a previous article [H. Bergeron, J. Math. Phys. 42, 3983 (2001)], we
presented a method to obtain a continuous transition from classical to quantum
mechanics starting from the usual phase space formulation of classical
mechanics. This procedure was based on a Koopman-von Neumann approach where
classical equations are reformulated into a quantumlike form. In this article,
we develop a different derivation of quantum equations, based on purely
classical stochastic arguments, taking some elements from the
Bohm-Fenyes-Nelson approach. This study starts from a remark noticed by
different authors [M. Born, Physics in My Generation (Pergamon Press, London,
1956); E. Prugovecki, Stochastic Quantum Mechanics and Quantum Spacetime
(Reidel, Dordrecht, 1986)], suggesting that physical continuous observables are
stochastic by nature. Following this idea, we study how intrinsic stochastic
properties can be introduced into the framework of classical mechanics. Then we
analyze how the quantum theory can emerge from this modified classical
framework. This approach allows us to show that the transition from classical
to quantum formalism (for a spinless particle) does not require real
postulates, but rather soft generalizations.


title:
An Application of Renormalization Group Techniques to Classical
  Information Theory

abstract:
  We apply Renormalization Group (RG) techniques to Classical Information
Theory, in the limit of large codeword size $n$. In particular, we apply RG
techniques to (1) noiseless coding (i.e., a coding used for compression) and
(2) noisy coding (i.e., a coding used for channel transmission). Shannon's
"first" and "second" theorems refer to (1) and (2), respectively. Our RG
technique uses composition class (CC) ideas, so we call our technique
Composition Class Renormalization Group (CCRG). Often, CC's are called "types"
instead of CC's, and their theory is referred to as the "Method of Types". For
(1) and (2), we find that the probability of error can be expressed as an Error
Function whose argument contains variables that obey renormalization group
equations. We describe a computer program called WimpyRG-C1.0 that implements
the ideas of this paper. C++ source code for WimpyRG-C1.0 is publicly
available.


title: Berry phase for a spin 1/2 in a classical fluctuating field

abstract:
  The effect of fluctuations in the classical control parameters on the Berry
phase of a spin 1/2 interacting with a adiabatically cyclically varying
magnetic field is analyzed. It is explicitly shown that in the adiabatic limit
dephasing is due to fluctuations of the dynamical phase.


title: Bohmian Mechanics and Quantum Field Theory

abstract:
  We discuss a recently proposed extension of Bohmian mechanics to quantum
field theory. For more or less any regularized quantum field theory there is a
corresponding theory of particle motion, which in particular ascribes
trajectories to the electrons or whatever sort of particles the quantum field
theory is about. Corresponding to the nonconservation of the particle number
operator in the quantum field theory, the theory describes explicit creation
and annihilation events: the world lines for the particles can begin and end.


title:
Entanglement in quantum computers described by the XXZ model with
  defects

abstract:
  We investigate how to generate maximally entangled states in systems
characterized by the Hamiltonian of the XXZ model with defects. Some proposed
quantum computers are described by such model. We show how the defects can be
used to obtain EPR states and W states when one or two excitations are
considered.


title:
Application of the geometric measure of entanglement to three-qubit
  mixed states

abstract:
  The geometric measure of entanglement, originated by Shimony and by Barnum
and Linden, is determined for a family of tripartite mixed states consisting of
aribitrary mixtures of GHZ, W, and inverted-W states. For this family of
states, other measures of entanglement, such as entanglement of formation and
relative entropy of entanglement, have not been determined. The results for the
geometric measure of entanglement are compared with those for negativity, which
are also determined. The results for the geometric measure of entanglement and
the negativity provide examples of the determination of entanglement for
nontrivial mixed multipartite states.


title: BBGKY Hierarchy Underlying Many Particle Quantum Mechanics

abstract:
  Recently, the one particle quantum mechanics has been obtained in the
framework of an entirely classical subquantum kinetics. In the present paper we
argue that, within the same scheme and without any additional assumption, it is
possible to obtain also the $n$-particle non relativistic quantum mechanics.
The main goal of the present effort is to show that the classical BBGKY
hierarchical equation, for the $n$-particle reduced distribution function, is
the ancestor of the $n$-particle Schr\"odinger equation. On the other hand we
show that within the scenario of the subquantum structure of quantum particle,
the Fisher information measure emerges naturally in quantum mechanics.


title: $Z_3$-graded Symmetries in Quantum Mechanics

abstract:
  In this paper we consider $Z_3$-graded topological symmetries (TSs) in one
dimensional quantum mechanics. We give a classification of one dimensional
quantum systems possessing these symmetries and show that different classes
correspond to a positive integer $N$.


abstract:
  Three different manifestations of the quantum Zeno effect are discussed,
compared and shown to be physically equivalent. We look at frequent projective
measurements, frequent unitary "kicks" and strong continuous coupling. In all
these cases, the Hilbert space of the system splits into invariant "Zeno"
subspaces, among which any transition is hindered.


title: Quantum mechanics as a sociology of matter

abstract:
  Analogies between quantum mechanics and sociology lead to the hypothesis that
quantum objects are complex products of evolution. Like biological objects they
are able to receive, to work on, and to spread semantic information. In general
meaning we can name it "consciousness". The important ability of consciousness
is ability to predict future. Key words: Evolution, consciousness, information,
quantum mechanics, EPR, decoherence.


title: Mathematical Models of Contemporary Elementary Quantum Computing Devices

abstract:
  Computations with a future quantum computer will be implemented through the
operations by elementary quantum gates. It is now well known that the
collection of 1-bit and 2-bit quantum gates are universal for quantum
computation, i.e., any n-bit unitary operation can be carried out by
concatenations of 1-bit and 2-bit elementary quantum gates.
  Three contemporary quantum devices--cavity QED, ion traps and quantum
dots--have been widely regarded as perhaps the most promising candidates for
the construction of elementary quantum gates. In this paper, we describe the
physical properties of these devices, and show the mathematical derivations
based on the interaction of the laser field as control with atoms, ions or
electron spins, leading to the following: (i) the 1-bit unitary rotation gates;
and (ii) the 2-bit quantum phase gates and the controlled-not gate. This paper
is aimed at providing a sufficiently self-contained survey account of
analytical nature for mathematicians, physicists and computer scientists to aid
interdisciplinary understanding in the research of quantum computation.


title: On amplification of light in the continuous EPR state

abstract:
  Two schemes of amplification of two-mode squeezed light in the continuous
variable EPR-state are considered. They are based on the integrals of motion,
which allow conserving quantum correlations whereas the power of each mode may
increase. One of these schemes involves a three-photon parametric process in a
nonlinear transparent medium and second is a Raman type interaction of light
with atomic ensemble.


title: A note on verification procedures for quantum noiseless subsystems

abstract:
  We establish conditions under which the experimental verification of quantum
error-correcting behavior against a linear set of error operators $\ce$
suffices for the verification of noiseless subsystems of an error algebra $\ca$
contained in $\ce$. From a practical standpoint, our results imply that the
verification of a noiseless subsystem need not require the explicit
verification of noiseless behavior for all possible initial states of the
syndrome subsystem.


title: Orthopositronium: Annihilation of positron in gaseous neon

abstract:
  On the basis of phenomenological model of the orthopositronium annihilation
"isotope anomaly" in gaseous neon (lifetime spectra, positrons source Na-22)
the realistic estimation of an additinal mode ~0.2%) of the orthopositronium
annihilation is received.


title: Entanglement cost of generalised measurements

abstract:
  Bipartite entanglement is one of the fundamental quantifiable resources of
quantum information theory. We propose a new application of this resource to
the theory of quantum measurements. According to Naimark's theorem any rank 1
generalised measurement (POVM) M may be represented as a von Neumann
measurement in an extended (tensor product) space of the system plus ancilla.
By considering a suitable average of the entanglements of these measurement
directions and minimising over all Naimark extensions, we define a notion of
entanglement cost E_min(M) of M.
  We give a constructive means of characterising all Naimark extensions of a
given POVM. We identify various classes of POVMs with zero and non-zero cost
and explicitly characterise all POVMs in 2 dimensions having zero cost. We
prove a constant upper bound on the entanglement cost of any POVM in any
dimension. Hence the asymptotic entanglement cost (i.e. the large n limit of
the cost of n applications of M, divided by n) is zero for all POVMs.
  The trine measurement is defined by three rank 1 elements, with directions
symmetrically placed around a great circle on the Bloch sphere. We give an
analytic expression for its entanglement cost. Defining a normalised cost of
any d-dimensional POVM by E_min(M)/log(d), we show (using a combination of
analytic and numerical techniques) that the trine measurement is more costly
than any other POVM with d>2, or with d=2 and ancilla dimension 2. This
strongly suggests that the trine measurement is the most costly of all POVMs.


title: How to encode the states of two non-entangled qubits in one qutrit?

abstract:
  A new scheme of quantum coding is presented. The scheme concerns the quantum
states to which Schumacher's compression does not apply. It is shown that two
qubits can be encoded in a single qutrit in such a way that one can faithfully
reconstruct the state of one qubit. Decision on which of these two qubits is to
be reconstructed can be made long after the encoding took place. The scheme
succeeds with the average probability of 2/3.


title: Quantum query complexity of graph connectivity

abstract:
  Harry Buhrman et al gave an Omega(sqrt n) lower bound for monotone graph
properties in the adjacency matrix query model. Their proof is based on the
polynomial method. However for some properties stronger lower bounds exist. We
give an Omega(n^{3/2}) bound for Graph Connectivity using Andris Ambainis'
method, and an O(n^{3/2} log n) upper bound based on Grover's search algorithm.
In addition we study the adjacency list query model, where we have almost
matching lower and upper bounds for Strong Connectivity of directed graphs.


title: Remarks on Mohrhoff's Interpretation of Quantum Mechanics

abstract:
  In a recently proposed interpretation of quantum mechanics, U. Mohrhoff
advocates original and thought-provoking views on space and time, the
definition of macroscopic objects, and the meaning of probability statements.
The interpretation also addresses a number of questions about factual events
and the nature of reality. The purpose of this note is to examine several
issues raised by Mohrhoff's interpretation, and to assess whether it helps
providing solutions to the long-standing problems of quantum mechanics.


title:
Spin Relaxation Caused by Thermal Excitations of High Frequency Modes of
  Cantilever Vibrations

abstract:
  We consider the process of spin relaxation in the oscillating
cantilever-driven adiabatic reversals technique in magnetic resonance force
microscopy. We simulated the spin relaxation caused by thermal excitations of
the high frequency cantilever modes in the region of the Rabi frequency of the
spin sub-system. The minimum relaxation time obtained in our simulations is
greater but of the same order of magnitude as one measured in recent
experiments. We demonstrated that using a cantilever with nonuniform
cross-sectional area may significantly increase spin relaxation time.


title:
Spectral representation of the Casimir Force Between a Sphere and a
  Substrate

abstract:
  We calculate the Casimir force in the non-retarded limit between a spherical
nanoparticle and a substrate, and we found that high-multipolar contributions
are very important when the sphere is very close to the substrate. We show that
the highly inhomegenous electromagnetic field induced by the presence of the
substrate, can enhance the Casimir force by orders of magnitude, compared with
the classical dipolar approximation.


title: Quantum Seals

abstract:
  A quantum seal is a way of encoding a classical message into quantum states,
so that everybody can read the message error-free, but at the same time the
sender and all intended readers who have some prior knowledge of the quantum
seal, can check if the seal has been broken and the message read. The
verification is done without reading nor disturbing the sealed message.


title: Finite-Dimensional PT-Symmetric Hamiltonians

abstract:
  This paper investigates finite-dimensional representations of PT-symmetric
Hamiltonians. In doing so, it clarifies some of the claims made in earlier
papers on PT-symmetric quantum mechanics. In particular, it is shown here that
there are two ways to extend real symmetric Hamiltonians into the complex
domain: (i) The usual approach is to generalize such Hamiltonians to include
complex Hermitian Hamiltonians. (ii) Alternatively, one can generalize real
symmetric Hamiltonians to include complex PT-symmetric Hamiltonians. In the
first approach the spectrum remains real, while in the second approach the
spectrum remains real if the PT symmetry is not broken. Both generalizations
give a consistent theory of quantum mechanics, but if D>2, a D-dimensional
Hermitian matrix Hamiltonian has more arbitrary parameters than a D-dimensional
PT-symmetric matrix Hamiltonian.


title: Shor's Algorithm for Factoring Large Integers

abstract:
  This work is a tutorial on Shor's factoring algorithm by means of a worked
out example. Some basic concepts of Quantum Mechanics and quantum circuits are
reviewed. It is intended for non-specialists which have basic knowledge on
undergraduate Linear Algebra.


title: Quantum spin pumping with adiabatically modulated magnetic barrier's

abstract:
  A quantum pump device involving magnetic barriers produced by the deposition
of ferro magnetic stripes on hetero-structure's is investigated. The device for
dc- transport does not provide spin-polarized currents, but in the adiabatic
regime, when one modulates two independent parameters of this device, spin-up
and spin-down electrons are driven in opposite directions, with the net result
being that a finite net spin current is transported with negligible charge
current. We also analyze our proposed device for inelastic-scattering and
spin-orbit scattering. Strong spin-orbit scattering and more so inelastic
scattering have a somewhat detrimental effect on spin/charge ratio especially
in the strong pumping regime. Further we show our pump to be almost noiseless,
implying an optimal quantum spin pump.

categories: quant-ph cond-mat.mes-hall math-ph math.MP physics.pop-ph


title: Negative result measurements in mesoscopic systems

abstract:
  We investigate measurement of electron transport in quantum dot systems by
using single-electron transistor as a noninvasive detector. It is demonstrated
that such a detector can operate in the ``negative-result measurement'' regime.
In this case the measured current is not distorted, providing that it is a
non-coherent one. For a coherent transport, however, the possibility of
observing a particular state out of coherent superposition leads to distortion
of a measured current even in the ``negative-result measurement'' regime. The
corresponding decoherence rate is obtained in the framework of quantum rate
equations.


title: Interference of Quantum Channels

abstract:
  We show how interferometry can be used to characterise certain aspects of
general quantum processes, in particular, the coherence of completely positive
maps. We derive a measure of coherent fidelity, maximum interference visibility
and the closest unitary operator to a given physical process under this
measure.


title: Unity gain and non-unity gain quantum teleportation

abstract:
  We investigate continuous variable quantum teleportation. We discuss the
methods presently used to characterize teleportation in this regime, and
propose an extension of the measures proposed by Grangier and Grosshans
\cite{Grangier00}, and Ralph and Lam \cite{Ralph98}. This new measure, the gain
normalized conditional variance product $\mathcal{M}$, turns out to be highly
significant for continuous variable entanglement swapping procedures, which we
examine using a necessary and sufficient criterion for entanglement. We
elaborate on our recent experimental continuous variable quantum teleportation
results \cite{Bowen03}, demonstrating success over a wide range of
teleportation gains. We analyze our results using fidelity; signal transfer,
and the conditional variance product; and a measure derived in this paper, the
gain normalized conditional variance product.


title: Continuous variable polarization entanglement, experiment and analysis

abstract:
  We generate and characterise continuous variable polarization entanglement
between two optical beams. We first produce quadrature entanglement, and by
performing local operations we transform it into a polarization basis. We
extend two entanglement criteria, the inseparability criteria proposed by Duan
{\it et al.}\cite{Duan00} and the Einstein-Podolsky-Rosen paradox criteria
proposed by Reid and Drummond\cite{Reid88}, to Stokes operators; and use them
to charactise the entanglement. Our results for the Einstein-Podolsky-Rosen
paradox criteria are visualised in terms of uncertainty balls on the
Poincar\'{e} sphere. We demonstrate theoretically that using two quadrature
entangled pairs it is possible to entangle three orthogonal Stokes operators
between a pair of beams, although with a bound $\sqrt{3}$ times more stringent
than for the quadrature entanglement.


title: Hamiltonian monodromy as lattice defect

abstract:
  The analogy between monodromy in dynamical (Hamiltonian) systems and defects
in crystal lattices is used in order to formulate some general conjectures
about possible types of qualitative features of quantum systems which can be
interpreted as a manifestation of classical monodromy in quantum finite
particle (molecular) problems.


title: Quantum coin tossing and bit-string generation in the presence of noise

abstract:
  We discuss the security implications of noise for quantum coin tossing
protocols. We find that if quantum error correction can be used, so that noise
levels can be made arbitrarily small, then reasonable security conditions for
coin tossing can be framed so that results from the noiseless case will
continue to hold. If, however, error correction is not available (as is the
case with present day technology), and significant noise is present, then
tossing a single coin becomes problematic. In this case, we are led to consider
random n-bit string generation in the presence of noise, rather than
single-shot coin tossing. We introduce precise security criteria for n-bit
string generation and describe an explicit protocol that could be implemented
with present day technology. In general, a cheater can exploit noise in order
to bias coins to their advantage. We derive explicit upper bounds on the
average bias achievable by a cheater for given noise levels.


title: Experimental Demonstration of Quantum Lattice Gas Computation

abstract:
  We report an ensemble nuclear magnetic resonance (NMR) implementation of a
quantum lattice gas algorithm for the diffusion equation. The algorithm employs
an array of quantum information processors sharing classical information, a
novel architecture referred to as a type-II quantum computer. This concrete
implementation provides a test example from which to probe the strengths and
limitations of this new computation paradigm. The NMR experiment consists of
encoding a mass density onto an array of 16 two-qubit quantum information
processors and then following the computation through 7 time steps of the
algorithm. The results show good agreement with the analytic solution for
diffusive dynamics. We also describe numerical simulations of the NMR
implementation. The simulations aid in determining sources of experimental
errors, and they help define the limits of the implementation.


title:
Tomographic Quantum Cryptography: Equivalence of Quantum and Classical
  Key Distillation

abstract:
  The security of a cryptographic key that is generated by communication
through a noisy quantum channel relies on the ability to distill a shorter
secure key sequence from a longer insecure one. For an important class of
protocols, which exploit tomographically complete measurements on entangled
pairs of any dimension, we show that the noise threshold for classical
advantage distillation is identical with the threshold for quantum entanglement
distillation. As a consequence, the two distillation procedures are equivalent:
neither offers a security advantage over the other.


title: Coherent population trapping in the stochastic limit

abstract:
  A 2-level atom with degenerate ground state interacting with a quantum field
is investigated. We show, that the field drives the state of the atom to a
stationary state, which is non-unique, but depends on the initial state of the
system through some conserved quantities. This non-uniqueness follows from the
degeneracy of the ground state of the atom, and when the ground subspace is
two-dimensional, the family of stationary states will depend on a
one-dimensional parameter. Only one of the stationary states in this family is
a pure state, and this state coincides with the known non-coupled population
trapped state (zero population in the excited level. Another one stationary
state corresponds to an equal weight mixture of the excited level and of the
coupled state.


title:
Cooling and Low Energy State Preparation for 3-local Hamiltonians are
  FQMA-complete

abstract:
  We introduce the quantum complexity class FQMA. This class describes the
complexity of generating a quantum state that serves as a witness for a given
QMA problem. In a certain sense, FQMA is the quantum analogue of FNP (function
problems associated with NP). The latter describes the complexity of finding a
succinct proof for a NP decision problem. Whereas all FNP problems can be
reduced to NP, there is no obvious reduction of FQMA to QMA since the solution
of FQMA is a quantum state and the solution of QMA the answer yes or no.
  We consider quantum state generators that get classical descriptions of
3-local Hamiltonians on n qubits as input and prepare low energy states for
these systems as output. We show that such state generators can be used to
prepare witnesses for QMA problems. Hence low energy state preparation is
FQMA-complete. Our proofs are extensions of the proofs by Kitaev et al. and
Kempe and Regev for the QMA-completeness of k-local Hamiltonian problems. We
show that FQMA can be solved by preparing thermal equilibrium states with an
appropriate temperature decreasing as the reciprocal of a polynomial in n.


title: Multiparticle Bell's inequalities involving many measurement settings

abstract:
  We present a prescription for obtaining Bell's inequalities for N>2 observers
involving more than two alternative measurement settings. We give examples of
some families of such inequalities. The inequalities are violated by certain
classes of states for which all standard Bell's inequalities with two
measurement settings per observer are satisfied.


title:
Simulating entangled sources by classically correlated sources and
  quantum imaging

abstract:
  We discuss the problem of when a set of measurements made on an entangled
source can be simulated with a classically correlated source. This is discussed
in general and some examples are given. The question of which aspects of
quantum imaging can be simulated by classically correlated sources is examined.


title:
Pseudopotential model of ultracold atomic collisions in quasi-one- and
  two-dimensional traps

abstract:
  We describe a model for s-wave collisions between ground state atoms in
optical lattices, considering especially the limits of quasi-one and two
dimensional axisymmetric harmonic confinement. When the atomic interactions are
modelled by an s-wave Fermi-pseudopotential, the relative motion energy
eigenvalues can easily be obtained. The results show that except for a bound
state, the trap eigenvalues are consistent with one- and two- dimensional
scattering with renormalized scattering amplitudes. For absolute scattering
lengths large compared with the tightest trap width, our model predicts a novel
bound state of low energy and nearly-isotropic wavefunction extending on the
order of the tightest trap width.


title: Optimal conclusive teleportation of quantum states

abstract:
  Quantum teleportation of qudits is revisited. In particular, we analyze the
case where the quantum channel corresponds to a non-maximally entangled state
and show that the success of the protocol is directly related to the problem of
distinguishing non-orthogonal quantum states. The teleportation channel can be
seen as a coherent superposition of two channels, one of them being a maximally
entangled state thus, leading to perfect teleportation and the other,
corresponding to a non-maximally entangled state living in a subspace of the
d-dimensional Hilbert space. The second channel leads to a teleported state
with reduced fidelity. We calculate the average fidelity of the process and
show its optimality.


title: An atom mirror etched from a hard drive

abstract:
  We describe the fabrication of an atom mirror by etching of a common hard
drive, and we report the observation of specular retroreflection of 11 uk
cesium atoms using this mirror. The atoms were trapped and cooled above the
hard drive using the mirror magneto-optical trap technique, and upon release,
two full bounces were detected. The hard drive atom mirror will be a useful
tool for both atom optics and quantum computation.


title:
Comment on "Quantitative wave-particle duality in multibeam
  interferometers"

abstract:
  In a recent paper [Phys. Rev. {\bf A64}, 042113 (2001)] S. D\"urr proposed an
interesting multibeam generalization of the quantitative formulation of
interferometric wave-particle duality, discovered by Englert for two-beam
interferometers. The proposed generalization is an inequality that relates a
generalized measure of the fringe visibility, to certain measures of the
maximum amount of which-way knowledge that can be stored in a which-way
detector. We construct an explicit example where, with three beams in a pure
state, the scheme proposed by D\"{u}rr leads to the possibility of an ideal
which-way detector, that can achieve a better path-discrimination, at the same
time as a better fringe visibility. In our opinion, this seems to be in
contrast with the intuitive idea of complementarity, as it is implemented in
the two-beams case, where an increase in path discrimination always implies a
decrease of fringe visibility, if the beams and the detector are in pure
states.


title:
Conditional generation of arbitrary multimode entangled states of light
  with linear optics

abstract:
  We propose a universal scheme for the probabilistic generation of an
arbitrary multimode entangled state of light with finite expansion in Fock
basis. The suggested setup involves passive linear optics, single photon
sources, strong coherent laser beams, and photodetectors with single-photon
resolution. The efficiency of this setup may be greatly enhanced if, in
addition, a quantum memory is available.


title: Exact remote state preparation for multiparties

abstract:
  We discuss the exact remote state preparation protocol of special ensembles
of qubits at multiple locations. We also present generalization of this
protocol for higher dimensional Hilbert space systems for multiparties. Using
the `dark states', the analogue of singlet EPR pair for multiparties in higher
dimension as quantum channel, we show several instances of remote state
preparation protocol using multiparticle measurement and classical
communication.


title:
Structure of states which satisfy strong subadditivity of quantum
  entropy with equality

abstract:
  We give an explicit characterisation of the quantum states which saturate the
strong subadditivity inequality for the von Neumann entropy. By combining a
result of Petz characterising the equality case for the monotonicity of
relative entropy with a recent theorem by Koashi and Imoto, we show that such
states will have the form of a so-called short quantum Markov chain, which in
turn implies that two of the systems are independent conditioned on the third,
in a physically meaningful sense. This characterisation simultaneously
generalises known necessary and sufficient entropic conditions for quantum
error correction as well as the conditions for the achievability of the Holevo
bound on accessible information.


title:
Measurement induced entanglement and quantum computation with atoms in
  optical cavities

abstract:
  We propose a method to prepare entangled states and implement quantum
computation with atoms in optical cavities. The internal state of the atoms are
entangled by a measurement of the phase of light transmitted through the
cavity. By repeated measurements an entangled state is created with certainty,
and this entanglement can be used to implement gates on qubits which are stored
in different internal degrees of freedom of the atoms. This method, based on
measurement induced dynamics, has a higher fidelity than schemes making use of
controlled unitary dynamics.


title: Genralized Robustness of Entanglement

abstract:
  The robustness of entanglement results of Vidal and Tarrach considered the
problem whereby an entangled state is mixed with a separable state so that the
overall state becomes non-entangled. In general it is known that there are also
cases when entangled states are mixed with other entangled states and where the
sum is separable. In this paper, we treat the more general case where entangled
states can be mixed with any states so that the resulting mixture is
unentangled. It is found that entangled pure states for this generalized case
have the same robustness as the restricted case of Vidal and Tarrach.


title: Group Theory and Quasiprobability Integrals of Wigner Functions

abstract:
  The integral of the Wigner function of a quantum mechanical system over a
region or its boundary in the classical phase plane, is called a
quasiprobability integral. Unlike a true probability integral, its value may
lie outside the interval [0,1]. It is characterized by a corresponding
selfadjoint operator, to be called a region or contour operator as appropriate,
which is determined by the characteristic function of that region or contour.
The spectral problem is studied for commuting families of region and contour
operators associated with concentric disks and circles of given radius a. Their
respective eigenvalues are determined as functions of a, in terms of the
Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in
Hilbert space carrying the positive discrete series representations of the
algebra su(1,1)or so(2,1). The explicit relation between the spectra of
operators associated with disks and circles with proportional radii, is given
in terms of the dicrete variable Meixner polynomials.


title:
Geometrical Conditions for CPTP Maps and their Application to a Quantum
  Repeater and a State-dependent Quantum Cloning Machine

abstract:
  We address the problem of finding optimal CPTP (completely positive, trace
preserving) maps between a set of binary pure states and another set of binary
generic mixed state in a two dimensional space. The necessary and sufficient
conditions for the existence of such CPTP maps can be discussed within a simple
geometrical picture. We exploit this analysis to show the existence of an
optimal quantum repeater which is superior to the known repeating strategies
for a set of coherent states sent through a lossy quantum channel. We also show
that the geometrical formulation of the CPTP mapping conditions can be a
simpler method to derive a state-dependent quantum (anti) cloning machine than
the study so far based on the explicit solution of several constraints imposed
by unitarity in an extended Hilbert space.


title:
Quantum initial value representations using approximate Bohmian
  trajectories

abstract:
  Quantum trajectories, originating from the de Broglie-Bohm (dBB) hydrodynamic
description of quantum mechanics, are used to construct time-correlation
functions in an initial value representation (IVR). The formulation is fully
quantum mechanical and the resulting equations for the correlation functions
are similar in form to their semi-classical analogs but do not require the
computation of the stability or monodromy matrix or conjugate points. We then
move to a {\em local} trajectory description by evolving the cumulants of the
wave function along each individual path. The resulting equations of motion are
an infinite hierarchy, which we truncate at a given order. We show that
time-correlation functions computed using these approximate quantum
trajectories can be used to accurately compute the eigenvalue spectrum for
various potential systems.


title: A geometric proof of the Kochen-Specker no-go theorem

abstract:
  We give a short geometric proof of the Kochen-Specker no-go theorem for
non-contextual hidden variables models. Note added to this version: I
understand from Jan-Aake Larsson that the construction we give here actually
contains the original Kochen-Specker construction as well as many others (Bell,
Conway and Kochen, Schuette, perhaps also Peres).


title: On the reality of EPR paradox

abstract:
  We argue that the so-called entangled states in quantum theory are not
something exceptional, deserving a special attention in our efforts to
understand conceptual foundations of quantum world. They appear by constructing
the basis states of a compound system via the basis states of entering
subsystems and describe it as a wholeness. While a system is considered as a
wholeness, the individual members, forming the entangled state, have no
physical meaning. In consequence, there is no physical ground for Einstein,
Podolsky and Rosen (EPR) correlations arising in a process of decaying the
system, being in the entangled state, into its constituent parts. The same
regards to Bell's introduced non-locality of quantum world.


title:
On the suppression of the diffusion and the quantum nature of a cavity
  mode. Optical bistability; forces and friction in driven cavities

abstract:
  A new analytical method is presented here, offering a physical view of driven
cavities where the external field cannot be neglected. We introduce a new
dimensionless complex parameter, intrinsically linked to the cooperativity
parameter of optical bistability, and analogous to the scaled Rabbi frequency
for driven systems where the field is classical. Classes of steady states are
iteratively constructed and expressions for the diffusion and friction
coefficients at lowest order also derived. They have in most cases the same
mathematical form as their free-space analog. The method offers a semiclassical
explanation for two recent experiments of one atom trapping in a high Q cavity
where the excited state is significantly saturated. Our results refute both
claims of atom trapping by a quantized cavity mode, single or not. Finally, it
is argued that the parameter newly constructed, as well as the groundwork of
this method, are at least companions of the cooperativity parameter and its
mother theory. In particular, we lay the stress on the apparently more
fundamental role of our structure parameter.


title: Quantum Computing and Error Correction

abstract:
  The main ideas of quantum error correction are introduced. These are
encoding, extraction of syndromes, error operators, and code construction. It
is shown that general noise and relaxation of a set of 2-state quantum systems
can always be understood as a combination of Pauli operators acting on the
system. Each quantum error correcting code allows a subset of these errors to
be corrected. In many situations the noise is such that the remaining
uncorrectable errors are unlikely to arise, and hence quantum error correction
has a high probability of success. In order to achieve the best noise tolerance
in the presence of noise and imprecision throughout the computer, a
hierarchical construction of a quantum computer is proposed.


title: Broken Promises and Quantum Algorithms

abstract:
  In the black-box model, problems constrained by a `promise' are the only ones
that admit a quantum exponential speedup over the best classical algorithm in
terms of query complexity. The most prominent example of this is the
Deutsch-Jozsa algorithm. More recently, Wim van Dam put forward an algorithm
for unstructured problems (i.e., those without a promise). We consider the
Deutsch-Jozsa algorithm with a less restrictive (or `broken') promise and study
the transition to an unstructured problem. We compare this to the success of
van Dam's algorithm. These are both compared with a standard classical sampling
algorithm. The Deutsch-Jozsa algorithm remains good as the problem initially
becomes less structured, but the van Dam algorithm can be adapted so as to
become superior to the Deutsch-Jozsa algorithm as the promise is weakened.


title: Realistic Decoherence Free Subspaces

abstract:
  Decoherence free subspaces (DFS) is a theoretical tool towards experimental
implementation of quantum information storage and processing. However, they
represent an experimental challenge, since conditions for their existence are
very stringent. This work explores the situation in which a system of $N$
oscillators coupled to a bath of harmonic oscillators is close to satisfy the
conditions for the existence of DFS. We show, in the Born-Markov limit and for
small deviations from separability and degeneracy conditions, that there are
{\emph{weak decoherence subspaces}} which resemble the original notion of DFS.


title: Optimal Lewenstein-Sanpera Decomposition for some Biparatite Systems

abstract:
  It is shown that for a given bipartite density matrix and by choosing a
suitable separable set (instead of product set) on the separable-entangled
boundary, optimal Lewenstein-Sanpera (L-S) decomposition can be obtained via
optimization for a generic entangled density matrix. Based on this, We obtain
optimal L-S decomposition for some bipartite systems such as $2\otimes 2$ and
$2\otimes 3$ Bell decomposable states, generic two qubit state in Wootters
basis, iso-concurrence decomposable states, states obtained from BD states via
one parameter and three parameters local operations and classical
communications (LOCC), $d\otimes d$ Werner and isotropic states, and a one
parameter $3\otimes 3$ state. We also obtain the optimal decomposition for
multi partite isotropic state. It is shown that in all $2\otimes 2$ systems
considered here the average concurrence of the decomposition is equal to the
concurrence. We also show that for some $2\otimes 3$ Bell decomposable states
the average concurrence of the decomposition is equal to the lower bound of the
concurrence of state presented recently in [Buchleitner et al,
quant-ph/0302144], so an exact expression for concurrence of these states is
obtained. It is also shown that for $d\otimes d$ isotropic state where
decomposition leads to a separable and an entangled pure state, the average
I-concurrence of the decomposition is equal to the I-concurrence of the state.
  Keywords: Quantum entanglement, Optimal Lewenstein-Sanpera decomposition,
Concurrence, Bell decomposable states, LOCC}
  PACS Index: 03.65.Ud


title: Entanglement assisted capacity of the broadband lossy channel

abstract:
  We calculate the entanglement assisted capacity of a multimode bosonic
channel with loss. As long as the efficiency of the channel is above 50%, the
superdense coding effect can be used to transmit more bits than those that can
be stored in the message sent down the channel. Bounds for the other capacities
of the multimode channel are also provided.


title:
Size-dependent decoherence of excitonic states in semiconductor
  microcrystallites

abstract:
  The size-dependent decoherence of the exciton states resulting from the
spontaneous emission is investigated in a semiconductor spherical
microcrystallite under condition $a_{B}\ll R_{0}\leq\lambda$. In general, the
larger size of the microcrystallite corresponds to the shorter coherence time.
If the initial state is a superposition of two different excitonic coherent
states, the coherence time depends on both the overlap of two excitonic
coherent states and the size of the microcrystallite. When the system with
fixed size is initially in the even or odd coherent states, the larger average
number of the excitons corresponds to the faster decoherence. When the average
number of the excitons is given, the bigger size of the microcrystallite
corresponds to the faster decoherence. The decoherence of the exciton states
for the materials GaAs and CdS is numerically studied by our theoretical
analysis.


title: Polarization squeezing with cold atoms

abstract:
  We study the interaction of a nearly resonant linearly polarized laser beam
with a cloud of cold cesium atoms in a high finesse optical cavity. We show
theoretically and experimentally that the cross-Kerr effect due to the
saturation of the optical transition produces quadrature squeezing on both the
mean field and the orthogonally polarized vacuum mode. An interpretation of
this vacuum squeezing as polarization squeezing is given and a method for
measuring quantum Stokes parameters for weak beams via a local oscillator is
developed.


title: Observables and States p-Mechanics

abstract:
  This is an up-to-date survey of the p-mechanical construction (see
funct-an/9405002, quant-ph/9610016, math-ph/0007030, quant-ph/0212101,
quant-ph/0303142), which is a consistent physical theory suitable for a
simultaneous description of classical and quantum mechanics. Observables in
p-mechanics are defined to be convolution operators on the Heisenberg group
H^n. Under irreducible representations of H^n the p-observables generate
corresponding observables in classical and quantum mechanics. p-States are
defined as positive linear functionals on p-observables. It is shown that both
states and observables can be realised as certain sets of
functions/distributions on the Heisenberg group. The dynamical equations for
both p-observables and p-states are provided. The construction is illustrated
by the forced and unforced harmonic oscillators. Connections with the
contextual interpretation of quantum mechanics are discussed. Keywords:
Classical mechanics, quantum mechanics, Moyal brackets, Poisson brackets,
commutator, Heisenberg group, orbit method, deformation quantisation,
symplectic group, representation theory, metaplectic representation, Berezin
quantisation, Weyl quantisation, Segal--Bargmann--Fock space, coherent states,
wavelet transform, Liouville equation, contextual interpretation, interaction
picture, forced harmonic oscillator.


title: Quantum mechanics and low energy nucleon dynamics

abstract:
  We discuss the problem of consistency of quantum mechanics as applied to low
energy nucleon dynamics with the symmetries of QCD. It is shown that the
dynamics consistent with these symmetries is not governed by the Schrodinger
equation. We present a new way to formulate the effective theory of nuclear
forces as an inevitable consequence of the basic principles of quantum
mechanics and the symmetries of strong interactions. We show that being
formulated in this way the effective theory of nuclear forces can be put on the
same firm theoretical grounds as the quantum mechanics of atomic phenomena. In
this case the effective theory allows one to describe with a given accuracy not
only two-nucleon scattering, but also the evolution of nucleon systems, and
places the constraints on the off-shell behavior of the two-nucleon
interaction. In this way we predict the off-shell behavior of the S wave
two-nucleon T-matrix at very low energies when the pionless theory is
applicable. Further extensions and applications of this approach are discussed.


title:
Locality and measurements within the SR model for an objective
  interpretation of quantum mechanics

abstract:
  One of the authors has recently propounded an SR (semantic realism) model
which shows, circumventing known no-go theorems, that an objective
(noncontextual, hence local) interpretation of quantum mechanics (QM) is
possible. We consider here compound physical systems and show why the proofs of
nonlocality of QM do not hold within the SR model. We also discuss quantum
measurement theory within this model, note that the objectification problem
disappears since the measurement of any property simply reveals its unknown
value, and show that the projection postulate can be considered as an
approximate law, valid FAPP (for all practical purposes). Finally, we provide
an intuitive justification for some unusual features of the SR model.


title: A complete set of covariants of the four qubit system

abstract:
  We obtain a complete and minimal set of 170 generators for the algebra of
$SL(2,\C)^{\times 4}$-covariants of a binary quadrilinear form. Interpreted in
terms of a four qubit system, this describes in particular the algebraic
varieties formed by the orbits of local filtering operations in its projective
Hilbert space. Also, this sheds some light on the local unitary invariants, and
provides all the possible building blocks for the construction of entanglement
measures for such a system.


title: Distinguishability of complete and unextendible product bases

abstract:
  It is not always possible to distinguish multipartite orthogonal states if
only local operation and classical communication (LOCC) are allowed. We prove
that we cannot distinguish the states of an unextendible product basis (UPB) by
LOCC even when infinite resources (infinite-dimensional ancillas, infinite
number of operations). Moreover we give a necessary and sufficient condition
for the LOCC distinguishability of complete product bases.


title:
Resonant nonstationary amplification of polychromatic laser pulses and
  conical emission in an optically dense ensemble of neon metastable atoms

abstract:
  Experimental and numerical investigation of single-beam and pump-probe
interaction with a resonantly absorbing dense extended medium under strong and
weak field-matter coupling is presented. Significant probe beam amplification
and conical emission were observed. Under relatively weak pumping and high
medium density, when the condition of strong coupling between field and
resonant matter is fulfilled, the probe amplification spectrum has a form of
spectral doublet. Stronger pumping leads to the appearance of a single peak of
the probe beam amplification at the transition frequency. The greater probe
intensity results in an asymmetrical transmission spectrum with amplification
at the blue wing of the absorption line and attenuation at the red one. Under
high medium density, a broad band of amplification appears. Theoretical model
is based on the solution of the Maxwell-Bloch equations for a two-level system.
Different types of probe transmission spectra obtained are attributed to
complex dynamics of a coherent medium response to broadband polychromatic
radiation of a multimode dye laser.


title: The Brody-Hughston Fisher Information Metric

abstract:
  We study the interrelationships between the Fisher information metric
recently introduced, on the basis of maximum entropy considerations, by Brody
and Hughston (quant-ph/9906085) and the monotone metrics, as explicated by Petz
and Sudar. This new metric turns out to be not strictly monotone in nature, and
to yield (via its normalized volume element) a prior probability distribution
over the Bloch ball of two-level quantum systems that is less noninformative
than those obtained from any of the monotone metrics, even the minimal monotone
(Bures) metric. We best approximate the additional information contained in the
Brody-Hughston prior over that contained in the Bures prior by constructing a
certain Bures posterior probability distribution. This is proportional to the
product of the Bures prior and a likelihood function based on four pairs of
spin measurements oriented along the diagonal axes of an inscribed cube.


title: Two-photon interference without bunching two photons

abstract:
  We report an interference experiment in which the two-photon entangled state
interference cannot be pictured in terms of the overlap and bunching of two
individual photons on a beamsplitter. We also demonstrate that two-photon
interference, or photon bunching effect on a beamsplitter, does not occur if
the two-photon Feynman amplitudes are distinguishable, even though individual
photons do overlap on a beamsplitter. Therefore, two-photon interference cannot
be viewed as interference of two individual photons, rather it should be viewed
as two-photon or biphoton interfering with itself. The results may also be
useful for studying decoherence management in entangled two-qubit systems as we
observe near complete restoration of quantum interference after the qubit
pairs, generated by a femtosecond laser pulse, went through certain
birefringent elements.


title: Interaction-free generation of entanglement

abstract:
  In this paper, we study how to generate entanglement by interaction-free
measurement. Using Kwiat et al.'s interferometer, we construct a two-qubit
quantum gate that changes a particle's trajectory according to the other
particle's trajectory. We propose methods for generating the Bell state from an
electron and a positron and from a pair of photons by this gate. We also show
that using this gate, we can carry out the Bell measurement with the
probability of 3/4 at the maximum and execute a controlled-NOT operation by the
method proposed by Gottesman and Chuang with the probability of 9/16 at the
maximum. We estimate the success probability for generating the Bell state by
our procedure under imperfect interaction.


title: Unambiguous quantum state filtering

abstract:
  In this paper, we consider the generalized measurement where one particular
quantum signal is unambiguously extracted from a set of non-commutative quantum
signals and the other signals are filtered out. Simple expressions for the
maximum detection probability and its POVM are derived. We applyl such
unambiguous quantum state filtering to evaluation of the sensing of decoherence
channels. The bounds of the precision limit for a given quantum state of probes
and possible device implementations are discussed.


title: Deterministic Secure Direct Communication Using Mixed state

abstract:
  We show an improved ping-pong protocol which is based on the protocol showed
by Kim Bostrom and Timo Felbinger [Phys. Rev. Lett. 89, 187902 (2002);
quant-ph/0209040]. We show that our protocol is asymptotically secure key
distribution and quasisecure direct communication using a single photon
resource. And this protocol can be can be carried out with great efficiency and
speed using today's technology.


title: Quantum Information as Reduced Classical Information

abstract:
  It is shown on a simple classical model of a quantum particle at rest that
information contained into the quantum state (quantum information) can be
obtained by integrating the corresponding probability distribution on phase
space, i.e. by reduction of the information contained into the classical state.


title: Quantum cryptography with continuous alphabet

abstract:
  A new quantum cryptography protocol, based on all unselected states of a
qubit as a sort of alphabet with continuous set of letters, is proposed. Its
effectiveness is calculated and shown to be essentially higher than those of
the other known protocols.


title: Experimental demonstration of quantum source coding

abstract:
  We report an experimental demonstration of Schumacher's quantum noiseless
coding theorem. Our experiment employs a sequence of single photons each of
which represents three qubits. We initially prepare each photon in one of a set
of 8 non-orthogonal codeword states corresponding to the value of a block of
three binary letters. We use quantum coding to compress this quantum data into
a two-qubit quantum channel and then uncompress the two-qubit channel to
restore the original data with a fidelity approaching the theoretical limit.


title: Exceeding classical capacity limit in quantum optical channel

abstract:
  The amount of information transmissible through a communications channel is
determined by the noise characteristics of the channel and by the quantities of
available transmission resources. In classical information theory, the amount
of transmissible information can be increased twice at most when the
transmission resource (e.g. the code length, the bandwidth, the signal power)
is doubled for fixed noise characteristics. In quantum information theory,
however, the amount of information transmitted can increase even more than
twice. We present a proof-of-principle demonstration of this super-additivity
of classical capacity of a quantum channel by using the ternary symmetric
states of a single photon, and by event selection from a weak coherent light
source. We also show how the super-additive coding gain, even in a small code
length, can boost the communication performance of conventional coding
technique.


title:
Creation of effective magnetic fields in optical lattices: The
  Hofstadter butterfly for cold neutral atoms

abstract:
  We investigate the dynamics of neutral atoms in a 2D optical lattice which
traps two distinct internal states of the atoms in different columns. Two Raman
lasers are used to coherently transfer atoms from one internal state to the
other, thereby causing hopping between the different columns. By adjusting the
laser parameters appropriately we can induce a non vanishing phase of particles
moving along a closed path on the lattice. This phase is proportional to the
enclosed area and we thus simulate a magnetic flux through the lattice. This
setup is described by a Hamiltonian identical to the one for electrons on a
lattice subject to a magnetic field and thus allows us to study this equivalent
situation under very well defined controllable conditions. We consider the
limiting case of huge magnetic fields -- which is not experimentally accessible
for electrons in metals -- where a fractal band structure, the Hofstadter
butterfly, characterizes the system.


title: Adiabatic quantum search algorithm for structured problems

abstract:
  The study of quantum computation has been motivated by the hope of finding
efficient quantum algorithms for solving classically hard problems. In this
context, quantum algorithms by local adiabatic evolution have been shown to
solve an unstructured search problem with a quadratic speed-up over a classical
search, just as Grover's algorithm. In this paper, we study how the structure
of the search problem may be exploited to further improve the efficiency of
these quantum adiabatic algorithms. We show that by nesting a partial search
over a reduced set of variables into a global search, it is possible to devise
quantum adiabatic algorithms with a complexity that, although still
exponential, grows with a reduced order in the problem size.


title:
Locally accessible information: How much can the parties gain by
  cooperating?

abstract:
  We investigate measurements of bipartite ensembles restricted to local
operations and classical communication and find a universal Holevo-like upper
bound on the locally accessible information. We analyze our bound and exhibit a
class of states which saturate it. Finally, we link the bound to the problem of
quantification of the nonlocality of the operations necessary to extract
locally unaccessible information.


title: Bures volume of the set of mixed quantum states

abstract:
  We compute the volume of the N^2-1 dimensional set M_N of density matrices of
size N with respect to the Bures measure and show that it is equal to that of a
N^2-1 dimensional hyper-halfsphere of radius 1/2. For N=2 we obtain the volume
of the Uhlmann 3-D hemisphere, embedded in R^4. We find also the area of the
boundary of the set M_N and obtain analogous results for the smaller set of all
real density matrices. An explicit formula for the Bures-Hall normalization
constants is derived for an arbitrary N.


title: Entanglement of formation for symmetric Gaussian states

abstract:
  We show that for a fixed amount of entanglement, two-mode squeezed states are
those that maximize Einstein-Podolsky-Rosen-like correlations. We use this fact
to determine the entanglement of formation for all symmetric Gaussian states
corresponding to two modes. This is the first instance in which this measure
has been determined for genuine continuous variable systems.


title: A new method for the solution of the Schrodinger equation

abstract:
  We present a new method for the solution of the Schrodinger equation
applicable to problems of non-perturbative nature. The method works by
identifying three different scales in the problem, which then are treated
independently: An asymptotic scale, which depends uniquely on the form of the
potential at large distances; an intermediate scale, still characterized by an
exponential decay of the wave function and, finally, a short distance scale, in
which the wave function is sizable. The key feature of our method is the
introduction of an arbitrary parameter in the last two scales, which is then
used to optimize a perturbative expansion in a suitable parameter. We apply the
method to the quantum anharmonic oscillator and find excellent results.


title:
Spin-based all-optical quantum computation with quantum dots:
  understanding and suppressing decoherence

abstract:
  We present an all-optical implementation of quantum computation using
semiconductor quantum dots. Quantum memory is represented by the spin of an
excess electron stored in each dot. Two-qubit gates are realized by switching
on trion-trion interactions between different dots. State selectivity is
achieved via conditional laser excitation exploiting Pauli exclusion principle.
Read-out is performed via a quantum-jump technique. We analyze the effect on
our scheme's performance of the main imperfections present in real quantum
dots: exciton decay, hole mixing and phonon decoherence. We introduce an
adiabatic gate procedure that allows one to circumvent these effects, and
evaluate quantitatively its fidelity.


title:
Decoherence of the flux-based superconducting qubit in an integrated
  circuit environment

abstract:
  Superconducting, flux-based qubits are promising candidates for the
construction of a large scale quantum computer. We present an explicit quantum
mechanical calculation of the coherent behavior of a flux based quantum bit in
a noisy experimental environment such as an integrated circuit containing bias
and control electronics. We show that non-thermal noise sources, such as bias
current fluctuations and magnetic coupling to nearby active control circuits,
will cause decoherence of a flux-based qubit on a timescale comparable to
recent experimental coherence time measurements.


title:
PT symmetric models in more dimensions and solvable square-well versions
  of their angular Schroedinger equations

abstract:
  For any central potential V in D dimensions, the angular Schroedinger
equation remains the same and defines the so called hyperspherical harmonics.
For non-central models, the situation is more complicated. We contemplate two
examples in the plane: (1) the partial differential Calogero's three-body model
(without centre of mass and with an impenetrable core in the two-body
interaction), and (2) the Smorodinsky-Winternitz' superintegrable harmonic
oscillator (with one or two impenetrable barriers). These examples are solvable
due to the presence of the barriers. We contemplate a small complex shift of
the angle. This creates a problem: the barriers become "translucent" and the
angular potentials cease to be solvable, having the sextuple-well form for
Calogero model and the quadruple or double well form otherwise. We mimic the
effect of these potentials on the spectrum by the multiple, purely imaginary
square wells and tabulate and discuss the result in the first nontrivial
double-well case.


title: Bohmian trajectories on a toroidal surface

abstract:
  Bohmian trajectories on the toroidal surface T^2 are determined from
eigenfunctions of the Schrodinger equation. An expression for the monodromy
matrix M(t) on a curved surface is developed and eigenvalues of M(t) on T^2
calculated. Lyapunov exponents for trajectories on T^2 are found for some
trajectories to be of order unity.


title: Weak localisation of light by atoms with quantum internal structure

abstract:
  The interference contrast observed in coherent backscattering by cold atoms
is drastically reduced with respect to classical disordered media. We study the
impact of the degeneracy of the resonant atomic dipole transition on multiple
scattering of polarised photons. An analytical treatment allows to derive the
diffusion coefficient and depolarisation times for the average light intensity,
and dephasing times for the weak localisation corrections. The calculated CBS
signals reproduce the experimental results.


title: The role of phase space geometry in Heisenberg's uncertainty relation

abstract:
  Aiming towards a geometric description of quantum theory, we study the
coherent states-induced metric on the phase space, which provides a geometric
formulation of the Heisenberg uncertainty relations (both the position-momentum
and the time-energy ones). The metric also distinguishes the original
uncertainty relations of Heisenberg from the ones that are obtained from
non-commutativity of operators. Conversely, the uncertainty relations can be
written in terms of this metric only, hence they can be formulated for any
physical system, including ones with non-trivial phase space. Moreover, the
metric is a key ingredient of the probability structure of continuous-time
histories on phase space. This fact allows a simple new proof the impossibility
of the physical manifestation of the quantum Zeno and anti-Zeno paradoxes.
Finally, we construct the coherent states for a spinless relativistic particle,
as a non-trivial example by which we demonstrate our results.


title:
Maximizing the Hilbert space for a finite number of distinguishable
  quantum states

abstract:
  We consider a quantum system with a finite number of distinguishable quantum
states, which may be partitioned freely by a number of quantum particles,
assumed to be maximally entangled. We show that if we partition the system into
a number of qudits, then the Hilbert space dimension is maximized when each
quantum particle is allowed to represent a qudit of order $e$. We demonstrate
that the dimensionality of an entangled system, constrained by the total number
quantum states, partitioned so as to maximize the number of qutrits will always
exceed the dimensionality of other qudit partitioning. We then show that if we
relax the requirement of partitioning the system into qudits, but instead let
the particles exist in any given state, that the Hilbert space dimension is
greatly increased.


title: Spin squeezing criterion with local unitary invariance

abstract:
  We propose a new spin squeezing criterion for arbitrary multi-qubit states
that is invariant under local unitary operations. We find that, for arbitrary
pure two-qubit states, spin squeezing is equivalent to entanglement, and
multi-qubit states are entangled if this new spin squeezing parameter is less
than 1.


title: Quantum Search on Bounded-Error Inputs

abstract:
  Suppose we have n algorithms, quantum or classical, each computing some
bit-value with bounded error probability. We describe a quantum algorithm that
uses O(sqrt{n}) repetitions of the base algorithms and with high probability
finds the index of a 1-bit among these n bits (if there is such an index). This
shows that it is not necessary to first significantly reduce the error
probability in the base algorithms to O(1/poly(n)) (which would require
O(sqrt{n}log n) repetitions in total). Our technique is a recursive
interleaving of amplitude amplification and error-reduction, and may be of more
general interest. Essentially, it shows that quantum amplitude amplification
can be made to work also with a bounded-error verifier. As a corollary we
obtain optimal quantum upper bounds of O(sqrt{N}) queries for all
constant-depth AND-OR trees on N variables, improving upon earlier upper bounds
of O(sqrt{N}polylog(N)).


title:
Experimental verification of a fully inseparable tripartite
  continuous-variable state

abstract:
  A continuous-variable tripartite entangled state is experimentally generated
by combining three independent squeezed vacuum states and the variances of its
relative positions and total momentum are measured. We show that the measured
values violate the separability criteria based on the sum of these quantities
and prove the full inseparability of the generated state.


title: Quantum computation based on d-level cluster states

abstract:
  The concept of qudit (a d-level system) cluster state is proposed by
generalizing the qubit cluster state (Phys. Rev. Lett. \textbf{86}, 910 (2001))
according to the finite dimensional representations of quantum plane algebra.
We demonstrate their quantum correlations and prove a theorem which guarantees
the availability of the qudit cluster states in quantum computation. We
explicitly construct the network to show the universality of the one-way
computer based on the defined qudit cluster states and single-qudit
measurement. And the corresponding protocol of implementing one-way quantum
computer can be suggested with the high dimensional "Ising" model which can be
found in many magnetic systems.


title: Revisiting the Schrodinger probability current

abstract:
  We revisit the definition of the probability current for the Schrodinger
equation. First, we prove that the Dirac probability currents of stationary
wave functions of the hydrogen atom and of the isotrop harmonic oscillator are
not nil and correspond to a circular rotation of the probability. Then, we
recall how it is necessary to add to classical Pauli and Schrodinger currents,
an additional spin-dependant current, the Gordan current. Consequently, we get
a circular probability current in the Schrodinger approximation for the
hydrogen atom and the isotrop harmonic oscillator.


title: Eutactic quantum codes

abstract:
  We consider sets of quantum observables corresponding to eutactic stars.
Eutactic stars are systems of vectors which are the lower dimensional
``shadow'' image, the orthogonal view, of higher dimensional orthonormal bases.
Although these vector systems are not comeasurable, they represent redundant
coordinate bases with remarkable properties. One application is quantum secret
sharing.


title: Simple criteria for projective measurements with linear optics

abstract:
  We derive a set of criteria to decide whether a given projection measurement
can be, in principle, exactly implemented solely by means of linear optics. The
derivation can be adapted to various detection methods, including photon
counting and homodyne detection. These criteria enable one to obtain easily
No-Go theorems for the exact distinguishability of orthogonal quantum states
with linear optics including the use of auxiliary photons and conditional
dynamics.


title:
Nuclear magnetic resonance implementation of the Deutsch-Jozsa algorithm
  using different initial states

abstract:
  The Deutsch-Jozsa algorithm distinguishes constant functions from balanced
functions with a single evaluation. In the first part of this work, we present
simulations of the nuclear magnetic resonance (NMR) application of the
Deutsch-Jozsa algorithm to a 3-spin system for all possible balanced functions.
Three different kinds of initial states are considered: a thermal state, a
pseudopure state, and a pair (difference) of pseudopure states. Then,
simulations of several balanced functions and the two constant functions of a
5-spin system are described. Finally, corresponding experimental spectra
obtained by using a 16-frequency pulse to create an input equivalent to either
a constant function or a balanced function are presented, and the results are
compared with those obtained from computer simulations.


title:
Purity of Gaussian states: measurement schemes and time-evolution in
  noisy channels

abstract:
  We present a systematic study of the purity for Gaussian states of
single-mode continuous variable systems. We prove the connection of purity to
observable quantities for these states, and show that the joint measurement of
two conjugate quadratures is necessary and sufficient to determine the purity
at any time. The statistical reliability and the range of applicability of the
proposed measurement scheme is tested by means of Monte Carlo simulated
experiments. We then consider the dynamics of purity in noisy channels. We
derive an evolution equation for the purity of general Gaussian states both in
thermal and squeezed thermal baths. We show that purity is maximized at any
given time for an initial coherent state evolving in a thermal bath, or for an
initial squeezed state evolving in a squeezed thermal bath whose asymptotic
squeezing is orthogonal to that of the input state.


title: Paradox of Quantum Information

abstract:
  The notion of quantum information related to the two different perspectives
of the global and local states is examined. There is circularity in the
definition of quantum information because we can speak only of the information
of systems that have been specifically prepared. In particular, we examine the
final state obtained by applying unitary transformations on a single qubit that
belongs to an entangled pair.


title: Nonunitary quantum circuit

abstract:
  A quantum circuit is generalized to a nonunitary one whose constituents are
nonunitary gates operated by quantum measurement. It is shown that a specific
type of one-qubit nonunitary gates, the controlled-NOT gate, as well as all
one-qubit unitary gates constitute a universal set of gates for the nonunitary
quantum circuit, without the necessity of introducing ancilla qubits. A
reversing measurement scheme is used to improve the probability of successful
nonunitary gate operation. A quantum NAND gate and Abrams-Lloyd's nonlinear
gate are analyzed as examples. Our nonunitary circuit can be used to reduce the
qubit overhead needed to ensure fault-tolerant quantum computation.


title: Weakly nonlocal fluid mechanics - the Schrodinger equation

abstract:
  A weakly nonlocal extension of ideal fluid dynamics is derived from the
Second Law of thermodynamics. It is proved that in the reversible limit the
additional pressure term can be derived from a potential. The requirement of
the additivity of the specific entropy function determines the quantum
potential uniquely. The relation to other known derivations of Schr\"odinger
equation (stochastic, Fisher information, exact uncertainty) is clarified.


title: Quantum Simulations of Physics Problems

abstract:
  If a large Quantum Computer (QC) existed today, what type of physical
problems could we efficiently simulate on it that we could not simulate on a
classical Turing machine? In this paper we argue that a QC could solve some
relevant physical "questions" more efficiently. The existence of one-to-one
mappings between different algebras of observables or between different Hilbert
spaces allow us to represent and imitate any physical system by any other one
(e.g., a bosonic system by a spin-1/2 system). We explain how these mappings
can be performed showing quantum networks useful for the efficient evaluation
of some physical properties, such as correlation functions and energy spectra.


title: Generic Quantum Fourier Transforms

abstract:
  The quantum Fourier transform (QFT) is the principal algorithmic tool
underlying most efficient quantum algorithms. We present a generic framework
for the construction of efficient quantum circuits for the QFT by
``quantizing'' the separation of variables technique that has been so
successful in the study of classical Fourier transform computations.
Specifically, this framework applies the existence of computable Bratteli
diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient
quantum circuits for the QFT over a wide variety a finite Abelian and
non-Abelian groups, including all group families for which efficient QFTs are
currently known and many new group families. Moreover, the method gives rise to
the first subexponential-size quantum circuits for the QFT over the linear
groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime
power q.


title: Quantum diffusion on a cyclic one dimensional lattice

abstract:
  The quantum diffusion of a particle in an initially localized state on a
cyclic lattice with N sites is studied. Diffusion and reconstruction time are
calculated. Strong differences are found for even or odd number of sites and
the limit N->infinit is studied. The predictions of the model could be tested
with micro - and nanotechnology devices.


title: Reliability of the beamsplitter based Bell-state measurement

abstract:
  A linear 50/50 beamsplitter, together with a coincidence measurement, has
been widely used in quantum optical experiments, such as teleportation, dense
coding, etc., for interferometrically distinguishing, measuring, or projecting
onto one of the four two-photon polarization Bell-states $|\psi^{(-)}>$. In
this paper, we demonstrate that the coincidence measurement at the output of a
beamsplitter cannot be used as an absolute identifier of the input state
$|\psi^{(-)}>$ nor as an indication that the input photons have projected to
the $|\psi^{(-)}>$ state.


title: Observation of correlated-photon statistics using a single detector

abstract:
  We report experimental observations of correlated-photon statistics in the
single-photon detection rate. The usual quantum interference in a two-photon
polarization interferometer always accompanies a dip in the single detector
counting rate, regardless of whether a dip or peak is seen in the coincidence
rate. This effect is explained by taking into account all possible photon
number states that reach the detector, rather than considering just the state
post-selected by the coincidence measurement. We also report an
interferometeric scheme in which the interference peak or dip in coincidence
corresponds directly to a peak or dip in the single-photon detection rate.


title: Geometric phases for non-degenerate and degenerate mixed states

abstract:
  This paper focuses on the geometric phase of general mixed states under
unitary evolution. Here we analyze both non-degenerate as well as degenerate
states. Starting with the non-degenerate case, we show that the usual procedure
of subtracting the dynamical phase from the total phase to yield the geometric
phase for pure states, does not hold for mixed states. To this end, we furnish
an expression for the geometric phase that is gauge invariant. The parallelity
conditions are shown to be easily derivable from this expression. We also
extend our formalism to states that exhibit degeneracies. Here with the
holonomy taking on a non-abelian character, we provide an expression for the
geometric phase that is manifestly gauge invariant. As in the case of the
non-degenerate case, the form also displays the parallelity conditions clearly.
Finally, we furnish explicit examples of the geometric phases for both the
non-degenerate as well as degenerate mixed states.


title: A simplification of entanglement purification

abstract:
  An idea of hybrid maps is proposed to establish standard entanglement
purification protocols which guarantee to purify any distillable state to a
desired maximally entangled pure state all by the standard purification local
operations and classical communications. The protocols proposed in this work,
in which two state transformations are used, perform better than the IBM and
Oxford protocols in the sense that they require fewer operation times in
yielding a same amount of the desired pure state. One of the proposed protocol
in this work can even lead to a higher improved output yield when it is
combined with the hashing protocol, as compared with the combined algorithm
consisting of the Oxford and the hashing protocol.


title:
Teleportation scheme implementing the Universal Optimal Quantum Cloning
  Machine and the Universal NOT gate

abstract:
  The universal quantum cloning machine and the universal NOT gate acting on a
single qubit can be implemented very generally by slightly modifying the
protocol of quantum state teleportation. The experimental demonstration of the
1 to 2 cloning process according to the above scheme has been realized for a
qubit encoded in photon polarization.


title: Unitary realizations of the ideal phase measurement

abstract:
  We explicitly construct a large class of unitary transformations that allow
to perform the ideal estimation of the phase-shift on a single-mode radiation
field. The ideal phase distribution is obtained by heterodyne detection on two
radiation modes after the interaction.


title:
Full quantum solutions to the resonant four-wave mixing of two
  single-photon wave packets

abstract:
  We analyze both analytically and numerically the resonant four-wave mixing of
two co-propagating single-photon wave packets. We present analytic expressions
for the two-photon wave function and show that soliton-type quantum solutions
exist which display a shape-preserving oscillatory exchange of excitations
between the modes. Potential applications including quantum information
processing are discussed.


title: On deciding whether a Boolean function is constant or not

abstract:
  We study the probability of making an error if, by querying an oracle a fixed
number of times, we declare constant a randomly chosen n-bit
  Boolean function. We compare the classical and the quantum case, and we
determine for how many oracle-queries k and for how many bits n one querying
procedure is more efficient than the other.


title: Quantum vs classical computation: a proposal opening a new perspective

abstract:
  We develop a classical model of computation (the S model) which captures some
important features of quantum computation, and which allows to design fast
algorithms for solving specific problems. In particular, we show that Deutsch's
problem can be trated within the S model of computation in the same way as
within quantum computation; also Grover's search problem of an unsorted
database finds a surprisingly fast solution. The correct understanding of these
results put into a new perspective the relationship between quantum and
classical computation.


title: Decoherence-Free Subspaces in Quantum Key Distribution

abstract:
  We demonstrate that two recent innovations in the field of practical quantum
key distribution (one-way autocompensation and passive detection) are closely
related to the methods developed to protect quantum computations from
decoherence. We present a new scheme that combines these advantages, and
propose a practical implementation of this scheme that is feasible using
existing technology.


title: The Communication Cost of Simulating Bell Correlations

abstract:
  What classical resources are required to simulate quantum correlations? For
the simplest and most important case of local projective measurements on an
entangled Bell pair state, we show that exact simulation is possible using
local hidden variables augmented by just one bit of classical communication.
Certain quantum teleportation experiments, which teleport a single qubit,
therefore admit a local hidden variables model.