title:
Quantum scissors: teleportation of single-mode optical states by means
  of a nonlocal single photon

abstract:
  We employ the quantum state of a single photon entangled with the vacuum
(|1,0>-|0,1>), generated by a photon incident upon a symmetric beam splitter,
to teleport single-mode quantum states of light by means of the Bennett
protocol. Teleportation of coherent states results in truncation of their Fock
expansion to the first two terms. We analyze the teleported ensembles by means
of homodyne tomography and obtain fidelities of up to 99 per cent for low
source state amplitudes. This work is an experimental realization of the
quantum scissors device proposed by Pegg, Phillips and Barnett (Phys. Rev.
Lett. 81, 1604 (1998))


title:
Integrals over Products of Distributions from Manifest Coordinate
  Invariance of Perturbation Expansions of Path Integrals in Curved Space

abstract:
  We show that the requirement of manifest coordinate invariance of
perturbatively defined quantum-mechanical path integrals in curved space leads
to an extension of the theory of distributions by specifying unique rules for
integrating products of distributions. The rules are derived using equations of
motion and partial integration, while keeping track of certain minimal features
stemming from the unique definition of all singular integrals in 1 - epsilon
dimensions. Our rules guarantee complete agreement with much more cumbersome
calculations in 1- epsilon dimensions where the limit epsilon --> 0 is taken at
the end. In contrast to our previous papers where we solved the same problem
for an infinite time interval or zero temperature, we consider here the more
involved case of finite-time (or non-zero temperature) amplitudes.


title:
Spin-Mediated Consciousness: Theory, Experimental Studies, Further
  Development & Related Topics

abstract:
  We postulate that consciousness is intrinsically connected to quantum spin
since the latter is the origin of quantum effects in both Bohm and Hestenes
quantum formulisms and a fundamental quantum process associated with the
structure of space-time. Applying these ideas to the particular structures and
dynamics of the brain, we have developed a detailed model of quantum
consciousness. We have also carried out experiments from the perspective of our
theory to test the possibility of quantum-entangling the quantum entities
inside the brain with those of an external chemical substance. We found that
applying magnetic pulses to the brain when an anaesthetic was placed in between
caused the brain to feel the effect of said anaesthetic as if the test subject
had actually inhaled the same. We further found that drinking water exposed to
magnetic pulses, laser light or microwave when an anaesthetic was placed in
between also causes brain effects in various degrees. Additional experiments
indicate that the said brain effect is indeed the consequence of quantum
entanglement. Recently we have studied non-local effects in simple physics
systems. We have found that the pH value, temperature and gravity of a liquid
in the detecting reservoirs can be non-locally affected through manipulating
another liquid in a remote reservoir quantum-entangled with the former. In
particular, the pH value changes in the same direction as that being
manipulated; the temperature can change against that of local environment; and
the gravity can change against local gravity. We suggest that they are mediated
by quantum entanglement between nuclear and/or electron spins in treated liquid
and discuss the profound implications of these results. This paper now also
includes materials on further development of the theory and related topics.


title: An introduction to quantum game theory

abstract:
  The application of the methods of quantum mechanics to game theory provides
us with the ability to achieve results not otherwise possible. Both linear
superpositions of actions and entanglement between the players' moves can be
exploited. We provide an introduction to quantum game theory and review the
current status of the subject.


title: KMS States on the Square of White Noise Algebra

abstract:
  It was shown in [AFS00] that there are only three types of irreducible
unitary representations theta of sl_2. Using the Schurmann triple one can
associate with each theta a number of representations of the square of white
noise (SWN) algebra A. However, in analogy with the Boson, Fermion and
q-deformed case, we expect that some interesting non irreducible
representations of sl_2 may result in GNS representations of KMS states
associated with some evolutions on A. In the present paper determine the
structure of the *--endomorphisms of the SWN algebra, induced by linear maps in
the 1--particle Hilbert algebra, we introduce the SWN analogue of the quasifree
evolutions and find the explicit form of the KMS states associated with some of
them.


title:
Preparation of multi-party entanglement of individual photons and atomic
  ensembles

abstract:
  An experimental feasible scheme is proposed to generate
Greenberger-Horne-Zeilinger (GHZ) type of maximal entanglement. Distinguishing
from the previous schemes, this entanglement can be chosen between either
atomic ensembles (stationary qubit) or individual photons (flying qubit),
according to the difference applications we desire for it. The physical
requirements of the scheme are moderate and well fit the present experimental
techinque.


title:
Trajectories and Particle Creation and Annihilation in Quantum Field
  Theory

abstract:
  We develop a theory based on Bohmian mechanics in which particle world lines
can begin and end. Such a theory provides a realist description of creation and
annihilation events and thus a further step towards a "beable-based"
formulation of quantum field theory, as opposed to the usual "observable-based"
formulation which is plagued by the conceptual difficulties--like the
measurement problem--of quantum mechanics.


title: Relaxation of quantum states under energy perturbations

abstract:
  The energy-based stochastic extension of the Schrodinger equation is perhaps
the simplest mathematically rigourous and physically plausible model for the
reduction of the wave function. In this article we apply a new simulation
methodology for the stochastic framework to analyse formulae for the dynamics
of a particle confined to a square-well potential. We consider the situation
when the width of the well is expanded instantaneously. Through this example we
are able to illustrate in detail how a quantum system responds to an energy
perturbation, and the mechanism, according to the stochastic evolutionary law,
by which the system relaxes spontaneously into one of the stable eigenstates of
the Hamiltonian. We examine in particular how the expectation value of the
Hamiltonian and the probability distribution for the position of the particle
change in time. An analytic expression for the typical timescale of relaxation
is derived. We also consider the small perturbation limit, and discuss the
relation between the stochastic framework and the quantum adiabatic theorem.


title: Two roles of relativistic spin operators

abstract:
  Operators that are associated with several important quantities, like angular
momentum, play a double role: they are both generators of the symmetry group
and ``observables.'' The analysis of different splittings of angular momentum
into "spin" and "orbital" parts reveals the difference between these two roles.
We also discuss a relation of different choices of spin observables to the
violation of Bell inequalities.


title: Cooperative three- and four- player quantum games

abstract:
  A cooperative multi-player quantum game played by 3 and 4 players has been
studied. Quantum superposed operator is introduced in this work which solves
the non-zero sum difficulty in previous treatment. The role of quantum
entanglement of the initial state is discussed in details.


title: Complex Extension of Quantum Mechanics

abstract:
  It is shown that the standard formulation of quantum mechanics in terms of
Hermitian Hamiltonians is overly restrictive. A consistent physical theory of
quantum mechanics can be built on a complex Hamiltonian that is not Hermitian
but satisfies the less restrictive and more physical condition of space-time
reflection symmetry (PT symmetry). Thus, there are infinitely many new
Hamiltonians that one can construct to explain experimental data. One might
expect that a quantum theory based on a non-Hermitian Hamiltonian would violate
unitarity. However, if PT symmetry is not spontaneously broken, it is possible
to construct a previously unnoticed physical symmetry C of the Hamiltonian.
Using C, an inner product is constructed whose associated norm is positive
definite. This construction is completely general and works for any
PT-symmetric Hamiltonian. Observables exhibit CPT symmetry, and the dynamics is
governed by unitary time evolution. This work is not in conflict with
conventional quantum mechanics but is rather a complex generalisation of it.


title: Quantum dynamics as a physical resource

abstract:
  How useful is a quantum dynamical operation for quantum information
processing? Motivated by this question we investigate several strength measures
quantifying the resources intrinsic to a quantum operation. We develop a
general theory of such strength measures, based on axiomatic considerations
independent of state-based resources. The power of this theory is demonstrated
with applications to quantum communication complexity, quantum computational
complexity, and entanglement generation by unitary operations.


title: Quantum information science as an approach to complex quantum systems

abstract:
  What makes quantum information science a science? These notes explore the
idea that quantum information science may offer a powerful approach to the
study of complex quantum systems. We discuss how to quantify complexity in
quantum systems, and argue that there are two qualitatively different types of
complex quantum system. We also explore ways of understanding complex quantum
dynamics by quantifying the strength of a quantum dynamical operation as a
physical resource. This is the text for a talk at the ``Sixth International
Conference on Quantum Communication, Measurement and Computing'', held at MIT,
July 2002. Viewgraphs for the talk may be found at http://www.qinfo.org/talks/.


title:
Nuclear Magnetic Resonance Implemenations of Remote State Preparation of
  Arbitary Longitudinal Qubit and Remote State Measurement of a Qubit

abstract:
  A qubit chosen from equatorial or polar great circles on a Bloch sphere can
be remotely prepared with an Einstain-Podolsky-Rosen (EPR) state shared and a
cbit communication. We generalize this protocal into an arbitrary longitudinal
qubit on the Bloch sphere in which the azimuthal angle phi can be an arbitrary
value instead of only being zero. The generalized scheme was experimentally
realized using liquid-state nuclear magnetic resonance (NMR) techniques. Also,
we have experimentally demonstrated remote state measurement (RSM) on an
arbitary qubit proposed by Pati.


title: On the Phase Covariant Quantum Cloning

abstract:
  It is known that in phase covariant quantum cloning the equatorial states on
the Bloch sphere can be cloned with a fidelity higher than the optimal bound
established for universal quantum cloning. We generalize this concept to
include other states on the Bloch sphere with a definite $z$ component of spin.
It is shown that once we know the $z$ component, we can always clone a state
with a fidelity higher than the universal value and that of equatorial states.
We also make a detailed study of the entanglement properties of the output
copies and show that the equatorial states are the only states which give rise
to separable density matrix for the outputs.


title:
Experimental demonstration of the interferometric complementarity of
  one- and two-particle interference in a bulk Nuclear Magnetic Resonance
  ensemble

abstract:
  We analyze an interferometric complementarity between one- and two-particle
interference in the general case: $V_{i}^{2}+V_{12}^{2}\leq 1$ $(i=1$, $2)$,
and further examine the relation among one-particle interference visibility
$V_{i}$, two-particle interference visibility $V_{12}$ and the predication
$P_{i}$ of the path of a single particle. An equality
$V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1$ $(i=1$, $2)$ is achieved for any pure
two-particle source, which implies the condition of the complementarity
relation to reach the upper bound and its relation to another interferometric
complementarity between path information and interference visibility of a
single particle. Meanwhile, the relationships of the complementarities and the
entanglement $E$ of the composite system are also investigated. Using nuclear
magnetic resonance techniques, the two-particle interferometric complementarity
was experimentally tested with the ensemble-averaged spin states, including two
extreme cases and an intermediate case.


title: Quantum retrodiction in open systems

abstract:
  Quantum retrodiction involves finding the probabilities for various
preparation events given a measurement event. This theory has been studied for
some time but mainly as an interesting concept associated with time asymmetry
in quantum mechanics. Recent interest in quantum communications and
cryptography, however, has provided retrodiction with a potential practical
application. For this purpose quantum retrodiction in open systems should be
more relevant than in closed systems isolated from the environment. In this
paper we study retrodiction in open systems and develop a general master
equation for the backward time evolution of the measured state, which can be
used for calculating preparation probabilities. We solve the master equation,
by way of example, for the driven two-level atom coupled to the electromagnetic
field.


title: Covariant Linear Response Theory of Relativistic QED Plasmas

abstract:
  We start from the QED Lagrangian to describe a charged many-particle system
coupled to the radiation field. A covariant density matrix approach to kinetic
theory of QED plasmas, subjected to a strong external electro-magnetic field
has recently been developed [1,2]. We use the hyperplane formalism in order to
perform a manifest covariant quantization and to implement initial correlations
to the solution of the Liouville-von Neumann equation. A perturbative expansion
in orders of the fine structure constant for the correlation functions as well
as the statistical operator is applied. The non-equilibrium state of the system
is given within generalized linear response theory. Expressions for the
susceptibility tensor, describing the plasma response, are calculated within
different approximations, like the RPA approximation or considering collisions
within the Born-approximation. In particular, the process of relativistic
inverse bremsstrahlung in a plasma is discussed.


title:
Stochastic unraveling of time-local quantum master equations beyond the
  Lindblad class

abstract:
  A new method for stochastic unraveling of general time-local quantum master
equations (QME) which involve the reduced density operator at time t only is
proposed. The present kind of jump algorithm enables a numerically efficient
treatment of QMEs which are not of Lindblad form. So it opens new large fields
of application for stochastic methods. The unraveling can be achieved by
allowing for trajectories with negative weight. We present results for the
quantum Brownian motion and the Redfield QMEs as test examples. The algorithm
can also unravel non-Markovian QMEs when they are in a time-local form like in
the time-convolutionless formalism.


title:
Quantum entanglement swapping can be tested with type I parametric down
  conversion

abstract:
  We propose a very simple scheme to test the quantum enatanglement swapping in
a priori. In the scheme, we only assume the photon detector can distinguish the
vacuum and non-vacuum Fock state rather than the exact Fock number states.


title:
Classical information and Mermin's non-technical proof of the theorem of
  Bell

abstract:
  We show that Mermin's reasoning against our refutation of his non-technical
proof for Bell-type inequalities is of limited significance or contains
mathematical inconsistencies that, when taken into account, do not permit his
proof to go forward. Our refutation therefore stands.


title: Quantum Causality, Stochastics, Trajectories and Information

abstract:
  A history of the discovery of quantum mechanics and paradoxes of its
interpretation is reconsidered from the modern point of view of quantum
stochastics and information. It is argued that in the orthodox quantum
mechanics there is no place for quantum phenomenology such as events. The
development of quantum measurement theory, initiated by von Neumann, and Bell's
conceptual critics of hidden variable theories indicated a possibility for
resolution of this crisis. This can be done by divorcing the algebra of the
dynamical generators and an extended algebra of the potential (quantum) and the
actual (classical) observables. The latter, called beables, form the center of
the algebra of all observables, as the only visible (macroscopic) observables
must be compatible with any hidden (microscopic) observable.
  It is shown that within this approach quantum causality can be rehabilitated
within event enhanced quantum mechanics (eventum mechanics) in the form of a
superselection rule for compatibility of the consistent histories with the
statistically predictable future. The application of this rule in the form of
the nondemolition principle leads to the statistical inference of the von
Neumann projection postulate, and also to the more general quantum information
dynamics for instantaneous events, spontaneous localizations (i.e. quantum
jumps), and state diffusions (i.e. continuous trajectories). This gives a
dynamical solution, in the form of a Dirac boundary value problem and reduced
filtering equations, of the notorious decoherence and measurement problems
which was tackled unsuccessfully by many famous mathematicians and physicists
starting with von Neumann, Schroedinger and Bohr.


title: How much state assignments can differ

abstract:
  The state that an observer attributes to a quantum system depends on the
information available to that observer. If two or more observers have different
information about a single system, they will in general assign different
states. Is there any restriction on what states can be assigned, given
reasonable assumptions about how the observers use their information? We derive
necessary and sufficient conditions for a group of general density matrices to
characterize what different people may know about one and the same physical
system. These conditions are summarized by a single criterion, which we term
compatibility.


title: Separability of rank two quantum states on multiple quantum spaces

abstract:
  Explicit sufficient and necessary conditions for separability of
$N$-dimensional rank two multiparty quantum mixed states are presented. A
nonseparability inequality is also given, for the case where one of the
eigenvectors corresponding to nonzero eigenvalues of the density matrix is
maximally entangled.


title:
Measurements of Diffusion Resonances for the Atom Optics Quantum Kicked
  Rotor

abstract:
  We present experimental observations of diffusion resonances for the quantum
kicked rotor with weak decoherence. Cold caesium atoms are subject to a pulsed
standing wave of near-resonant light, with spontaneous emission providing
environmental coupling. The mean energy as a function of the pulse period is
determined during the late-time diffusion regime for a constant probability of
spontaneous emission per unit time. Structure in the late-time energy is seen
to increase with physical kicking strength. The observed structure is related
to Shepelyansky's predictions of the initial quantum diffusion rates.


title:
Simple optical measurement of the overlap and fidelity of quantum
  states: An experiment

abstract:
  We present the experimental results of measurements of the overlap of both
pure and mixed polarization states of photons. The fidelity and purity of mixed
states were also measured. The experimental apparatus exploits the fact that a
beam splitter can distinguish the singlet Bell state from the other Bell
states, i.e., it realizes projections into the symmetric and antisymmetric
subspaces of photons' Hilbert space.


title:
Tackling Systematic Errors in Quantum Logic Gates with Composite
  Rotations

abstract:
  We describe the use of composite rotations to combat systematic errors in
single qubit quantum logic gates and discuss three families of composite
rotations which can be used to correct off-resonance and pulse length errors.
Although developed and described within the context of NMR quantum computing
these sequences should be applicable to any implementation of quantum
computation.


title:
High order correlations of generic pure states of finite-dimensional
  quantum systems are determined by lower order correlations

abstract:
  We show that almost every pure state of multi-party quantum systems (each of
whose local Hilbert space has the same dimension) is completely determined by
the state's reduced density matrices of a fraction of the parties; this
fraction is less than about two-thirds of the parties for states of large
numbers of parties. In other words once the reduced states of this fraction of
the parties have been specified, there is no further freedom in the state.


title: Decoherence of Semiclassical Wigner Functions

abstract:
  The Lindblad equation governs general markovian evolution of the density
operator in an open quantum system. An expression for the rate of change of the
Wigner function as a sum of integrals is one of the forms of the Weyl
representation for this equation. The semiclassical description of the Wigner
function in terms of chords, each with its classically defined amplitude and
phase, is thus inserted in the integrals, which leads to an explicit
differential equation for the Wigner function. All the Lindblad operators are
assumed to be represented by smooth phase space functions corresponding to
classical variables. In the case that these are real, representing hermitian
operators, the semiclassical Lindblad equation can be integrated. There results
a simple extension of the unitary evolution of the semiclassical Wigner
function, which does not affect the phase of each chord contribution, while
dampening its amplitude. This decreases exponentially, as governed by the time
integral of the square difference of the Lindblad functions along the classical
trajectories of both tips of each chord. The decay of the amplitudes is shown
to imply diffusion in energy for initial states that are nearly pure.
Projecting the Wigner function onto an orthogonal position or momentum basis,
the dampening of long chords emerges as the exponential decay of off-diagonal
elements of the density matrix.


title: A number-phase Wigner function

abstract:
  One of the most prominent quasiprobability functions in quantum mechanics is
the Wigner function that gives the right marginal probability functions if
integrated over position or momentum. Here we depart from the definition of the
position-momentum Wigner function to, in analogy, construct a number-phase
Wigner function that, if summed over photon numbers gives the correct phase
distribution and integrated over phase gives the right photon distribution.


title: Direct measurement of the Q-function in a lossy cavity

abstract:
  We show that the Q-function corresponding to an electromagnetic field in a
lossy cavity can be directly measured by means of a simple scheme, therefore
allowing the knowledge of the state of the field despite dissipation.


title: Quantum bits and superposition displaced Fock states of the cavity field

abstract:
  We study the effects of counter rotating terms in the interaction of
quantized light with a two-level atom, by using the method of small rotations.
We give an expression for the wave function of the composed system atom plus
field and point out one initial wave function that generates a quantum bit of
the electromagnetic field with arbitrary amplitudes.


title: Multipartite Entanglement and Quantum State Exchange

abstract:
  We investigate multipartite entanglement in relation to the theoretical
process of quantum state exchange. In particular, we consider such entanglement
for a certain pure state involving two groups of N trapped atoms. The state,
which can be produced via quantum state exchange, is analogous to the
steady-state intracavity state of the subthreshold optical nondegenerate
parametric amplifier. We show that, first, it possesses some 2N-way
entanglement. Second, we place a lower bound on the amount of such entanglement
in the state using a novel measure called the entanglement of minimum bipartite
entropy.


title:
Comment on ``Experimental Simulation of Two-Particle Quantum
  Entanglement using Classical Fields''

abstract:
  We assert that the reported results consitute an empirical counterexample to
Bell's theorem


title:
Observation of Collective-Emission-Induced Cooling inside an Optical
  Cavity

abstract:
  We report the observation of collective-emission-induced, velocity-dependent
light forces. One third of a falling sample containing 3 x 10^6 cesium atoms
illuminated by a horizontal standing wave is stopped by cooperatively emitting
light into a vertically oriented confocal resonator. We observe decelerations
up to 1500 m/s^2 and cooling to temperatures as low as 7 uK, well below the
free space Doppler limit. The measured forces substantially exceed those
predicted for a single two-level atom.


title: Design of photonic crystal microcavities for cavity QED

abstract:
  We discuss the optimization of optical microcavity designs based on 2D
photonic crystals for the purpose of strong coupling between the cavity field
and a single neutral atom trapped within a hole. We present numerical
predictions for the quality factors and mode volumes of localized defect modes
as a function of geometric parameters, and discuss some experimental challenges
related to the coupling of a defect cavity to gas-phase atoms.


title:
Experimental implementation of generalized Grover's algorithm of
  multiple marked states and its application

abstract:
  Generalized Grover's searching algorithm for the case in which there are
multiple marked states is demonstrated on a nuclear magnetic resonance (NMR)
quantum computer. The entangled basis states (EPR states) are synthesized using
the algorithm.


title: Stokes operator squeezed continuous variable polarization states

abstract:
  We investigate quantum correlations in continuous wave polarization squeezed
laser light generated from one and two optical parametric amplifiers,
respectively. A general expression of how Stokes operator variances decompose
into two mode quadrature operator variances is given. Stokes parameter variance
spectra for four different polarization squeezed states have been measured and
compared with a coherent state. Our measurement results are visualized by
three-dimensional Stokes operator noise volumes mapped on the quantum Poincare
sphere. We quantitatively compare the channel capacity of the different
continuous variable polarization states for communication protocols. It is
shown that squeezed polarization states provide 33% higher channel capacities
than the optimum coherent beam protocol.


title: Quantum mechanics and free will: counter-arguments

abstract:
  Since quantum mechanics (QM) was formulated, many voices have claimed this to
be the basis of free will in the human beings. Basically, they argue that free
will is possible because there is an ontological indeterminism in the natural
laws, and that the mind is responsible for the wave function collapse of
matter, which leads to a choice among the different possibilities for the body.
However, I defend the opposite thesis, that free will cannot be defended in
terms of QM. First, because indeterminism does not imply free will, it is
merely a necessary condition but not enough to defend it. Second, because all
considerations about an autonomous mind sending orders to the body is against
our scientific knowledge about human beings; in particular, neither
neurological nor evolutionary theory can admit dualism. The quantum theory of
measurement can be interpreted without the intervention of human minds, but
other fields of science cannot contemplate the mentalist scenario, so it is
concluded that QM has nothing to say about the mind or free will, and its
scientific explanation is more related to biology than to physics. A fatalistic
or materialist view, which denies the possibility of a free will, makes much
more sense in scientific terms.


title: Pseudo-digital quantum bits

abstract:
  Quantum computers are analog devices; thus they are highly susceptible to
accumulative errors arising from classical control electronics. Fast
operation--as necessitated by decoherence--makes gating errors very likely. In
most current designs for scalable quantum computers it is not possible to
satisfy both the requirements of low decoherence errors and low gating errors.
Here we introduce a hardware-based technique for pseudo-digital gate operation.
We perform self-consistent simulations of semiconductor quantum dots, finding
that pseudo-digital techniques reduce operational error rates by more than two
orders of magnitude, thus facilitating fast operation.


title: Wave packets of a harmonic oscillator with various degrees of rigidity

abstract:
  The time evolution of wave packets in a harmonic oscillator potential is
studied. Some new results for the most general case are obtained. A natural
number, called ``degree of rigidity'', is introduced to describe qualitatively
how much the shape of a wave packet is changed with time. Two classes of wave
packets with an arbitrarily given degree of rigidity are presented.


title: Rapid Data Search using Adiabatic Quantum Computation

abstract:
  We show that by a suitable choice of time-dependent Hamiltonian, the search
for a marked item in an unstructured database can be achieved in unit time,
using Adiabatic Quantum Computation. This is a considerable improvement over
the O(sqrt(N)) time required in previous algorithms. The trade-off is that in
the intermediate stages of the computation process, the ground state energy of
the computer increases to a maximum of O(sqrt(N)), before returning to zero at
the end of the process.


title: Measurement, Filtering and Control in Quantum Open Dynamical Systems

abstract:
  A Markovian model for a quantum automata, i.e. an open quantum dynamical
discrete-time system with input and output channels and a feedback, is
described. A dynamical theory of quantum discrete-time adaptive measurements
and multi-stage quantum statistical decisions is developed and applied to the
optimal feedback control problem for the quantum dynamical objects. Quantum
analogies of Stratonovich non-stationary filtering, and Bellman quantum
dynamical programming in the discrete time are derived.
  A Gaussian Langevin model of the quantum one-dimensional linear Markovian
dynamical system matched with a quantum linear transmission line as an
input-output quantum noisy channel is studied. The optimal quantum multi-stage
decision rule consisting of a classical linear optimal control strategy and the
quantum optimal filtering of the noise is found. The latter contains the
optimal quantum coherent measurement on the output of the line and the
recursive processing by the Kalman filter.
  A time-continuous limit of the above model is considered, and the quantum
nondemolition measurement, time-continuous filtering and the optimal dynamical
programming are found in this limit. All the results are illustrated by an
example of the optimal control problem for a quantum open oscillator matched to
a quantum transmission line.


title: Beable trajectories for revealing quantum control mechanisms

abstract:
  The dynamics induced while controlling quantum systems by optimally shaped
laser pulses have often been difficult to understand in detail. A method is
presented for quantifying the importance of specific sequences of quantum
transitions involved in the control process. The method is based on a
``beable'' formulation of quantum mechanics due to John Bell that rigorously
maps the quantum evolution onto an ensemble of stochastic trajectories over a
classical state space. Detailed mechanism identification is illustrated with a
model 7-level system. A general procedure is presented to extract mechanism
information directly from closed-loop control experiments. Application to
simulated experimental data for the model system proves robust with up to 25%
noise.


title:
On the Heisenberg principle, namely on the information-disturbance
  trade-off in a quantum measurement

abstract:
  Common misconceptions on the Heisenberg principle are reviewed, and the
original spirit of the principle is reestablished in terms of the trade-off
between information retrieved by a measurement and disturbance on the measured
system. After analyzing the possibility of probabilistically reversible
measurements, along with erasure of information and undoing of disturbance,
general information-disturbance trade-offs are presented, where the disturbance
of the measurement is related to the possibility in principle of undoing its
effect.


title: Entanglement, Quantum Entropy and Mutual Information

abstract:
  The operational structure of quantum couplings and entanglements is studied
and classified for semifinite von Neumann algebras. We show that the
classical-quantum correspondences such as quantum encodings can be treated as
diagonal semi-classical (d-) couplings, and the entanglements characterized by
truly quantum (q-) couplings, can be regarded as truly quantum encodings. The
relative entropy of the d-compound and entangled states leads to two different
types of entropy for a given quantum state: the von Neumann entropy, which is
achieved as the maximum of mutual information over all d-entanglements, and the
dimensional entropy, which is achieved at the standard entanglement -- true
quantum entanglement, coinciding with a d-entanglement only in the case of pure
marginal states. The d- and q- information of a quantum noisy channel are
respectively defined via the input d- and q- encodings, and the q-capacity of a
quantum noiseless channel is found as the logarithm of the dimensionality of
the input algebra. The quantum capacity may double the classical capacity,
achieved as the supremum over all d-couplings, or encodings, bounded by the
logarithm of the dimensionality of a maximal Abelian subalgebra.


title:
Creating superpositions that correspond to efficiently integrable
  probability distributions

abstract:
  We give a simple and efficient process for generating a quantum superposition
of states which form a discrete approximation of any efficiently integrable
(such as log concave) probability density functions.


title:
Quantum Computing Simulation Optimizations and Operational Errors on
  Various 2-qubit Multiplier Circuits

abstract:
  Since simulating quantum computers requires exponentially more classical
resources, efficient algorithms are extremely helpful. We analyze algorithms
that create single qubit and specific controlled qubit matrix representations
of gates.
  Additionally, we use the simulator to investigate errors based on different
probability distributions and to investigate the robustness of different
2-qubit multiplier circuits in the presence of operational errors.


title:
Mediated Entanglement And Correlations In A Star Network Of Interacting
  Spins

abstract:
  We investigate analytically a star network of spins, in which all spins
interact exclusively with a central spin through Heisenberg XX couplings of
equal strength. We find that the central spin correlates and entangles the
other spins at zero temperature to a degree that depends on the total number of
spins. Surprisingly, the entanglement depends on the evenness or oddness of
this number and some correlations are substantial even for an infinite
collection of spins. We show how symmetric multi-party states for optimal
sharing and splitting of entanglement can be obtained in this system using a
magnetic field.


title: On Entangled Information and Quantum Capacity

abstract:
  The pure quantum entanglement is generalized to the case of mixed compound
states on an operator algebra to include the classical and quantum encodings as
particular cases. The true quantum entanglements are characterized by quantum
couplings which are described as transpose-CP, but not Completely Positive
(CP), trace-normalized linear positive maps of the algebra.
  The entangled (total) information is defined in this paper as a relative
entropy of the conditional (the derivative of the compound state with respect
to the input) and the unconditional output states. Thus defined the total
information of the entangled states leads to two different types of the entropy
for a given quantum state: the von Neumann entropy, or c-entropy, which is
achieved as the supremum of the information over all c-entanglements and thus
is semi-classical, and the true quantum entropy, or q-entropy, which is
achieved at the standard entanglement.
  The q-capacity, defined as the supremum over all entanglements, coincides
with the topological entropy. In the case of the simple algebra it doubles the
c-capacity, coinciding with the rank-entropy. The conditional q-entropy based
on the q-entropy, is positive, unlike the von Neumann conditional entropy, and
the q-information of a quantum channel is proved to be additive.


title:
Correspondence between continuous variable and discrete quantum systems
  of arbitrary dimensions

abstract:
  We establish a mapping between a continuous variable (CV) quantum system and
a discrete quantum system of arbitrary dimension. This opens up the general
possibility to perform any quantum information task with a CV system as if it
were a discrete system of arbitrary dimension. The Einstein-Podolsky-Rosen
state is mapped onto the maximally entangled state in any finite dimensional
Hilbert space and thus can be considered as a universal resource of
entanglement. As an explicit example of the formalism a two-mode CV entangled
state is mapped onto a two-qutrit entangled state.


title: Unconditional Continuous Variable Dense Coding

abstract:
  We investigate the conditions under which unconditional dense coding can be
achieved using continuous variable entanglement. We consider the effect of
entanglement impurity and detector efficiency and discuss experimental
verification. We conclude that the requirements for a strong demonstration are
not as stringent as previously thought and are within the reach of present
technology.


title:
Universal Quantum Computation using Exchange Interactions and
  Teleportation of Single-Qubit Operations

abstract:
  We show how to construct a universal set of quantum logic gates using control
over exchange interactions and single- and two-spin measurements only.
Single-spin unitary operations are teleported instead of being executed
directly, thus eliminating a major difficulty in the construction of several of
the most promising proposals for solid-state quantum computation, such as
spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons
on helium. Contrary to previous proposals dealing with this difficulty, our
scheme requires no encoding redundancy. We also discuss an application to
superconducting phase qubits.


title: Comment on "Nonadiabatic Conditional Geometric Phase Shift with NMR"

abstract:
  We clarify that the nonadiabatic scheme based on a parallel extension of the
adiabatic scenario cannot realize the desired goal of quantum computation.


title: Evaluating holonomic quantum computation: beyond adiabatic limitation

abstract:
  The proposal of the optical scheme for holonomic quantum computation is
evaluated based on dynamical resolution to the system beyond adiabatic
limitation. The time-dependent Schr\"{o}dinger equation is exactly solved by
virtue of the cranking representation and gauge transformation approach.
Besides providing rigorous confirmation to holonomies of the geometrical
prediction that holds for the ideally adiabatic situation, the dynamical
resolution enables one to evaluate elaborately the amplitude of the
nonadiabatic deviation, so that the errors induced to the quantum computation
can be explicitly estimated.


title:
Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum
  Probability

abstract:
  We develop a systematic approach to quantum probability as a theory of
rational betting in quantum gambles. In these games of chance the agent is
betting in advance on the outcomes of several (finitely many) incompatible
measurements. One of the measurements is subsequently chosen and performed and
the money placed on the other measurements is returned to the agent. We show
how the rules of rational betting imply all the interesting features of quantum
probability, even in such finite gambles. These include the uncertainty
principle and the violation of Bell's inequality among others. Quantum gambles
are closely related to quantum logic and provide a new semantics to it. We
conclude with a philosophical discussion on the interpretation of quantum
mechanics.


title: Absorption problems for quantum walks in one dimension

abstract:
  This paper treats absorption problems for the one-dimensional quantum walk
determined by a 2 times 2 unitary matrix U on a state space {0,1,...,N} where N
is finite or infinite by using a new path integral approach based on an
orthonormal basis P, Q, R and S of the vector space of complex 2 times 2
matrices. Our method studied here is a natural extension of the approach in the
classical random walk.


title:
Weisskopf-Wigner Decay Theory for the Energy-Driven Stochastic
  Schr\"odinger Equation

abstract:
  We generalize the Weisskopf-Wigner theory for the line shape and transition
rates of decaying states to the case of the energy-driven stochastic
Schr\"odinger equation that has been used as a phenomenology for state vector
reduction. Within the standard approximations used in the Weisskopf-Wigner
analysis, and assuming that the perturbing potential inducing the decay has
vanishing matrix elements within the degenerate manifold containing the
decaying state, the stochastic Schr\"odinger equation linearizes. Solving the
linearized equations, we find no change from the standard analysis in the line
shape or the transition rate per unit time. The only effect of the stochastic
terms is to alter the early time transient behavior of the decay, in a way that
eliminates the quantum Zeno effect. We apply our results to estimate
experimental bounds on the parameter governing the stochastic effects.


title: Bohm's interpretation and maximally entangled states

abstract:
  Several no-go theorems showed the incompatibility between the locality
assumption and quantum correlations obtained from maximally entangled spin
states. We analyze these no-go theorems in the framework of Bohm's
interpretation. The mechanism by which non-local correlations appear during the
results of measurements performed on distant parts of entangled systems is
explicitly put into evidence in terms of Bohmian trajectories. It is shown that
a GHZ like contradiction of the type+1=-1 occurs for well-chosen initial
positions of the Bohmian trajectories and that it is this essential
non-classical feature that makes it possible to violate the locality condition.


title: Qubits from Number States and Bell Inequalities for Number Measurements

abstract:
  Bell inequalities for number measurements are derived via the observation
that the bits of the number indexing a number state are proper qubits.
Violations of these inequalities are obtained from the output state of the
nondegenerate optical parametric amplifier.


title:
Optimal discrimination of mixed quantum states involving inconclusive
  results

abstract:
  We propose a generalized discrimination scheme for mixed quantum states. In
the present scenario we allow for certain fixed fraction of inconclusive
results and we maximize the success rate of the quantum-state discrimination.
This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the
Helstrom one. We formulate the extremal equations for the optimal positive
operator valued measure describing the discrimination device and establish a
criterion for its optimality. We also devise a numerical method for efficient
solving of these extremal equations.


title: Comment on a suggested Kochen-Specker test

abstract:
  A suggestion for an observational test of the difference between quantum
mechanics and noncontextual hidden variables theories requires the measurement
of a product of two commuting observables without measuring either observable
separately. A proposal has been made for doing this, but it is shown to be
problematic.


title: Relativistic Doppler effect in quantum communication

abstract:
  When an electromagnetic signal propagates in vacuo, a polarization detector
cannot be rigorously perpendicular to the wave vector because of diffraction
effects. The vacuum behaves as a noisy channel, even if the detectors are
perfect. The ``noise'' can however be reduced and nearly cancelled by a
relative motion of the observer toward the source. The standard definition of a
reduced density matrix fails for photon polarization, because the
transversality condition behaves like a superselection rule. We can however
define an effective reduced density matrix which corresponds to a restricted
class of positive operator-valued measures. There are no pure photon qubits,
and no exactly orthogonal qubit states.


title: Doppler cooling of an optically dense cloud of trapped atoms

abstract:
  We have studied a general technique for laser cooling a cloud of polarized
trapped atoms down to the Doppler temperature. A one-dimensional optical
molasses using polarized light cools the axial motional degree of freedom of
the atoms in the trap. Cooling of the radial degrees of freedom can be modelled
by reabsorption of scattered photons in the optically dense cloud. We present
experimental results for a cloud of chromium atoms in a magnetic trap. A simple
model based on rate equations shows quantitative agreement with the
experimental results. This scheme allows us to readily prepare a dense cloud of
atoms in a magnetic trap with ideal starting conditions for evaporative
cooling.


title: Engineering Functional Quantum Algorithms

abstract:
  Suppose that a quantum circuit with K elementary gates is known for a unitary
matrix U, and assume that U^m is a scalar matrix for some positive integer m.
We show that a function of U can be realized on a quantum computer with at most
O(mK+m^2log m) elementary gates. The functions of U are realized by a generic
quantum circuit, which has a particularly simple structure. Among other
results, we obtain efficient circuits for the fractional Fourier transform.


title:
Compression of sources of probability distributions and density
  operators

abstract:
  We study the problem of efficient compression of a stochastic source of
probability distributions. It can be viewed as a generalization of Shannon's
source coding problem. It has relation to the theory of common randomness, as
well as to channel coding and rate--distortion theory: in the first two
subjects ``inverses'' to established coding theorems can be derived, yielding a
new approach to proving converse theorems, in the third we find a new proof of
Shannon's rate--distortion theorem.
  After reviewing the known lower bound for the optimal compression rate, we
present a number of approaches to achieve it by code constructions. Our main
results are: a better understanding of the known lower bounds on the
compression rate by means of a strong version of this statement, a review of a
construction achieving the lower bound by using common randomness which we
complement by showing the optimal use of the latter within a class of
protocols. Then we review another approach, not dependent on common randomness,
to minimizing the compression rate, providing some insight into its
combinatorial structure, and suggesting an algorithm to optimize it.
  The second part of the paper is concerned with the generalization of the
problem to quantum information theory: the compression of mixed quantum states.
Here, after reviewing the known lower bound we contribute a strong version of
it, and discuss the relation of the problem to other issues in quantum
information theory.


title: Topological Protection and Quantum Noiseless Subsystems

abstract:
  Encoding and manipulation of quantum information by means of topological
degrees of freedom provides a promising way to achieve natural fault-tolerance
that is built-in at the physical level. We show that this topological approach
to quantum information processing is a particular instance of the notion of
computation in a noiseless quantum subsystem. The latter then provide the most
general conceptual framework for stabilizing quantum information and for
preserving quantum coherence in topological and geometric systems.


title: Entanglement in the One-dimensional Kondo Necklace Model

abstract:
  We discuss the thermal and magnetic entanglement in the one-dimensional Kondo
necklace model. Firstly, we show how the entanglement naturally present at zero
temperature is distributed among pairs of spins according to the strength of
the two couplings of the chain, namely, the Kondo exchange interaction and the
hopping energy. The effect of the temperature and the presence of an external
magnetic field is then investigated, being discussed the adjustment of these
variables in order to control the entanglement available in the system. In
particular, it is indicated the existence of a critical magnetic field above
which the entanglement undergoes a sharp variation, leading the ground state to
a completely unentangled phase.


title:
Optimization of three-dimensional micropost microcavities for cavity
  quantum electrodynamics

abstract:
  This article presents a detailed analysis, based on the first-principles
finite-difference time-domain method, of the resonant frequency, quality factor
(Q), mode volume (V), and radiation pattern of the fundamental (HE11) mode in a
three-dimensional distributed-Bragg-reflector (DBR) micropost microcavity. By
treating this structure as a one-dimensional cylindrical photonic crystal
containing a single defect, we are able to push the limits of Q/V beyond those
achievable by standard micropost designs, based on the simple rules established
for planar DBR microcavities. We show that some of the rules that work well for
designing large-diameter microposts (e.g., high-refractive index contrast) fail
to provide high-quality cavities with small diameters. By tuning the
thicknesses of mirror layers and the spacer, the number of mirror pairs, the
refractive indices of high and low refractive index regions, and the cavity
diameter, we are able to achieve Q as high as 10^4, together with a mode volume
of 1.6 cubic wavelengths of light in the high-refractive-index material. The
combination of high Q and small V makes these structures promising candidates
for the observation of such cavity quantum electrodynamics phenomena as strong
coupling between a quantum dot and the cavity field, and single-quantum-dot
lasing.


title: Quantum Adiabatic Evolution Algorithms with Different Paths

abstract:
  In quantum adiabatic evolution algorithms, the quantum computer follows the
ground state of a slowly varying Hamiltonian. The ground state of the initial
Hamiltonian is easy to construct; the ground state of the final Hamiltonian
encodes the solution of the computational problem. These algorithms have
generally been studied in the case where the "straight line" path from initial
to final Hamiltonian is taken. But there is no reason not to try paths
involving terms that are not linear combinations of the initial and final
Hamiltonians. We give several proposals for randomly generating new paths.
Using one of these proposals, we convert an algorithmic failure into a success.


title: NMR molecular photography

abstract:
  A procedure is described for storing a 2D pattern consisting of 32x32 = 1024
bits in a spin state of a molecular system and then retrieving the stored
information as a stack of NMR spectra. The system used is a nematic liquid
crystal, the protons of which act as spin clusters with strong intramolecular
interactions. The technique used is a programmable multi-frequency irradiation
with low amplitude. When it is applied to the liquid crystal, a large number of
coherent long-lived 1H response signals can be excited, resulting in a spectrum
showing many sharp peaks with controllable frequencies and amplitudes. The
spectral resolution is enhanced by using a second weak pulse with a 90 phase
shift, so that the 1024 bits of information can be retrieved as a set of
well-resolved pseudo-2D spectra reproducing the input pattern.


title: Quantum memory: Write, read and reset

abstract:
  A model is presented for the quantum memory, the content of which is a pure
quantum state. In this model, the fundamental operations of writing on,
reading, and resetting the memory are performed through scattering from the
memory. The requirement that the quantum memory must remain in a pure state
after scattering implies that the scattering is of a special type, and only
certain incident waves are admissible. An example, based on the Fermi
pseudo-potential in one dimension, is used to demonstrate that the requirements
on the scattering process are consistent and can be satisfied. This model is
compared with the commonly used model for the quantum memory; the most
important difference is that the spatial dimensions and interference play a
central role in the present model.


title: Maximal entanglement versus entropy for mixed quantum states

abstract:
  Maximally entangled mixed states are those states that, for a given
mixedness, achieve the greatest possible entanglement. For two-qubit systems
and for various combinations of entanglement and mixedness measures, the form
of the corresponding maximally entangled mixed states is determined primarily
analytically. As measures of entanglement, we consider entanglement of
formation, relative entropy of entanglement, and negativity; as measures of
mixedness, we consider linear and von Neumann entropies. We show that the forms
of the maximally entangled mixed states can vary with the combination of
(entanglement and mixedness) measures chosen. Moreover, for certain
combinations, the forms of the maximally entangled mixed states can change
discontinuously at a specific value of the entropy.


title:
A New Proof of the Channel Coding Theorem via Hypothesis Testing in
  Quantum Information Theory

abstract:
  A new proof of the direct part of the quantum channel coding theorem is shown
based on a standpoint of quantum hypothesis testing. A packing procedure of
mutually noncommutative operators is carried out to derive an upper bound on
the error probability, which is similar to Feinstein's lemma in classical
channel coding. The upper bound is used to show the proof of the direct part
along with a variant of Hiai-Petz's theorem in quantum hypothesis testing.


title:
Detected jump-error correcting quantum codes, quantum error designs and
  quantum computation

abstract:
  The recently introduced detected-jump correcting quantum codes are capable of
stabilizing qubit-systems against spontaneous decay processes arising from
couplings to statistically independent reservoirs. These embedded quantum codes
exploit classical information about which qubit has emitted spontaneously and
correspond to an active error-correcting code embedded in a passive
error-correcting code. The construction of a family of one detected jump-error
correcting quantum codes is shown and the optimal redundancy, encoding and
recovery as well as general properties of detected jump-error correcting
quantum codes are discussed. By the use of design theory multiple jump-error
correcting quantum codes can be constructed. The performance of one jump-error
correcting quantum codes under non-ideal conditions is studied numerically by
simulating a quantum memory and Grover's algorithm.


title: Decoherence of molecular wave packets in an anharmonic potential

abstract:
  The time evolution of anharmonic molecular wave packets is investigated under
the influence of the environment consisting of harmonic oscillators. These
oscillators represent photon or phonon modes and assumed to be in thermal
equilibrium. Our model explicitly incorporates the fact that in the case of a
nonequidistant spectrum the rates of the environment induced transitions are
different for each transition. The nonunitary time evolution is visualized by
the aid of the Wigner function related to the vibrational state of the
molecule. The time scale of decoherence is much shorter than that of
dissipation, and gives rise to states which are mixtures of localized states
along the phase space orbit of the corresponding classical particle. This
behavior is to a large extent independent of the coupling strength, the
temperature of the environment and also of the initial state.


title: Lewenstein-Sanpera Decomposition for Iso-concurrence Decomposable States

abstract:
  We obtain Lewenstein-Sanpera decomposition of iso-concurrence decomposable
states of $2\otimes 2$ quantum systems. It is shown that in these systems
average concurrence of the decomposition is equal to the concurrence of the
state and also it is equal to the amount of violation of positive partial
transpose criterion. It is also shown that the product states introduced by
Wootters in [W. K. Wootters, Phys. Rev. Lett. {\bf 80} 2245 (1998)] form the
best separable approximation ensemble for these states.


title: Quantum computation with unknown parameters

abstract:
  We show how it is possible to realize quantum computations on a system in
which most of the parameters are practically unknown. We illustrate our results
with a novel implementation of a quantum computer by means of bosonic atoms in
an optical lattice. In particular we show how a universal set of gates can be
carried out even if the number of atoms per site is uncertain.


title:
Generation of many-particle entanglement in an ion trap by adiabatic
  ground-state transitions

abstract:
  We discuss the creation of many-particle entanglement in an ion trap where
all ions are simultaneously coupled to bichromatic laser fields. It is shown
that in a time-averaged, coarse-grained picture the system can be mapped onto a
spin ensemble with controllable collective interactions. An adiabatic change of
laser parameters allows a transfer from separable to entangled eigenstates of
the many-particle Hamiltonian. Of particular interest is a transition in the
ground state which in some cases corresponds to a quantum phase transition. The
influence of decoherence mechanisms can be substantially reduced if at all
times a sufficiently large energy gap between the ground state and the first
excited state is maintained.


title: Experimental realization of a continuous version of the Grover algorithm

abstract:
  A continuous, analog version of the Grover algorithm is realized using NMR.
The system studied is 23Na in a liquid crystal medium. The presence of
quadrupolar coupling makes the spin I=3/2 nucleus a 2-qubit system. Applying a
specially designed pulse sequence, the time evolution of the spin density
operator is described in an interaction representation which has no external
time-dependent radio-frequency fields. This approach is used to implement one
instance of the continuous Grover search for the transform of a uniform state
to a target state, and the implementation provides a clear physical
interpretation of the algorithm. The experimental results are in good agreement
with the theory.


title: Comment on "Measuring the Orbital Angular Momentum of a Single Photon"

abstract:
  Optical modes with different orbital angular momentums (OAMs) per photon may
be sorted by Mach-Zehnder interferometers incorporated with beam rotators,
without resorting to OAM mode converters.


title:
Forcing a unitary transformation by an external field: comparing two
  approaches based on optimal control theory

abstract:
  A quantum gate is realized by specific unitary transformations operating on
states representing qubits. Considering a quantum system employed as an element
in a quantum computing scheme, the task is therefore to enforce the
pre-specified unitary transformation. This task is carried out by an external
time dependent field. Optimal control theory has been suggested as a method to
compute the external field which alters the evolution of the system such that
it performs the desire unitary transformation. This study compares two recent
implementations of optimal control theory to find the field that induces a
quantum gate. The first approach is based on the equation of motion of the
unitary transformation. The second approach generalizes the state to state
formulation of optimal control theory. This work highlight the formal relation
between the two approaches.


title: Qualitative insights on fundamental mechanics

abstract:
  The gap between classical mechanics and quantum mechanics has an important
interpretive implication: the Universe must have an irreducible fundamental
level, which determines the properties of matter at higher levels of
organization. We show that the main parameters of any fundamental model must be
theory-independent. They cannot be predicted, because they cannot have internal
causes. However, it is possible to describe them in the language of classical
mechanics. We invoke philosophical reasons in favor of a specific model, which
treats particles as sources of real waves. Experimental considerations for
gravitational, electromagnetic, and quantum phenomena are outlined.


title: A semi-quantum version of the game of Life

abstract:
  A version of John Conway's game of Life is presented where the normal binary
values of the cells are replaced by oscillators which can represent a
superposition of states. The original game of Life is reproduced in the
classical limit, but in general additional properties not seen in the original
game are present that display some of the effects of a quantum mechanical Life.
In particular, interference effects are seen.


title:
Maximal violation of Clauser-Horne-Shimony-Holt inequality for two
  qutrits

abstract:
  Bell-Clauser-Horne-Shimony-Holt inequality (in terms of correlation
functions) of two qutrits is studied in detail by employing tritter
measurements. A uniform formula for the maximum value of this inequality for
tritter measurements is obtained. Based on this formula, we show that
non-maximally entangled states violate the Bell-CHSH inequality more strongly
than the maximally entangled one. This result is consistent with what was
obtained by Ac{\'{i}}n {\it et al} [Phys. Rev. A {\bf 65}, 052325 (2002)] using
the Bell-Clauser-Horne inequality (in terms of probabilities).


title: Spin & Statistics in Nonrelativistic Quantum Mechanics, I

abstract:
  A necessary and sufficient condition for Pauli's spin-statistics relation is
given for nonrelativistic anyons, bosons, and fermions in two and three spatial
dimensions.
  For any point particle species in two spatial dimensions, denote by J the
total (i.e., spin plus orbital) angular momentum of a single particle, and
denote by j the total angular momentum of the corresponding two-particle system
with respect to its center of mass. In three spatial dimensions, write J_z and
j_z for the z-components of these vector operators.
  In two spatial dimensions, the spin statistics connection holds if and only
if there exists a unitary operator U such that j=2UJU^*. In three dimensions,
the analogous relation cannot hold as it stands, but restricting it to an
appropriately chosen subspace of the state space yields a sufficient and
necessary condition for the spin-statistics connection.


title: Efficient distillation beyond qubits

abstract:
  We provide generalizations of known two-qubit entanglement distillation
protocols for arbitrary Hilbert space dimensions. The protocols, which are
analogues of the hashing and breeding procedures, are adapted to bipartite
quantum states which are diagonal in a basis of maximally entangled states. We
show that the obtained rates are optimal, and thus equal to the distillable
entanglement, for a (d-1) parameter family of rank deficient states. Methods to
improve the rates for other states are discussed. In particular, for isotropic
states it is shown that the rate can be improved such that it approaches the
relative entropy of entanglement in the limit of large dimensions.


title: Comparison of unitary transforms

abstract:
  We analyze the problem of comparing unitary transformations. The task is to
decide, with minimal resources and maximal reliability, whether two given
unitary transformations are identical or different. It is possible to make such
comparisons without obtaining any information about the individual
transformations. Different comparison strategies are presented and compared
with respect to their efficiency. With an interferometric setup, it is possible
to compare two unitary transforms using only one test particle. Another
strategy makes use of a two-particle singlet state. This strategy is more
efficient than using a non-entangled two-particle test state, thus
demonstrating the benefit of entanglement. Generalisations to higher
dimensional transforms and to more than two transformations are made.


title: Altering the remote past

abstract:
  An abstract treatment of Bell inequalities is proposed, in which the
parameters characterizing Bell's observable can be times rather than
directions. The violation of a Bell inequality might then be taken to mean that
a property of a system can be changed by the timing of a distant measurement,
which could take place in the future.


title: Secure quantum key distribution with an uncharacterized source

abstract:
  We prove the security of the Bennett-Brassard (BB84) quantum key distribution
protocol for an arbitrary source whose averaged states are basis-independent, a
condition that is automatically satisfied if the source is suitably designed.
The proof is based on the observation that, to an adversary, the key extraction
process is equivalent to a measurement in the sigma_x-basis performed on a pure
sigma_z-basis eigenstate. The dependence of the achievable key length on the
bit error rate is the same as that established by Shor and Preskill for a
perfect source, indicating that the defects in the source are efficiently
detected by the protocol.


title: Bohmian trajectories and quantum phase space distributions

abstract:
  We prove that most quasi-distributions can be written in a form similar to
that of the de Broglie-Bohm distribution, except that ordinary products are
replaced by some suitable non-commutative star product. In doing so, we show
that the Hamilton-Jacobi trajectories and the concept of "classical pure state"
are common features to all phase space formulations of quantum mechanics.
Furthermore, these results provide an explicit quantization prescription for
classical distributions.


title: Conditional phase shifts using trapped atoms

abstract:
  We describe a scheme for producing conditional nonlinear phase shifts on
two-photon optical fields using an interaction with one or more ancilla
two-level atomic systems. The conditional field state transformations are
induced by using high efficiency fluorescence shelving measurements on the
atomic ancilla. The scheme can be nearly deterministic and is of obvious
benefit for quantum information applications.


title:
A suggested interpretation of the quantum theory in terms of
  discontinuous motion of particles

abstract:
  We present a theory of discontinuous motion of particles in continuous
space-time. We show that the simplest nonrelativistic evolution equation of
such motion is just the Schroedinger equation in quantum mechanics. This
strongly implies what quantum mechanics describes is discontinuous motion of
particles. Considering the fact that space-time may be essentially discrete
when considering gravity, we further present a theory of discontinuous motion
of particles in discrete space-time. We show that its evolution may naturally
result in the dynamical collapse process of the wave function, and this
collapse will bring about the appearance of continuous motion of objects in the
macroscopic world.


title:
Lower bound on the relative error of mixed-state cloning and related
  operations

abstract:
  We extend the concept of the relative error to mixed-state cloning and
related physical operations, in which the ancilla contains some a priori
information about the input state. The lower bound on the relative error is
obtained. It is shown that this result contributes to the stronger no-cloning
theorem.


title:
Continuous quantum nondemolition feedback and unconditional atomic spin
  squeezing

abstract:
  We discuss the theory and experimental considerations of a quantum feedback
scheme for producing deterministically reproducible spin squeezing. Continuous
nondemolition atom number measurement from monitoring a probe field
conditionally squeezes the sample. Simultaneous feedback of the measurement
results controls the quantum state such that the squeezing becomes
unconditional. We find that for very strong cavity coupling and a limited
number of atoms, the theoretical squeezing approaches the Heisenberg limit.
Strong squeezing will still be produced at weaker coupling and even in free
space (thus presenting a simple experimental test for quantum feedback). The
measurement and feedback can be stopped at any time, thereby freezing the
sample with a desired amount of squeezing.


title: Assumptions Underlying Bell's Inequalities

abstract:
  There are several versions of Bell's inequalities, proved in different
contexts, using different sets of assumptions. The discussions of their
experimental violation often disregard some required assumptions and use loose
formulations of others. The issue, to judge from recent publications, continues
to cause misunderstandings. We present a very simple but general proof of
Bell's inequalities, identifying explicitly the complete set of assumptions
required.


title: Polarization Entangled W State using Parametric Down-Conversion

abstract:
  An experimental scheme for preparing a polarization entangled W states from
four photons emitted by parametric down-conversion is proposed. We consider two
different configurations and a method of improving the yield by using single
photon sources. In the proposed scheme, one uses only linear optical elements
and photon detectors, so that this scheme is feasible by current technologies.


title: Deformation quantization in the teaching of quantum mechanics

abstract:
  We discuss the deformation quantization approach for the teaching of quantum
mechanics. This approach has certain conceptual advantages which make its
consideration worthwhile. In particular, it sheds new light on the relation
between classical and quantum mechanics. We demionstrate how it can be used to
solve specific problems and clarify its relation to conventional quantization
and path integral techniques. We also discuss its recent applications in
relativistic quantum field theory.


title: Planck's scale dissipative effects in atom interferometry

abstract:
  Atom interferometers can be used to study phenomena leading to
irreversibility and dissipation, induced by the dynamics of fundamental objects
(strings and branes) at a large mass scale. Using an effective, but physically
consistent description in terms of a master equation of Lindblad form, the
modifications of the interferometric pattern induced by the new phenomena are
analyzed in detail. We find that present experimental devices can in principle
provide stringent bounds on the new effects.


title: Fundamental Limits for Coherent Manipulation on Atom Chips

abstract:
  The limitations for the coherent manipulation of neutral atoms with
fabricated solid state devices, so-called `atom chips', are addressed.
Specifically, we examine the dominant decoherence mechanism, which is due to
the magnetic noise originating from the surface of the atom chip. It is shown
that the contribution of fluctuations in the chip wires at the shot noise level
is not negligible. We estimate the coherence times and discuss ways to increase
them. Our main conclusion is that future advances should allow for coherence
times as long as one second, a few micrometers away from the surface.


title:
Producing the event ready two photon polarization EPR state with linear
  optics devices

abstract:
  We propose a scheme to produce the maximally two photon polarization
entangled state(EPR state) with single photon sources and the linear optics
devices. In particular, our scheme requires the photon detectors only to
distinguish the vacuum and non-vacuum Fock number states. A sophisticated
photon detector distinguishing one or two photon states is unnecessary.


title: Quantum games and social norms. The quantum ultimatum game

abstract:
  The noncooperative Nash equilibrium solution of classical games corresponds
to a rational expectations attitude on the part of the players. However, in
many cases, games played by human players have outcomes very different from
Nash equilibria. A restricted version of quantum games is proposed to
implement, in mathematical games, the interplay of self-interest and
internalized social norms that rules human behavior.


title: Classical Dynamics as Constrained Quantum Dynamics

abstract:
  We show that the classical mechanics of an algebraic model are implied by its
quantizations. An algebraic model is defined, and the corresponding classical
and quantum realizations are given in terms of a spectrum generating algebra.
Classical equations of motion are then obtained by constraining the quantal
dynamics of an algebraic model to an appropriate coherent state manifold. For
the cases where the coherent state manifold is not symplectic, it is shown that
there exist natural projections onto classical phase spaces. These results are
illustrated with the extended example of an asymmetric top.


title:
A perturbative approach to non-Markovian stochastic Schr\"odinger
  equations

abstract:
  In this paper we present a perturbative procedure that allows one to
numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations,
for a wide range of memory functions. To illustrate this procedure numerical
results are presented for a classically driven two level atom immersed in a
environment with a simple memory function. It is observed that as the order of
the perturbation is increased the numerical results for the ensembled average
state $\rho_{\rm red}(t)$ approach the exact reduced state found via
Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].


title:
Schemes for generating W state of paths and W state of polarization
  photons

abstract:
  In this paper, we give two very simple schemes to produce two kinds of W
states, one kind is path W state with one photon and the other is multiphoton
photon polarization W state. These schemes just need a common commercial
multiport fiber coupler and single photon sources, they are feasible by current
technologies.


title: On Pay-off induced Quantum Games

abstract:
  In recent years methods have been proposed to extend classical game theory
into the quantum domain. This paper explores further extensions of these ideas
that may have a substantial potential for further research. Upon reformulating
quantum game theory as a theory of classical games played by "quantum players"
I take a constructive approach. The roles of the players and the arbiter are
investigated for clues on the nature of the quantum game space.
  Upon examination of the role of the arbiter, a possible non-commutative
nature of pay-off operators can be deduced. I investigate a sub-class of games
in which the pay-off operators satisfy non-trivial commutation relations.
Non-abelian pay-off operators can be used to generate whole families of quantum
games.


title:
Entanglement of two atomic samples by quantum non-demolition
  measurements

abstract:
  This paper presents simulations of the state vector dynamics for a pair of
atomic samples which are being probed by phase shift measurements on an optical
beam passing through both samples. We show how measurements, which are
sensitive to different atomic components, serve to prepare states which are
close to being maximally entangled.


title: Non-Perturbative Renormalization Group Analysis in Quantum Mechanics

abstract:
  We analyze quantum mechanical systems using the non-perturbative
renormalization group (NPRG). The NPRG method enables us to calculate quantum
corrections systematically and is very effective for studying non-perturbative
dynamics. We start with anharmonic oscillators and proceed to asymmetric double
well potentials, supersymmetric quantum mechanics and many particle systems.


title:
Quantum interference with photon pairs created in spatially separated
  sources

abstract:
  We report on a quantum interference experiment to probe the coherence between
two photons coming from non degenerate photon pairs at telecom wavelength
created in spatially separated sources. The two photons are mixed on a beam
splitter and we observe a reduction of up to 84% in the coincidence count rate
when the photons are made indistinguishable. This experiment constitutes an
important step towards the realization of quantum teleportation and
entanglement swapping with independent sources.


title:
Lindbladian Evolution with Selfadjoint Lindblad Operators as Averaged
  Random Unitary Evolution

abstract:
  It is shown how any Lindbladian evolution with selfadjoint Lindblad
operators, either Markovian or nonMarkovian, can be understood as an averaged
random unitary evolution. Both mathematical and physical consequences are
analyzed. First a simple and fast method to solve this kind of master equations
is suggested and particularly illustrated with the phase-damped master equation
for the multiphoton resonant Jaynes-Cummings model in the rotating-wave
approximation. A generalization to some intrinsic decoherence models present in
the literature is included. Under the same philosophy a proposal to generalize
the Jaynes-Cummings model is suggested whose predictions are in accordance with
experimental results in cavity QED and in ion traps. A comparison with
stochastic dynamical collapse models is also included.


title: Damped Quantum Interference using Stochastic Calculus

abstract:
  It is shown how the phase-damping master equation, either in Markovian and
nonMarkovian regimes, can be obtained as an averaged random unitary evolution.
This, apart from offering a common mathematical setup for both regimes, enables
us to solve this equation in a straightforward manner just by solving the
Schrodinger equation and taking the stochastic expectation value of its
solutions after an adequate modification. Using the linear entropy as a figure
of merit (basically the loss of quantum coherence) the distinction of four
kinds of environments is suggested.


title:
Universal Sets of Quantum Gates for Detected Jump-Error Correcting
  Quantum Codes

abstract:
  A universal set of quantum gates is constructed for the recently developed
jump-error correcting quantum codes. These quantum codes are capable of
correcting errors arising from the spontaneous decay of distinguishable qubits
into statistically independent reservoirs. The proposed universal quantum gates
are constructed with the help of Heisenberg- and Ising-type Hamiltonians acting
on these physical qubits. This way it is guaranteed that the relevant error
correcting code space is not left at any time even during the application of
one of these quantum gates. The proposed entanglement gate is particularly well
suited for scalable quantum processing units whose elementary registers are
based on four-qubit systems.


title: Gauge invariance and the Dirac free field energy

abstract:
  Dirac field theory is assumed to be gauge invariant. However it is well known
that a calculation of the polarization tensor yields a non-gauge invariant
result. The reason for this has been shown to be due to the fact that for Dirac
theory to be gauge invariant there must be no lower bound to the free field
energy. Here an additional proof will be presented to show that this is,
indeed, the case.


title:
Classicality of spin-coherent states via entanglement and
  distinguishability

abstract:
  We investigate the classical nature of the spin coherent states. In addition
to being minimum uncertainty states, as the size of the spin, S, increases, the
classical nature is seen to increase in two respects: in their resistance to
entanglement generation (when passed through a beam splitter) and in the
distinguishability of the states. In the infinite S limit the spin coherent
state is a subclass of the optical coherent states (namely the subclass of
orthogonal optical coherent states). These states generate no entanglement and
are obviously completely distinguishable. The decline of the generated
entanglement, and in this sense increase in classicality with S, is very slow
and dependent on the amplitude z of the state. Surprisingly we find that for
|z| > 1 there is an initial increase in entanglement followed by an extremely
gradual decline to zero. The distinguishability, on the other hand, quickly
becomes classical for all z. We illustrate the distinguishability of spin
coherent states in a novel manner using the representation of Majorana.


title: Experimental demonstration of a controlled-NOT wave-packet gate

abstract:
  We report the experimental demonstration of a controlled-NOT (CNOT) quantum
logic gate between motional and internal state qubits of a single ion where, as
opposed to previously demonstrated gates, the conditional dynamics depends on
the extent of the ion's wave-packet. Advantages of this CNOT gate over one
demonstrated previously are its immunity from Stark shifts due to off-resonant
couplings and the fact that an auxiliary internal level is not required. We
characterize the gate logic through measurements of the post-gate ion state
populations for both logic basis and superposition input states, and we
demonstrate the gate coherence via an interferometric measurement.


title:
Experimental demonstration of a technique to generate arbitrary quantum
  superposition states

abstract:
  Using a single, harmonically trapped $^9$Be$^+$ ion, we experimentally
demonstrate a technique for generation of arbitrary states of a two-level
particle confined by a harmonic potential. Rather than engineering a single
Hamiltonian that evolves the system to a desired final sate, we implement a
technique that applies a sequence of simple operations to synthesize the state.


title:
Experimental demonstration of quantum state tomography and qubit-qubit
  interactions for rare-earth-ion based solid state qubits

abstract:
  We report on the implementation of quantum state tomography for an ensemble
of Eu$^{3+}$ dopant ions in a \YSO crystal. The tomography was applied to a
qubit based on one of the ion's optical transitions. The qubit was manipulated
using optical pulses and measurements were made by observing the optical free
induction in a phase sensitive manner. Fidelities of $>90$% for the combined
preparation and measurement process were achieved. Interactions between the
ions due to the change in the ions' permanent electric dipole moment when
excited optically were also measured. In light of these results, the ability to
do multi-qubit quantum computation using this system is discussed.


title: Improving the Success Probability for Shor's Factoring Algorithm

abstract:
  Given n=p*q with p and q prim and y in Z_{p*q}^*. Shor's Algorithm computes
the order r of y, i.e. y^r=1 (mod n). If r=2k is even and y^k \ne -1 (mod n) we
can easily compute a non trivial factor of n: gcd(y^k-1,n). In the original
paper it is shown that a randomly chosen y is usable for factoring with
probabily {1/2}. In this paper we will show an efficient possibility to improve
the lower bound of this probability by selecting only special y in Z_n^* to
{3/4}, so we are able to reduce the fault probabilty in the worst case from
{1/2} to {1/4}.


title: Quantum testers for hidden group properties

abstract:
  We construct efficient or query efficient quantum property testers for two
existential group properties which have exponential query complexity both for
their decision problem in the quantum and for their testing problem in the
classical model of computing. These are periodicity in groups and the common
coset range property of two functions having identical ranges within each coset
of some normal subgroup. Our periodicity tester is efficient in Abelian groups
and generalizes, in several aspects, previous periodicity testers. This is
achieved by introducing a technique refining the majority correction process
widely used for proving robustness of algebraic properties. The periodicity
tester in non-Abelian groups and the common coset range tester are query
efficient.


title:
Bohmian particle trajectories in relativistic bosonic quantum field
  theory

abstract:
  We study the de Broglie-Bohm interpretation of bosonic relativistic quantum
mechanics and argue that the negative densities and superluminal velocities
that appear in this interpretation do not lead to inconsistencies. After that,
we study particle trajectories in bosonic quantum field theory. A new
continuously changing hidden variable - the effectivity of a particle (a number
between 0 and 1) - is postulated. This variable leads to a causal description
of processes of particle creation and destruction. When the field enters one of
nonoverlapping wave-functional packets with a definite number of particles,
then the effectivity of the particles corresponding to this packet becomes
equal to 1, while that of all other particles becomes equal to 0.


title: Classical Limit of Demagnetization in a Field Gradient

abstract:
  We calculate the rate of decrease of the expectation value of the transverse
component of spin for spin-1/2 particles in a magnetic field with a spatial
gradient, to determine the conditions under which a previous classical
description is valid. A density matrix treatment is required for two reasons.
The first arises because the particles initially are not in a pure state due to
thermal motion. The second reason is that each particle interacts with the
magnetic field and the other particles, with the latter taken to be via a
2-body central force. The equations for the 1-body Wigner distribution
functions are written in a general manner, and the places where quantum
mechanical effects can play a role are identified. One that may not have been
considered previously concerns the momentum associated with the magnetic field
gradient, which is proportional to the time integral of the gradient. Its
relative magnitude compared with the important momenta in the problem is a
significant parameter, and if their ratio is not small some non-classical
effects contribute to the solution.
  Assuming the field gradient is sufficiently small, and a number of other
inequalities are satisfied involving the mean wavelength, range of the force,
and the mean separation between particles, we solve the integro- partial
differential equations for the Wigner functions to second order in the strength
of the gradient. When the same reasoning is applied to a different problem with
no field gradient, but having instead a gradient to the z-component of
polarization, the connection with the diffusion coefficient is established, and
we find agreement with the classical result for the rate of decrease of the
transverse component of magnetization.


title: No time loophole in Bell's theorem; the Hess-Philipp model is non-local

abstract:
  Hess and Philipp have recently claimed that proofs of Bell's theorem have
overlooked the possibility of time dependence in local hidden variables, hence
the theorem has not been proven true. Moreover they present what is claimed to
be a local realistic model of the EPR correlations. If this is true then Bell's
theorem is not just unproven, but false. We refute both claims. Firstly we
explain why time is not an issue in Bell's theorem, and secondly show that
their hidden variables model violates Einstein separability. Hess and Philipp
have overlooked the freedom of the experimenter to choose settings of a
measurement apparatus at will: any setting could be in force during the same
time period.


title: Counter-Intuitive Vacuum-Stimulated Raman Scattering

abstract:
  Vacuum-stimulated Raman scattering in strongly coupled atom-cavity systems
allows one to generate free-running single photon pulses on demand. Most
properties of the emitted photons are well defined, provided spontaneous
emission processes do not contribute. Therefore, electronic excitation of the
atom must not occur, which is assured for a system adiabatically following a
dark state during the photon-generation process. We experimentally investigate
the conditions that must be met for adiabatic following in a time-of-flight
driven system, with atoms passing through a cavity and a pump beam oriented
transverse to the cavity axis. From our results, we infer the optimal intensity
and relative pump-beam position with respect to the cavity axis.


title:
Total suppression of a large spin tunneling barrier in quantum adiabatic
  computation

abstract:
  We apply a quantum adiabatic evolution algorithm to a combinatorial
optimization problem where the cost function depends entirely on the of the
number of unit bits in a n-bit string (Hamming weight). The solution of the
optimization problem is encoded as a ground state of the problem Hamiltonian
H_p for the z-projection of a total spin-n/2. We show that tunneling barriers
for the total spin can be completely suppressed during the algorithm if the
initial Hamiltonian has its ground state extended in the space of the
z-projections of the spin. This suppression takes place even if the cost
function has deep and well separated local minima. We provide an intuitive
picture for this effect and show that it guarantees the polynomial complexity
of the algorithm in a very broad class of cost functions. We suggest a simple
example of the Hamiltonian for the adiabatic evolution: H(tau) = (1-tau) hat
S_{x}^{2} + tau H_p, with parameter tau slowly varying in time between 0 and 1.
We use WKB analysis for the large spin to estimate the minimum energy gap
between the two lowest adiabatic eigenvalues of H(tau).


title: Cartan Calculus via Pauli Matrices

abstract:
  In this paper we will provide a new operatorial counterpart of the
path-integral formalism of classical mechanics developed in recent years. We
call it new because the Jacobi fields and forms will be realized via finite
dimensional matrices. As a byproduct of this we will prove that all the
operations of the Cartan calculus, such as the exterior derivative, the
interior contraction with a vector field, the Lie derivative and so on, can be
realized by means of suitable tensor products of Pauli and identity matrices.


title: A single photoelectron transistor for quantum optical communications

abstract:
  A single photoelectron can be trapped and its photoelectric charge detected
by a source/drain channel in a transistor. Such a transistor photodetector can
be useful for flagging the safe arrival of a photon in a quantum repeater. The
electron trap can be photo-ionized and repeatedly reset for the arrival of
successive individual photons. This single photoelectron transistor (SPT)
operating at the lambda = 1.3 mu m tele-communication band, was demonstrated by
using a windowed-gate double-quantum-well InGaAs/InAlAs/InP heterostructure
that was designed to provide near-zero electron g-factor. The g-factor
engineering allows selection rules that would convert a photon's polarization
to an electron spin polarization. The safe arrival of the photo-electric charge
would trigger the commencement of the teleportation algorithm.


title:
Comments on Struyve and Baere's paper on experiments to distinguish
  Bohmian mechanics from quantum mechanics

abstract:
  It is shown in detail why the arguments put forward by Struyve and Baere
(quant-ph/0108038) against my conclusions are incorrect.


title: Entanglement in particle-detector interactions

abstract:
  It is predicted by Schrodinger's equation that entanglement will occur in the
interaction between detector and particle. We provide an analysis of the
entanglement using the Gurvitz model of double-dot and detector. New results on
entangled doubled-dots are provided as well as implications on Quantum
Information processing.


title: A lattice of Magneto-Optical and Magnetic traps for cold atoms

abstract:
  We describe basic periodic trapping configurations for ultracold atoms above
surfaces. The approach is based on a simple wire grid and can be scaled to
provide large arrays of periodically arranged magnetic or magneto-optical
traps. The unit cells of the trap lattices are based on crossed wire segments.
By alternating the current directions in the wires of the grid it can be
distinguished between 3 basic lattice configurations. As a first demonstration,
we used macroscopic wires in a 2 layer configuration to realize the unit cells
of the lattices. With this experimental setup, we observe two of the basic unit
cells and an array of 2x2 magneto optical traps.


title: The quantum to classical transition for random walks

abstract:
  We look at two possible routes to classical behavior for the discrete quantum
random walk on the line: decoherence in the quantum ``coin'' which drives the
walk, or the use of higher-dimensional coins to dilute the effects of
interference. We use the position variance as an indicator of classical
behavior, and find analytical expressions for this in the long-time limit; we
see that the multicoin walk retains the ``quantum'' quadratic growth of the
variance except in the limit of a new coin for every step, while the walk with
decoherence exhibits ``classical'' linear growth of the variance even for weak
decoherence.


title:
An experimental investigation of criteria for continuous variable
  entanglement

abstract:
  We generate a pair of entangled beams from the interference of two amplitude
squeezed beams. The entanglement is quantified in terms of EPR-paradox [Reid88]
and inseparability [Duan00] criteria, with observed results of $\Delta^{2}
X_{x|y}^{+} \Delta^{2} X_{x|y}^{-} = 0.58 \pm 0.02$ and $\sqrt{\Delta^{2} X_{x
\pm y}^{+} \Delta^{2} X_{x \pm y}^{-}} =
  0.44 \pm 0.01$, respectively. Both results clearly beat the standard quantum
limit of unity. We experimentally analyze the effect of decoherence on each
criterion and demonstrate qualitative differences. We also characterize the
number of required and excess photons present in the entangled beams and
provide contour plots of the efficacy of quantum information protocols in terms
of these variables.


title: Complex worlds from simple rules?

abstract:
  Can the apparent complexity we observe in the real world be generated from
simple initial conditions via simple, deterministic rules?


title: Analysing a complementarity experiment on the quantum-classical boundary

abstract:
  The complementarity experiment reported in Bertet [{\it{et al.}} (2001),
{\it{Nature}} {\bf{411}}, 166.] is discussed. The role played by entanglement
in reaching the classical limit is pointed out. Dissipative and thermal effects
of the cavity are calculated and a simple modification of the experiment is
proposed in order to observe the progressive loss of the capacity of ``quantum
erasing''as a manifestation of the classical limit of quantum mechanics.


title: Nonclassical effects in cold trapped ions inside a cavity

abstract:
  We investigate the dynamics of a cold trapped ion coupled to the quantized
field inside a high-finesse cavity, considering exact resonance between the
ionic internal levels and the field (carrier transition). We derive an
intensity-dependent hamiltonian in which terms proportional to the square of
the Lamb-Dicke parameter ($\eta$) are retained. We show that different
nonclassical effects arise in the dynamics of the ionic population inversion,
depending on the initial states of the vibrational motion/field and on the
values of $\eta$.


title: Decoherence can be useful in quantum walks

abstract:
  We present a study of the effects of decoherence in the operation of a
discrete quantum walk on a line, cycle and hypercube. We find high sensitivity
to decoherence, increasing with the number of steps in the walk, as the
particle is becoming more delocalised with each step. However, the effect of a
small amount of decoherence is to enhance the properties of the quantum walk
that are desirable for the development of quantum algorithms. Specifically, we
observe a highly uniform distribution on the line, a very fast mixing time on
the cycle, and more reliable hitting times across the hypercube.


title: Quantum computation using the Aharonov-Casher set up

abstract:
  It is argued that the Aharonov-Casher set up could be used as the basic
building block for quantum computation. We demonstrate explicitly in this
scenario one- and two-qubit phase shift gates that are fault tolerant to
deformations of the path when encircling two sites of the computational system
around each other.


title:
Quantum state filtering and discrimination between sets of Boolean
  functions

abstract:
  The problem of quantum state filtering consists of determining whether an
unknown quantum state, which is chosen from a known set of states, is either a
particular, specified state, or not. We consider this problem for the case that
the filtering procedure is required to be unambiguous, which necessitates
admitting inconclusive answers when the given states are not orthogonal. As an
application, we propose an efficient, probabilistic procedure for
distinguishing between sets of Boolean functions, which is an extension of the
Deutsch-Jozsa algorithm.