title:
Quantum-optical states in finite-dimensional Hilbert space. I. General
  formalism

abstract:
  The interest in quantum-optical states confined in finite-dimensional Hilbert
spaces has recently been stimulated by the progress in quantum computing,
quantum-optical state preparation, and measurement techniques, in particular,
by the development of the discrete quantum-state tomography. In the first part
of our review we present two essentially different approaches to define
harmonic oscillator states in the finite-dimensional Hilbert spaces. One of
them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys.
Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The
second method corresponds to the truncation scheme of Leo\'nski and Tana\'s
[Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states
related to these truncation schemes and find their explicit forms in the Fock
representation. We discuss finite-dimensional generalizations of coherent
states, phase coherent states, displaced number states, Schr\"odinger cats, and
squeezed vacuum. We show some intriguing properties of the states with the help
of the discrete Wigner function.


title: The Moyal-Lie Theory of Phase Space Quantum Mechanics

abstract:
  A Lie algebraic approach to the unitary transformations in Weyl quantization
is discussed. This approach, being formally equivalent to the
$\star$-quantization, is an extension of the classical Poisson-Lie formalism
which can be used as an efficient tool in the quantum phase space
transformation theory.


title: Measuring irreversible dynamics of a quantum harmonic oscillator

abstract:
  We show that the unitary evolution of a harmonic oscillator coupled to a
two-level system can be undone by a suitable manipulation of the two-level
system -- more specifically: by a quasi-instantaneous phase change. This
enables us to isolate the dissipative evolution to which the oscillator may be
exposed in addition. With this method we study the decoherence of a photon mode
in cavity QED, and that of the quantized harmonic motion of trapped ions. We
comment on the relation to spin echoes and multi-path interferometry.


title:
Huygens' principle, the free Schrodinger particle and the quantum
  anti-centrifugal force

abstract:
  Huygens' principle following from the d'Alembert wave equation is not valid
in two-dimensional space. A Schrodinger particle of vanishing angular momentum
moving freely in two dimensions experiences an attractive force - the quantum
anti-centrifugal force - towards its center. We connect these two phenomena by
comparing and contrasting the radial propagators of the d'Alembert wave
equation and of a free non-relativistic quantum mechanical particle in two and
three dimensions.


title: Violating Bell's inequality beyond Cirel'son's bound

abstract:
  Cirel'son inequality states that the absolute value of the combination of
quantum correlations appearing in the Clauser-Horne-Shimony-Holt (CHSH)
inequality is bound by $2 \sqrt 2$. It is shown that the correlations of two
qubits belonging to a three-qubit system can violate the CHSH inequality beyond
$2 \sqrt 2$. Such a violation is not in conflict with Cirel'son's inequality
because it is based on postselected systems. The maximum allowed violation of
the CHSH inequality, 4, can be achieved using a Greenberger-Horne-Zeilinger
state.


title: Some Comments On Bound State Eigenvalues of PT-Symmetric Potentials

abstract:
  Using purely physical arguments it is claimed that for ID Schrodinger
operators with complex PT- Symmatric potentials having a purely real attractive
potential well and a purely imaginary repulsive part,bound state eigenvalues
will be discrete and real.This has been illustrated with several potentials
possessing similar properties.


title: A General Phase Matching Condition for Quantum Searching Algorithm

abstract:
  A general consideration on the phase rotations in quantum searching algorithm
is taken in this work. As four phase rotations on the initial state, the marked
states, and the states orthogonal to them are taken account, we deduce a phase
matching condition for a successful search. The optimal options for these phase
are obtained consequently.


title: 'Photosynthetic' Quantum Computers?

abstract:
  Do quantum computers already exist in Nature? It is proposed that they do.
Photosynthesis is one example in which a 'quantum computer' component may play
a role in the 'classical' world of complex biological systems. A 'translation'
of the standard metabolic description of the 'front-end' light harvesting
complex in photosynthesis into the language of quantum computers is presented.
Biological systems represent an untapped resource for thinking about the design
and operation of hybrid quantum-classical computers and expanding our current
conceptions of what defines a 'quantum computer' in Nature.


title:
Exploring Hilbert Space: accurate characterisation of quantum
  information

abstract:
  We report the creation of a wide range of quantum states with controllable
degrees of entanglement and entropy using an optical two-qubit source based on
spontaneous parametric downconversion. The states are characterised using
measures of entanglement and entropy determined from tomographically determined
density matrices. The Tangle-Entropy plane is introduced as a graphical
representation of these states, and the theoretic upper bound for the maximum
amount of entanglement possible for a given entropy is presented. Such a
combination of general quantum state creation and accurate characterisation is
an essential prerequisite for quantum device development.


title:
Explicit Euler method for solving time dependent Schr\H{o}dinger
  equation

abstract:
  Using an explicit Euler substitution it was obtained a system of differential
equations, which can be used to find the solution of time-dependent
1-dimentional Schr\H{o}dinger equation for a general form of the time-dependent
potential.


title: Perfect cloning of harmonic oscillator coherent states is possible

abstract: We have withdrawn this paper due to a fatal flaw in eqn(38).


title: Quantum Cooperative Games

abstract:
  We study two forms of a symmetric cooperative game played by three players,
one classical and other quantum. In its classical form making a coalition gives
advantage to players and they are motivated to do so. However in its quantum
form the advantage is lost and players are left with no motivation to make a
coalition.


title: The 18-fold way

abstract:
  I shall consider each of the 18 claims made by Mohrhoff, and explain, in each
case, why I take the path opposite to the one by which he seeks to remove the
effects of our thoughts on the activities of our quantum mechanically described
brains.


title: Quantum entanglement without eigenvalue spectra

abstract:
  From the consideration of measuring bipartite mixed states by separable pure
states, we introduce algebraic sets in complex projective spaces for bipartite
mixed states as the degenerating locus of the measurement. These algebraic sets
are independent of the eigenvalues and only measure the "position" of
eigenvectors of bipartite mixed states. They are nonlocal invariants ie.,
remaining invariant after local unitary transformations. The algebraic sets
have to be the sum of the linear subspaces if the mixed states are separable,
and thus we give a "eigenvalue-free" criterion of separability.Based on our
criterion, examples are given to illustrate that entangled mixed states which
are invariant under partial transposition or fufill entropy and disorder
criterion of separability can be constructed systematically.We reveal that a
large part of quantum entanglement is independent of eigenvalue spectra and
develop a method to measure this part of quantum enatnglement.The results are
extended to multipartite case.


title: From Quantum Action to Quantum Chaos

abstract:
  We have recently suggested a quantum action, which has the form of a
classical action and takes into account quantum effects via renormalized action
parameters. Here we apply it to quantum chaos. We study a system in 2-D with
weak anharmonic coupling ($V_{coupl} \propto x^{2}y^{2}$) being classically
chaotic. We construct the quantum action at finite temperature. We compute
Poincar\'e sections of the quantum action at that temperature and compare it
with those of the classical action. We observe chaotic behavior in both cases.


title: A quantum Goldreich-Levin theorem with cryptographic applications

abstract:
  We investigate the Goldreich-Levin Theorem in the context of quantum
information. This result is a reduction from the computational problem of
inverting a one-way function to the problem of predicting a particular bit
associated with that function. We show that the quantum version of the
reduction -- between quantum one-way functions and quantum hard-predicates --
is quantitatively more efficient than the known classical version. Roughly
speaking, if the one-way function acts on n-bit strings then the overhead in
the reduction is by a factor of O(n/epsilon^2) in the classical case but only
by a factor of O(1/epsilon) in the quantum case, where 1/2 + epsilon is the
probability of predicting the hard-predicate. Moreover, we prove via a lower
bound that, in a black-box framework, the classical version of the reduction
cannot have overhead less than order n/epsilon^2.
  We also show that, using this reduction, a quantum bit commitment scheme that
is perfectly binding and computationally concealing can be obtained from any
quantum one-way permutation. This complements a recent result by Dumais, Mayers
and Salvail, where the bit commitment scheme is perfectly concealing and
computationally binding. We also show how to perform qubit commitment by a
similar approach.


title:
Generalized Continuity Equation and Modified Normalization in
  PT-Symmetric Quantum Mechanics

abstract:
  The continuity equation relating the change in time of the position
probability density to the gradient of the probability current density is
generalized to PT-symmetric quantum mechanics. The normalization condition of
eigenfunctions is modified in accordance with this new conservation law and
illustrated with some detailed examples.


title: Greenberger-Horne-Zeilinger paradoxes for N quNits

abstract:
  In this paper we show the series of Greenberger-Horne-Zeilinger paradoxes for
N maximally entangled N-dimensional quantum systems.


title: Polarization squeezing and continuous-variable polarization entanglement

abstract:
  The Stokes-parameter operators and the associated Poincare sphere, which
describe the quantum-optical polarization properties of light, are defined and
their basic properties are reviewed. The general features of the Stokes
operators are illustrated by evaluation of their means and variances for a
range of simple polarization states. Some of the examples show polarization
squeezing, in which the variances of one or more Stokes parameters are smaller
than the coherent-state value. The main object of the paper is the application
of these concepts to bright squeezed light. It is shown that a light beam
formed by interference of two orthogonally-polarized quadrature-squeezed beams
exhibits squeezing in some of the Stokes parameters. Passage of such a primary
polarization-squeezed beam through suitable optical components generates a pair
of polarization-entangled light beams with the nature of a two-mode squeezed
state. The use of pairs of primary polarization-squeezed light beams leads to
substantially increased entanglement and to the generation of EPR-entangled
light beams. The important advantage of these nonclassical polarization states
for quantum communication is the possibility of experimentally determining all
of the relevant conjugate variables of both squeezed and entangled fields using
only linear optical elements followed by direct detection.


title:
Entropy production due to coupling to a heat bath in the kicked rotor
  problem

abstract:
  Considering a kicked rotor coupled to a model heat bath both the classical
and quantum entropy productions are calculated exactly. Starting with an
initial wave packet, the von Neuman entropy as a function of time is determined
from the reduced density matrix while the Liouville evolution of the
corresponding Husimi distribution provides us with the classical entropy. It is
found that both these entropies agree reasonably satisfying the same asymptotic
growth law and more importantly both are proportional to the classical
Liapounov exponent.


title: Qubit authentication

abstract:
  Secure communication requires message authentication. In this paper we
address the problem of how to authenticate quantum information sent through a
quantum channel between two communicating parties with the minimum amount of
resources. Specifically, our objective is to determine whether one elementary
quantum message (a qubit) can be authenticated with a key of minimum length. We
show that, unlike the case of classical-message quantum authentication, this is
not possible.


title: Conservation of Orbital Angular Momentum in Stimulated Down-Conversion

abstract:
  We report on an experiment demonstrating the conservation of orbital angular
momentum in stimulated down-conversion. The orbital angular momentum is not
transferred to the individual beams of the spontaneous down-conversion, but it
is conserved when twin photons are taken individually. We observe the
conservation law for an individual beam of the down-conversion through
cavity-free stimulated emission.


title: Classicality of quantum information processing

abstract:
  The ultimate goal of the classicality programme is to quantify the amount of
quantumness of certain processes. Here, classicality is studied for a
restricted type of process: quantum information processing (QIP). Under special
conditions, one can force some qubits of a quantum computer into a classical
state without affecting the outcome of the computation. The minimal set of
conditions is described and its structure is studied. Some implications of this
formalism are the increase of noise robustness, a proof of the quantumness of
mixed state quantum computing and a step forward in understanding the very
foundation of QIP.


title:
A Non-Adiabatic Controlled Not Gate for the Kane Solid State Quantum
  Computer

abstract:
  The method of iterated resolvents is used to obtain an effective Hamiltonian
for neighbouring qubits in the Kane solid state quantum computer. In contrast
to the adiabatic gate processes inherent in the Kane proposal we show that free
evolution of the qubit-qubit system, as generated by this effective
Hamiltonian, combined with single qubit operations, is sufficient to produce a
controlled-NOT (c-NOT) gate. Thus the usual set of universal gates can be
obtained on the Kane quantum computer without the need for adiabatic switching
of the controllable parameters as prescribed by Kane. Both the fidelity and
gate time of this non-adiabatic c-NOT gate are determined by numerical
simulation.


title: Global entanglement in multiparticle systems

abstract:
  We define a polynomial measure of multiparticle entanglement which is
scalable, i.e., which applies to any number of spin-1/2 particles. By
evaluating it for three particle states, for eigenstates of the one dimensional
Heisenberg antiferromagnet and on quantum error correcting code subspaces, we
illustrate the extent to which it quantifies global entanglement. We also apply
it to track the evolution of entanglement during a quantum computation.


title: On the structure of covariant phase observables

abstract:
  We study the mathematical structure of covariant phase observables. Such an
observable can alternatively be expressed as a phase matrix, as a sequence of
unit vectors, as a sequence of phase states, or as an equivalent class of
covariant trace-preserving operations. Covariant generalized operator measures
are defined by structure matrices which form a W*-algebra with phase matrices
as its subset. The properties of the Radon-Nikodym derivatives of phase
probability measures are studied.


title: Perspectives on a Solid State NMR Quantum Computer

abstract:
  A quantum information processing device, based on bulk solid state NMR of the
quasi-one dimensional material hydroxyapatite, is proposed following the
magnetic resonance force microscopy work of Yamamoto et al (quant-ph/0009122).
In a macroscopic sample of hydroxyapatite, our solid state NMR model yields a
limit of 10^8 qubits imposed by physics, while development of current
technological considerations should allow an upper bound in the range of
hundreds to thousands of qubits.


title: On Quantum - Classical Correspondence for Baker's Map

abstract:
  Quantum baker`s map is a model of chaotic system. We study quantum dynamics
for the quantum baker's map. We use the Schack and Caves symbolic description
of the quantum baker`s map. We find an exact expression for the expectation
value of the time dependent position operator. A relation between quantum and
classical trajectories is investigated. Breakdown of the quantum-classical
correspondence at the logarithmic timescale is rigorously established.


title: Generalized measurements by linear elements

abstract:
  I give a first characterization of the class of generalized measurements that
can be exactly realized on a pair of qudits encoded in indistinguishable
particles, by using only linear elements and particle detectors. Two immediate
results follow from this characterization. (i) The Schmidt number of each POVM
element cannot exceed the number of initial particles. This rules out any
possibility of performing perfect Bell-measurements for qudits. (ii) The
maximum probability of performing a generalized incomplete Bell-measurement is
1/2.


title:
Time dependence of occupation numbers and thermalization time in closed
  chaotic many-body systems

abstract:
  We study the time evolution of occupation numbers for interacting
Fermi-particles in the situation when exact compound states are "chaotic". This
situation is generic for highly excited many-particles states in heavy nuclei,
complex atoms, quantum dots, spin systems and quantum computer models.
Numerical data show perfect agreement with a simple theory for the onset of
thermalization in close systems of interacting particles.

categories: quant-ph cond-mat.stat-mech nlin.CD nucl-th physics.atom-ph


title: Polynomial-Time Simulation of Pairing Models on a Quantum Computer

abstract:
  We propose a polynomial-time algorithm for simulation of the class of pairing
Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The
algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap
between ground and first excited states, and provides a test of the
applicability of the BCS Hamiltonian to mesoscopic superconducting systems,
such as ultra-small metallic grains.


title: On the nonadiabatic geometric quantum gates

abstract:
  Motivated for the fault tolerant quantum computation, quantum gate by
adiabatic geometric phase shift is extensively investigated. In this paper, we
demonstrate the nonadiabatic scheme for the geometric phase shift and
conditional geometric phase shift. Essentially, the new scheme is simply to add
an appropriate additional field. With this additional field, the state
evolution can be controlled exactly on a dynamical phase free path. Geometric
quantum gates for single qubit and the controlled NOT gate for two qubits are
given.


title: Quantum stochastic equation for the low density limit

abstract:
  A new derivation of quantum stochastic differential equation for the
evolution operator in the low density limit is presented. We use the
distribution approach and derive a new algebra for quadratic master fields in
the low density limit by using the energy representation. We formulate the
stochastic golden rule in the low density limit case for a system coupling with
Bose field via quadratic interaction. In particular the vacuum expectation
value of the evolution operator is computed and its exponential decay is shown.


title: The N-box paradox in orthodox quantum mechanics

abstract:
  The prediction of the N-box paradox, that whichever box is opened will
contain the record of the particle having passed through it, is traced to a
failure to specify whether the other boxes are distinguishable or
indistinguishable. These correspond to different ways of lifting the degeneracy
of a certain measurement, and have incompatible consequences.


title:
Degrees of controllability for quantum systems and applications to
  atomic systems

abstract:
  Precise definitions for different degrees of controllability for quantum
systems are given, and necessary and sufficient conditions are discussed. The
results are applied to determine the degree of controllability for various
atomic systems with degenerate energy levels and transition frequencies.


title: Phase-selective reversible quantum decoherence in cavity QED experiment

abstract:
  New feasible cavity QED experiment is proposed to analyse reversible quantum
decoherence in consequence of quantum complementarity and entanglement.
Utilizing the phase selective manipulations with enviroment, it is demonstrated
how the complementarity particularly induces a preservation of visibility,
whereas quantum decoherence is more progressive due to pronounced entanglement
between system and enviroment. This effect can be directly observed using the
proposed cavity QED measurements.


title:
A polynomial-time solution to the parity problem on an NMR quantum
  computer

abstract:
  An efficient quantum algorithm is proposed to solve in polynomial time the
parity problem, one of the hardest problems both in conventional quantum
computation and in classical computation, on NMR quantum computers. It is based
on the quantum parallelism principle in a quantum ensemble, the selective
decoherence manipulation, and the NMR phase-sensitive measurement. The quantum
circuit for the quantum algorithm is designed explicitly.


title: Generation of arbitrary two dimensional motional state of a trapped ion

abstract:
  We present a scheme to generate an arbitrary two-dimensional quantum state of
motion of a trapped ion. This proposal is based on a sequence of laser pulses,
which are tuned appropriately to control transitions on the sidebands of two
modes of vibration. Not more than $(M+1)(N+1)$ laser pulses are needed to
generate a pure state with upper phonon number $M$ and $N$ in the $x$ and $y$
direction respectively.


title:
The one-way quantum computer - a non-network model of quantum
  computation

abstract:
  A one-way quantum computer works by only performing a sequence of one-qubit
measurements on a particular entangled multi-qubit state, the cluster state. No
non-local operations are required in the process of computation. Any quantum
logic network can be simulated on the one-way quantum computer. On the other
hand, the network model of quantum computation cannot explain all ways of
processing quantum information possible with the one-way quantum computer. In
this paper, two examples of the non-network character of the one-way quantum
computer are given. First, circuits in the Clifford group can be performed in a
single time step. Second, the realisation of a particular circuit --the
bit-reversal gate-- on the one-way quantum computer has no network
interpretation. (Submitted to J. Mod. Opt, Gdansk ESF QIT conference issue.)


title:
A device for feasible fidelity, purity, Hilbert-Schmidt distance and
  entanglement witness measurements

abstract:
  A generic model of measurement device which is able to directly measure
commonly used quantum-state characteristics such as fidelity, overlap, purity
and Hilbert-Schmidt distance for two general uncorrelated mixed states is
proposed. In addition, for two correlated mixed states, the measurement
realizes an entanglement witness for Werner's separability criterion. To
determine these observables, the estimation only one parameter - the visibility
of interference, is needed. The implementations in cavity QED, trapped ion and
electromagnetically induced transparency experiments are discussed.


title: Quantization of Non-Hamiltonian Systems

abstract:
  In this paper a generalization of Weyl quantization which maps a dynamical
operator in a function space to a dynamical superoperator in an operator space
is suggested. Quantization of dynamical operator, which cannot be represented
as Poisson bracket with some function, is considered. The usual Weyl
quantization of observables can be derived as a specific case of suggested
quantization if dynamical operator is an operator of multiplication on a
function. This approach allows to define consistent Weyl quantization of
non-Hamiltonian and dissipative systems. Examples of the harmonic oscillator
with friction and a system which evolves by Fokker-Planck-type equation are
considered.


title: To the finite information content of the physically existing reality

abstract:
  Every physical measuring needs a finite, different from zero measurement time
and provides information in form of the choice of a measurement result from all
possible measurement results. If infinitely many (different) measurement
results would be possible, the choice of a measurement result could deliver an
infinite quantity of information. But the results of physical measurings (of
finite duration) never deliver an infinite quantity of information, they
describe past, finite reality. Therefore the set of all possible measurement
results a priori is finite. In the physical reality only a finite information
quantity can be processed within a finite time interval. For mathematical
models whose representation requires a processing of an infinite quantity of
information, for example irrational numbers, no (exact) equivalent exists in
the physical reality. So mathematical calculations, which have an equivalent in
physical reality, can include only rational (finitely many elementary)
combinations of rational numbers. Conclusions arise from this for the
foundations of mathematical physics.


title: Algorithm for Computing Excited States in Quantum Theory

abstract:
  Monte Carlo techniques have been widely employed in statistical physics as
well as in quantum theory in the Lagrangian formulation. However, in the
conventional approach, it is extremely difficult to compute the excited states.
Here we present a different algorithm: the Monte Carlo Hamiltonian method,
designed to overcome the difficulties of the conventional approach. As a new
example, application to the Klein-Gordon field theory is shown.


title:
Superluminal information transmission using a double-double-slit
  apparatus

abstract: This paper has been withdrawn


title: Role of entanglement in two-photon imaging

abstract:
  The use of entangled photons in an imaging system can exhibit effects that
cannot be mimicked by any other two-photon source, whatever the strength of the
correlations between the two photons. We consider a two-photon imaging system
in which one photon is used to probe a remote (transmissive or scattering)
object, while the other serves as a reference. We discuss the role of
entanglement versus correlation in such a setting, and demonstrate that
entanglement is a prerequisite for achieving distributed quantum imaging.


title:
Completeness of photon-added squeezed vacuum and one-photon-states and
  of photon-added coherent states on a circle

abstract:
  A discrete completeness relation and a continuous one with a positive measure
are found for the photon-added squeezed vacuum states. Extension to the
photon-added squeezed one-photon states is considered. Photon-added coherent
states on a circle are introduced. Their normalization and unity resolution
relation are given.


title:
Generalized coherent states associated with the C_{\lambda}-extended
  oscillator

abstract:
  Two new types of coherent states associated with the C_{\lambda}-extended
oscillator, where C_{\lambda} is the cyclic group of order \lambda, are
introduced. The first ones include as special cases both the Barut-Girardello
and the Perelomov su(1,1) coherent states for \lambda=2, as well as the
annihilation-operator coherent states of the C_{\lambda}-extended oscillator
spectrum generating algebra for higher \lambda values. The second ones, which
are eigenstates of the C_{\lambda}-extended oscillator annihilation operator,
extend to higher \lambda values the paraboson coherent states, to which they
reduce for \lambda=2. All these states satisfy a unity resolution relation in
the C_{\lambda}-extended oscillator Fock space (or in some subspace thereof).
They give rise to Bargmann representations of the latter, wherein the
generators of the C_{\lambda}-extended oscillator algebra are realized as
differential-operator-valued matrices (or differential operators). The
statistical and squeezing properties of the new coherent states are
investigated over a wide range of parameters and some interesting nonclassical
features are exhibited.


title: Relativity and EPR Entanglement: Comments

abstract:
  Recent experiment by Zhinden et al (Phys. Rev {\bf A} 63 02111, 2001)
purports to test compatibility between relativity and quantum mechanics in the
classic EPR setting. We argue that relativity has no role in the EPR argument
based solely on non-relativistic quantum formalism. It is suggested that this
interesting experiment may have significance to address fundamental questions
on quantum probability.


title:
Beyond the Fokker-Planck equation: Stochastic Simulation of Complete
  Wigner representation for the Optical Parametric Oscillator

abstract:
  We demonstrate a method which allows the stochastic modelling of quantum
systems for which the generalised Fokker-Planck equation in the phase space
contains derivatives of higher than second order. This generalises quantum
stochastics far beyond the quantum-optical paradigm of three and four-wave
mixing problems to which these techniques have so far only been applicable. To
verify our method, we model a full Wigner representation for the optical
parametric oscillator, a system where the correct results are well known and
can be obtained by other methods.

categories: quant-ph cond-mat.stat-mech math-ph math.MP physics.comp-ph


title: Entanglement, joint measurement, and state reduction

abstract:
  Entanglement is perhaps the most important new feature of the quantum world.
It is expressed in quantum theory by the joint measurement formula. We prove
the formula for self-adjoint observables from a plausible assumption, which for
spacelike separated measurements is an expression of relativistic causality.
State reduction is simply a way to express the JMF after one measurement has
been made, and its result known.


title: Inverse Quantum Zeno Effect in Quantum Oscillations

abstract:
  It is shown that inverse quantum Zeno effect (IZE) may exist in a three-level
system with Rabi oscillations between discrete atomic states. The experiment to
observe IZE in such a system is proposed.


title: A Proposed Quantum Low Density Parity Check Code

abstract:
  We propose a new CSS code based on the finite geometry low density parity
check code of Kou, Lin, and Fossorier.


title: A simple model of quantum trajectories

abstract:
  Quantum trajectory theory, developed largely in the quantum optics community
to describe open quantum systems subjected to continuous monitoring, has
applications in many areas of quantum physics. In this paper I present a simple
model, using two-level quantum systems (q-bits), to illustrate the essential
physics of quantum trajectories and how different monitoring schemes correspond
to different ``unravelings'' of a mixed state master equation. I also comment
briefly on the relationship of the theory to the Consistent Histories formalism
and to spontaneous collapse models.


title: On Classical and Quantum Cryptography

abstract:
  Lectures on classical and quantum cryptography. Contents: Private key
cryptosystems. Elements of number theory. Public key cryptography and RSA
cryptosystem. Shannon`s entropy and mutual information. Entropic uncertainty
relations. The no cloning theorem. The BB84 quantum cryptographic protocol.
Security proofs. Bell`s theorem. The EPRBE quantum cryptographic protocol.

categories: quant-ph cond-mat.mes-hall cs.IT hep-th math-ph math.IT math.MP


title: Local Realistic Model for Two-Particle Einstein-Podolsky-Rosen Pairs

abstract:
  A local realistic model for quantum mechanics of two-particle
Einstein-Podolsky-Rosen pairs is proposed. In this model, it is the strict
obedience of conservation laws in each event at the quantum level that uphold
the perfect correlation of two spatially-separated particles, instead of
nonlocality in the orthodox formulation of quantum mechanics. Therefore, one
can conclude that all components of the spin of two particles, and the position
and momentum of a particle can be measured simultaneously. The proposed model
yields the same statistical prediction on an ensemble of individual particles
as the orthodox formulation does. This suggests that the wave function is not a
complete description of individual particle as assumed in the orthodox
formulation, but only a statistical description of an ensemble of particles.


title: Relation between complementarity and nonlocality under decoherence

abstract:
  Relations connecting violation of any Bell inequalities and the
complementarity between visibility and distinguishability in the
interferometric experiments with different sources of decoherence are
presented. A boundary of local-realistic explanation of the which-way
complementarity is discussed in dependence on the choice of independent or
collective tests of nonlocality.


title:
Dynamics of open quantum systems initially entangled with environment:
  Beyond the Kraus representation

abstract:
  We present a general analysis of the role of initial correlations between the
open system and an environment on quantum dynamics of the open system.


title: Geometry of entangled states, Bloch spheres and Hopf fibrations

abstract:
  We discuss a generalization to 2 qubits of the standard Bloch sphere
representation for a single qubit, in the framework of Hopf fibrations of high
dimensional spheres by lower dimensional spheres. The single qubit Hilbert
space is the 3-dimensional sphere S3. The S2 base space of a suitably oriented
S3 Hopf fibration is nothing but the Bloch sphere, while the circular fibres
represent the qubit overall phase degree of freedom. For the two qubits case,
the Hilbert space is a 7-dimensional sphere S7, which also allows for a Hopf
fibration, with S3 fibres and a S4 base. A main striking result is that
suitably oriented S7 Hopf fibrations are entanglement sensitive. The relation
with the standard Schmidt decomposition is also discussed


title: A Storage Ring for Neutral Atoms

abstract:
  We have demonstrated a storage ring for ultra-cold neutral atoms. Atoms with
mean velocities of 1 m/s corresponding to kinetic energies of ~100 neV are
confined to a 2 cm diameter ring by magnetic forces produced by two
current-carrying wires. Up to 10^6 atoms are loaded at a time in the ring, and
7 revolutions are clearly observed. Additionally, we have demonstrated multiple
loading of the ring and deterministic manipulation of the longitudinal velocity
distribution of the atoms using applied laser pulses. Applications of this ring
include large area atom interferometers and cw monochromatic atomic beam
generation.


title: On the stochastic mechanics of the free relativistic particle

abstract:
  Given a positive energy solution of the Klein-Gordon equation, the motion of
the free, spinless, relativistic particle is described in a fixed Lorentz frame
by a Markov diffusion process with non-constant diffusion coefficient. Proper
time is an increasing stochastic process and we derive a probabilistic
generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A
random time-change transformation provides the bridge between the $t$ and the
$\tau$ domain. In the $\tau$ domain, we obtain an $\M^4$-valued Markov process
with singular and constant diffusion coefficient. The square modulus of the
Klein-Gordon solution is an invariant, non integrable density for this Markov
process. It satisfies a relativistically covariant continuity equation.


title:
Non Linear Compton Scattering of Strong Laser Radiation on Channeled
  Particles in a Crystal

abstract:
  A version for intense $\gamma $-ray radiation based on the multiphoton
scattering of strong laser radiation on relativistic particle beam channeled in
a crystal is proposed. The scheme is considered when the incident laser beam
and charged paricles beam are counter-propagating and the laser radiation is
resonant to the energy levels of transversal motion of channeled particles.


title:
Numerical simulation of Einstein-Podolsky-Rosen experiments in a local
  hidden variables model

abstract:
  We simulate correlation measurements of entangled photons numerically. The
model employed is strictly local. In our model correlations arise from a phase,
connecting the electromagnetic fields of the two photons at their separate
points of measurement. We sum up coincidences for each pair individually and
model the operation of a polarizer beam splitter numerically. The results thus
obtained differ substantially from the classical results. In addition, we
analyze the effects of decoherence and non-ideal beam splitters. It is shown
that under realistic experimental conditions the Bell inequalities are violated
by more than 30 standard deviations.


title:
A recursion technique for deriving renormalized perturbation expansions
  for one-dimensional anharmonic oscillator

abstract:
  A new recursion procedure for deriving renormalized perturbation expansions
for the one-dimensional anharmonic oscillator is offered. Based upon the
$\hbar$-expansions and suitable quantization conditions, the recursion formulae
obtained have the same simple form both for ground and excited states and can
be easily applied to any renormalization scheme. As an example, the
renormalized expansions for the sextic anharmonic oscillator are considered.


title: Classical and Quantum Propagation of Chaos

abstract:
  This article examines the relationship between classical and quantum
propagation of chaos. (In this context, "chaos" refers to the Boltzmann's
Ansatz of molecular disorder, not to chaotic dynamics.) Classical propagation
of chaos is shown to occur when quantum systems that propagate quantum
molecular chaos are suitably prepared, allowed to evolve without interference,
and then observed.


title:
Mean field loops versus quantum anti-crossing nets in trapped
  Bose-Einstein condensates

abstract:
  We study a Bose-Einstein condensate trapped in an asymmetric double well
potential. Solutions of the time-independent Gross-Pitaevskii equation reveal
intrinsic loops in the energy (or chemical potential) level behavior when the
shape of the potential is varied. We investigate the corresponding behavior of
the quantum (many-body) energy levels. Applying the two-mode approximation to
the bosonic field operators, we show that the quantum energy levels create an
anti-crossing net inside the region bounded by the loop of the mean field
solution.


title: Explicit conversion from the Casimir force to Planck's law of radiation

abstract:
  The Casimir force has its origin in finite modification of the infinite
zero-point energy induced by a specific boundary condition for the spatial
configuration. In terms of the imaginary-time formalism at finite temperature,
the root of Planck's law of radiation can be traced back to finite modification
of the infinite vacuum energy induced by the periodic boundary condition in the
temporal direction. We give the explicit conversion from the Casimir force to
Planck's law of radiation, which shows the apparent correspondence between the
system bounded by parallel conducting plates and the thermodynamic system. The
temperature inversion symmetry and the duality relation in the thermodynamics
are also discussed. We conclude that the effective temperature characterized by
the spatial extension should no longer be regarded as genuine temperature.


title: Simulating Physical Phenomena by Quantum Networks

abstract:
  Physical systems, characterized by an ensemble of interacting elementary
constituents, can be represented and studied by different algebras of
observables or operators. For example, a fully polarized electronic system can
be investigated by means of the algebra generated by the usual fermionic
creation and annihilation operators, or by using the algebra of Pauli
(spin-1/2) operators. The correspondence between the two algebras is given by
the Jordan-Wigner isomorphism. As we previously noted similar one-to-one
mappings enable one to represent any physical system in a quantum computer. In
this paper we evolve and exploit this fundamental concept in quantum
information processing to simulate generic physical phenomena by quantum
networks. We give quantum circuits useful for the efficient evaluation of the
physical properties (e.g, spectrum of observables or relevant correlation
functions) of an arbitrary system with Hamiltonian $H$.


title:
Larmor precession and barrier tunneling time of a neutral spinning
  particle

abstract:
  The Larmor precession of a neutral spinning particle in a magnetic field
confined to the region of a one dimensional-rectangular barrier is investigated
for both a nonrelativistic and a relativistic incoming particle. The spin
precession serves as a clock to measure the time spent by a quantum particle
traversing a potential barrier. With the help of general spin coherent state it
is explicitly shown that the precession time is equal to the dwell time in both
the nonrelativistic and relativistic cases. We also present a numerical
estimation of the precession time showing an apparent superluminal tunneling.


title:
Experimental realization of 7-qubit universal perfect controlled-NOT and
  controlled square-root NOT gates

abstract:
  The controlled-NOT gate and controlled square-root NOT gate play an important
role in quantum algorithm. This article reports the experimental results of
these two universal quantum logic gates (controlled square-root NOT gate and
controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a
simple experimental method to measure and correct the error in the controlled
phase-shift gate, which is helpful to construct a more perfect phase-shift gate
experimentally and can also be used in more qubits discrete Fourier
transformation.


title: Aspects of mutually unbiased bases in odd prime power dimensions

abstract:
  We rephrase the Wootters-Fields construction [Ann. Phys., {\bf 191}, 363
(1989)] of a full set of mutually unbiased bases in a complex vector space of
dimensions $N=p^r$, where $p$ is an odd prime, in terms of the character
vectors of the cyclic group $G$ of order $p$. This form may be useful in
explicitly writing down mutually unbiased bases for $N=p^r$.


title: Quantum Computing and Shor`s Factoring Algorithm

abstract:
  Lectures on quantum computing. Contents: Algorithms. Quantum circuits.
Quantum Fourier transform. Elements of number theory. Modular exponentiation.
Shor`s algorithm for finding the order. Computational complexity of Schor`s
algorithm. Factoring integers. NP-complete problems.


title:
Measurement of the photonic de Broglie wavelength of biphotons generated
  by spontaneous parametric down-conversion

abstract:
  Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the
measurement of the photonic de Broglie wavelength of an entangled photon pair
(a biphoton) generated by spontaneous parametric down-conversion. The observed
interference manifests the concept of the photonic de Broglie wavelength. The
result also provides a proof-of-principle of the quantum lithography that
utilizes the reduced interferometric wavelength.


title: Quantum Computing in a Macroscopic Dark Period

abstract:
  Decoherence-free subspaces allow for the preparation of coherent and
entangled qubits for quantum computing. Decoherence can be dramatically
reduced, yet dissipation is an integral part of the scheme in generating stable
qubits and manipulating them via one and two bit gate operations. How this
works can be understood by comparing the system with a three-level atom
exhibiting a macroscopic dark period. In addition, a dynamical explanation is
given for a scheme based on atoms inside an optical cavity in the strong
coupling regime and we show how spontaneous emission by the atoms can be highly
suppressed.


title: An arbitrated quantum signature scheme

abstract:
  The general principle for a quantum signature scheme is proposed and
investigated based on ideas from classical signature schemes and quantum
cryptography. The suggested algorithm is implemented by a symmetrical quantum
key cryptosystem and Greenberger-Horne-Zeilinger (GHZ) triplet states and
relies on the availability of an arbitrator. We can guarantee the unconditional
security of the algorithm, mostly due to the correlation of the GHZ triplet
states and the use of quantum one-time pads.


title:
Non locality, closing the detection loophole and communication
  complexity

abstract:
  It is shown that the detection loophole which arises when trying to rule out
local realistic theories as alternatives for quantum mechanics can be closed if
the detection efficiency $\eta$ is larger than $\eta \geq d^{1/2} 2^{-0.0035d}$
where $d$ is the dimension of the entangled system. Furthermore it is argued
that this exponential decrease of the detector efficiency required to close the
detection loophole is almost optimal. This argument is based on a close
connection that exists between closing the detection loophole and the amount of
classical communication required to simulate quantum correlation when the
detectors are perfect.


title: Quantum key distribution with bright entangled beams

abstract:
  We suggest a quantum cryptographic scheme using continuous EPR-like
correlations of bright optical beams. For binary key encoding, the continuous
information is discretized in a novel way by associating a respective
measurement, amplitude or phase, with a bit value "1" or "0". The secure key
distribution is guaranteed by the quantum correlations. No pre-determined
information is sent through the quantum channel contributing to the security of
the system.


title: Clifford algebras, noncommutative tori and universal quantum computers

abstract:
  Recently author suggested [quant-ph/0010071] an application of Clifford
algebras for construction of a "compiler" for universal binary quantum computer
together with later development [quant-ph/0012009] of the similar idea for a
non-binary base. The non-binary case is related with application of some
extension of idea of Clifford algebras. It is noncommutative torus defined by
polynomial algebraic relations of order l. For l=2 it coincides with definition
of Clifford algebra. Here is presented the joint consideration and comparison
of both cases together with some discussion on possible physical consequences.


title: Quantum techniques using continuous variables of light

abstract:
  We present schemes for the generation and evaluation of continuous variable
entanglement of bright optical beams and give a brief overview of the variety
of optical techniques and quantum communication applications on this basis. A
new entanglement-based quantum interferometry scheme with bright beams is
suggested. The performance of the presented schemes is independent of the
relative interference phase which is advantageous for quantum communication
applications.


title: Submicroscopic Deterministic Quantum Mechanics

abstract:
  So-called hidden variables introduced in quantum mechanics by de Broglie and
Bohm have changed their initial enigmatic meanings and acquired quite
reasonable outlines of real and measurable characteristics. The start viewpoint
was the following: All the phenomena, which we observe in the quantum world,
should reflect structural properties of the real space. Thus the scale 10^{-28}
cm at which three fundamental interactions (electromagnetic, weak, and strong)
intersect has been treated as the size of a building block of the space. The
appearance of a massive particle is associated with a local deformation of the
cellular space, i.e. deformation of a cell. The mechanics of a moving particle
that has been constructed is deterministic by its nature and shows that the
particle interacts with cells of the space creating elementary excitations
called "inertons". The further study has disclosed that inertons are a
substructure of the matter waves which are described by the orthodox wave
\psi-function formalism. The concept has allowed resolving the spin problem.
The theory, or more exactly, the existence of inertons, has been verified
experimentally: in rarefied gases, inerton clouds of atoms' electrons interact
with a strong laser pulse; in a solid, atom's inertons induce an additional
harmonic potential that contributes to the interatomic interaction (metal
specimens and the KIO_3*HIO_3 crystal).


title: How to Quantize Phases and Moduli!

abstract:
  A typical classical interference pattern of two waves with intensities I_1,
I_2 and relative phase phi = phi_2-phi_1 may be characterized by the 3
observables p = sqrt{I_1 I_2}, p cos\phi and -p sin\phi. They are, e.g. the
starting point for the semi-classical operational approach by Noh, Fougeres and
Mandel (NFM) to the old and notorious phase problem in quantum optics.
Following a recent group theoretical quantization of the symplectic space S =
{(phi in R mod 2pi, p > 0)} in terms of irreducible unitary representations of
the group SO(1,2) the present paper applies those results to that controversial
problem of quantizing moduli and phases of complex numbers: The Poisson
brackets of the classical observables p cos\phi, -p sin\phi and p > 0 form the
Lie algebra of the group SO(1,2). The corresponding self-adjoint generators
K_1, K_2 and K_3 of that group may be obtained from its irreducible unitary
representations. For the positive discrete series the modulus operator K_3 has
the spectrum {k+n, n = 0, 1,2,...; k > 0}. Self-adjoint operators for cos phi
and sin phi can be defined as ((1/K_3)K_1 + K_1/K_3)/2 and -((1/K_3)K_2 +
K_2/K_3)/2 which have the theoretically desired properties for k > or = 0.5.
The approach advocated here solves, e.g. the modulus-phase quantization problem
for the harmonic oscillator and appears to provide a full quantum theoretical
basis for the NFM-formalism.

categories: quant-ph hep-th math-ph math.MP physics.atom-ph


title:
Generation of entangled states and error protection from adiabatic
  avoided level crossings

abstract:
  We consider the environment-affected dynamics of $N$ self-interacting
particles living in one-dimensional double wells. Two topics are dealt with.
First, we consider the production of entangled states of two-level systems. We
show that by adiabatically varying the well biases we may dynamically generate
maximally entangled states, starting from initially unentangled product states.
Entanglement degradation due to a common type of environmental influence is
then computed by solving a master equation. However, we also demonstrate that
entanglement production is unaffected if the system-environment coupling is of
the type that induces ``motional narrowing''. As our second but related topic,
we construct a different master equation that seamlessly merges error
protection/detection dynamics for quantum information with the environmental
couplings responsible for producing the errors in the first place. Adiabatic
avoided crossing schemes are used in both topics.


title:
The unity between quantum field computation, real computation, and
  quantum computation

abstract:
  It is indicated that principal models of computation are indeed significantly
related. The quantum field computation model contains the quantum computation
model of Feynman. (The term "quantum field computer" was used by Freedman.)
Quantum field computation (as enhanced by Wightman's model of quantum field
theory) involves computation over the continuum which is remarkably related to
the real computation model of Smale. The latter model was established as a
generalization of Turing computation. All this is not surprising since it is
well known that the physics of quantum field theory (which includes Einstein's
special relativity) contains quantum mechanics which in turn contains classical
mechanics. The unity of these computing models, which seem to have grown
largely independently, could shed new light into questions of computational
complexity, into the central P (Polynomial time) versus NP (Non-deterministic
Polynomial time) problem of computer science, and also into the description of
Nature by fundamental physics theories.


title: ROM-based computation: quantum versus classical

abstract:
  We introduce a model of computation based on read only memory (ROM), which
allows us to compare the space-efficiency of reversible, error-free classical
computation with reversible, error-free quantum computation. We show that a
ROM-based quantum computer with one writable qubit is universal, whilst two
writable bits are required for a universal classical ROM-based computer. We
also comment on the time-efficiency advantages of quantum computation within
this model.


title:
Entanglement and Properties of Composite Quantum Systems: a Conceptual
  and Mathematical Analysis

abstract:
  Various topics concerning the entanglement of composite quantum systems are
considered with particular emphasis concerning the strict relations of such a
problem with the one of attributing objective properties to the constituents.
Most of the paper deals with composite systems in pure states. After a detailed
discussion and a precise formal analysis of the case of systems of
distinguishable particles, the problems of entanglement and the one of the
properties of subsystems of systems of identical particles are thourougly
discussed. This part is the most interesting and new and it focuses various
subtle questions which have never been adequately discussed in the literature.
Some inappropriate assertions which appeared in recent papers are analyzed. The
relations of the main subject of the paper with the nonlocal aspects of quantum
mechanics, as well as with the possibility of deriving Bell's inequality are
also considered.


title:
Squeezed light from microstructured fibres: towards free space quantum
  cryptography

abstract:
  Amplitude squeezed pulsed light has been produced using a microstructured
silica fibre. By spectrally filtering after the nonlinear propagation in the
fibre a squeezing value of -1.7dB has been measured. A quantum key distribution
scheme based on squeezed light from such microstructured fibres is proposed.


title:
Nonstationary Casimir effect in cavities with two resonantly coupled
  modes

abstract:
  We study the peculiarities of the nonstationary Casimir effect (creation of
photons in cavities with moving boundaries) in the special case of two
resonantly coupled modes with frequencies $\omega_0$ and $(3\Delta)\omega_0$,
parametrically excited due to small amplitude oscillations of the ideal cavity
wall at the frequency $2\omega_0(1\delta)$ (with $|\delta|,|\Delta|\ll 1$). The
effects of thermally induced oscillations in time dependences of the mean
numbers of created photons and the exchange of quantum purities between the
modes are discovered. Squeezing and photon distributions in each modes are
calculated for initial vacuum and thermal states. A possibility of compensation
of detunings is shown.


title: General Multimode Squeezed States

abstract:
  By the complex multimode Bogoliubov transformation, we obtain the general
forms of squeeze operators and squeezed states including squeezed vacuum
states, squeezed coherent states, squeezed Fock states and squeezed coherent
Fock states, for a general multimode boson system. We decompose the squeezed
operator into disentangling form in normal ordering to simplify the expressions
of the squeezed states. We also calculate the statistical properties of the SS.
Furthermore we prove that if it is non-degenerate, a Bogoliubov transformation
matrix can be decomposed into three basic matrix, by which we can not only
check the criterion of the minimum uncertainty state (MUS) found by Milburn,
but also prove that except the special cases, any multimode squeezed state is
MUS after the original creation and annihilation operators rotate properly. We
also discuss some special cases of the three basic matrices. Finally we give an
analytical results of a two-mode system as an example.


title:
Reducing Constraints on Quantum Computer Design by Encoded Selective
  Recoupling

abstract:
  The requirement of performing both single-qubit and two-qubit operations in
the implementation of universal quantum logic often leads to very demanding
constraints on quantum computer design. We show here how to eliminate the need
for single-qubit operations in a large subset of quantum computer proposals:
those governed by isotropic and XXZ,XY-type anisotropic exchange interactions.
Our method employs an encoding of one logical qubit into two physical qubits,
while logic operations are performed using an analogue of the NMR selective
recoupling method.


title: Probabilistic instantaneous quantum computation

abstract:
  The principle of teleportation can be used to perform a quantum computation
even before its quantum input is defined. The basic idea is to perform the
quantum computation at some earlier time with qubits which are part of an
entangled state. At a later time a generalized Bell state measurement is
performed jointly on the then defined actual input qubits and the rest of the
entangled state. This projects the output state onto the correct one with a
certain exponentially small probability. The sufficient conditions are found
under which the scheme is of benefit.


title: Atom Interferometers: Beyond Complementarity Principles

abstract:
  Complementarity lies at the heart of conceptual foundation of orthodox
quantum mechanics. The wave-particle duality makes it impossible to tell which
slit each particle passes through and still observe an interference pattern in
a Young's double-slit experiment. In this paper, this duality is appraised
under the standard formulation of quantum mechanics for atom interferometers.
It is found that the internal freedoms like electronic states of an atom can be
used to detect the which-path information of each atom while uphold the
interference pattern of atoms when the center-of-mass motion of atoms is
detected.


title:
Entanglement, quantum phase transitions, and density matrix
  renormalization

abstract:
  We investigate the role of entanglement in quantum phase transitions, and
show that the success of the density matrix renormalization group (DMRG) in
understanding such phase transitions is due to the way it preserves
entanglement under renormalization. We provide a reinterpretation of the DMRG
in terms of the language and tools of quantum information science which allows
us to rederive the DMRG in a physically transparent way. Motivated by our
reinterpretation we suggest a modification of the DMRG which manifestly takes
account of the entanglement in a quantum system. This modified renormalization
scheme is shown,in certain special cases, to preserve more entanglement in a
quantum system than traditional numerical renormalization methods.


title:
About Some Problems Raised by the Relativistic Form of De-Broglie--Bohm
  Theory of Pilot Wave

abstract:
  The standard relativistic de-Broglie--Bohm theory has the problems of
tacyonic solutions and the incorrect non-relativistic limit. In this paper we
obtain a relativistic theory, not decomposing the relativistic wave equations
but looking for a generalization of non-relativistic Bohmian theory in such a
way that the correct non-relativistic limit emerges. In this way we are able to
construct a relativistic de-Broglie--Bohm theory both for a single particle and
for a many-particle system. At the end, the theory is extended to the curved
space-time and the connection with quantum gravity is discussed.


title: The phase representation of covariant phase observables

abstract:
  Covariant phase observables are obtained by defining simple conditions for
mappings from the set of phase wave functions (unit vectors of the Hardy space)
to the set of phase probability densities. The existence of phase probability
density for any phase wave function, the existence of interference effects, and
the natural phase shift covariance are those simple conditions. The
nonlocalizability of covariant phase observables is proved.


title: A nonlocal classical perspective on quantum electrodynamics

abstract:
  The ideas behind the nonlocal classical statistical field theory model for
the quantized Klein-Gordon field introduced in Morgan(2001, quant-ph/0106141)
are extended to accommodate quantum electrodynamics. The anticommutation rules
for the quantized Dirac spinor field are given a classical interpretation as a
relativistically covariant modification of the minimal coupling interaction
between the classical electromagnetic field and a classical Dirac spinor field.


title:
Variable length universal entanglement concentration by local operations
  and its application to teleportation and dense coding

abstract:
  Using invariance of the $n$-th tensored state w.r.t. the $n$-th symmetric
group, we propose a 'variable length' universal entanglement concentration
without classical communication. Like variable length data compression,
arbitrary unknown states are concentrated into perfect Bell states and not
approximate Bell states and the number of Bell states obtained is equal to the
optimal rate asymptotically with the probability 1. One of the point of our
scheme is that we need no classical communication at all. Using this method, we
can construct a universal teleportation and a universal dense coding.


title:
Environmental Influence on the Measurement Process in Stochastic
  Reduction Models

abstract:
  We consider the energy-driven stochastic state vector reduction equation for
the density matrix, which for pure state density matrices can be written in two
equivalent forms. We use these forms to discuss the decoupling of the noise
terms for independent subsystems, and to construct ``environmental'' stochastic
density matrices whose time-independent expectations are the usual quantum
statistical distributions. We then consider a measurement apparatus weakly
coupled to an external environment, and show that in mean field (Hartree)
approximation the stochastic equation separates into independent equations for
the apparatus and environment, with the Hamiltonian for the apparatus augmented
by the environmental expectation of the interaction Hamiltonian. We use the
Hartree approximated equation to study a simple accretion model for the
interaction of the apparatus with its environment, as part of a more general
discussion of when the stochastic dynamics predicts state vector reduction, and
when it predicts the maintenance of coherence. We also discuss the magnitude of
decoherence effects acting during the reduction process. Our analysis supports
the suggestion that a measurement takes place when the different outcomes are
characterized by sufficiently distinct environmental interactions for the
reduction process to be rapidly driven to completion.


title: A quantum computer based on electrons floating on liquid helium

abstract:
  Electrons on a helium surface form a quasi two-dimensional system which
displays the highest mobility reached in condensed matter physics. We propose
to use this system as a set of interacting quantum bits. We will briefly
describe the system and discuss how the qubits can be addressed and
manipulated, including interqubit excitation transfer. The working frequency of
the proposed quantum computer is ~1GHz. The relaxation rate can be at least 5
orders of magnitude smaller, for low temperatures.


title:
Coherent Control of Magneto-optical Rotation in Inhomogeneously
  Broadened Medium

abstract:
  We extend our earlier investigations [Opt. Commun. {\bf 179}, 97 (2000)] on
the enhancement of magneto-optical rotation (MOR) to include inhomogeneous
broadening. We introduce a control field that counter-propagates with respect
to the probe field. We derive analytical results for the susceptibilities
corresponding to the two circular polarization components of the probe field.
  From the analytical results we identify and numerically demonstrate the
region of parameters where significantly large magneto-optical rotation (MOR)
can be obtained. From the numerical results we isolate the significance of the
magnetic field and the control field in enhancement of MOR. The control field
opens up many new regions of the frequencies of the probe where large
magneto-optical rotation occurs. We also report that a large enhancement of MOR
can be obtained by operating the probe and control field in two-photon
resonance condition.


title:
Improved Hamilton-Jacobi Quantization for Nonholonomic Constrained
  System

abstract:
  The nonholonomic constrained system with second-class constraints is
investigated using the Hamilton-Jacobi (HJ) quantization scheme to yield the
complete equations of motion of the system. Although the integrability
conditions in the HJ scheme are equivalent to the involutive relations for the
first-class constrained system in the improved Dirac quantization method (DQM),
one should elaborate the HJ scheme by using the improved DQM in order to obtain
the first-class Hamiltonian and the corresponding effective Lagrangian having
the BRST invariant nonholonomic constrained system.


title: Four qubits can be entangled in nine different ways

abstract:
  We consider a single copy of a pure four-partite state of qubits and
investigate its behaviour under the action of stochastic local quantum
operations assisted by classical communication (SLOCC). This leads to a
complete classification of all different classes of pure states of four-qubits.
It is shown that there exist nine families of states corresponding to nine
different ways of entangling four qubits. The states in the generic family give
rise to GHZ-like entanglement. The other ones contain essentially 2- or 3-qubit
entanglement distributed among the four parties. The concept of concurrence and
3-tangle is generalized to the case of mixed states of 4 qubits, giving rise to
a seven parameter family of entanglement monotones. Finally, the SLOCC
operations maximizing all these entanglement monotones are derived, yielding
the optimal single copy distillation protocol.


title: Nullification of the Nullification

abstract:
  A recent claim by Meyer, Kent and Clifton (MKC), that their models
``nullify'' the Kochen-Specker theorem, has attracted much comment. In this
paper we present a new counter-argument, based on the fact that a classical
measurement reveals, not simply a pre-existing value, but pre-existing
classical information. In the MKC models measurements do not generally reveal
pre-existing classical information. Consequently, the Kochen-Specker theorem is
not nullified. We go on to prove a generalized version of the Kochen-Specker
theorem, applying to non-ideal quantum measurements. The theorem was inspired
by the work of Simon et al and Larsson (SBZL). However, there is a loophole in
SBZL's argument, which means that their result is invalid (operational
non-contextuality is not inconsistent with the empirical predictions of quantum
mechanics). Our treatment resolves this difficulty. We conclude by discussing
the question, whether the MKC models can reproduce the empirical predictions of
quantum mechanics.


title: Quantum version of the Monty Hall problem

abstract:
  A version of the Monty Hall problem is presented where the players are
permitted to select quantum strategies. If the initial state involves no
entanglement the Nash equilibrium in the quantum game offers the players
nothing more than can be obtained with a classical mixed strategy. However, if
the initial state involves entanglement of the qubits of the two players, it is
advantageous for one player to have access to a quantum strategy while the
other does not. Where both players have access to quantum strategies there is
no Nash equilibrium in pure strategies, however, there is a Nash equilibrium in
quantum mixed strategies that gives the same average payoff as the classical
game.


title: A new application of non-canonical maps in quantum mechanics

abstract:
  A proof is given that an invertible and a unitary operator can be used to
reproduce the effect of a q-deformed commutator of annihilation and creation
operators. In other words, the original annihilation and creation operators are
mapped into new operators, not conjugate to each other, whose standard
commutator equals the identity plus a correction proportional to the original
number operator. The consistency condition for the existence of this new set of
operators is derived, by exploiting the Stone theorem on 1-parameter unitary
groups. The above scheme leads to modified equations of motion which do not
preserve the properties of the original first-order set for annihilation and
creation operators. Their relation with commutation relations is also studied.


title: From Spectral Relaxation to Quantified Decoherence

abstract:
  Quantum information processing (QIP) requires thorough assessment of
decoherence. Atoms or ions prepared for QIP often become addressed by radiation
within schemes of alternating microwave-optical double resonance. A
well-defined amount of decoherence may be applied to the system when spurious
resonance light is admitted simultaneously with the driving radiation. This
decoherence is quantified in terms of longitudinal and transversal relaxation.
It may serve for calibrating observed decoherence as well as for testing
error-correcting quantum codes.


title: On a Problem in Quantum Summation

abstract:
  We consider the computation of the mean of sequences in the quantum model of
computation. We determine the query complexity in the case of sequences which
satisfy a $p$-summability condition for $1\le p<2$. This settles a problem left
open in Heinrich (2001).


title: An all silicon quantum computer

abstract:
  A solid-state implementation of a quantum computer composed entirely of
silicon is proposed. Qubits are Si-29 nuclear spins arranged as chains in a
Si-28 (spin-0) matrix with Larmor frequencies separated by a large magnetic
field gradient. No impurity dopants or electrical contacts are needed.
Initialization is accomplished by optical pumping, algorithmic cooling, and
pseudo-pure state techniques. Magnetic resonance force microscopy is used for
readout. This proposal takes advantage of many of the successful aspects of
solution NMR quantum computation, including ensemble measurement, RF control,
and long decoherence times, but it allows for more qubits and improved
initialization.


title: Using entanglement improves precision of quantum measurements

abstract:
  We show how entanglement can be used to improve the estimation of an unknown
transformation. Using entanglement is always of benefit, in improving either
the precision or the stability of the measurement. Examples relevant for
applications are illustrated, for either qubits and continuous variables


title: How much state assignments can differ

abstract:
  We derive necessary and sufficient conditions for a group of density matrices
to characterize what different people may know about one and the same physical
system.


title:
Counterfactual Statements and Weak Measurements: an Experimental
  Proposal

abstract:
  A recent analysis [quant-ph/0104062] suggests that weak measurements can be
used to give observational meaning to counterfactual reasoning in quantum
physics. A weak measurement is predicted to assign a negative unit population
to a specific state in an interferometric Gedankenexperiment proposed by Hardy.
We propose an experimental implementation with trapped ions of the
Gedankenexperiment and of the weak measurement. In our standard quantum
mechanical analysis of the proposal no states have negative population, but we
identify the registration of a negative population by particles being displaced
on average in the direction opposite to a force acting upon them.


title: Dynamical Casimir effect without boundary conditions

abstract:
  The moving-mirror problem is microscopically formulated without invoking the
external boundary conditions. The moving mirrors are described by the quantized
matter field interacting with the photon field, forming dynamical cavity
polaritons: photons in the cavity are dressed by electrons in the moving
mirrors. The effective Hamiltonian for the polariton is derived, and
corrections to the results based on the external boundary conditions are
discussed.


title: Particle localization and the Notion of Einstein Causality

abstract:
  The notion of Einstein causality, i.e. the limiting role of the velocity of
light in the transmission of signals, is discussed. It is pointed out that
Nimtz and coworkers use the notion of signal velocity in a different sense from
Einstein and that their experimental results are in full agreement with
Einstein causality in its ordinary sense. We also show that under quite general
assumptions instantaneous spreading of particle localization occurs in quantum
theory, relativistic or not, with fields or without. We discuss if this affects
Einstein causality.


title: Impurity Scattering Induced Entanglement of Ballistic Electrons

abstract:
  We show how entanglement between two conduction electrons is generated in the
presence of a localized magnetic impurity embedded in an otherwise ballistic
conductor of special geometry. This process is a generalization of
beam-splitter mediated entanglement generation schemes with a localized spin
placed at the site of the beam splitter. Our entangling scheme is unconditional
and robust to randomness of the initial state of the impurity. The entangled
state generated manifests itself in noise reduction of spin-dependent currents.


title: Nonlinear Micromechanical Casimir Oscillator

abstract:
  The Casimir force between uncharged metallic surfaces originates from quantum
mechanical zero point fluctuations of the electromagnetic field. We demonstrate
that this quantum electrodynamical effect has a profound influence on the
oscillatory behavior of microstructures when surfaces are in close proximity
(<= 100 nm). Frequency shifts, hysteretic behavior and bistability caused by
the Casimir force are observed in the frequency response of a periodically
driven micromachined torsional oscillator.


title:
Efficient Classical Simulation of Continuous Variable Quantum
  Information Processes

abstract:
  We obtain sufficient conditions for the efficient simulation of a continuous
variable quantum algorithm or process on a classical computer. The resulting
theorem is an extension of the Gottesman-Knill theorem to continuous variable
quantum information. For a collection of harmonic oscillators, any quantum
process that begins with unentangled Gaussian states, performs only
transformations generated by Hamiltonians that are quadratic in the canonical
operators, and involves only measurements of canonical operators (including
finite losses) and suitable operations conditioned on these measurements can be
simulated efficiently on a classical computer.


title: Geometry of Quantum Theory: Weyl-Kahler Space

abstract:
  A new space namely the Weyl-Kahler is proposed to the quantum state space.
Some of the physical consequences are discussed.


title: Weak force detection with superposed coherent states

abstract:
  We investigate the utility of non classical states of simple harmonic
oscillators, particularly a superposition of coherent states, for sensitive
force detection. We find that like squeezed states a superposition of coherent
states allows displacement measurements at the Heisenberg limit. Entangling
many superpositions of coherent states offers a significant advantage over a
single mode superposition states with the same mean photon number.


title:
"Extrinsic" and "intrinsic" data in quantum measurements: asymptotic
  convex decomposition of positive operator valued measures

abstract:
  We study the problem of separating the data produced by a given quantum
measurement (on states from a memoryless source which is unknown except for its
average state), described by a positive operator valued measure (POVM), into a
"meaningful" (intrinsic) and a "not meaningful" (extrinsic) part. We are able
to give an asymptotically tight separation of this form, with the "intrinsic"
data quantfied by the Holevo mutual information of a certain state ensemble
associated to the POVM and the source, in a model that can be viewed as the
asymptotic version of the convex decomposition of POVMs into extremal ones.
This result is applied to a similar separation therorem for quantum instruments
and quantum operations, in their Kraus form. Finally we comment on links to
related subjects: we stress the difference between data and information (in
particular by pointing out that information typically is strictly less than
data), derive the Holevo bound from our main result, and look at its classical
case: we show that this includes the solution to the problem of
extrinsic/intrinsic data separation with a known source, then compare with the
well-known notion of sufficient statistics. The result on decomposition of
quantum operations is used to exhibit a new aspect of the concept of entropy
exchange of an open dynamics. An appendix collects several estimates for mixed
state fidelity and trace norm distance, that seem to be new, in particular a
construction of canonical purification of mixed states that turns out to be
valuable to analyze their fidelity.


title: A more efficient variant of the Oxford protocol

abstract:
  An alternative presentation of the Oxford purification protocol is obtained
by using dynamical variables. I suggest to introduce the degree of separability
as a purification parameter, where the purified state has a smaller degree of
separability than the initial one. An improved version of the Oxford protocol
is described, in which local unitary transformations optimize each step.


title: Entanglement induced by a single-mode heat environment

abstract:
  A thermal field, which frequently appears in problems of decoherence,
provides us with minimal information about the field. We study the interaction
of the thermal field and a quantum system composed of two qubits and find that
such a chaotic field with minimal information can nevertheless entangle the
qubits which are prepared initially in a separable state. This simple model of
a quantum register interacting with a noisy environment allows us to understand
how memory of the environment affects the state of a quantum register.


title: Comment on "Evolution of a Quasi-Stationary State"

abstract:
  Approximately forty years ago it was realized that the time development of
decaying systems might not be precisely exponential. Rolf Winter (Phys. Rev.
{\bf 123}, 1503 (1961)) analyzed the simplest nontrivial system - a particle
tunneling out of a well formed by a wall and a delta-function. He calculated
the probability current just outside the well and found irregular oscillations
on a short time scale followed by an exponential decrease followed by more
oscillations and finally by a decrease as a power of the time. We have
reanalyzed this system, concentrating on the survival probability of the
particle in the well rather than the probability current, and find a different
short time behavior.


title: Communication and measurement with squeezed states

abstract:
  The principles are elaborated which underlie the applications of general
nonclassical states to communication and measurement systems. Relevant
classical communication concepts are reviewed. Communication and measurement
processes are compared. The possible advantages of nonclassical states in
classical information transfer are assessed. The significance of novel quantum
amplifiers and duplicators in communication is emphasized. A general approach
is developed for determining the ultimate accuracy limit in quantum measurement
systems. It is found that bandwidth or mode number is a most important
parameter and ultrahigh precision measurement is possible in systems with a
fixed energy but many modes. The problem of the standard quantum limit in
monitoring the position of a free mass is also addressed.


title: How unconditionally secure quantum bit commitment is possible

abstract:
  Bit commitment involves the submission of evidence from one party to another
so that the evidence can be used to confirm a later revealed bit value by the
first party, while the second party cannot determine the bit value from the
evidence alone. It is widely believed that unconditionally secure quantum bit
commitment is impossible due to quantum entanglement cheating, which is
codified in a general impossibility theorem. In this paper, the scope of this
general impossibility proof is analyzed, and gaps are found. Two variants of a
bit commitment scheme utilizing anonymous quantum states and decoy states are
presented. In the first variant, the exact verifying measurement is independent
of the committed bit value, thus the second party can make it before the first
party opens, making possible an unconditional security proof based on
no-cloning. In the second variant, the impossibility proof fails because
quantum entanglement purification of a mixed state does not render the protocol
determinate. Whether impossibility holds in this or similar protocols is an
open question, although preliminary results already show that the impossibility
proof cannot work as it stands.


title: Quantum entanglement without eigenvalue spectra:multipartite case

abstract:
  We introduce algebriac sets in the products of complex projective spaces for
multipartite mixed states, which are independent of their eigenvalues and only
measure the "position" of their eigenvectors, as their non-local invariants
(ie. remaining invariant after local untary transformations). These invariants
are naturally arised from the physical consideration of checking multipartite
mixed states by measuring them with multipartite separable pure states. The
algebraic sets have to be the sum of linear subspaces if the multipartite mixed
state is separable, and thus we give a new separability criterion of
multipartite mixed states. A continuous family of 4-party mixed states, whose
members are separable for any 2:2 cut and entangled for any 1:3 cut (thus bound
entanglement if 4 parties are isolated), is constructed and studied from our
invariants and separability criterion. Examples of LOCC-incomparable entangled
tripartite pure states are given to show it is hopeless to characterize the
entanglement properties of tripartite pure states by only using the eigenvalue
speactra of their partial traces. We also prove that at least $n^2+n-1$ terms
of separable pure states, which are "orthogonal" in some sence, are needed to
write a generic pure state in $H_A^{n^2} \otimes H_B^{n^2} \otimes H_C^{n^2}$
as a linear combination of them.


title:
Nonclassical character of statistical mixtures of the single-photon and
  vacuum optical states

abstract:
  We demonstrate, theoretically and experimentally, that statistical mixtures
of the vacuum state |0> and the single-photon Fock state |1> are nonclassical
according to the Vogel criterion (W. Vogel, Phys. Rev. Lett. 84, 1849 (2000)),
regardless of the vacuum fraction. The ensembles are synthesized via
conditional measurements on biphotons generated by means of parametric
downconversion, and their quadrature statistics are measured using balanced
homodyne detection. A comparative review of various quantum state
nonclassicality criteria is presented.


title: Quantum collision states for positive charges in an octahedral cage

abstract:
  One-electron energy levels are studied for a configuration of two positive
charges inside an octahedral cage, the vertices of the cage being occupied by
atoms with a partially filled shell. Although ground states correspond to large
separations, there are relatively low-lying states with large collision
probabilities. Electromagnetic radiation fields used to excite the quantum
collisional levels may provide a means to control nuclear reactions. However,
given the scale of the excitation energies involved, this mechanism cannot
provide an explanation for the unexplained ``cold fusion'' events.


title: de Broglie's pilot wave theory for the Klein-Gordon equation

abstract:
  We illustrate, using a simple model, that in the usual formulation the
time-component of the Klein-Gordon current is not generally positive definite
even if one restricts allowed solutions to those with positive frequencies.
Since in de Broglie's theory of particle trajectories the particle follows the
current this leads to difficulties of interpretation, with the appearance of
trajectories which are closed loops in space-time and velocities not limited
from above. We show that at least this pathology can be avoided if one uses a
covariant extension of the canonical formulation of relativistic point particle
dynamics proposed by Gitman and Tyutin.


title: Quantum Operations, State Transformations and Probabilities

abstract:
  In quantum operations, probabilities characterise both the degree of the
success of a state transformation and, as density operator eigenvalues, the
degree of mixedness of the final state. We give a unified treatment of
pure-to-pure state transformations, covering both probabilistic and
deterministic cases. We then discuss the role of majorization in describing the
dynamics of mixing in quantum operations. The conditions for mixing enhancement
for all initial states are derived. We show that mixing is monotonically
decreasing for deterministic pure-to-pure transformations, and discuss the
relationship between these transformations and deterministic LOCC entanglement
transformations.


title: Spectral Structure of Quantum Line with a Defect

abstract:
  We study the spectral properties of one-dimensional quantum wire with a
single defect. We reveal the existence of the non-trivial topological
structures in the spectral space of the system, which are behind the exotic
quantum phenomena that have lately been found in the system.

categories: quant-ph cond-mat.mes-hall gr-qc hep-th math-ph math.MP


title: Transformations of q-boson and q-fermion algebras

abstract:
  We investigate the algebras satisfied by q-deformed boson and fermion
oscillators, in particular the transformations of the algebra from one form to
another. Based on a specific algebra proposed in recent literature, we show
that the algebra of deformed fermions can be transformed to that of undeformed
standard fermions. Furthermore we also show that the algebra of q-deformed
fermions can be transformed to that of undeformed standard bosons.


title:
Universal Simulation of Hamiltonians Using a Finite Set of Control
  Operations

abstract:
  Any quantum system with a non-trivial Hamiltonian is able to simulate any
other Hamiltonian evolution provided that a sufficiently large group of unitary
control operations is available. We show that there exist finite groups with
this property and present a sufficient condition in terms of group characters.
We give examples of such groups in dimension 2 and 3. Furthermore, we show that
it is possible to simulate an arbitrary bipartite interaction by a given one
using such groups acting locally on the subsystems.


title: Universal simulation of Hamiltonian dynamics for qudits

abstract:
  What interactions are sufficient to simulate arbitrary quantum dynamics in a
composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial
solution to this problem in the form of an efficient algorithm to simulate any
desired two-body Hamiltonian evolution using any fixed two-body entangling
N-qubit Hamiltonian, and local unitaries. We extend this result to the case
where the component systems have D dimensions. As a consequence we explain how
universal quantum computation can be performed with any fixed two-body
entangling N-qudit Hamiltonian, and local unitaries.


title: Fragility of Thermodynamically-Abnormal Ground States of Finite Systems

abstract:
  We study a general macroscopic quantum system of a finite size, which will
exhibit a symmetry breaking if the system size goes to infinity, when the
system interacts with an environment. We evaluate the decoherence rates of the
anomalously fluctuating vacuum (AFV), which is the symmetric ground state, and
the pure phase vacua (PPVs). By making full use of the locality and huge
degrees of freedom, we show that there can exist an interaction with an
environment which makes the decoherence rate of the AFV anomalously fast,
whereas PPVs are less fragile.


title: Quantum Encodings in Spin Systems and Harmonic Oscillators

abstract:
  We show that higher-dimensional versions of qubits, or qudits, can be encoded
into spin systems and into harmonic oscillators, yielding important advantages
for quantum computation. Whereas qubit-based quantum computation is adequate
for analyses of quantum vs classical computation, in practice qubits are often
realized in higher-dimensional systems by truncating all but two levels,
thereby reducing the size of the precious Hilbert space. We develop natural
qudit gates for universal quantum computation, and exploit the entire
accessible Hilbert space. Mathematically, we give representations of the
generalized Pauli group for qudits in coupled spin systems and harmonic
oscillators, and include analyses of the qubit and the infinite-dimensional
limits.


title:
Quasi-uniform approximation for the radial Schr\"odinger equation with
  power-law potentials

abstract:
  The uniformly valid approximation to solutions of the radial Schr\"odinger
equation with power-law potentials are obtained by means of the explicit
summation of the leading constituent WKB series.


title:
Improved Quantum Communication Complexity Bounds for Disjointness and
  Equality

abstract:
  We prove new bounds on the quantum communication complexity of the
disjointness and equality problems. For the case of exact and non-deterministic
protocols we show that these complexities are all equal to n+1, the previous
best lower bound being n/2. We show this by improving a general bound for
non-deterministic protocols of de Wolf. We also give an O(sqrt{n}c^{log^*
n})-qubit bounded-error protocol for disjointness, modifying and improving the
earlier O(sqrt{n}log n) protocol of Buhrman, Cleve, and Wigderson, and prove an
Omega(sqrt{n}) lower bound for a large class of protocols that includes the
BCW-protocol as well as our new protocol.


title: QED using the nilpotent formalism

abstract:
  The nilpotent formalism for the Dirac equation, outlined in previous
papers,is applied to QED. It is shown that what is usually described as
'renormalization' is effectively a statement of the fact that the nilpotent
formulation is automatically second quantized and constrains the field into
producing finite values for fundamental quantities.


title: On Quantum Versions of the Yao Principle

abstract:
  The classical Yao principle states that the complexity R_epsilon(f) of an
optimal randomized algorithm for a function f with success probability
1-epsilon equals the complexity max_mu D_epsilon^mu(f) of an optimal
deterministic algorithm for f that is correct on a fraction 1-epsilon of the
inputs, weighed according to the hardest distribution mu over the inputs. In
this paper we investigate to what extent such a principle holds for quantum
algorithms. We propose two natural candidate quantum Yao principles, a ``weak''
and a ``strong'' one. For both principles, we prove that the quantum
bounded-error complexity is a lower bound on the quantum analogues of max mu
D_epsilon^mu(f). We then prove that equality cannot be obtained for the
``strong'' version, by exhibiting an exponential gap. On the other hand, as a
positive result we prove that the ``weak'' version holds up to a constant
factor for the query complexity of all symmetric Boolean functions


title:
Quantum key distribution using non-classical photon number correlations
  in macroscopic light pulses

abstract:
  We propose a new scheme for quantum key distribution using macroscopic
non-classical pulses of light having of the order 10^6 photons per pulse.
Sub-shot-noise quantum correlation between the two polarization modes in a
pulse gives the necessary sensitivity to eavesdropping that ensures the
security of the protocol. We consider pulses of two-mode squeezed light
generated by a type-II seeded parametric amplification process. We analyze the
security of the system in terms of the effect of an eavesdropper on the bit
error rates for the legitimate parties in the key distribution system. We also
consider the effects of imperfect detectors and lossy channels on the security
of the scheme.


title: Tomography and spectroscopy as quantum computations

abstract:
  Determining the state of a system and measuring properties of its evolution
are two of the most important tasks a physicist faces. For the first purpose
one can use tomography, a method that after subjecting the system to a number
of experiments determines all independent elements of the density matrix. For
the second task, one can resort to spectroscopy, a set of techniques used to
determine the spectrum of eigenvalues of the evolution operator. In this
letter, we show that tomography and spectroscopy can be naturally interpreted
as dual forms of quantum computation. We show how to adapt the simplest case of
the well-known phase estimation quantum algorithm to perform both tasks, giving
it a natural interpretation as a simulated scattering experiment. We show how
this algorithm can be used to implement an interesting form of tomography by
performing a direct measurement of the Wigner function of a quantum system. We
present results of such measurements performed on a system of three qubits
using liquid state NMR quantum computation techniques in a sample of
trichloroethylene. Remarkable analogies with other experiments are discussed.


title: A Note on Invariants and Entanglements

abstract:
  The quantum entanglements are studied in terms of the invariants under local
unitary transformations. A generalized formula of concurrence for
$N$-dimensional quantum systems is presented. This generalized concurrence has
potential applications in studying separability and calculating entanglement of
formation for high dimensional mixed quantum states.


title: Generic Quantum Block Compression

abstract:
  A generic approach for compiling any classical block compression algorithm
into a quantum block compression algorithm is presented. Using this technique,
compression asymptoticaly approaching the von Neumann entropy of a qubit source
can be achieved. The automatically compiled algorithms are competitive (in time
and space complexity) with hand constructed quantum block compression
algorithms.


title:
Quantum, classical and semiclassical analyses of photon statistics in
  harmonic generation

abstract:
  In this review, we compare different descriptions of photon-number statistics
in harmonic generation processes within quantum, classical and semiclassical
approaches. First, we study the exact quantum evolution of the harmonic
generation by applying numerical methods including those of Hamiltonian
diagonalization and global characteristics. We show explicitly that the
harmonic generations can indeed serve as a source of nonclassical light. Then,
we demonstrate that the quasi-stationary sub-Poissonian light can be generated
in these quantum processes under conditions corresponding to the so-called
no-energy-transfer regime known in classical nonlinear optics. By applying
method of classical trajectories, we demonstrate that the analytical
predictions of the Fano factors are in good agreement with the quantum results.
On comparing second and higher harmonic generations in the no-energy-transfer
regime, we show that the highest noise reduction is achieved in third-harmonic
generation with the Fano-factor of the third harmonic equal to 13/16.


title: Implementing the quantum random walk

abstract:
  Recently, several groups have investigated quantum analogues of random walk
algorithms, both on a line and on a circle. It has been found that the quantum
versions have markedly different features to the classical versions. Namely,
the variance on the line, and the mixing time on the circle increase
quadratically faster in the quantum versions as compared to the classical
versions. Here, we propose a scheme to implement the quantum random walk on a
line and on a circle in an ion trap quantum computer. With current ion trap
technology, the number of steps that could be experimentally implemented will
be relatively small. However, we show how the enhanced features of these walks
could be observed experimentally. In the limit of strong decoherence, the
quantum random walk tends to the classical random walk. By measuring the degree
to which the walk remains `quantum', this algorithm could serve as an important
benchmarking protocol for ion trap quantum computers.


title: Efficient Quantum Computation using Coherent States

abstract:
  Universal quantum computation using optical coherent states is studied. A
teleportation scheme for a coherent-state qubit is developed and applied to
gate operations. This scheme is shown to be robust to detection inefficiency.


title: Qubits as Parafermions

abstract:
  Qubits are neither fermions nor bosons. A Fock space description of qubits
leads to a mapping from qubits to parafermions: particles with a hybrid
boson-fermion quantum statistics. We study this mapping in detail, and use it
to provide a classification of the algebras of operators acting on qubits.
These algebras in turn classify the universality of different classes of
physically relevant qubit-qubit interaction Hamiltonians. The mapping is
further used to elucidate the connections between qubits, bosons, and fermions.
These connections allow us to share universality results between the different
particle types. Finally, we use the mapping to study the quantum computational
power of certain anisotropic exchange Hamiltonians. In particular, we prove
that the XY model with nearest-neighbor interactions only is not
computationally universal. We also generalize previous results about universal
quantum computation with encoded qubits to codes with higher rates.


title: Qubit Channels Can Require More Than Two Inputs to Achieve Capacity

abstract:
  We give examples of qubit channels that require three input states in order
to achieve the Holevo capacity.