title: Generalization of the entanglement of formation for multi-party systems

abstract:
  We present the generalization of the entanglement of formation for
three-party systems in a pure state. For three qubit system we derive out its
explicit and closed expression which is a linear combination of the binary
entropy functions with various arguments, and these arguments are clearly
determined in terms of the components of state vector of three qubits. As a
reasonable measure of entanglement, the main behaviors and elementary
properties of this generalized entanglement of formation are showed through
discussing some important and interesting examples. Moreover, we propose how to
extend our definition to a mixed state in according to the familiar idea. Then,
we suggest the generalization of the entanglement of formation for multi-party
systems which is consistent with the regular definition for two-party systems
and our definition for three-party systems.


title: Absorption by cold Fermi atoms in a harmonic trap

abstract:
  We study the absorption spectrum for a strongly degenerate Fermi gas confined
in a harmonic trap. The spectrum is calculated using both the exact summation
and also the Thomas-Fermi (TF) approximation. In the latter case, relatively
simple analytical expressions are obtained for the absorption lineshape at
large number of trapped atoms. At zero temperature, the approximated lineshape
is characterized by a $(1-z^2)^{5/2}$ dependence which agrees well with the
exact numerical calculations. At non-zero temperature, the spectrum becomes
broader, although remains non-Gaussian as long as the fermion gas is
degenerate. The changes in the trap frequency for an electronically excited
atom can introduce an additional line broadening.


title: Hiding bits in Bell states

abstract:
  We present a scheme for hiding bits in Bell states that is secure even when
the sharers Alice and Bob are allowed to carry out local quantum operations and
classical communication. We prove that the information that Alice and Bob can
gain about a hidden bit is exponentially small in $n$, the number of qubits in
each share, and can be made arbitrarily small for hiding multiple bits. We
indicate an alternative efficient low-entanglement method for preparing the
shared quantum states. We discuss how our scheme can be implemented using
present-day quantum optics.


title:
Reply to the comment on `` Manipulating the frequency-entangled states
  by an acoustic-optical modulator''

abstract:
  In the paper [1], authors claim that the scheme for entanglement swapping
using an acoustic-optical modulator [2] is flaw. In this reply, we show there
is a trivial mistake in the scheme [2], but the main conclusion is still
correct, that is, the acoustic-optical modulator can be used to manipulate the
frequency-entangled state.


title:
Ptolemyness of conventional program for microcosm investigations and
  alternative research program

abstract:
  It is shown that the conventional approach to microcosm investigations uses
an incorrect supposition (incorrect space-time model) whose incorrectness is
compensated by means of additional hypotheses, known as quantum mechanics
principles. Such a conception reminds the Ptolemaic doctrine of celestial
mechanics. Alternative research program, which uses a more correct space-time
model and does not need additional hypotheses (quantum principles) for free
explanations of quantum effects, is suggested. If the more correct space-time
model were known in the beginning of XXth century, when research of microcosm
started, quantum mechanics could develop in other way. The alternative research
program appeared with a secular delay, because all this time the necessary
mathematical technique was not available for researchers. Absence of necessary
mathematical technique is connected with some prejudices which have been
overcame at the construction of new conception of geometry and that of
statistical description. Basic statements of the new mathematical technique and
principles of its application in alternative research program are presented in
the paper.


title: Quadrupole Contribution in Semiclassical Radiation Theory

abstract:
  Within the frame-work of semiclassical theory two-level approximation in
atomic system has been considered. Model proposed by M.D. Crisp and E.T. Jaynes
has been modified. It has been shown that the time-dependent frequency shift
depends on the higher multipole moments, retained in the Taylor expansion of
electromagnetic field.


title: Quantum Algorithmic Entropy

abstract:
  We extend algorithmic information theory to quantum mechanics, taking a
universal semicomputable density matrix (``universal probability'') as a
starting point, and define complexity (an operator) as its negative logarithm.
  A number of properties of Kolmogorov complexity extend naturally to the new
domain. Approximately, a quantum state is simple if it is within a small
distance from a low-dimensional subspace of low Kolmogorov complexity. The von
Neumann entropy of a computable density matrix is within an additive constant
from the average complexity. Some of the theory of randomness translates to the
new domain.
  We explore the relations of the new quantity to the quantum Kolmogorov
complexity defined by Vitanyi (we show that the latter is sometimes as large as
2n - 2log n and the qubit complexity defined by Berthiaume, Dam and Laplante.
The ``cloning'' properties of our complexity measure are similar to those of
qubit complexity.


title: Fidelity of a t-error correcting quantum code with more than t errors

abstract:
  It is important to study the behavior of a t-error correcting quantum code
when the number of errors is greater than t, because it is likely that there
are also small errors besides t large correctable errors. We give a lower bound
for the fidelity of a t-error correcting stabilizer code over a general
memoryless channel, allowing more than t errors. We also show that the fidelity
can be made arbitrary close to 1 by increasing the code length.


title:
Fejer average and the short term behaviors of a wave packet in infinite
  square well

abstract:
  The first two period behaviors of a quantum wave packet in an infinite square
well potential is studied. First, the short term behavior of expectation value
of a quantity on an equally weighted wave packet (EWWP) is in classical limit
proved to reproduce the Fej'{e}r average of the Fourier series decomposition of
the corresponding classical quantity. Second, in order to best mimic the
classical behavior, a nice relation between number $N$ of stationary states in
the EWWP with the average quantum number $n$ as $N\thickapprox \sqrt{n}$ is
revealed. Third, since the Fej\'{e}r average can only approximate the classical
quantity, it carries an uncertainty which in large quantum number case is
almost the same as the quantum uncertainty.


title: String Matching in ${\tilde O}(\sqrt{n}+\sqrt{m})$ Quantum Time

abstract:
  We show how to determine whether a given pattern p of length m occurs in a
given text t of length n in ${\tilde O}(\sqrt{n}+\sqrt{m})$\footnote{${\tilde
O}$ allows for logarithmic factors in m and $n/m$} time, with inverse
polynomial failure probability. This algorithm combines quantum searching
algorithms with a technique from parallel string matching, called {\em
Deterministic Sampling}.


title: Optimal Creation of Entanglement Using a Two--Qubit Gate

abstract:
  We consider a general unitary operator acting on two qubits in a product
state. We find the conditions such that the state of the qubits after the
action is as entangled as possible. We also consider the possibility of using
ancilla qubits to increase the entanglement.


title: Quantum Computation with Ballistic Electrons

abstract:
  We describe a solid state implementation of a quantum computer using
ballistic single electrons as flying qubits in 1D nanowires. We show how to
implement all the steps required for universal quantum computation: preparation
of the initial state, measurement of the final state and a universal set of
quantum gates. An important advantage of this model is the fact that we do not
need ultrafast optoelectronics for gate operations. We use cold programming (or
pre-programming), i.e., the gates are set before launching the electrons; all
programming can be done using static electric fields only.


title: Quantum Finite State Transducers

abstract:
  We introduce quantum finite state transducers (qfst), and study the class of
relations which they compute. It turns out that they share many features with
probabilistic finite state transducers, especially regarding undecidability of
emptiness (at least for low probability of success). However, like their
`little brothers', the quantum finite automata, the power of qfst is
incomparable to that of their probabilistic counterpart. This we show by
discussing a number of characteristic examples.


title: On the fidelity of two pure states

abstract:
  The fidelity of two pure states (also known as transition probability) is a
symmetric function of two operators, and well-founded operationally as an event
probability in a certain preparation-test pair. Motivated by the idea that the
fidelity is the continuous quantum extension of the combinatorial equality
function, we enquire whether there exists a symmetric operational way of
obtaining the fidelity. It is shown that this is impossible. Finally, we
discuss the optimal universal approximation by a quantum operation.


title: Effect of symmetry breaking on level curvature distributions

abstract:
  We derive an exact general formalism that expresses the eigenvector and the
eigenvalue dynamics as a set of coupled equations of motion in terms of the
matrix elements dynamics. Combined with an appropriate model Hamiltonian, these
equations are used to investigate the effect of the presence of a discrete
symmetry in the level curvature distribution. An explanation of the unexpected
behavior of the data regarding frequencies of acoustic vibrations of quartz
block is provided.


title: NMR implementation of a building block for scalable quantum computation

abstract:
  We report the implementation of the central building block of the
Schulman-Vazirani procedure for fully polarizing a subset of two-level quantum
systems which are initially only partially polarized. This procedure consists
of a sequence of unitary operations and incurs only a quasi-linear overhead in
the number of quantum systems and operations required. The key building block
involves three quantum systems and was implemented on a homonuclear three-spin
system using room temperature liquid state nuclear magnetic resonance (NMR)
techniques. This work was inspired by the state initialization challenges in
current NMR quantum computers but also shines new light on polarization
transfer in NMR.


title:
Efficient Quantum Key Distribution Scheme And Proof of Its Unconditional
  Security

abstract:
  We devise a simple modification that essentially doubles the efficiency of
the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We
also prove the security of our modified scheme against the most general
eavesdropping attack that is allowed by the laws of physics. The first major
ingredient of our scheme is the assignment of significantly different
probabilities to the different polarization bases during both transmission and
reception, thus reducing the fraction of discarded data.
  A second major ingredient of our scheme is a refined analysis of accepted
data: We divide the accepted data into various subsets according to the basis
employed and estimate an error rate for each subset *separately*.
  We then show that such a refined data analysis guarantees the security of our
scheme against the most general eavesdropping strategy, thus generalizing
  Shor and Preskill's proof of security of BB84 to our new scheme. Up till now,
most proposed proofs of security of single-particle type quantum key
distribution schemes have relied heavily upon the fact that the bases are
chosen uniformly, randomly and independently. Our proof removes this symmetry
requirement.


title: Optimal phase estimation and square root measurement

abstract:
  We present an optimal strategy having finite outcomes for estimating a single
parameter of the displacement operator on an arbitrary finite dimensional
system using a finite number of identical samples. Assuming the uniform {\it a
priori} distribution for the displacement parameter, an optimal strategy can be
constructed by making the {\it square root measurement} based on uniformly
distributed sample points. This type of measurement automatically ensures the
global maximality of the figure of merit, that is, the so called average score
or fidelity. Quantum circuit implementations for the optimal strategies are
provided in the case of a two dimensional system.


title: Creating Bell states and decoherence effects in quantum dots system

abstract:
  We show how to improve the efficiency for preparing Bell states in coupled
two quantum dots system. A measurement to the state of driven quantum laser
field leads to wave function collapse. This results in highly efficiency
preparation of Bell states. The effect of decoherence on the efficiency of
generating Bell states is also discussed in this paper. The results show that
the decoherence does not affect the relative weight of $|00>$ and $|11>$ in the
output state, but the efficiency of finding Bell states.


title:
Quantum-mechanical tunneling: differential operators, zeta-functions and
  determinants

abstract:
  We consider in detail the quantum-mechanical problem associated with the
motion of a one-dimensional particle under the action of the double-well
potential. Our main tool will be the euclidean (imaginary time) version of the
path-integral method. Once we perform the Wick rotation, the euclidean equation
of motion is the same as the usual one for the point particle in real time,
except that the potential at issue is turned upside down. In doing so, our
double-well potential becomes a two-humped potential. As required by the
semiclassical approximation we may study the quadratic fluctuations over the
instanton which represents in this context the localised finite-action
solutions of the euclidean equation of motion. The determinants of the
quadratic differential operators are evaluated by means of the zeta-function
method. We write in closed form the eigenfunctions as well as the energy
eigenvalues corresponding to such operators by using the shape-invariance
symmetry. The effect of the multi-instantons configurations is also included in
this approach.


title: New optimal tests of quantum nonlocality

abstract:
  We explore correlation polytopes to derive a set of all Boole-Bell type
conditions of possible classical experience which are both maximal and
complete. These are compared with the respective quantum expressions for the
Greenberger-Horne-Zeilinger (GHZ) case and for two particles with spin state
measurements along three directions.


title: The spinor equation for the electromagnetic field

abstract:
  We develop a spinor equation of the electromagnetic field, which is
equivalent to the Maxwell equation and has a similar form as the Dirac
equation. The spinor is the very conjugate momentum of the vector potential in
the Lagrangian mechanics. In this framework the electromagnetic field described
by the spinor exhibits the SU(2) internal symmetry. The quantization and the
problem of longinal and scalar photons are disscussed.


title: Symmetries and solutions of the three-dimensional Paul trap

abstract:
  Using the symmetries of the three-dimensional Paul trap, we derive the
solutions of the time-dependent Schr\"odinger equation for this system, in both
Cartesian and cylindrical coordinates. Our symmetry calculations provide
insights that are not always obvious from the conventional viewpoint.


title:
On the units of bipartite entanglement: Is sixteen ounces of
  entanglement always equal to one pound?

abstract:
  In a good physical theory dimensionless quantities such as the ratio m_p /
m_e of the mass of the proton to the mass of the electron do not depend on the
system of units being used. This paper demonstrates that one widely used method
for defining measures of entanglement violates this principle. Specifically, in
this approach dimensionless ratios E(rho) / E(sigma) of entanglement measures
may depend on what state is chosen as the basic unit of entanglement. This
observation leads us to suggest three novel approaches to the quantification of
entanglement. These approaches lead to unit-free definitions for the
entanglement of formation and the distillable entanglement, and suggest natural
measures of entanglement for multipartite systems. We also show that the
behaviour of one of these novel measures, the entanglement of computation, is
related to some open problems in computational complexity.


title: Introduction to quantum information theory

abstract:
  This is an expanded and revised text for a fifteen minute talk given at the
University of Queensland Physics Camp, September 2000. The focus is on the
goals and motivations for studying quantum information theory, rather than on
technical results.


title: Sharp Quantum vs. Classical Query Complexity Separations

abstract:
  We obtain the strongest separation between quantum and classical query
complexity known to date -- specifically, we define a black-box problem that
requires exponentially many queries in the classical bounded-error case, but
can be solved exactly in the quantum case with a single query (and a polynomial
number of auxiliary operations). The problem is simple to define and the
quantum algorithm solving it is also simple when described in terms of certain
quantum Fourier transforms (QFTs) that have natural properties with respect to
the algebraic structures of finite fields. These QFTs may be of independent
interest, and we also investigate generalizations of them to noncommutative
finite rings.


title:
Separable approximations of density matrices of composite quantum
  systems

abstract:
  We investigate optimal separable approximations (decompositions) of states
rho of bipartite quantum systems A and B of arbitrary dimensions MxN following
the lines of Ref. [M. Lewenstein and A. Sanpera, Phys. Rev. Lett. 80, 2261
(1998)]. Such approximations allow to represent in an optimal way any density
operator as a sum of a separable state and an entangled state of a certain
form. For two qubit systems (M=N=2) the best separable approximation has a form
of a mixture of a separable state and a projector onto a pure entangled state.
We formulate a necessary condition that the pure state in the best separable
approximation is not maximally entangled. We demonstrate that the weight of the
entangled state in the best separable approximation in arbitrary dimensions
provides a good entanglement measure. We prove in general for arbitrary M and N
that the best separable approximation corresponds to a mixture of a separable
and an entangled state which are both unique. We develop also a theory of
optimal separable approximations for states with positive partial transpose
(PPT states). Such approximations allow to decompose any density operator with
positive partial transpose as a sum of a separable state and an entangled PPT
state. We discuss procedures of constructing such decompositions.


title: Efficient Quantum Algorithms for Shifted Quadratic Character Problems

abstract:
  We introduce the Shifted Legendre Symbol Problem and some variants along with
efficient quantum algorithms to solve them. The problems and their algorithms
are different from previous work on quantum computation in that they do not
appear to fit into the framework of the Hidden Subgroup Problem. The classical
complexity of the problem is unknown despite the various results on the
irregularity of Legendre Sequences.


title: Information-Theoretic Description of No-go Theorem of a Bit Commitment

abstract:
  We give a comprehensive and constructive proof of the no-go theorem of a bit
commitment given by Mayers, Lo, and Chau from the viewpoint of quantum
information theory. It is shown that there is a trade-off relation between
information acquired by Bob during the commitment phase and the ability to
change a commit bit by Alice during the opening phase. It is clarified that a
protocol that is unbiased to both Alice and Bob cannot be, at the same time,
secure against both parties. Fundamental physical constraints that govern this
no-go theorem are also discussed.


title: Quantum channel locally interacting with environment

abstract:
  The quantum channel subject to local interaction with two-level environment
is studied. The two-level environment is regarded as a quantum bit (qubit) as
well as a pair of particles owned by Alice and Bob. The amount of entanglement
initially shared by Alice and Bob is distributed among these three qubits due
to the interaction. In this model, we show that the singlet fraction of the
decohered quantum channel is uniquely determined by the distributed
entanglement. When the decohered quantum channel is used under the standard
teleportation scheme, the optimal teleportation fidelity is well understood by
considering the remaining entanglement between environment and transmitted
state.


title: The Bargmann representation for the quantum mechanics on a sphere

abstract:
  The Bargmann representation is constructed corresponding to the coherent
states for a particle on a sphere introduced in: K. Kowalski and J.
Rembielinski, J. Phys. A: Math. Gen. 33, 6035 (2000). The connection is
discussed between the introduced formalism and the standard approach based on
the Hilbert space of square integrable functions on a sphere S^2.


title: Quantum Chaos and the Black Body Radiation

abstract:
  We discuss a mechanical model which mimics the main features of the radiation
matter interaction in the black body problem. The pure classical dynamical
evolution, with a simple discretization of the action variables, leads to the
Stefan- Boltzmann law and to the Planck distribution without any additional
statistical assumption.


title:
On the reversible extraction of classical information from a quantum
  source

abstract:
  Consider a source E of pure quantum states with von Neumann entropy S. By the
quantum source coding theorem, arbitrarily long strings of signals may be
encoded asymptotically into S qubits/signal (the Schumacher limit) in such a
way that entire strings may be recovered with arbitrarily high fidelity.
Suppose that classical storage is free while quantum storage is expensive and
suppose that the states of E do not fall into two or more orthogonal subspaces.
We show that if E can be compressed with arbitrarily high fidelity into A
qubits/signal plus any amount of auxiliary classical storage then A must still
be at least as large as the Schumacher limit S of E. Thus no part of the
quantum information content of E can be faithfully replaced by classical
information. If the states do fall into orthogonal subspaces then A may be less
than S, but only by an amount not exceeding the amount of classical information
specifying the subspace for a signal from the source.


title: Quantum Cloning and Distributed Measurements

abstract:
  We study measurements on various subsystems of the output of a universal 1 to
2 cloning machine, and establish a correspondence between these measurements at
the output and effective measurements on the original input. We show that one
can implement sharp effective measurement elements by measuring only two out of
the three output systems. Additionally, certain complete sets of sharp
measurements on the input can be realised by measurements on the two clones.
Furthermore, we introduce a scheme that allows to restore the original input in
one of the output bits, by using measurements and classical communication -- a
protocol that resembles teleportation.


title:
Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum
  trajectory treatment

abstract:
  Quantum feedback can stabilize a two-level atom against decoherence
(spontaneous emission), putting it into an arbitrary (specified) pure state.
This requires perfect homodyne detection of the atomic emission, and
instantaneous feedback. Inefficient detection was considered previously by two
of us. Here we allow for a non-zero delay time $\tau$ in the feedback circuit.
Because a two-level atom is a nonlinear optical system, an analytical solution
is not possible. However, quantum trajectories allow a simple numerical
simulation of the resulting non-Markovian process. We find the effect of the
time delay to be qualitatively similar to that of inefficient detection. The
solution of the non-Markovian quantum trajectory will not remain fixed, so that
the time-averaged state will be mixed, not pure. In the case where one tries to
stabilize the atom in the excited state, an approximate analytical solution to
the quantum trajectory is possible. The result, that the purity ($P=2{\rm
Tr}[\rho^{2}]-1$) of the average state is given by $P=1-4\gamma\tau$ (where
$\gamma$ is the spontaneous emission rate) is found to agree very well with the
numerical results.


title: Entangled-State Lithography: Tailoring any Pattern with a Single State

abstract:
  We demonstrate a systematic approach to Heisenberg-limited lithographic image
formation using four-mode reciprocal binominal states. By controlling the
exposure pattern with a simple bank of birefringent plates, any pixel pattern
on a $(N+1) \times (N+1)$ grid, occupying a square with the side half a
wavelength long, can be generated from a $2 N$-photon state.


title:
Extended covariance under nonlinear canonical transformation in Weyl
  quantization

abstract:
  A theory of nonunitary-invertible as well as unitary canonical
transformations is formulated in the context of Weyl's phase space
representations. Exact solutions of the transformation kernels and the phase
space propagators are given for the three fundamental canonical maps as
fractional-linear, gauge and contact (point) transformations. Under the
nonlinear maps a phase space representation is mapped to another phase space
representation thereby extending the standard concept of covariance. This
extended covariance allows Dirac-Jordan transformation theory to naturally
emerge from the Hilbert space representations in the Weyl quantization.

categories: quant-ph cond-mat.stat-mech hep-th math-ph math.MP nlin.CD nlin.SI physics.optics


title: Zeno and anti-Zeno effects for photon polarization dephasing

abstract:
  We discuss a simple, experimentally feasible scheme, which elucidates the
principles of controlling ("engineering") the reservoir spectrum and the
spectral broadening incurred by repeated measurements. This control can yield
either the inhibition (Zeno effect) or the acceleration (anti-Zeno effect) of
the quasi-exponential decay of the observed state by means of frequent
measurements. In the discussed scheme, a photon is bouncing back and forth
between two perfect mirrors, each time passing a polarization rotator. The
horizontal and vertical polarizations can be viewed as analogs of an excited
and a ground state of a two level system (TLS). A polarization beam splitter
and an absorber for the vertically polarized photon are inserted between the
mirrors, and effect measurements of the polarization. The polarization angle
acquired in the electrooptic polarization rotator can fluctuate randomly, e.g.,
via noisy modulation. In the absence of an absorber the polarization
randomization corresponds to TLS decay into an infinite-temperature reservoir.
The non-Markovian nature of the decay stems from the many round-trips required
for the randomization. We consider the influence of the polarization
measurements by the absorber on this non-Markovian decay, and develop a theory
of the Zeno and anti-Zeno effects in this system.


title: Quantum Strategy Without Entanglement

abstract:
  In this paper we quantize the Card Game. In the classical version of this
game, one player (Alice) can always win with propability 2/3. But when the
other player (Bob) is allowed to apply quantum strategy, the original unfair
game turns into a fair and zero-sum game. Further more, the procedure in which
Bob perform his quantum strategy does not include any ingredient of
entanglement.


title:
Competition-induced shifts of spectral peaks in photon coincidence
  spectroscopy

abstract:
  We show that shifts in locations of two-photon coincidence spectral peaks,
for a bichromatically-driven two-level atom passing through a single-mode
cavity, are due to competition between excitation pathways for a
Jaynes-Cummings system. We also discuss an analogous shift of (single-photon)
spectral peaks for a driven three-level V-system, which demonstrates that
competition between excitation pathways is also important in this simple
system.


title: Quantum Computation with Harmonic Oscillators

abstract:
  By encoding a qudit in a harmonic oscillator and investigating the infinite
limit, we give an entirely new realization of continuous-variable quantum
computation. The generalized Pauli group is generated by number and phase
operators for harmonic oscillators. We describe a physical realization in terms
of modes in a microwave cavity, coupled via a standard Kerr nonlinearity.


title:
Multiparticle Quantum Superposition and Stimulated Entanglement by
  Parity Selective Amplification of Entangled States

abstract:
  A multiparticle quantum superposition state has been generated by a novel
phase-selective parametric amplifier of an entangled two-photon state. This
realization is expected to open a new field of investigations on the
persistence of the validity of the standard quantum theory for systems of
increasing complexity, in a quasi decoherence-free environment. Because of its
nonlocal structure the new system is expected to play a relevant role in the
modern endeavor on quantum information and in the basic physics of
entanglement.


title: Diese verdammte quantenspringerei

abstract:
  It is argued that the conventional formulation of quantum mechanics is
inadequate: the usual interpretation of the mathematical formalism in terms of
the results of measurements cannot be applied to situations in which
discontinuous transitions ("quantum jumps) are observed as they happen, since
nothing that can be called a measurement happens at the moment of observation.
Attempts to force such observations into the standard mould lead to absurd
results: "a watched pot never boils". Experiments show both that this result is
correct when the experiment does indeed consist of a series of measurements,
and that it is not when the experiment consists of a period of observation:
quantum jumps do happen. The possibilities for improving the formalism by
incorporating transitions in the basic postulates are reviewed, and a
satisfactory postulate is obtained by modifying a suggestion of Bell's. This
requires a distinction between the external description of the whole of a
physical system and internal descriptions which are themselves physical events
in the system. It is shown that this gives correct results for simple unstable
systems and for the quantum-jump experiments.


title: Teleportation: from probability distributions to quantum states

abstract:
  The role of the off-diagonal density matrix elements of the entangled pair is
investigated in quantum teleportation of a qbit. The dependence between them
and the off-diagonal elements of the teleported density matrix is shown to be
linear. In this way the ideal quantum teleportation is related to an entirely
classical communication protocol: the one-time pad cypher. The latter can be
regarded as the classical counterpart of Bennett's quantum teleportation
scheme. The quantum-to-classical transition is demonstrated on the statistics
of a gedankenexperiment.


title: Why am I me? and why is my world so classical?

abstract:
  This is an attempt to apply Nagel's distinction between internal and external
statements to the interpretation of quantum mechanics. I propose that this
distinction resolves the contradiction between unitary evolution and the
projection postulate. I also propose a more empirically realistic version of
the projection postulate. The result is a version of Everett's relative-state
interpretation, including a proposal for how probabilities are to be
understood.
  Based on a talk given at the 9th UK Foundations of Physics meeting in
Birmingham on 12 September 2000.


title: Quantum Rate-Distortion Theory for I.I.D. Sources

abstract:
  We formulate quantum rate-distortion theory in the most general setting where
classical side information is included in the tradeoff. Using a natural
distortion measure based on entanglement fidelity and specializing to the case
of an unrestricted classical side channel, we find the exact quantum
rate-distortion function for a source of isotropic qubits. An upper bound we
believe to be exact is found in the case of biased sources. We establish that
in this scenario optimal rate-distortion codes produce no entropy exchange with
the environment of any individual qubit.


title: The Observer in the Quantum Experiment

abstract:
  A goal of most interpretations of quantum mechanics is to avoid the apparent
intrusion of the observer into the measurement process. Such intrusion is
usually seen to arise because observation somehow selects a single actuality
from among the many possibilities represented by the wavefunction. The issue is
typically treated in terms of the mathematical formulation of the quantum
theory. We attempt to address a different manifestation of the quantum
measurement problem in a theory-neutral manner. With a version of the two-slit
experiment, we demonstrate that an enigma arises directly from the results of
experiments. Assuming that no observable physical phenomena exist beyond those
predicted by the theory, we argue that no interpretation of the quantum theory
can avoid a measurement problem involving the observer.


title: Decoherence of a Pointer by a Gas Reservoir

abstract:
  We study the effect of the environment on the process of the measurement of a
state of a microscopic spin half system. The measuring apparatus is a heavy
particle, whose center of mass coordinates can be considered at the end of the
measurement as approximately classical, and thus can be used as a pointer. The
state of the pointer, which is the result of its interaction with the spin, is
transformed into a mixed state by the coupling of the pointer to the
environment. The environment is considered to be a gas reservoir, whose
particles interact with the pointer. This results in a Fokker-Planck equation
for the reduced density matrix of the pointer. The solution of the equation
shows that the quantum coherences, which are characteristic to the entangled
state between the probabilities to find the pointer in one of two positions,
decays exponentially fast in time. We calculate the exponential decay function
of this decoherence effect, and express it in terms of the parameters of the
model.


title:
Quantum interferometric optical lithography:towards arbitrary
  two-dimensional patterns

abstract:
  As demonstrated by Boto et al. [Phys. Rev. Lett. 85, 2733 (2000)], quantum
lithography offers an increase in resolution below the diffraction limit. Here,
we generalize this procedure in order to create patterns in one and two
dimensions. This renders quantum lithography a potentially useful tool in
nanotechnology.


title: A New Class of PT-symmetric Hamiltonians with Real Spectra

abstract:
  We investigate complex PT-symmetric potentials, associated with quasi-exactly
solvable non-hermitian models involving polynomials and a class of rational
functions. We also look for special solutions of intertwining relations of SUSY
Quantum Mechanics providing a partnership between a real and a complex
PT-symmetric potential of the kind mentioned above. We investigate conditions
sufficient to ensure the reality of the full spectrum or, for the quasi-exactly
solvable systems, the reality of the energy of the finite number of levels.


title:
Schr\"{o}dinger cat state of trapped ions in harmonic and anharmonic
  oscillator traps

abstract:
  We examine the time evolution of a two level ion interacting with a light
field in harmonic oscillator trap and in a trap with anharmonicities. The
anharmonicities of the trap are quantified in terms of the deformation
parameter $\tau $ characterizing the q-analog of the harmonic oscillator trap.
Initially the ion is prepared in a Schr\"{o}dinger cat state. The entanglement
of the center of mass motional states and the internal degrees of freedom of
the ion results in characteristic collapse and revival pattern. We calculate
numerically the population inversion I(t), quasi-probabilities $Q(t),$ and
partial mutual quantum entropy S(P), for the system as a function of time.
Interestingly, small deformations of the trap enhance the contrast between
population inversion collapse and revival peaks as compared to the zero
deformation case. For \beta =3 and $4,(% \beta $ determines the average number
of trap quanta linked to center of mass motion) the best collapse and revival
sequence is obtained for \tau =0.0047 and \tau =0.004 respectively. For large
values of \tau decoherence sets in accompanied by loss of amplitude of
population inversion and for \tau \sim 0.1 the collapse and revival phenomenon
disappear. Each collapse or revival of population inversion is characterized by
a peak in S(P) versus t plot. During the transition from collapse to revival
and vice-versa we have minimum mutual entropy value that is S(P)=0. Successive
revival peaks show a lowering of the local maximum point indicating a
dissipative irreversible change in the ionic state. Improved definition of
collapse and revival pattern as the anharminicity of the trapping potential
increases is also reflected in the Quasi- probability versus t plots.


title:
Bounds on the generalized entanglement of formation for multi-party
  systems

abstract:
  We present a general method to find the upper and lower bounds on the
generalized entanglement of formation for multi-party systems. The upper and
lower bounds can be expressed in terms of the bi-partite entanglements of
formation and/or entropies of various subsystems. The examples for tri- and
four-party systems in the both pure states and mixed states are given. We also
suggest a little modified definition of generalized entanglement of formation
for multi-party systems if EPR pairs are thought of belonging to the set of
maximally entangled states.


title:
Selecting molecules in the vibrational and rotational ground state by
  deflection

abstract:
  A beam of diatomic molecules scattered off a standing wave laser mode splits
according to the rovibrational quantum state of the molecules. Our numerical
calculation shows that single state resolution can be achieved by properly
tuned, monochromatic light. The proposed scheme allows for selecting
non-vibrating and non-rotating molecules from a thermal beam, implementing a
laser Maxwell's demon to prepare a rovibrationally cold molecular ensemble.


title: Quantum Jacobi fields in Hamiltonian mechanics

abstract:
  Jacobi fields of classical solutions of a Hamiltonian mechanical system are
quantized in the framework of vertical-extended Hamiltonian formalism. Quantum
Jacobi fields characterize quantum transitions between classical solutions.


title:
Experimental Test of Complementarity by Nuclear Magnetic Resonance
  Techniques

abstract:
  We have tested complementarity for the ensemble-averaged spin states of
nuclei $^{13}$C in the molecule of $^{13}$CHCl$_{3}$ by the use of the spin
states of another nuclei $^{1}$H as the path marker. It turns out that the
wave-particle duality holds when one merely measures the probability density of
quantum states, and that the wave- and particle-like behavior is simultaneously
observed with the help of measuring populations and coherence in a single
nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and
causes of the appearance and disappearance of the wave behavior are analysed.


title: On the LOCC Classification of Bipartite Density Matrices

abstract:
  We provide a unifying framework for exact, probabilistic, and approximate
conversions by local operations and classical communication (LOCC) between
bipartite states. This framework allows us to formulate necessary and
sufficient conditions for LOCC conversions from pure states to mixed states and
it provides necessary conditions for LOCC conversions between mixed states. The
central idea is the introduction of convex sets for exact, probabilistic, and
approximate conversions, which are closed under LOCC operations and which are
largely characterized by simple properties of pure states.


title:
su(2) and su(1,1) displaced number states and their nonclassical
  properties

abstract:
  We study su(2) and su(1,1) displaced number states. Those states are
eigenstates of density-dependent interaction systems of quantized radiation
field with classical current. Those states are intermediate states
interpolating between number and displaced number states. Their photon number
distribution, statistical and squeezing properties are studied in detail. It is
show that these states exhibit strong nonclassical properties.


title: Stochastic description for open quantum systems

abstract:
  A linear open quantum system consisting of a harmonic oscillator linearly
coupled to an infinite set of independent harmonic oscillators is considered;
these oscillators have a general spectral density function and are initially in
a Gaussian state. Using the influence functional formalism a formal Langevin
equation can be introduced to describe the system's fully quantum properties
even beyond the semiclassical regime. It is shown that the reduced Wigner
function for the system is exactly the formal distribution function resulting
from averaging both over the initial conditions and the stochastic source of
the formal Langevin equation. The master equation for the reduced density
matrix is then obtained in the same way a Fokker-Planck equation can always be
derived from a Langevin equation characterizing a stochastic process. We also
show that a subclass of quantum correlation functions for the system can be
deduced within the stochastic description provided by the Langevin equation. It
is emphasized that when the system is not Markovian more information can be
extracted from the Langevin equation than from the master equation.

categories: quant-ph cond-mat.stat-mech gr-qc hep-ph


title: Giant Radiative Interactions Among Distant Atoms

abstract:
  We examine the feasibility of enhancing the fundamental radiative
interactions between distant atoms. We present general arguments for producing
enhancement. In particular, we show how giant dipole-dipole interaction can be
produced by considering dipoles placed close to micron sized silica spheres.
The giant interaction arises as the whispering gallery modes can resonantly
couple the dipoles.


title: On the level spacing distribution in quantum graphs

abstract:
  We derive a formula for the level spacing probability distribution in quantum
graphs. We apply it to simple examples and we discuss its relation with
previous work and its possible application in more general cases. Moreover, we
derive an exact and explicit formula for the level spacing distribution of
integrable quantum graphs.


title: Slow-light pulses in moving media

abstract:
  Slow light in moving media reaches a paradoxical regime when the flow speed
of the medium approaches the group velocity of light. Pulses can penetrate a
region where a counter-propagating flow exceeds the group velocity. When the
counter-flow slows down pulses are reflected.


title: Schrodinger's Cataplex

abstract:
  We discuss elementary entwiners that cross-weave the variables of certain
integrable models: Liouville, sine-Gordon, and sinh-Gordon field theories in
two-dimensional spacetime, and their quantum mechanical reductions. First we
define a complex time parameter that varies from one energy-shell to another.
Then we explain how field propagators can be simply expressed in terms of
elementary functions through the combination of an evolution in this complex
time and a duality transformation.


title: Tunable whispering gallery modes for spectroscopy and CQED experiments

abstract:
  We have tuned the whispering gallery modes of a fused silica micro- resonator
over nearly 1 nm at 800 nm, i.e.over half of a free spectral range or the
equivalent of 10^6 linewidths of the resonator.This has been achieved by a new
method based on the stretching of a two-stem microsphere.The devices described
below will permit new Cavity-QED experiments with this ultra high .nesse
optical resonator when it is desirable to optimise its coupling to emitters
with given transition frequencies. The tuning capability demonstrated is
compatible with both UHV and low temperature operation which should be useful
for future experiments with laser cooled atoms or single quantum dots.A general
overview of the current state of the art in microspheres is given as well as a
more general introduction.


title:
Approximate Decoherence of Histories and 't Hooft's Deterministic
  Quantum Theory

abstract:
  This paper explores the possibility that an exactly decoherent set of
histories may be constructed from an approximately decoherent set by small
distortions of the operators characterizing the histories. In particular, for
the case of histories of positions and momenta, this is achieved by doubling
the set of operators and then finding, amongst this enlarged set, new position
and momentum operators which commute, so decohere exactly, and which are
``close'' to the original operators. The enlarged, exactly decoherent, theory
has the same classical dynamics as the original one, and coincides with the
so-called deterministic quantum theories of the type recently studied by 't
Hooft. These results suggest that the comparison of standard and deterministic
quantum theories may provide an alternative method of characterizing emergent
classicality. A side-product is the surprising result that histories of momenta
in the quantum Brownian motion model (for the free particle in the
high-temperature limit) are exactly decoherent.


title:
On the mystery of quantum probabilistic rule: trigonometric and
  hyperbolic probabilistic behaviours

abstract:
  We demonstrate the quantum probabilistic rule (which differ from classical
Bayes' formula by the cosinus factor) can be obtained on purely classical basis
as a consequence of the perturbation effect of preparation procedures. In any
case the interference can be easily simulated for macrosystems. Moreover, we
obtain the classification of all possible transformations of probablities which
can arise via perturbation effects. There are two main transformation classes:
with trigonometric and hyperbolic ("interference") perturbations of classical
Bayes' formula. Quantum probabilistic rule is just a particular case of
trigonometric probablistic behaviour. Hyperbolic probablistic behaviour can be
easily simulated. However, the question of its observation for "real physical
phenomena" is open.


title:
Dynamical diffraction in sinusoidal potentials: uniform approximations
  for Mathieu functions

abstract:
  Eigenvalues and eigenfunctions of Mathieu's equation are found in the short
wavelength limit using a uniform approximation (method of comparison with a
`known' equation having the same classical turning point structure) applied in
Fourier space. The uniform approximation used here relies upon the fact that by
passing into Fourier space the Mathieu equation can be mapped onto the simpler
problem of a double well potential. The resulting eigenfunctions (Bloch waves),
which are uniformly valid for all angles, are then used to describe the
semiclassical scattering of waves by potentials varying sinusoidally in one
direction. In such situations, for instance in the diffraction of atoms by
gratings made of light, it is common to make the Raman-Nath approximation which
ignores the motion of the atoms inside the grating. When using the
eigenfunctions no such approximation is made so that the dynamical diffraction
regime (long interaction time) can be explored.


title: On 1-qubit channels

abstract:
  The entropy H_T(rho) of a state rho with respect to a channel T and the
Holevo capacity of the channel require the solution of difficult variational
problems. For a class of 1-qubit channels, which contains all the extremal
ones, the problem can be significantly simplified by associating an Hermitian
antilinear operator theta to every channel of the considered class. The
concurrence of the channel can be expressed by theta and turns out to be a flat
roof. This allows to write down an explicit expression for H_T. Its maximum
would give the Holevo (1-shot) capacity.


title: Loading of a Bose-Einstein condensate in the boson-accumulation regime

abstract:
  We study the optical loading of a trapped Bose-Einstein condensate by
spontaneous emission of atoms in excited electronic state in the
Boson-Accumulation Regime. We generalize the previous simplified analysis of
ref. [Phys. Rev. A 53, 2466 (1996)], to a 3D case in which more than one trap
level of the excited state trap is considered. By solving the corresponding
quantum many-body master equation, we demonstrate that also for this general
situation the photon reabsorption can help to increase the condensate fraction.
Such effect could be employed to realize a continuous atom laser, and to
overcome condensate losses.


title:
Local Realistic Theories and Quantum Mechanics for the two-neutral-kaon
  system

abstract:
  The predictions of local realistic theories for the observables concerning
the evolution of a $K^0\bar{K}^0$ quantum entangled pair (created in the decay
of the $\phi$-meson) are discussed. It is shown, in agreement with Bell's
theorem, that the most general local hidden-variable model fails in reproducing
the whole set of quantum-mechanical joint probabilities. We achieve these
conclusion by employing two different approaches. In a first one the local
realistic observables are deduced from the most general premises concerning
locality and realism, and Bell-like inequalities are not employed. The other
approach makes use of Bell's inequalities. Within the former scheme, under
particular conditions for the detection times, the discrepancy between quantum
mechanics and local realism for the time-dependent asymmetry turns out to be
not less than 20%. The same incompatibility can be made evident by means of a
Bell-type test by employing both Wigner's and (once properly normalized
probabilities are used) Clauser-Holt-Shimony-Holt's inequalities. Because of
the relatively low experimental accuracy, the data obtained by the CPLEAR
collaboration for the asymmetry parameter do not allow for a decisive test of
local realism. Such a test, both with and without the use of Bell's
inequalities, should be feasible in the future at the Frascati $\Phi$-factory.


title: An Exponentially Fast Quantum Search Algorithm

abstract: This paper has been withdrawn by the authors.


title: Maximally entangled mixed states of two qubits

abstract:
  We consider mixed states of two qubits and show under which global unitary
operations their entanglement is maximized. This leads to a class of states
that is a generalization of the Bell states. Three measures of entanglement are
considered: entanglement of formation, negativity and relative entropy of
entanglement. Surprisingly all states that maximize one measure also maximize
the others. We will give a complete characterization of these generalized Bell
states and prove that these states for fixed eigenvalues are all equivalent
under local unitary transformations. We will furthermore characterize all
nearly entangled states closest to the maximally mixed state and derive a new
lower bound on the volume of separable mixed states.


title: Local filtering operations on two qubits

abstract:
  We consider one single copy of a mixed state of two qubits and investigate
how its entanglement changes under local quantum operations and classical
communications (LQCC) of the type $\rho'\sim (A\otimes B)\rho(A\otimes
B)^{\dagger}$. We consider a real matrix parameterization of the set of density
matrices and show that these LQCC operations correspond to left and right
multiplication by a Lorentz matrix, followed by normalization. A constructive
way of bringing this matrix into a normal form is derived. This allows us to
calculate explicitly the optimal local filterin operations for concentrating
entanglement. Furthermore we give a complete characterization of the mixed
states that can be purified arbitrary close to a Bell state. Finally we obtain
a new way of calculating the entanglement of formation.


title:
Generation of coherent superposition of Fock states in a cavity.
  Entanglement of atomic coherent states

abstract:
  A scheme for preparation of coherent superposition of Fock states of
electromagnetic field is constructed. The superposition state is created inside
the cavity via a strong interaction of a four-level atom with quantum field of
the cavity and classic laser fields. We demonstrate the possibility to create
desired arbitrary superposition of the cavity Fock states just by changing the
relative delay of the fields. Then, as another application of our model, we
study a means of creating entanglement of neutral four-level atoms using
different sequences of interactions with the cavity and laser fields.


title: Continuous loading of a magnetic trap

abstract:
  We have realized a scheme for continuous loading of a magnetic trap (MT).
^{52}Cr atoms are continuously captured and cooled in a magneto-optical trap
(MOT). Optical pumping to a metastable state decouples atoms from the cooling
light. Due to their high magnetic moment (6 Bohr magnetons), low-field seeking
metastable atoms are trapped in the magnetic quadrupole field provided by the
MOT. Limited by inelastic collisions between atoms in the MOT and in the MT, we
load 10^8 metastable atoms at a rate of 10^8 atoms/s below 100 microkelvin into
the MT. After loading we can perform optical repumping to realize a MT of
ground state chromium atoms.


title: Multi-Dimensional Hermite Polynomials in Quantum Optics

abstract:
  We study a class of optical circuits with vacuum input states consisting of
Gaussian sources without coherent displacements such as down-converters and
squeezers, together with detectors and passive interferometry (beam-splitters,
polarisation rotations, phase-shifters etc.). We show that the outgoing state
leaving the optical circuit can be expressed in terms of so-called
multi-dimensional Hermite polynomials and give their recursion and
orthogonality relations. We show how quantum teleportation of photon
polarisation can be modelled using this description.


title: Generalizing the Heisenberg uncertainty relation

abstract:
  The proof of the Heisenberg uncertainty relation is modified to produce two
improvements: (a) the resulting inequality is stronger because it includes the
covariance between the two observables, and (b) the proof lifts certain
restrictions on the state to which the relation is applied, increasing its
generality. The restrictions necessary for the standard inequality to apply are
not widely known, and they are discussed in detail. The classical analog of the
Heisenberg relation is also derived, and the two are compared. Finally, the
modified relation is used to address the apparent paradox that eigenfunctions
of the z component of angular momentum L_z do not satisfy the \phi-L_z
Heisenberg relation; the resolution is that the restrictions mentioned above
make the usual inequality inapplicable to these states. The modified relation
does apply, however, and it is shown to be consistent with explicit
calculations.


title:
The Relaxation Method for Solving the Schrodinger Equation in
  Configuration Space with the Coulomb and Linear Potentials

abstract:
  The non-relativistic Schrodinger equation with the linear and Coulomb
potentials is solved numerically in configuration space using the relaxation
method. The numerical method presented in this paper is a plain explicit
Schrodinger solver which is conceptually simple and is suitable for advanced
undergraduate research.


title: Separable states are more disordered globally than locally

abstract:
  A remarkable feature of quantum entanglement is that an entangled state of
two parties, Alice (A) and Bob (B), may be more disordered locally than
globally. That is, S(A) > S(A,B), where S(.) is the von Neumann entropy. It is
known that satisfaction of this inequality implies that a state is
non-separable. In this paper we prove the stronger result that for separable
states the vector of eigenvalues of the density matrix of system AB is
majorized by the vector of eigenvalues of the density matrix of system A alone.
This gives a strong sense in which a separable state is more disordered
globally than locally and a new necessary condition for separability of
bipartite states in arbitrary dimensions. We also investigate the extent to
which these conditions are sufficient to characterize separability, exhibiting
examples that show separability cannot be characterized solely in terms of the
local and global spectra of a state. We apply our conditions to give a simple
proof that non-separable states exist sufficiently close to the completely
mixed state of $n$ qudits.


title: Searching with Quantum Computers

abstract:
  This article introduces quantum computation by analogy with probabilistic
computation. A basic description of the quantum search algorithm is given by
representing the algorithm as a C program in a novel way.


title: On the Qualitative Theory of Non-Gamov Decay States

abstract:
  Complex potential transformations which add imaginary parts to chosen energy
levels are given and qualitatively explained. Unexpected shape similarity of
potential perturbations for real and imaginary E-shifts of bound states are
exhibited. The imaginary E-shifts in the continuous spectrum lead to a
surprising quasi-periodic field raking up initial propagating waves into
localized states. Complex periodic potentials without lacunas (!) are
constructed. The fission of quasi-bound states when neighbour complex
eigenvalues approach one another is demonstrated. E-shift algorithms represent
wide classes of exactly solvable quantum models for non-self-adjoint operators.


title: Berry's phase for compact Lie groups

abstract:
  The Lie group adiabatic evolution determined by a Lie algebra parameter
dependent Hamiltonian is considered. It is demonstrated that in the case when
the parameter space of the Hamiltonian is a homogeneous K\"ahler manifold its
fundamental K\"ahler potentials completely determine Berry geometrical phase
factor. Explicit expressions for Berry vector potentials (Berry connections)
and Berry curvatures are obtained using the complex parametrization of the
Hamiltonian parameter space. A general approach is exemplified by the Lie
algebra Hamiltonians corresponding to SU(2) and SU(3) evolution groups.


title:
A geometrical approach to non-adiabatic transitions in quantum theory:
  applications to NMR, over-barrier reflection and parametric excitation of
  quantum oscillator

abstract:
  This article deals with non-adiabatic processes (i.e. processes excluded by
the adiabatic theorem) from the geometrical (group-theoretical) point of view.
An approximated formula for the probabilities of the non-adiabatic transitions
is derived in the adiabatic regime for the case when the parameter-dependent
Hamiltonian represents a smooth curve in the Lie algebra and the quantal
dynamics is determined by the corresponding Lie group evolution operator. We
treat the spin precession in a time-dependent magnetic field and the
over-barrier reflection problem in a uniform way using the first-order
dynamical equations on SU(2) and $SU(1.1)$ group manifolds correspondingly.
  A comparison with analytic solutions for simple solvable models is provided.


title: Algorithmic Theories of Everything

abstract:
  The probability distribution P from which the history of our universe is
sampled represents a theory of everything or TOE. We assume P is formally
describable. Since most (uncountably many) distributions are not, this imposes
a strong inductive bias. We show that P(x) is small for any universe x lacking
a short description, and study the spectrum of TOEs spanned by two Ps, one
reflecting the most compact constructive descriptions, the other the fastest
way of computing everything. The former derives from generalizations of
traditional computability, Solomonoff's algorithmic probability, Kolmogorov
complexity, and objects more random than Chaitin's Omega, the latter from
Levin's universal search and a natural resource-oriented postulate: the
cumulative prior probability of all x incomputable within time t by this
optimal algorithm should be 1/t. Between both Ps we find a universal
cumulatively enumerable measure that dominates traditional enumerable measures;
any such CEM must assign low probability to any universe lacking a short
enumerating program. We derive P-specific consequences for evolving observers,
inductive reasoning, quantum physics, philosophy, and the expected duration of
our universe.

categories: quant-ph cs.AI cs.CC cs.LG hep-th math-ph math.MP physics.comp-ph


title: Frequently Asked Questions about Decoherence

abstract:
  We give a short, critical review of the issue of decoherence. We establish
the most general framework in which decoherence can be discussed, how it can be
quantified and how it can be measured. We focus on environment induced
decoherence and its degree of usefulness for the interpretation of quantum
theory. We finally discuss the emergence of a classical world. An overall
emphasis is given in pointing at common fallacies and misconceptions.


title:
Teleportation of entangled states and dense coding using a multiparticle
  quantum channel

abstract:
  A set of protocols for teleportation and dense coding tasks with the use of a
N particle quantum channel, presented by entangled states of the GHZ class, is
introduced, when N>2. Using a found representation for the multiparticle
entangled states of the GHZ class, it has shown, that for dense coding schemes
enhancement of the classical capacity of the channel due from entanglement is
N/N-1. If N>2 there is no one - to -one correspondence between teleportation
and dense coding schemes in comparison with the EPR channel is exploited. A set
of schemes, for which two additional operations as entanglement and
disentanglement are permitted, is considered.


title: Stochastic Reduction in Nonlinear Quantum Mechanics

abstract:
  Stochastic extensions of the Schrodinger equation have attracted attention
recently as plausible models for state reduction in quantum mechanics. Here we
formulate a general approach to stochastic Schrodinger dynamics in the case of
a nonlinear state space of the type proposed by Kibble. We derive a number of
new identities for observables in the nonlinear theory, and establish general
criteria on the curvature of the state space sufficient to ensure collapse of
the wave function.


title:
Quantum versus Classical Domains for Teleportation with Continuous
  Variables

abstract:
  Fidelity F{classical} = 1/2 has been established as setting the boundary
between classical and quantum domains in the teleportation of coherent states
of the electromagnetic field (S. L. Braunstein, C. A. Fuchs, and H. J. Kimble,
J. Mod. Opt. 47, 267 (2000)). Two recent papers by P. Grangier and F. Grosshans
(quant-ph/0009079 and quant-ph/0010107) introduce alternate criteria for
setting this boundary and as a result claim that the appropriate boundary
should be F = 2/3. Although larger fidelities would lead to enhanced
teleportation capabilities, we show that the new conditions of Grangier and
Grosshans are largely unrelated to the questions of entanglement and
Bell-inequality violations that they take to be their primary concern. With
regard to the quantum-classical boundary, we demonstrate that fidelity
F{classical} = 1/2 remains the appropriate point of demarcation. The claims of
Grangier and Grosshans to the contrary are simply wrong, as we show by an
analysis of the conditions for nonseparability (that complements our earlier
treatment) and by explicit examples of Bell-inequality violations.


title: Perturbative corrections to photon coincidence spectroscopy

abstract:
  Photon coincidence spectroscopy is a promising technique for probing the
nonlinear regime of cavity quantum electrodynamics in the optical domain,
however its accuracy is mitigated by two factors: higher-order photon
correlations, which contribute to an enhanced pair count rate, and
non-simultaneity of emitted photon pairs from the optical cavity. We show that
the technique of photon coincidence spectroscopy is effective in the presence
of these effects if the quantitative predictions are adjusted to include
non-simultaneity and higher-order correlations.


title: Entangled Quantum Clocks for Measuring Proper-Time Difference

abstract:
  We report that entangled pairs of quantum clocks (non-degenerate quantum
bits) can be used as a specialized detector for precisely measuring difference
of proper-times that each constituent quantum clock experiences. We describe
why the proposed scheme would be more precise in the measurement of proper-time
difference than a scheme of two-separate-quantum-clocks. We consider
possibilities that the proposed scheme can be used in precision test of the
relativity theory.


title: Singular potentials and absorption problem in Quantum Mechanics

abstract:
  We discuss a possible approach to the absorption problem in Quantum Mechanics
based on using of singular attractive potentials in the corresponding
Schr\"{o}dinger equations. Possible criteria for selection of exact solutions
of these equations are considered and it is shown that different models of
absorption can be realized by a special choice of exact solutions. As an
example, the motion of charged particles in the Aharonov-Bohm (AB) and the
scalar attractive $\rho^{-2}$ potentials is investigated in detail. Other
attractive potentials are briefly considered.


title:
Nuclear magnetic resonance spectrum of 31P donors in silicon quantum
  computer

abstract:
  The influence of the electric field created by a gate potential of the
silicon quantum computer on the hyperfine interaction constant (HIC) is
obtained. The errors due to technological inaccuracy of location of donor atoms
under a gate are evaluated. The energy spectra of electron-nuclear spin system
of two interacting donor atoms with various values of HIC are calculated. The
presence of two pairs of anticrossing levels in the ground electronic state is
shown. Parameters of the structure at which errors rate can be greatly
minimized are found.


title: Optimal encoding and decoding of a spin direction

abstract:
  For a system of N spins 1/2 there are quantum states that can encode a
direction in an intrinsic way. Information on this direction can later be
decoded by means of a quantum measurement. We present here the optimal encoding
and decoding procedure using the fidelity as a figure of merit. We compute the
maximal fidelity and prove that it is directly related to the largest zeroes of
the Legendre and Jacobi polynomials. We show that this maximal fidelity
approaches unity quadratically in 1/N. We also discuss this result in terms of
the dimension of the encoding Hilbert space.


title: Levels of Reality as Source of Quantum Indeterminacy

abstract:
  We show that the notion of "levels of Reality" introduced by Werner
Heisenberg in his "Manuscript of 1942" (1984) and by myself (1983-1985) could
explain the quantum indeterminacy. General epistemological implications of this
notion are also studied.


title: Mechanical analogy for the wave-particle: helix on a vortex filament

abstract:
  The small amplitude-to-thread ratio helical configuration of a vortex
filament in the ideal fluid behaves exactly as de Broglie wave. The
complex-valued algebra of quantum mechanics finds a simple mechanical
interpretation in terms of differential geometry of the space curve. The wave
function takes the meaning of the velocity with which the helix rotates about
the screw axis. The helices differ in type of the screw - right or left-handed.
Two kinds of the helical waves deflect in the inhomogeneous fluid vorticity
field in the same way as spin particles in the Stern-Gerlach experiment.

categories: quant-ph nlin.PS physics.ed-ph physics.flu-dyn


title: Noncommutative tori and universal sets of non-binary quantum gates

abstract:
  A problem of universality in simulation of evolution of quantum system and in
theory of quantum computations is related with the possibility of expression or
approximation of arbitrary unitary transformation by composition of specific
unitary transformations (quantum gates) from given set. In an earlier paper
(quant-ph/0010071) application of Clifford algebras to constructions of
universal sets of binary quantum gates $U_k \in U(2^n)$ was shown. For
application of a similar approach to non-binary quantum gates $U_k \in U(l^n)$
in present work is used rational noncommutative torus ${\Bbb T}^{2n}_{1/l}$. A
set of universal non-binary two-gates is presented here as one example.


title: Bell's Theorem and Locality in Space

abstract:
  Bell's theorem states that some quantum correlations can not be represented
by classical correlations of separated random variables. It has been
interpreted as incompatibility of the requirement of locality with quantum
mechanics. We point out that in fact the space part of the wave function was
neglected in the proof of Bell's theorem. However this space part is crucial
for considerations of property of locality of quantum system. Actually the
space part leads to an extra factor in quantum correlations and as a result the
ordinary proof of Bell's theorem fails in this case. We present a criterium of
locality in a realist theory of hidden variables. It is argued that predictions
of quantum mechanics for Gaussian wave functions can be consistent with Bell's
inequalities and hence Einstein's local realism is restored in this case.

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


title: Symmetries, Quantum Geometry, and the Fundamental Interactions

abstract:
  A generalized Noether's theorem and the operational determination of a
physical geometry in quantum physics are used to motivate a quantum geometry
consisting of relations between quantum states that are defined by a universal
group. Making these relations dynamical implies the non local effect of the
fundamental interactions on the wave function, as in the Aharonov-Bohm effect
and its generalizations to non Abelian gauge fields and gravity. The usual
space-time geometry is obtained as the classical limit of this quantum geometry
using the quantum state space metric.


title:
Efficacy of non-locality theorems "without inequalities" for pairs of
  spin 1/2 particles

abstract:
  We prove that recent theorems of non-locality without inequalities are not
effective, for systems of two spacelike separated 2-level sub-systems, in
proving non-locality of any empirically valid theory sharing a set of
correlations with quantum theory.


title:
A Unified Treatment for XXX-Heisenberg Model and Haldane-Shastry Model
  Using Shift Operators

abstract:
  A unified treatment is developed for the XXX-Heisenberg model and a
long-ranged interaction model (the $H_2$ in Haldane-Shastry model) from the
point of view of shift operators (or raising and lowering operators), based on
which the energy spectra of the spin-chain models are determined. Some physical
discussions are also made.


title:
Quantum dynamical theory for squeezing the output of a Bose-Einstein
  condensate

abstract:
  A linear quantum dynamical theory for squeezing the output of the trapped
Bose-Einstein condensate is presented with the Bogoliubov approximation. We
observe that the non-classical properties, such as sub-Poisson distribution and
quadrature squeezing effect, mutually oscillate between the quantum states of
the applied optical field and the resulting atom laser beam with time. In
particular, it is shown that an initially squeezed optical field will lead to
squeezing in the outcoupled atomic beam at later times.


title: Optimal estimation of quantum dynamics

abstract:
  We construct the optimal strategy for the estimation of an unknown unitary
transformation $U\in SU(d)$. This includes, in addition to a convenient
measurement on a probe system, finding which is the best initial state on which
$U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to
estimate simultaneously both the direction and the strength of a magnetic
field, and shows how to use a spin 1/2 particle to transmit information about a
whole coordinate system instead of only a direction in space.


title:
Complete parameterization, and invariance, of diffusive quantum
  trajectories for Markovian open systems

abstract:
  The state matrix $\rho$ for an open quantum system with Markovian evolution
obeys a master equation. The master equation evolution can be unraveled into
stochastic nonlinear trajectories for a pure state $P$, such that on average
$P$ reproduces $\rho$. Here we give for the first time a complete
parameterization of all diffusive unravelings (in which $P$ evolves
continuously but non-differentiably in time). We give an explicit measurement
theory interpretation for these quantum trajectories, in terms of monitoring
the system's environment. We also introduce new classes of diffusive
unravelings that are invariant under the linear operator transformations under
which the master equation is invariant. We illustrate these invariant
unravelings by numerical simulations. Finally, we discuss generalized gauge
transformations as a method of connecting apparently disparate descriptions of
the same trajectories by stochastic Schr\"odinger equations, and their
invariance properties.


title: Time and Information

abstract:
  The relationship between 'information' and 'time' is explored in order to
look for a 'solution' to the 'Problem of Time'. 'Time' is found to be the
result of the conversion of energy into 'information'. The 'time' number or
label we assign to 'events' can be manufactured by processing information
'flowing' from a Feynman Clock (FC), via a 'signal', to a Feynman Detector (FD)
in causal networks. Macroscopic arrows of time are built from the irreversible
Quantum Arrow of Time (QAT) associated with unstable or excited states of
quantum systems. The QAT is shown to be connected to the thermodynamic arrow of
time. Collective Excitations, and causal networks provide a means for
understanding 'time' in complex systems. The ordered set of the 'time' numbers
labeling 'events' can be used to construct the 'direction' and 'dimension'
associated with the usual conception of a 'time' axis or 'time' coordinate in
quantum, classical and realtivistic mechanics.


title: Coherence-Preserving Quantum Bits

abstract:
  Real quantum systems couple to their environment and lose their intrinsic
quantum nature through the process known as decoherence. Here we present a
method for minimizing decoherence by making it energetically unfavorable. We
present a Hamiltonian made up solely of two-body interactions between four
two-level systems (qubits) which has a two-fold degenerate ground state. This
degenerate ground state has the property that any decoherence process acting on
an individual physical qubit must supply energy from the bath to the system.
Quantum information can be encoded into the degeneracy of the ground state and
such coherence-preserving qubits will then be robust to local decoherence at
low bath temperatures. We show how this quantum information can be universally
manipulated and indicate how this approach may be applied to a quantum dot
quantum computer.


title: Control of a Coupled Two Spin System Without Hard Pulses

abstract:
  Constructive methods for controlling a coupled, two spin system via bounded
amplitude, piecewise sinusoidal fields are provided. The fields are incident at
the alrmor frequencies and take one of two phase values


title: Phase Conjugation of Continuous Quantum Variables

abstract:
  The phase conjugation of an unknown Gaussian state cannot be realized
perfectly by any physical process. A semi-classical argument is used to derive
a tight lower bound on the noise that must be introduced by an approximate
phase conjugation operation. A universal transformation achieving the optimal
imperfect phase conjugation is then presented, which is the continuous
counterpart of the universal-NOT transformation for quantum bits. As a
consequence, it is also shown that more information can be encoded into a pair
of conjugate Gaussian states than using twice the same state.


title: Speakable and unspeakable after John Bell

abstract:
  `Philosophy' was speakable for John Bell but is not for many physicists. The
border between philosophy and physics is here illustrated through Brownian
motion and Bell experiments. `Measurement', however, was unspeakable for Bell.
His insistence that the physics of quantum measurement should not be confined
to the laboratory and that physics is concerned with the big world outside
leads us to examples from zoology, meteorology and cosmology.


title:
Distilling a Greenberger-Horne-Zeilinger State From an Arbitrary Pure
  State of Three Qubits

abstract:
  We present a general algorithm to achieve local operators which can produce
the GHZ state for an arbitrary given three-qubit state. Thus the distillation
process of the state can be realized optimally. The algorithm is shown to be
sufficient for the three-qubit state on account of the fact that any state for
which this distillation algorithm is invalid cannot be distilled to the GHZ
state by any local actions. Moreover, an analytical result of distillation
operations is achieved for the general state of three qubits.


title: Non-perturbative solution of nonlinear Heisenberg equations

abstract:
  A new non-perturbative method of solution of the nonlinear Heisenberg
equations in the finite-dimensional subspace is illustrated. The method, being
a counterpart of the traditional Schrodinger picture method, is based on a
finite operator expansion into the elementary processes. It provides us with
the insight into the nonlinear quantal interaction from the different point of
view. Thus one can investigate the nonlinear system in both pictures of quantum
mechanics.


title: A general computer program for the Bell detection loophole

abstract:
  The difference between ideal experiments to test Bell's weak nonlocality and
the real experiments leads to loopholes. Ideal experiments involve either
inequalities (Bell) or equalities (Greenberger, Horne, Zeilinger). Every real
experiment has its own critical inequalities, which are almost all more
complicated than the corresponding ideal inequalities and equalities. If one of
these critical inequalities is violated, then the detection loophole is closed,
with no further assumptions. If all the critical inequalities are satisfied,
then it remains open, unless further assumptions are made. The computer program
described here and published on the website
http://www.strings.ph.qmw.ac.uk/QI/main.htm obtains the critical inequalities
for any real experiment, given the number of allowed settings of the angles and
the corresponding possible output signals for a single run. Given all the
necessary conditional probabilities or rates, it tests whether all these
inequalities are satisfied.


title: Continuous variable cloning via network of parametric gates

abstract:
  We propose an experimental scheme for the cloning machine of continuous
quantum variables through a network of parametric amplifiers working as
input-output four-port gates.


title: Feasible Entanglement Purification for Quantum Communication

abstract:
  The distribution of entangled states between distant locations will be
essential for the future large scale realization of quantum communication
schemes such as quantum cryptography and quantum teleportation. Because of the
unavoidable noise in the quantum communication channel, the entanglement
between two particles is more and more degraded the further they propagate.
Entanglement purification is thus essential to distill highly entangled states
from less entangled ones. Existing general purification protocols are based on
the quantum controlled-NOT (CNOT) or similar quantum logic operations, which
are very difficult to implement experimentally. Present realizations of CNOT
gates are much too imperfect to be useful for long-distance quantum
communication. Here we present a feasible scheme for the entanglement
purification of general mixed entangled states, which does not require any CNOT
operations, but only simple linear optical elements. Since the perfection of
such elements is very high, the local operations necessary for purification can
be performed with the required precision. Our procedure is within the reach of
current technology and should significantly simplify the implementation of
long-distance quantum communication.


title:
Comment on the Possibility of a Geometric Constraint in the Schroedinger
  Quantum Mechanics

abstract:
  It is shown that the geometric constraint advocated in [R. S. Kaushal, Mod.
Phys. Lett. A 15 (2000) 1391] is trivially satisfied. Therefore, such a
constraint does not exist. We also point out another flaw in Kaushal's paper.


title:
New high-efficiency source of photon pairs for engineering quantum
  entanglement

abstract:
  We have constructed an efficient source of photon pairs using a
waveguide-type nonlinear device and performed a two-photon interference
experiment with an unbalanced Michelson interferometer. Parametric
down-converted photons from the nonlinear device are detected by two detectors
located at the output ports of the interferometer. Because the interferometer
is constructed with two optical paths of different length, photons from the
shorter path arrive at the detector earlier than those from the longer path. We
find that the difference of arrival time and the time window of the coincidence
counter are important parameters which determine the boundary between the
classical and quantum regime. When the time window of the coincidence counter
is smaller than the arrival time difference, fringes of high visibility
(80$\pm$ 10%) were observed. This result is only explained by quantum theory
and is clear evidence for quantum entanglement of the interferometer's optical
paths.


title: Modified relative entropy of entanglement for multi-party systems

abstract:
  We present the modified relative entropy of entanglement for multi-party
systems by a given relative density matrix which is spanned by a linear
combination of the direct products of so-called basis of relative density
matrices and reduced density matrices for every party. For three qubit system
in a pure state we derive out the explicit and closed expression of our
relative density matrix which is a function of the components of the state
vector of three qubits. Through computing the modified relative entropy of
entanglement of some important and interesting examples, we display the main
behaviors and elementary properties of the modified relative entropy of
entanglement and compare it with the generalized entanglement of formation.
Moreover, we also propose an assistant, as the upper bound, of the modified
relative entropy of entanglement.


title: Atom Optics with Microfabricated Optical Elements

abstract:
  We introduce a new direction in the field of atom optics, atom
interferometry, and neutral-atom quantum information processing. It is based on
the use of microfabricated optical elements. With these elements versatile and
integrated atom optical devices can be created in a compact fashion. This
approach opens the possibility to scale, parallelize, and miniaturize atom
optics for new investigations in fundamental research and application. It will
lead to new, compact sources of ultracold atoms, compact sensors based on
matter wave interference and new approaches towards quantum computing with
neutral atoms. The exploitation of the unique features of the quantum
mechanical behavior of matter waves and the capabilities of powerful
state-of-the-art micro- and nanofabrication techniques lend this approach a
special attraction.


title: Remarks on the Extended Characteristic Uncertainty Relations

abstract:
  Three remarks concerning the form and the range of validity of the
state-extended characteristic uncertainty relations (URs) are presented. A more
general definition of the uncertainty matrix for pure and mixed states is
suggested. Some new URs are provided.


title: Realization of quantum process tomography in NMR

abstract:
  Quantum process tomography is a procedure by which the unknown dynamical
evolution of an open quantum system can be fully experimentally characterized.
We demonstrate explicitly how this procedure can be implemented with a nuclear
magnetic resonance quantum computer. This allows us to measure the fidelity of
a controlled-not logic gate and to experimentally investigate the error model
for our computer. Based on the latter analysis, we test an important assumption
underlying nearly all models of quantum error correction, the independence of
errors on different qubits.


title: A quantum-copying machine for equatorial qubits

abstract:
  Bu\v{z}ek and Hillery proposed a universal quantum-copying machine (UQCM)
(i.e., transformation) to analyze the possibility of cloning arbitrary states.
The UQCM copies quantum-mechanical states with the quality of its output does
not depend on the input. We propose a slightly different transformation to
analyze a restricted set of input states. We impose the conditions (I) the
density matrices of the two output states are the same, and that (II) the
distance between input density operator and the output density operators is
input state independent. Using Hilbert-Schmidt norm and Bures fidelity, we show
that our transformation can achieves the bound of the fidelity.


title:
Exact solutions for classical few-body systems from the multichannel
  quantum inverse problem

abstract:
  A surprising "duality" of the Newton equation with time-dependent forces and
the stationary Schroedinger equation is discussed. Wide classes of exact
solutions not known before for few-body Newton equations are generated directly
from exactly solvable multichannel models discovered in quantum mechanics due
to the inverse problem and the supersymmetry (SUSYQ) approach. The application
of this duality to the control of the stability (bifurcations) of classical
motions is suggested.


title: Teleportation of general finite dimensional quantum systems

abstract:
  Teleportation of finite dimensional quantum states by a non-local entangled
state is studied. For a generally given entangled state, an explicit equation
that governs the teleportation is presented. Detailed examples and the roles
played by the dimensions of the Hilbert spaces related to the sender, receiver
and the auxiliary space are discussed.


title:
Covariant geometric quantization of non-relativistic Hamiltonian
  mechanics

abstract:
  We provide geometric quantization of the vertical cotangent bundle V^*Q
equipped with the canonical Poisson structure. This is a momentum phase space
of non-relativistic mechanics with the configuration bundle Q -> R. The goal is
the Schrodinger representation of V^*Q. We show that this quantization is
equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R,
that makes the quantum algebra of non-relativistic mechanics an instantwise
algebra. Quantization of the classical evolution equation defines a connection
on this instantwise algebra, which provides quantum evolution in
non-relativistic mechanics as a parallel transport along time.


title:
Interfering with decay of a single photon in microwave cavities through
  single photon quantum non-demolition scheme

abstract:
  The decay of a single photon in a microwave cavity is shown to be retarded by
interaction with a resonant two-level atom in the experimental setup recently
developed by Nogues and co-workers [see G. Nogues, A. Rauschenbeutel, S.
Osnaghi, M. Brune, J. M. Raimond and S. Haroche, Nature vol 400, 239(1999)].
The effect may be interpreted in terms of the temporary removal of the photon
from the cavity thereby protecting it from the effects of the environment to
wich the cavity is coupled. Realistic parameters lead to a significative
increase of the survival probability of the photon subsequently to the
monitoring interaction.


title:
Preparation of pseudo-pure states by line-selective pulses in Nuclear
  Magnetic Resonance

abstract:
  A new method of preparing the pseudo-pure state of a spin system for quantum
computation in liquid nuclear magnetic resonance (NMR) was put forward and
demonstrated experimentally. Applying appropriately connected line-selective
pulses simultaneously and a field gradient pulse techniques we acquired
straightforwardly all pseudo-pure states for two qubits in a single experiment
much efficiently. The signal intensity with the pseudo-pure state prepared in
this way is the same as that of temporal averaging. Our method is suitable for
the system with arbitrary numbers of qubits. As an example of application, a
highly structured search algorithm----Hogg's algorithm was also performed on
the pseudo-pure state $\mid 00>$ prepared by our method.


title: A Neutral Atom and a Charged Wire: From Elastic scattering to Absorption

abstract:
  We solve the problem of a neutral atom interacting with a charged wire,
giving rise to an attractive 1/r^2 potential in two dimensions. We show how a
suitable average over all possible self-adjoint extensions of the radial
Schroedinger Hamiltonian eventually leads to the classical formula for
absorption of the atom, a formula shown to be in agreement with a recent
experiment.


title: Resonant photon creation in a three dimensional oscillating cavity

abstract:
  We analyze the problem of photon creation inside a perfectly conducting,
rectangular, three dimensional cavity with one oscillating wall. For some
particular values of the frequency of the oscillations the system is resonant.
We solve the field equation using multiple scale analysis and show that the
total number of photons inside the cavity grows exponentially in time. This is
also the case for slightly off-resonance situations. Although the spectrum of a
cavity is in general non equidistant, we show that the modes of the
electromagnetic field can be coupled, and that the rate of photon creation
strongly depends on this coupling. We also analyze the thermal enhancement of
the photon creation.


title:
Comments on: ``Weinberg's Nonlinear Quantum Mechanics and
  Einstein-Podolsky-Rosen paradox'', by Joseph Polchinski

abstract:
  Contrary to the opinion of J. Polchinski [Phys.Rev.Lett. {\bf 66}, 397-400
(1991)], the phenomenon of superluminal messages in nonlinear versions of
quantum mechanics is not a specific difficulty in a class of theories
formulated by S. Weinberg [Ann.Phys. (N.Y.), {\bf 194}, 336-386 (1989)]. It
appears in all schemes which try to enlarge the orthodox class of observables,
while conserving the traditional structure of the pure and mixed states.


title: A continuum local hidden variable model for the EPR experiment

abstract:
  The paper is withdrawn by the author, due to the fact that in Larsson's
Phys.Lett. A256 (1999) 245-252 (quant-ph/9901074) a similar model was published
with even higher efficiency.


title:
Chaotic atomic population oscillations between two coupled Bose-Einstein
  condensates with time-dependent asymmetric trap potential

abstract:
  We have investigated the chaotic atomic population oscillations between two
coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap
potential. In the perturbative regime, the population oscillations can be
described by the Duffing equation, and the chaotic oscillations near the
separatrix solution are analyzed. The sufficient-necessary conditions for
stable oscillations depend on the physical parameters and initial conditions
sensitively. The first-order necessary condition indicates that the Melnikov
function is equal to zero, so the stable oscillations are Melnikov chaotic. For
the ordinary parameters and initial conditions, the chaotic dynamics is
simulated with numerical calculation. If the damping is absent, with the
increasing of the trap asymmetry, the regular oscillations become chaotic
gradually, the corresponding stroboscopic Poincare sections (SPS) vary from a
single island to more islands, and then the chaotic sea. For the completely
chaotic oscillations, the long-term localization disappears and the short-term
localization can be changed from one of the BECs to the other through the route
of Rabi oscillation. When there exists damping, the stationary chaos
disappears, the transient chaos is a common phenomenon before regular stable
frequency locked oscillations. And proper damping can keep localization
long-lived.


title:
Diagonalization of Hamiltonians, uncertainty matrices and Robertson
  inequality

abstract:
  The problem of diagonalization of Hamiltonians of N-dimensional boson systems
by means of time-dependent canonical transformations (CT) is considered, the
case of quadratic Hamiltonians being treated in greater detail. The unitary
generator of time-dependent CT which can transform any Hamiltonian to that of a
system of uncoupled stationary oscillators is constructed. The close
relationship between methods of canonical transformations, time-dependent
integrals of motion and dynamical symmetry is noted.
  The diagonalization and symplectic properties of the uncertainty matrix for
2N canonical observables are studied. It is shown that the normalized
uncertainty matrix is symplectic for the squeezed multimode Glauber coherent
states and for the squeezed Fock states with equal photon numbers in each mode.
The Robertson uncertainty relation for the dispersion matrix of canonical
observables is shown to be minimized in squeezed coherent states only.


title:
Communication of Spin Directions with Product States and Finite
  Measurements

abstract:
  Total spin eigenstates can be used to intrinsically encode a direction, which
can later be decoded by means of a quantum measurement. We study the optimal
strategy that can be adopted if, as is likely in practical applications, only
product states of $N$-spins are available. We obtain the asymptotic behaviour
of the average fidelity which provides a proof that the optimal states must be
entangled. We also give a prescription for constructing finite measurements for
general encoding eigenstates.


title:
Optimal cloning of coherent states with a linear amplifier and beam
  splitters

abstract:
  A transformation achieving the optimal symmetric N-to-M cloning of coherent
states is presented. Its implementation only requires a phase-insensitive
linear amplifier and a network of beam splitters. An experimental demonstration
of this continuous-variable cloner should therefore be in the scope of current
technology. The link between optimal quantum cloning and optimal amplification
of quantum states is also pointed out.


title: Analysis of Density Matrix reconstruction in NMR Quantum Computing

abstract:
  Reconstruction of density matrices is important in NMR quantum computing. An
analysis is made for a 2-qubit system by using the error matrix method. It is
found that the state tomography method determines well the parameters that are
necessary for reconstructing the density matrix in NMR quantum computations.
Analysis is also made for a simplified state tomography procedure that uses
fewer read-outs. The result of this analysis with the error matrix method
demonstrates that a satisfactory accuracy in density matrix reconstruction can
be achieved even in a measurement with the number of read-outs being largely
reduced.


title: Optical implementation of continuous-variable quantum cloning machines

abstract:
  We propose an optical implementation of the Gaussian continuous-variable
quantum cloning machines. We construct a symmetric N -> M cloner which
optimally clones coherent states and we also provide an explicit design of an
asymmetric 1 -> 2 cloning machine. All proposed cloning devices can be built
from just a single non-degenerate optical parametric amplifier and several beam
splitters.


title: Entanglement Manipulation and Concentration

abstract:
  We introduce a simple, experimentally realisable, entanglement manipulation
protocol for exploring mixed state entanglement. We show that for both
non-maximally entangled pure, and mixed polarisation-entangled two qubit
states, an increase in the degree of entanglement and purity, which we define
as concentration, is achievable.


title:
Coherent states and the quantization of 1+1-dimensional Yang-Mills
  theory

abstract:
  This paper discusses the canonical quantization of 1+1-dimensional Yang-Mills
theory on a spacetime cylinder, from the point of view of coherent states, or
equivalently, the Segal-Bargmann transform. Before gauge symmetry is imposed,
the coherent states are simply ordinary coherent states labeled by points in an
infinite-dimensional linear phase space. Gauge symmetry is imposed by
projecting the original coherent states onto the gauge-invariant subspace,
using a suitable regularization procedure. We obtain in this way a new family
of "reduced" coherent states labeled by points in the reduced phase space,
which in this case is simply the cotangent bundle of the structure group K.
  The main result explained here, obtained originally in a joint work of the
author with B. Driver, is this: The reduced coherent states are precisely those
associated to the generalized Segal-Bargmann transform for K, as introduced by
the author from a different point of view. This result agrees with that of K.
Wren, who uses a different method of implementing the gauge symmetry. The
coherent states also provide a rigorous way of making sense out of the quantum
Hamiltonian for the unreduced system.
  Various related issues are discussed, including the complex structure on the
reduced phase space and the question of whether quantization commutes with
reduction.


title: Comment on "Measurement of time of arrival in quantum mechanics"

abstract:
  The analysis of the model quantum clocks proposed by Aharonov et al. [Phys.
Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent
components, previously ignored. We also clarify the meaning of the operational
time of arrival distribution which had been investigated.