title: A quantum analog of Huffman coding

abstract:
  We analyze a generalization of Huffman coding to the quantum case. In
particular, we notice various difficulties in using instantaneous codes for
quantum communication. Nevertheless, for the storage of quantum information, we
have succeeded in constructing a Huffman-coding inspired quantum scheme. The
number of computational steps in the encoding and decoding processes of N
quantum signals can be made to be of polylogarithmic depth by a massively
parallel implementation of a quantum gate array. This is to be compared with
the O (N^3) computational steps required in the sequential implementation by
Cleve and DiVincenzo of the well-known quantum noiseless block coding scheme of
Schumacher. We also show that O(N^2(log N)^a) computational steps are needed
for the communication of quantum information using another Huffman-coding
inspired scheme where the sender must disentangle her encoding device before
the receiver can perform any measurements on his signals.


title: Measurement Process In a Two-Barrier System

abstract:
  The description of a measuring process, such as that which occurs when a
quantum point contact (QPC) detector is influenced by a nearby external
electron which can take up two possible positions, provides a interesting
application of the method of quantum damping. We find a number of new effects,
due to the complete treatment of phases afforded by the formalism, although our
results are generally similiar to those of other treatments, particularly to
those of Buks et al.
  These are effects depending on the phase shift in the detector, effects which
depend on the direction of the measuring current, and in addition to damping or
dissipative effects, an energy shift of the measured system. In particular, the
phase shift effect leads to the conclusion that there can be effects of
"observation" even when the two barriers in question pass the same current.
  The nature of the current through the barriers and its statistics is
discussed, giving a description of correlations in the current due to
"measurement" and of the origin of "telegraphic" signals.


title: Quantum Counting

abstract:
  We study some extensions of Grover's quantum searching algorithm. First, we
generalize the Grover iteration in the light of a concept called amplitude
amplification. Then, we show that the quadratic speedup obtained by the quantum
searching algorithm over classical brute force can still be obtained for a
large family of search problems for which good classical heuristics exist.
Finally, as our main result, we combine ideas from Grover's and Shor's quantum
algorithms to perform approximate counting, which can be seen as an amplitude
estimation process.


title: Remarks on Universal Quantum Computer

abstract: This paper has been superseded by quant-ph/9908074.


title:
Generalized Noiseless Quantum Codes utilizing Quantum Enveloping
  Algebras

abstract:
  A generalization of the results of Rasetti and Zanardi concerning avoiding
errors in quantum computers by using states preserved by evolution is
presented. The concept of dynamical symmetry is generalized from the level of
classical Lie algebras and groups to the level of dynamical symmetry based on
quantum Lie algebras and quantum groups (in the sense of Woronowicz). A natural
connection is proved between states preserved by representations of a quantum
group and states preserved by evolution with dynamical symmetry of the
appropriate universal enveloping algebra. Illustrative examples are discussed.


title: Schr\"odinger operators with complex potential but real spectrum

abstract:
  Several aspects of complex-valued potentials generating a real and positive
spectrum are discussed. In particular, we construct complex-valued potentials
whose corresponding Schr\"odinger eigenvalue problem can be solved
analytically.


title: Quantum Effects in Algorithms

abstract:
  We discuss some seemingly paradoxical yet valid effects of quantum physics in
information processing. Firstly, we argue that the act of ``doing nothing'' on
part of an entangled quantum system is a highly non-trivial operation and that
it is the essential ingredient underlying the computational speedup in the
known quantum algorithms. Secondly, we show that the watched pot effect of
quantum measurement theory gives the following novel computational possibility:
suppose that we have a quantum computer with an on/off switch, programmed ready
to solve a decision problem. Then (in certain circumstances) the mere fact that
the computer would have given the answer if it were run, is enough for us to
learn the answer, even though the computer is in fact not run.


title: Interfering resonances in a quantum billiard

abstract:
  We present a method for numerically obtaining the positions, widths and
wavefunctions of resonance states in a two dimensional billiard connected to a
waveguide. For a rectangular billiard, we study the dynamics of three resonance
poles lying separated from the other ones. As a function of increasing coupling
strength between the waveguide and the billiard two of the states become
trapped while the width of the third one continues to increase for all coupling
strengths. This behavior of the resonance poles is reflected in the time delay
function which can be studied experimentally.


title: Entangled Mixed States and Local Purification

abstract:
  Linden, Massar and Popescu have recently given an optimization argument to
show that a single two-qubit Werner state, or any other mixture of the
maximally entangled Bell states, cannot be purified by local operations and
classical communications. We generalise their result and give a simple
explanation. In particular, we show that no purification scheme using local
operations and classical communications can produce a pure singlet from any
mixed state of two spin-1/2 particles. More generally, no such scheme can
produce a maximally entangled state of any pair of finite-dimensional systems
from a generic mixed state. We also show that the Werner states belong to a
large class of states whose fidelity cannot be increased by such a scheme.


title: Lower Bounds of Quantum Search for Extreme Point

abstract:
  We show that Durr-Hoyer's quantum algorithm of searching for extreme point of
integer function can not be sped up for functions chosen randomly. Any other
algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect
answer for the functions with the single point of maximum chosen randomly with
probability converging to 1. The lower bound as $\Omega (\sqrt{2^n /b})$ was
established for the quantum search for solution of equations $f(x)=1$ where $f$
is a Boolean function with $b$ such solutions chosen at random with probability
converging to 1.


title: Time-Symmetrized Quantum Theory, Counterfactuals, and `Advanced Action'

abstract:
  Recent authors have raised objections to the counterfactual interpretation of
the Aharonov-Bergmann-Lebowitz (ABL) rule of time symmetrized quantum theory
(TSQT). I distinguish between two different readings of the ABL rule,
counterfactual and non-counterfactual, and confirm that TSQT advocate L.
Vaidman is employing the counterfactual reading to which these authors object.
Vaidman has responded to the objections by proposing a new kind of
time-symmetrized counterfactual, which he has defined in two different ways. It
is argued that neither definition succeeds in overcoming the objections, except
in a special case previously noted by Cohen and Hiley. In addition, a
connection is made between TSQT and Price's concept of `advanced action', which
further supports the special case discussed.


title:
Bose condensation in two dimensions with disorder: Gross-Pitaevskii
  approach

abstract:
  Bose condensation of interacting bosons in a two-dimensional random potential
is studied. The Gross-Pitaevskii equation is solved to determine the
spatially-varying order parameter and the localization length as a function of
the disorder, the interaction strength, and the condensate density. A finite
temperature of condensation is obtained thereby. The results are applied to
determination of the superradiant decay of excitons in a GaAs quantum well.


title: Levinson's theorem for the Schr\"{o}dinger equation in two dimensions

abstract:
  Levinson's theorem for the Schr\"{o}dinger equation with a cylindrically
symmetric potential in two dimensions is re-established by the Sturm-Liouville
theorem. The critical case, where the Schr\"{o}dinger equation has a finite
zero-energy solution, is analyzed in detail. It is shown that, in comparison
with Levinson's theorem in non-critical case, the half bound state for $P$
wave, in which the wave function for the zero-energy solution does not decay
fast enough at infinity to be square integrable, will cause the phase shift of
$P$ wave at zero energy to increase an additional $\pi$.


title: Levinson's Theorem for Non-local Interactions in Two Dimensions

abstract:
  In the light of the Sturm-Liouville theorem, the Levinson theorem for the
Schr\"{o}dinger equation with both local and non-local cylindrically symmetric
potentials is studied. It is proved that the two-dimensional Levinson theorem
holds for the case with both local and non-local cylindrically symmetric cutoff
potentials, which is not necessarily separable. In addition, the problems
related to the positive-energy bound states and the physically redundant state
are also discussed in this paper.


title: The Relativistic Levinson Theorem in Two Dimensions

abstract:
  In the light of the generalized Sturm-Liouville theorem, the Levinson theorem
for the Dirac equation in two dimensions is established as a relation between
the total number $n_{j}$ of the bound states and the sum of the phase shifts
$\eta_{j}(\pm M)$ of the scattering states with the angular momentum $j$:
$$\eta_{j}(M)+\eta_{j}(-M)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$$
$$~~~=\left\{\begin{array}{ll} (n_{j}+1)\pi &{\rm
when~a~half~bound~state~occurs~at}~E=M ~~{\rm and}~~ j=3/2~{\rm or}~-1/2\\
(n_{j}+1)\pi &{\rm when~a~half~bound~state~occurs~at}~E=-M~~{\rm and}~~
j=1/2~{\rm or}~-3/2\\ n_{j}\pi~&{\rm the~rest~cases} . \end{array} \right. $$
  \noindent The critical case, where the Dirac equation has a finite
zero-momentum solution, is analyzed in detail. A zero-momentum solution is
called a half bound state if its wave function is finite but does not decay
fast enough at infinity to be square integrable.


title: Prime decomposition and correlation measure of finite quantum systems

abstract:
  Under the name prime decomposition (pd), a unique decomposition of an
arbitrary $N$-dimensional density matrix $\rho$ into a sum of seperable density
matrices with dimensions given by the coprime factors of $N$ is introduced. For
a class of density matrices a complete tensor product factorization is
achieved. The construction is based on the Chinese Remainder Theorem and the
projective unitary representation of $Z_N$ by the discrete Heisenberg group
$H_N$. The pd isomorphism is unitarily implemented and it is shown to be
coassociative and to act on $H_N$ as comultiplication. Density matrices with
complete pd are interpreted as grouplike elements of $H_N$. To quantify the
distance of $\rho$ from its pd a trace-norm correlation index $\cal E$ is
introduced and its invariance groups are determined.


title: Estimates for practical quantum cryptography

abstract:
  In this article I present a protocol for quantum cryptography which is secure
against attacks on individual signals. It is based on the Bennett-Brassard
protocol of 1984 (BB84). The security proof is complete as far as the use of
single photons as signal states is concerned. Emphasis is given to the
practicability of the resulting protocol. For each run of the quantum key
distribution the security statement gives the probability of a successful key
generation and the probability for an eavesdropper's knowledge, measured as
change in Shannon entropy, to be below a specified maximal value.


title:
To Enjoy the Morning Flower in the Evening - What does the Appearance of
  Infinity in Physics Imply?

abstract:
  A new regularization - renormalization method with no explicit divergence, no
counterterm, no bare parameter and no arbitrary running mass scale is discussed
>. There is no difficulty of triviality and the Higgs mass in the standard
model is calculated to be 138 Gev.


title: Quantum computation based on particle statistics

abstract:
  In spite of their evident logical character, particle statistics symmetries
are not among the inherently quantum features exploited in quantum computation.
A difficulty may be that, being a constant of motion of a unitary evolution, a
particle statistics symmetry cannot affect the course of such an evolution. We
try to avoid this possible deadlock by introducing a generalized
(counterfactual, blunt) formulation where this type of symmetry becomes a
watchdog effect shaping the evolution of a unitary computation process. The
work is an exploration.


title: Entanglement and pseudomixtures

abstract:
  In a recent paper Sanpera et al. have shown, that for the simplest binary
composite systems any density matrix can be described in terms of only product
vectors. The purpose of this note is to show that posibillity of decomposing
any state as pseudomixtures does not depend on dimension of the subsystems.


title: Deterministic entanglement of two trapped ions

abstract:
  We have prepared the internal states of two trapped ions in both the
Bell-like singlet and triplet entangled states. In contrast to all other
experiments with entangled states of either massive particles or photons, we do
this in a deterministic fashion, producing entangled states on demand without
selection. The deterministic production of entangled states is a crucial
prerequisite for large-scale quantum computation.


title:
Volume of classical and quantum ensembles: geometric approach to entropy
  and information

abstract:
  It is shown for classical and quantum ensembles that there is a unique
quantity which has the properties of a "volume". This quantity is a function of
the ensemble entropy, and hence provides a geometric interpretation for the
latter. It further provides a geometric picture for deriving and unifying a
number of results in classical and quantum information theory, and for
discussing entropic uncertainty relations.


title: Quantum tomography as normalization of incompatible observations

abstract:
  Quantum states are successfully reconstructed using the maximum likelihood
estimation on the subspace where the measured projectors reproduce the identity
operator. Reconstruction corresponds to normalization of incompatible
observations. The proposed approach handles the noisy data corresponding to
realistic incomplete observation with finite resolution.


title: Quantum Zeno and quantum anti-Zeno effects

abstract:
  Consequences of the deviation from the linear on time quantum transition
probabilities leading to the nonexponential decay law and to the so-called Zeno
effect are analysed. Main features of the quantum Zeno and quantum anti-Zeno
effects for induced transitions are revealed on simple model systems.


title: Smearing Formula for Higher-Order Effective Classical Potentials

abstract:
  In the variational approach to quantum statistics, a smearing formula
describes efficiently the consequences of quantum fluctuations upon an
interaction potential. The result is an effective classical potential from
which the partition function can be obtained by a simple integral. In this
work, the smearing formula is extended to higher orders in the variational
perturbation theory. An application to the singular Coulomb potential exhibits
the same fast convergence with increasing orders that has been observed in
previous variational perturbation expansions of the anharmonic oscillator with
quartic potential.


title:
Semiclassical trajectory-coherent approximation in quantum mechanics:
  II. High order corrections to the Dirac operators in external electromagnetic
  field

abstract:
  High approximations of semiclassical trajectory-coherent states (TCS) and of
semiclassical Green function (in the class of semiclassically concentrated
states) for the Dirac operator with anomalous Pauli interaction are obtained.
For Schrodinger and Dirac operators trajectory-coherent representations are
constructed up to any precision with respect to h, h-->0.


title: Yang-Mills Equation and Bures Metric

abstract:
  It is shown that the connection form (gauge field) related to the
generalization of the Berry phase to mixed states proposed by Uhlmann satisfies
the source-free Yang-Mills equation *D*Dw=0, where the Hodge star is taken with
respect to the Bures metric on the space of finite dimensional nondegenerate
density matrices.


title:
SUSY Quantum Mechanics with Complex Superpotentials and Real Energy
  Spectra

abstract:
  We extend the standard intertwining relations used in Supersymmetrical (SUSY)
Quantum Mechanics which involve real superpotentials to complex
superpotentials. This allows to deal with a large class of non-hermitean
Hamiltonians and to study in general the isospectrality between complex
potentials. In very specific cases we can construct in a natural way
"quasi-complex" potentials which we define as complex potentials having a
global property such as to lead to a Hamiltonian with real spectrum. We also
obtained a class of complex transparent potentials whose Hamiltonian can be
intertwined to a free Hamiltonian. We provide a variety of examples both for
the radial problem (half axis) and for the standard one-dimensional problem
(the whole axis), including remarks concerning scattering problems.


title: Exactly Solvable Hydrogen-like Potentials and Factorization Method

abstract:
  A set of factorization energies is introduced, giving rise to a
generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for
the radial hydrogen-like Hamiltonian. An algebraic intertwining technique
involving such factorization energies leads to derive $n$-parametric families
of potentials in general almost-isospectral to the hydrogen-like radial
Hamiltonians. The construction of SUSY partner Hamiltonians with ground state
energies greater than the corresponding ground state energy of the initial
Hamiltonian is also explicitly performed.


title: Quantum Logic Gates in Optical Lattices

abstract:
  We propose a new system for implementing quantum logic gates: neutral atoms
trapped in a very far-off-resonance optical lattice. Pairs of atoms are made to
occupy the same well by varying the polarization of the trapping lasers, and
then a near-resonant electric dipole is induced by an auxiliary laser. A
controlled-NOT can be implemented by conditioning the target atomic resonance
on a resolvable level shift induced by the control atom. Atoms interact only
during logical operations, thereby suppressing decoherence.


title: The Anomalous Behaviour of Fermions in a Thin Wire

abstract:
  Motivated by the recent development of insulated nano-tubes and the attempts
to develop conducting nano wires in such tubes, we examine the Fermionic
behaviour in extremely thin wires. Although the one- dimensional problem has
been studied in detail over the years, it is an extreme idealization: We
consider the more realistic scenario of thin wires which are nevertheless three
dimensional. We show that the assembly of Fermions behaves as if it is below
the Fermi temperature, and in the limit of one dimension, in the ground state
as well. Thus there are indeed Bosonization features. These conclusions are
checked from an independent stand point.


title: Bohm Confirmed by NonRelativistic Quark Model

abstract:
  The effectiveness of the NonRelativistic Quark Model of hadrons can be
explained by Bohm's quantum theory applied to a fermion confined in a box, in
which the fermion is at rest because its kinetic energy is transformed into
PSI-field potential energy. Since that aspect of Bohm's quantum theory is not a
property of most other formulations of quantum theory, the effectiveness of the
NonRelativistic Quark Model confirms Bohm's quantum theory as opposed to those
others.


title: Convex probability domain of generalized quantum measurements

abstract:
  Generalized quantum measurements with N distinct outcomes are used for
determining the density matrix, of order d, of an ensemble of quantum systems.
The resulting probabilities are represented by a point in an N-dimensional
space. It is shown that this point lies in a convex domain having at most d^2-1
dimensions.


title:
Relativistic corrections to the energy spectra of completely confined
  particles

abstract:
  An analytical expression for the relativistic corrections to the energy
spectra of particles completely confined in an one-dimensional limited length
in real space is given, based upon the wave property of particles, the
relativistic energy-momentum relation and two mathematical equations.


title: Stochastic wave function approach to generalized master equations

abstract:
  A generalization of the stochastic wave function method is presented which
allows the unravelling of arbitrary linear quantum master equations which are
not necessarily in Lindblad form and, moreover, the explicit treatment of
memory effects by employing the time-convolutionless projection operator
technique. The crucial point of this construction is the description of the
open system in a doubled Hilbert space, which has already been successfully
used for the computation of multitime correlation functions.


title:
New approach to Epsilon-entropy and Its comparison with Kolmogorov's
  Epsilon-entropy

abstract:
  Kolmogorov introduced a concept of Epsilon-entropy to analyze information in
classical continuous system. The fractal dimension of geometrical sets was
introduced by Mandelbrot as a new criterion to analyze the complexity of these
sets. The Epsilon-entropy and the fractal dimension of a state in general
quantum system were introduced by one of the present authors in order to
characterize chaotic properties of general states.
  In this paper, we show that Epsilon-entropy of a state includes Kolmogorov
Epsilon-entropy, and the fractal dimension of a state describe fractal
structure of Gaussian measures.


title: Connections and Metrics Respecting Standard Purification

abstract:
  Standard purification interlaces Hermitian and Riemannian metrics on the
space of density operators with metrics and connections on the purifying
Hilbert-Schmidt space. We discuss connections and metrics which are well
adopted to purification, and present a selected set of relations between them.
A connection, as well as a metric on state space, can be obtained from a metric
on the purification space. We include a condition, with which this
correspondence becomes one-to-one. Our methods are borrowed from elementary
*-representation and fibre space theory. We lift, as an example, solutions of a
von Neumann equation, write down holonomy invariants for cyclic ones, and ``add
noise'' to a curve of pure states.


title: Quantum Circuits with Mixed States

abstract:
  We define the model of quantum circuits with density matrices, where
non-unitary gates are allowed. Measurements in the middle of the computation,
noise and decoherence are implemented in a natural way in this model, which is
shown to be equivalent in computational power to standard quantum circuits.
  The main result in this paper is a solution for the subroutine problem: The
general function that a quantum circuit outputs is a probabilistic function,
but using pure state language, such a function can not be used as a black box
in other computations. We give a natural definition of using general
subroutines, and analyze their computational power.
  We suggest convenient metrics for quantum computing with mixed states. For
density matrices we analyze the so called ``trace metric'', and using this
metric, we define and discuss the ``diamond metric'' on superoperators. These
metrics enable a formal discussion of errors in the computation.
  Using a ``causality'' lemma for density matrices, we also prove a simple
lower bound for probabilistic functions.


title: Supersymmetric Method for Constructing Quasi-Exactly Solvable Potentials

abstract:
  We propose a new method for constructing the quasi-exactly solvable (QES)
potentials with two known eigenstates using supersymmetric quantum mechanics.
General expression for QES potentials with explicitly known energy levels and
wave functions of ground state and excited state are obtained. Examples of new
QES potentials are considered.


title: Defeating classical bit commitments with a quantum computer

abstract:
  It has been recently shown by Mayers that no bit commitment scheme is secure
if the participants have unlimited computational power and technology. However
it was noticed that a secure protocol could be obtained by forcing the cheater
to perform a measurement. Similar situations had been encountered previously in
the design of Quantum Oblivious Transfer. The question is whether a classical
bit commitment could be used for this specific purpose. We demonstrate that,
surprisingly, classical unconditionally concealing bit commitments do not help.


title:
Good Quantum Convolutional Error Correction Codes And Their Decoding
  Algorithm Exist

abstract:
  Quantum convolutional code was introduced recently as an alternative way to
protect vital quantum information. To complete the analysis of quantum
convolutional code, I report a way to decode certain quantum convolutional
codes based on the classical Viterbi decoding algorithm. This decoding
algorithm is optimal for a memoryless channel. I also report three simple
criteria to test if decoding errors in a quantum convolutional code will
terminate after a finite number of decoding steps whenever the Hilbert space
dimension of each quantum register is a prime power. Finally, I show that
certain quantum convolutional codes are in fact stabilizer codes. And hence,
these quantum stabilizer convolutional codes have fault-tolerant
implementations.


title: Quantum Carpets made simple

abstract:
  We show that the concept of degeneracy is the key idea for understanding the
quantum carpet woven by a particle in the box.


title: Collective spontaneous emission in a q-deformed Dicke model

abstract:
  The q-deformation of a single quantized radiation mode interacting with a
collection of two level atoms is introduced, analysing its effects on the
cooperative behavior of the system.


title: Relativistic properties of marginal distributions

abstract:
  We study the properties of marginal distributions-projections of the phase
space representation of a physical system-under relativistic transforms. We
consider the Galileo case as well as the Lorentz transforms exploiting the
relativistic oscillator model used for describing the mass spectrum of
elementary particles.


title: Causality, particle localization and positivity of the energy

abstract:
  Positivity of the Hamiltonian alone is used to show that particles, if
initially localized in a finite region, immediately develop infinite tails.


title:
Transition from antibunching to bunching for two dipole-interacting
  atoms

abstract:
  It is known that there is a transition from photon antibunching to bunching
in the resonance fluorescence of a driven system of two two-level atoms with
dipole-dipole interaction when the atomic distance decreases and the other
parameters are kept fixed. We give a simple explanation for the underlying
mechanism which in principle can also be applied to other systems. PACS numbers
42.50.Ar, 42.50Fx


title:
Non-Markovian Quantum Fluctuations and Superradiance Near a Photonic
  Band Edge

abstract:
  We discuss a point model for the collective emission of light from N
two-level atoms in a photonic bandgap material, each with an atomic resonant
frequency near the edge of the gap. In the limit of a low initial occupation of
the excited atomic state, our system is shown to possess novel atomic spectra
and population statistics. For a high initial excited state population, mean
field theory suggests a fractionalized inversion and a macroscopic polarization
for the atoms in the steady state, both of which can be controlled by an
external d.c. field. This atomic steady state is accompanied by a non--zero
expectation value of the electric field operators for field modes located in
the vicinity of the atoms. The nature of homogeneous broadening near the band
edge is shown to differ markedly from that in free space due to non-Markovian
memory effects in the radiation dynamics. Non-Markovian vacuum fluctuations are
shown to yield a partially coherent steady state polarization with a random
phase. In contrast with the steady state of a conventional laser, near a
photonic band edge this coherence occurs as a consequence of photon
localization in the absence of a conventional cavity mode. We also introduce a
classical stochastic function with the same temporal correlations as the
electromagnetic reservoir, in order to stochastically simulate the effects of
vacuum fluctuations near a photonic band edge.


title: Exact Eigenanalyses of Certain N^m x N^m Density Matrices

abstract:
  We apply and extend recent results of Krattenthaler and Slater
(quant-ph/9612043), who sought quantum analogs of seminal work on universal
data compression of Clarke and Barron. KS obtained explicit formulas for the
eigenvalues and eigenvectors of the 2^m x 2^m density matrices gotten by
averaging the m-fold tensor products with themselves of the 2 x 2 density
matrices. The weighting was done with respect to a one-parameter family of
probability distributions, all the members of which are spherically-symmetric
over the "Bloch sphere" of two-level quantum systems. This family includes the
normalized volume element of the minimal monotone (Bures) metric. In this
letter, we conduct parallel analyses (for m =2,3,4), based on a natural measure
on the density matrices recently proposed by Zyczkowski, Horodecki, Sanpera and
Lewenstein (quant-ph/9804024) and find interesting similarities and differences
with the findings of KS. In addition, we are able to obtain exact analogous
results, based on the measure of ZHSL, for the twofold tensor products of the 3
x 3 density matrices.


title: Verifiable quantum oblivious transfer protocol based on entangled states

abstract: This paper has been withdrawn.


title:
Fermion-Boson Duality of One-dimensional Quantum Particles with
  Generalized Contact Interaction

abstract:
  For a system of spinless one-dimensional fermions, the non-vanishing
short-range limit of two-body interaction is shown to induce the wave-function
discontinuity. We prove the equivalence of this fermionic system and the
bosonic particle system with two-body $\delta$-function interaction with the
reversed role of strong and weak couplings.
  KEYWORDS: one-dimensional system, $\epsilon$-interaction, solvable many-body
problem, exact bosonization

categories: quant-ph cond-mat nlin.SI nucl-th solv-int


title: Fundamentals of quantum mutual entropy and capacity

abstract:
  The study of mutual entropy (information) and capacity in classica l system
was extensively done after Shannon by several authors like Kolmogor ov and
Gelfand. In quantum systems, there have been several definitions of t he mutual
entropy for classical input and quantum output. In 1983, the autho r defined
the fully quantum mechanical mutual entropy by means of the relati ve entropy
of Umegaki, and he extended it to general quantum systems by the relative
entropy of Araki and Uhlmann. When the author introduced the quantu m mutual
entropy, he did not indicate that it contains other definitions of the mutual
entropy including classical one, so that there exist several misu nderstandings
for the use of the mutual entropy (information) to compute the capacity of
quantum channels. Therefore in this note we point out that our quantum mutual
entropy generalizes others and where the m isuse occurs.


title: Violation of Bell inequalities by photons more than 10 km apart

abstract:
  A Franson-type test of Bell inequalities by photons 10.9 km apart is
presented. Energy-time entangled photon-pairs are measured using two-channel
analyzers, leading to a violation of the inequalities by 16 standard deviations
without subtracting accidental coincidences. Subtracting them, a 2-photon
interference visibility of 95.5% is observed, demonstrating that distances up
to 10 km have no significant effect on entanglement. This sets quantum
cryptography with photon pairs as a practical competitor to the schemes based
on weak pulses.


title: Stochastic Motion of an Open Bosonic String

abstract:
  We show that the classical stochastic motion of an open bosonic string leads
to the same results as the standard first quantization of this system. For
this, the diffusion constant governing the process has to be proportional to
\alpha ', the Regge slope parameter, which is the only constant, along with the
velocity of light, needed to describe the motion of a string.


title: Quantum theory of dispersive electromagnetic modes

abstract:
  A quantum theory of dispersion for an inhomogeneous solid is obtained, from a
starting point of multipolar coupled atoms interacting with an electromagnetic
field. The dispersion relations obtained are equivalent to the standard
classical Sellmeir equations obtained from the Drude-Lorentz model. In the
homogeneous (plane-wave) case, we obtain the detailed quantum mode structure of
the coupled polariton fields, and show that the mode expansion in all branches
of the dispersion relation is completely defined by the refractive index and
the group-velocity for the polaritons. We demonstrate a straightforward
procedure for exactly diagonalizing the Hamiltonian in one, two or
three-dimensional environments, even in the presence of longitudinal
phonon-exciton dispersion, and an arbitrary number of resonant transitions with
different frequencies. This is essential, since it is necessary to include at
least one phonon (I.R.) and one exciton (U.V.) mode, in order to accurately
represent dispersion in transparent solid media. Our method of diagonalization
does not require an explicit solution of the dispersion relation, but relies
instead on the analytic properties of Cauchy contour integrals over all
possible mode frequencies. When there is longitudinal phonon dispersion, the
relevant group-velocity term is modified so that it only includes the purely
electromagnetic part of the group velocity.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics. III.
  Pictures and integrals of motion

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. It's evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
  In this third part of our series we investigate the bundle analogues of the
conventional pictures of motion. In particular, there are found the state
sections and bundle morphisms corresponding to state vectors and observables
respectively. The equations of motion for these quantities are derived too.
Using the results obtained, we consider from the bundle view-point problems
concerning the integrals of motion. An invariant (bundle) necessary and
sufficient conditions for a dynamical variable to be an integral of motion are
found.


title: What information theory can tell us about quantum reality

abstract:
  An investigation of Einstein's ``physical'' reality and the concept of
quantum reality in terms of information theory suggests a solution to quantum
paradoxes such as the Einstein-Podolsky-Rosen (EPR) and the Schroedinger-cat
paradoxes. Quantum reality, the picture based on unitarily evolving
wavefunctions, is complete, but appears incomplete from the observer's point of
view for fundamental reasons arising from the quantum information theory of
measurement. Physical reality, the picture based on classically accessible
observables is, in the worst case of EPR experiments, unrelated to the quantum
reality it purports to reflect. Thus, quantum information theory implies that
only correlations, not the correlata, are physically accessible: the mantra of
the Ithaca interpretation of quantum mechanics.


title: Quantum computation with linear optics

abstract:
  We present a constructive method to translate small quantum circuits into
their optical analogues, using linear components of present-day quantum optics
technology only. These optical circuits perform precisely the computation that
the quantum circuits are designed for, and can thus be used to test the
performance of quantum algorithms. The method relies on the representation of
several quantum bits by a single photon, and on the implementation of universal
quantum gates using simple optical components (beam splitters, phase shifters,
etc.). The optical implementation of Brassard et al.'s teleportation circuit, a
non-trivial 3-bit quantum computation, is presented as an illustration.


title: Bell's inequalities, multiphoton states and phase space distributions

abstract:
  The connection between quantum optical nonclassicality and the violation of
Bell's inequalities is explored. Bell type inequalities for the electromagnetic
field are formulated for general states of quantised radiation and their
violation is connected to other nonclassical properties of the field. This is
achieved by considering states with an arbitrary number of photons and
carefully identifying the hermitian operators whose expectation values do not
admit any local hidden variable description. We relate the violation of these
multi-photon inequalities to properties of phase space distribution functions
such as the diagonal coherent state distribution function and the Wigner
function. Finally, the family of 4-mode states with Gaussian Wigner
distributions is analysed, bringing out in this case the connection of
violation of Bell type inequalities with the nonclassical property of
squeezing.


title:
Density-matrix approach to coherent transport and the measurement
  problem

abstract:
  Bloch-type equations for description of coherent transport in mesoscopic
systems are applied for a study of the continuous measurement process. Both the
detector and the measured system are described quantum mechanically. It is
shown that the Schr\"odinger evolution of the entire system cannot be
accommodated with the measurement collapse. The latter leads to quantum jumps
which can be experimentally detected.


title: Theory of atomic diffraction from evanescent waves

abstract:
  We review recent theoretical models and experiments dealing with the
diffraction of neutral atoms from a reflection grating, formed by a standing
evanescent wave. We analyze diffraction mechanisms proposed for normal and
grazing incidence, point out their scopes and confront the theory with
experiment.


title: Klein Tunnelling and the Klein Paradox

abstract:
  The Klein paradox is reassessed by considering the properties of a finite
square well or barrier in the Dirac equation. It is shown that spontaneous
positron emission occurs for a well if the potential is strong enough. The
vacuum charge and lifetime of the well are estimated. If the well is wide
enough, a seemingly constant current is emitted. These phenomena are transient
whereas the tunnelling first calculated by Klein is time-independent. Klein
tunnelling is a property of relativistic wave equations, not necessarily
connected to particle emission. The Coulomb potential is investigated in this
context: it is shown that a heavy nucleus of sufficiently large $Z$ will bind
positrons. Correspondingly, it is expected that as $Z$ increases the Coulomb
barrier will become increasingly transparent to positrons. This is an example
of Klein tunnelling.


title:
Superradiant Laser: First-Order Phase Transition and Non-stationary
  Regime

abstract:
  We solve the superradiant laser model in two limiting cases. First the
stationary low-pumping regime is considered where a first-order phase
transition in the semiclassical solution occurs. This discontinuity is smeared
out in the quantum regime. Second, we solve the model in the non-stationary
regime where we find a temporally periodic solution. For a certain parameter
range well separated pulses may occur.


title: The Halting Problem for Quantum Computers

abstract:
  We argue that the halting problem for quantum computers which was first
raised by Myers, is by no means solved, as has been claimed recently. We
explicitly demonstrate the difficulties that arise in a quantum computer when
different branches of the computation halt at different, unknown, times.


title: Force-Free Interactions and Nondispersive Phase Shifts in Interferometry

abstract:
  Zeilinger's observation that phenomena of the Aharonov-Bohm type lead to
nondispersive, i.e. energy-independent, phase shifts in interferometers is
generalized in a new proof which shows that the precise condition for
nondispersivity is a force-free interaction. The converse theorem is disproved
by a conceptual counter example. Applications to several nondispersive
interference phenomena are reviewed briefly. Those fall into two classes which
are objectively distinct from each other in that in the first class phase
shifts depend only on the topology of the interfering beam paths while in the
second class force-free physical interactions take place at identifiable points
along the path. Apparent disagreements in the literature about the topological
nature of the phenomena in the second class stem from differing definitions.


title: How Wigner Functions Transform Under Symplectic Maps

abstract:
  It is shown that, while Wigner and Liouville functions transform in an
identical way under linear symplectic maps, in general they do not transform
identically for nonlinear symplectic maps. Instead there are ``quantum
corrections'' whose hbar tending to zero limit may be very complicated.
Examples of the behavior of Wigner functions in this limit are given in order
to examine to what extent the corresponding Liouville densities are recovered.


title: Effective field theory of resonant 2-level atoms

abstract:
  The phenomenological two-level atom is re-analysed using the methods of
effective field theory. By presenting the Dicke-Jaynes-Cummings model in real
space, an exact diagonalization is accomplished going beyond the rotating wave
approximation. The meaning of the symmetries and conserved quantities in the
theory is discussed and the model is related to non-equilibrium field theory.
The structure of the solution raises a question about the rotating wave
approximation in quantum mechanics.


title: Bound entanglement can be activated

abstract:
  Bound entanglement is the noisy entanglement which cannot be distilled to a
singlet form. Thus it cannot be used alone for quantum communication purposes.
Here we show that, nevertheless, the bound entanglement can be, in a sense,
pumped into single pair of free entangled particles. It allows for
teleportation via the pair with the fidelity impossible to achieve without
support of bound entanglement. The result also suggests that the distillable
entanglement may be not additive.


title: Quantum Mechanics and Algorithmic Randomness

abstract:
  A long sequence of tosses of a classical coin produces an apparently random
bit string, but classical randomness is an illusion: the algorithmic
information content of a classically-generated bit string lies almost entirely
in the description of initial conditions. This letter presents a simple
argument that, by contrast, a sequence of bits produced by tossing a quantum
coin is, almost certainly, genuinely (algorithmically) random. This result can
be interpreted as a strengthening of Bell's no-hidden-variables theorem, and
relies on causality and quantum entanglement in a manner similar to Bell's
original argument.


title:
Operator Formulation of Classical Mechanics and the Problem of
  Measurement

abstract:
  The basic concepts of classical mechanics are given in the operator form. The
dynamical equation for a hybrid system, consisting of quantum and classical
subsystems, is introduced and analyzed in the case of an ideal nonselective
measurement. The nondeterministic evolution is found to be the consequence of
the superposition of two different deterministic evolutions.


title: Photon-added coherent states as nonlinear coherent states

abstract:
  The states $|\alpha,m>$, defined as ${a^{\dagger}}^{m}|\alpha>$ up to a
normalization constant and $m$ is a nonnegative integer, are shown to be the
eigenstates of $f(\hat{n},m)\hat{a}$ where $f(\hat{n},m)$ is a nonlinear
function of the number operator $\hat{n}$. The explicit form of $f(\hat{n},m)$
is constructed. The eigenstates of this operator for negative values of $m$ are
introduced. The properties of these states are discussed and compared with
those of the state $|\alpha,m >$.


title: Generating photon pulses with an oscillating cavity

abstract:
  We study the generation of photon pulses from thermal field fluctuations
through opto-mechanical coupling to a cavity with an oscillatory motion. Pulses
are regularly spaced and become sharp for a high finesse cavity.


title: Quantum secret sharing

abstract:
  Secret sharing is a procedure for splitting a message into several parts so
that no subset of parts is sufficient to read the message, but the entire set
is. We show how this procedure can be implemented using GHZ states. In the
quantum case the presence of an eavesdropper will introduce errors so that his
presence can be detected. We also show how GHZ states can be used to split
quantum information into two parts so that both parts are necessary to
reconstruct the original qubit.


title: Bound-State Problem in a One-Dimensional Cantor-like Potential

abstract:
  One of the best systems for the study of quantum chaos is the atomic nucleus.
A confined particle with general boundary conditions can present chaos and the
eigenvalue problem can exhibit this fact. We study a toy model in which the
potential has a Cantor-like form. The eigenvalue spectrum presents a Devil's
staircase ordering in the semi-classical limit.


title: Quantum Rate-Distortion Coding

abstract:
  I introduce rate-distortion theory for quantum coding, and derive a lower
bound, involving the coherent information, on the rate at which qubits must be
used to encode a quantum source with a given maximum level of distortion per
source emission. The convexity of the "information rate-distortion function"
which defines this bound is also derived.


title:
Internal structures of electrons and photons: the concept of extended
  particles revisited

abstract:
  The theoretical foundations of quantum mechanics and de Broglie--Bohm
mechanics are analyzed and it is shown that both theories employ a formal
approach to microphysics. By using a realistic approach it can be established
that the internal structures of extended particles comply with a wave-equation.
Including external potentials yields the Schrodinger equation, which, in this
context, is arbitrary due to internal energy components. The statistical
interpretation of wave functions in quantum theory as well as Heisenberg's
uncertainty relations are shown to be an expression of this, fundamental,
arbitrariness. Electrons and photons can be described by an identical
formalism, providing formulations equivalent to the Maxwell equations.
Electrostatic interactions justify the initial assumption of electron-wave
stability: the stability of electron waves can be referred to vanishing
intrinsic fields of interaction. The theory finally points out some fundamental
difficulties for a fully covariant formulation of quantum electrodynamics,
which seem to be related to the existing infinity problems in this field.


title: Building a frame and gauge free formulation of quantum mechanics

abstract:
  The wave function of quantum mechanics is not a boost invariant and gauge
invariant quantity. Correspondingly, reference frame dependence and gauge
dependence are inherited to most of the elements of the usual formulation of
quantum mechanics (including operators, states and events). If a frame
dependent and gauge dependent formalism is called, in short, a relative
formalism, then the aim of the paper is to establish an absolute, i.e., frame
and gauge free, reformulation of quantum mechanics. To fulfil this aim, we
develop absolute quantities and the corresponding equations instead of the wave
function and the Schr\"odinger equation. The absolute quantities have a more
direct physical interpretation than the wave function has, and the
corresponding equations express explicitly the independent physical aspects of
the system which are contained in the Schr\"odinger equation in a mixed and
more hidden form. Based on the absolute quantities and equations, events,
states and physical quantities are introduced also in an absolute way. The
formalism makes it possible to obtain some sharper versions of the uncertainty
relation and to extend the validity of Ehrenfest's theorem. The absolute
formulation allows wide extensions of quantum mechanics. To give examples, we
discuss two known nonlinear extensions and, in close detail, a dissipative
system. An argument is provided that the absolute formalism may lead to an
explanation of the Aharonov-Bohm effect purely in terms of the electromagnetic
field strength tensor. At last, on special relativistic and curved spacetimes,
absolute quantities and equations instead of the Klein-Gordon wave function and
equation are given, and their nonrelativistic limit is derived.


title: Quantum Nonlocality in Phase Space

abstract:
  We propose an experiment demonstrating the nonlocality of a quantum
singlet-like state generated from a single photon incident on a beam splitter.
Each of the two spatially separated apparatuses in the setup performs a
strongly unbalanced homodyning, employing a single photon counting detector. We
show that the correlation functions violating the Bell inequalities in the
proposed experiment are given by the joint two-mode Q-function and the Wigner
function of the optical singlet-like state. This establishes a direct
relationship between two intriguing aspects of quantum mechanics: the
nonlocality of entangled states and the noncommutativity of quantum
observables, which underlies the nonclassical structure of phase space
quasidistribution functions.


title: Nonlocality of Einstein-Podolsky-Rosen State in Wigner Representation

abstract:
  We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state,
though positive definite, provides a direct evidence of the nonlocal character
of this state. The proof is based on an observation that the Wigner function
describes correlations in the joint measurement of the phase space displaced
parity operator.


title: Comment on ``Possibility of quantum mechanics being nonlocal''

abstract:
  A recent proof, formulated in the symbolic language of modal logic, shows
that a well-defined formulation of the possibility mentioned in the title is
answered affirmatively. In the paper being commented upon several proposals
were made about how to translate this symbolic proof into prose, and it was
concluded, on the basis of those proposed translations, that either the proof
was invalid or that an unwarranted reality assumption was made. However, those
interpretations deviate in small but important ways from the precise logical
path followed in the proof. It is explained here how by staying on this path
one avoids the difficulties that those deviations engendered.


title: The Time's Arrow within the Uncertainty Quantum

abstract:
  A generalized framework is developed which uses a set description instead of
wavefunction to emphasize the role of the observer. Such a framework is found
to be very effective in the study of the measurement problem and time's arrow.
Measurement in classical and quantum theory is given a unified treatment. With
the introduction of the concept of uncertainty quantum which is the basic unit
of measurement, we show that the time's arrow within the uncertainty quantum is
just opposite to the time's arrow in the observable reality. A special constant
is discussed which explains our sensation of time and provides a permanent
substrate for all change. It is shown that the whole spacetime connects
together in a delicate structure.


title:
Thermal radiation and amplified spontaneous emission from a random
  medium

abstract:
  We compute the statistics of thermal emission from systems in which the
radiation is scattered chaotically, by relating the photocount distribution to
the scattering matrix - whose statistical properties are known from
random-matrix theory. We find that the super-Poissonian noise is that of a
black body with a reduced number of degrees of freedom. The general theory is
applied to a disordered slab and to a chaotic cavity, and is extended to
include amplifying as well as absorbing systems. We predict an excess noise of
amplified spontaneous emission in a random laser below the laser threshold.


title: Levinson theorem in two dimensions

abstract:
  A two-dimensional analogue of Levinson's theorem for nonrelativistic quantum
mechanics is established, which relates the phase shift at threshold(zero
momentum) for the $m$th partial wave to the total number of bound states with
angular momentum $m\hbar(m=0,1,2,...)$ in an attractive central field.


title:
On an attempt to resolve the EPR-Bell paradox via Reichenbachian concept
  of common cause

abstract:
  Reichenbach's Common Cause Principle claims that if there is correlation
between two events and none of them is directly causally influenced by the
other, then there must exist a third event that can, as a common cause, account
for the correlation. The EPR-Bell paradox consists in the problem that we
observe correlations between spatially separated events in the EPR-experiments,
which do not admit common-cause-type explanation; and it must therefore be
inevitably concluded, that, contrary to relativity theory, in the realm of
quantum physics there exists action at a distance, or at least superluminal
causal propagation is possible; that is, either relativity theory or
Reichenbach's common cause principle fails. By means of closer analyses of the
concept of common cause and a more precise reformulation of the EPR
experimental scenario, I will sharpen the conclusion we can draw from the
violation of Bell's inequalities. It will be explicitly shown that the
correla-tions we encounter in the EPR experiment could have common causes; that
is, Reichen-bach's Common Cause Principle does not fail in quantum mechanics.
Moreover, these common causes satisfy the locality conditions usually required.
In the Revised Version of the paper I added a Postscript from which it turns
out that the solution such obtained is, contrary to the original title,
incomplete. It turns out that a new problem arises: some combinations of the
common cause events do statistically cor-relate with the measurement
operations.

categories: quant-ph gr-qc hep-th math-ph math.MP physics.hist-ph physics.pop-ph


title: Levinson theorem for Dirac particles in two dimensions

abstract:
  The Levinson theorem for nonrelativistic quantum mechanics in two spatial
dimensions is generalized to Dirac particles moving in a central field. The
theorem relates the total number of bound states with angular momentum $j$
($j=\pm 1/2, \pm 3/2, ... $), $n_j$, to the phase shifts $\eta_j(\pm E_k)$ of
scattering states at zero momentum as follows: $\eta_j(\mu)+\eta_j(-\mu)=
n_j\pi$.


title:
Nonadiabatic geometric phase for the cyclic evolution of a
  time-dependent Hamiltonian system

abstract:
  The geometric phases of the cyclic states of a generalized harmonic
oscillator with nonadiabatic time-periodic parameters are discussed in the
framework of squeezed state. It is shown that the cyclic and quasicyclic
squeezed states correspond to the periodic and quasiperiodic solutions of an
effective Hamiltonian defined on an extended phase space, respectively. The
geometric phase of the cyclic squeezed state is found to be a phase-space area
swept out by a periodic orbit. Furthermore, a class of cyclic states are
expressed as a superposition of an infinte number of squeezed states. Their
geometric phases are found to be independent of $\hbar$, and equal to
$-(n+1/2)$ times the classical nonadiabatic Hannay angle.


title:
Quantum state transformation by dispersive and absorbing four-port
  devices

abstract:
  The recently derived input-output relations for the radiation field at a
dispersive and absorbing four-port device [T. Gruner and D.-G. Welsch, Phys.
Rev. A 54, 1661 (1996)] are used to derive the unitary transformation that
relates the output quantum state to the input quantum state, including
radiation and matter and without placing frequency restrictions. It is shown
that for each frequency the transformation can be regarded as a well-behaved
SU(4) group transformation that can be decomposed into a product of U(2) and
SU(2) group transformations. Each of them may be thought of as being realized
by a particular lossless four-port device. If for narrow-bandwidth radiation
far from the medium resonances the absorption matrix of the four-port device
can be disregarded, the well-known SU(2) group transformation for a lossless
device is recognized. Explicit formulas for the transformation of Fock-states
and coherent states are given.


title: Nested quantum search and NP-complete problems

abstract:
  A quantum algorithm is known that solves an unstructured search problem in a
number of iterations of order $\sqrt{d}$, where $d$ is the dimension of the
search space, whereas any classical algorithm necessarily scales as $O(d)$. It
is shown here that an improved quantum search algorithm can be devised that
exploits the structure of a tree search problem by nesting this standard search
algorithm. The number of iterations required to find the solution of an average
instance of a constraint satisfaction problem scales as $\sqrt{d^\alpha}$, with
a constant $\alpha<1$ depending on the nesting depth and the problem
considered. When applying a single nesting level to a problem with constraints
of size 2 such as the graph coloring problem, this constant $\alpha$ is
estimated to be around 0.62 for average instances of maximum difficulty. This
corresponds to a square-root speedup over a classical nested search algorithm,
of which our presented algorithm is the quantum counterpart.


title: Quantum Zeno Dynamics and Inhibition of Geometric Phase

abstract:
  If unitary evolution of a quantum system is interrupted by a sequence of
measurements we call the dynamics as quantum Zeno dynamics. We show that under
quantum Zeno dynamics not only the transition probability (leading to quantum
Zeno effect) but also phases are affected. We call this new effect as quantum
Zeno phase effect (QZPE) which says that under repeated measurements the
geometric phase of a quantum system can be inhibited. Since geometric phase
attributes a memory to a quatum system this result also proves that under
quantum Zeno dynamics the memory of a system can be erased. We have proposed a
neutron interference experiment where this prediction can be tested. We also
beleive that with Itano's kind of set up for two-level systems this prediction
can be tested. This will provide a new way of controlling phase shift in
interference experiment by doing repeated measurements.


title: Solvable potentials, non-linear algebras, and associated coherent states

abstract:
  Using the Darboux method and its relation with supersymmetric quantum
mechanics we construct all SUSY partners of the harmonic oscillator. With the
help of the SUSY transformation we introduce ladder operators for these partner
Hamiltonians and shown that they close a quadratic algebra. The associated
coherent states are constructed and discussed in some detail.


title:
Quantum limits and symphotonic states in free-mass gravitational-wave
  antennae

abstract:
  Quantum mechanics sets severe limits on the sensitivity and required
circulating energy in traditional free-mass gravitational-wave antennas. One
possible way to avoid these restrictions is the use of intracavity QND
measurements. We analyze a new QND observable, which possesses a number of
features that make it a promising candidate for such measurements and propose a
practical scheme for the realization of this measurement. In combination with
an advanced coordinate meter, this scheme makes it possible to lower
substantially the requirements on the circulating power.


title: Quantum telecloning and multiparticle entanglement

abstract:
  A quantum telecloning process combining quantum teleportation and optimal
quantum cloning from one input to M outputs is presented. The scheme relies on
the establishment of particular multiparticle entangled states, which function
as multiuser quantum information channels. The entanglement structure of these
states is analyzed and shown to be crucial for this type of information
processing.


title:
Could quantum statistical regularities derive from a measure on the
  boundary conditions of a classical universe?

abstract:
  The problem of defining the boundary conditions for the universe is
considered here in the framework of a classical dynamical theory, pointing out
that a measure on boundary conditions must be included in the theory in order
to explain the statistical regularities of evolution. It is then suggested that
quantum statistical regularities also could derive from this measure. An
explicit definition of such a measure is proposed, using both a simplified
model of the universe based on classical mechanics and the non-relativistic
quantum mechanics formalism. The peculiarity of such a measure is that it does
not apply to the initial conditions of the universe, i.e. to the initial
positions and momenta of particles, but to their initial and final positions,
from which the path is derived by means of the least action principle. This
formulation of the problem is crucial and it is supported by the observation
that it is incorrect to liken the determination of the boundary conditions of
the universe to the preparation of a laboratory system, in which the initial
conditions of the system are obviously determined. Some possible objections to
this theory are then discussed. Specifically, the EPR paradox is discussed, and
it is explained by showing that, in general, a measure on the boundary
conditions of the universe generates preinteractive correlations, and that in
the presence of such correlations Bell's inequality can no longer be proven
true. Finally, it is shown that if one broadens the dynamical scheme of the
theory to encompass phenomena such as particle decay and annihilation, the
least action principle allows for an indeterministic evolution of the system.


title: Fast versions of Shor's quantum factoring algorithm

abstract:
  We present fast and highly parallelized versions of Shor's algorithm. With a
sizable quantum computer it would then be possible to factor numbers with
millions of digits. The main algorithm presented here uses FFT-based fast
integer multiplication. The quick reader can just read the introduction and the
``Results'' section.


title: General radiation states and Bell's inequalities

abstract:
  The connection between quantum optical nonclassicality and the violation of
Bell's inequalities is explored. Bell type inequalities for the electromagnetic
field are formulated for general states(arbitrary number or photons, pure or
mixed) of quantised radiation and their violation is connected to other
nonclassical properties of the field. Classical states are shown to obey these
inequalities and for the family of centered Gaussian states the direct
connection between violation of Bell-type inequalities and squeezing is
established.


title: Exploiting Particle Statistics in Quantum Computation

abstract:
  We describe a plausible-speculative form of quantum computation which
exploits particle (fermionic, bosonic) statistics, under a generalized,
counterfactual interpretation thereof. In the idealized situation of an
isolated system, it seems that this form of computation yields to
NP-complete=P.


title:
Fundamentals of Relativity Providing Time, Distance and Velocity
  Standards

abstract:
  The paper presents an attempt to suggest an alternative way of considering
the fundamentals of Einstein's special relativity theory. Its formulation based
on introducing an inertial reference system by rigid linking of clocks to a
free entity to define proper time is self-contradictory since the operation of
rigid linking involves interaction which is excluded by definition for a free
entity. The way to overcome this inconsistency is proposed by postulating that
each free entity (object, particle) has to be ideal clocks by itself, providing
ideal internal time standards defined by the only intrinsic feature of a free
entity, namely its proper mass which means that de Broglie's periodic
phenomenon has to be considered as a fundamental principle needed to built the
special relativity, along with the principle of indistinguishability allowing
to define the particle's proper mass with ideal accuracy. Further, the internal
distance standard is provided by passing to Compton wavelength and the velocity
standard is introduced by means of Hubble's law. It is proposed to interpret
the wave function as an internal system of reference undergoing distortion when
external interaction is included.


title: Quantum Games and Quantum Strategies

abstract:
  We investigate the quantization of non-zero sum games. For the particular
case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma
if quantum strategies are allowed for. We also construct a particular quantum
strategy which always gives reward if played against any classical strategy.


title:
SU(N) x S_{m}-Invariant Eigenspaces of N^{m} x N^{m} Mean Density
  Matrices

abstract:
  We extend to additional probability measures and scenarios, certain of the
recent results of Krattenthaler and Slater (quant-ph/9612043), whose original
motivation was to obtain quantum analogs of seminal work on universal data
compression of Clarke and Barron. KS obtained explicit formulas for the
eigenvalues and eigenvectors of the 2^m x 2^m density matrices derived by
averaging the m-fold tensor products with themselves of the 2 x 2 density
matrices. The weighting was done with respect to a one-parameter (u) family of
probability distributions, all the members of which are spherically-symmetric
(SU(2)-invariant) over the ``Bloch sphere'' of two-level quantum systems. For u
= 1/2, one obtains the normalized volume element of the minimal monotone
(Bures) metric. In this paper, analyses parallel to those of KS are conducted,
based on an alternative "natural" measure on the density matrices recently
proposed by Zyczkowski, Horodecki, Sanpera, and Lewenstein (quant-ph/9804024).
The approaches of KS and that based on ZHSL are found to yield [1 + m/2]
identical SU(2) x S_{m}-invariant eigenspaces (but not coincident eigenvalues
for m > 3). Companion results, based on the SU(3) form of the ZHSL measure, are
obtained for the twofold and threefold tensor products of the 3 x 3 density
matrices. We find a rather remarkable limiting procedure (selection rule) for
recovering from these analyses, the (permutationally-symmetrized) multiplets of
SU(3) constructed from two or three particles. We also analyze the scenarios
(all for m = 2) N = 2 x 3, N= 2 x 3 x 2, N= 3 x 2 x 2 and N = 4 and, in
addition, generalize the ZHSL measure, so that it incorporates a family of
(symmetric) Dirichlet distributions (rather than simply the uniform
distribution), defined on the (N-1)-dimensional simplex of eigenvalues.


title: Two Classical Queries versus One Quantum Query

abstract:
  In this note we study the power of so called query-limited computers. We
compare the strength of a classical computer that is allowed to ask two
questions to an NP-oracle with the strength of a quantum computer that is
allowed only one such query. It is shown that any decision problem that
requires two parallel (non-adaptive) SAT-queries on a classical computer can
also be solved exactly by a quantum computer using only one SAT-oracle call,
where both computations have polynomial time-complexity. Such a simulation is
generally believed to be impossible for a one-query classical computer. The
reduction also does not hold if we replace the SAT-oracle by a general
black-box. This result gives therefore an example of how a quantum computer is
probably more powerful than a classical computer. It also highlights the
potential differences between quantum complexity results for general oracles
when compared to results for more structured tasks like the SAT-problem.


title:
An efficient scheme for the deterministic maximal entanglement of N
  trapped ions

abstract:
  We propose a method for generating maximally entangled states of N two-level
trapped ions. The method is deterministic and independent of the number of ions
in the trap. It involves a controlled-NOT acting simultaneously on all the ions
through a dispersive interaction. We explore the potential application of our
scheme for high precision frequency standards.


title:
Chaos, Thermodynamics and Quantum Mechanics: an Application to Celestial
  Dynamics

abstract:
  We address the issue of the quantum-classical correspondence in chaotic
systems using, as recently done by Zurek [e-print quant-ph/9802054], the solar
system as a whole as a case study: this author shows that the classicality of
the planetary motion is ensured by the environment-induced decoherence. We show
that equivalent results are provided by the theories of spontaneous
fluctuations and that these latter theories, in some cases, result in a still
faster process of decoherence. We show that, as an additional benefit, the
assumption of spontaneous fluctuation makes it possible to genuinely derive
thermodynamics from mechanics, namely, without implicitly assuming
thermodynamics.


title: Reconstruction of Liouvillian Superoperators

abstract:
  We show how to determine (reconstruct) a master equation governing the time
evolution of an open quantum system.
  We present a general algorithm for the reconstruction of the corresponding
Liouvillian superoperators. Dynamics of a two-level atom in various
environments is discussed in detail.


title: Robustness of entanglement

abstract:
  In the quest of completely describing entanglement in the general case of a
finite number of parties sharing a physical system of finite dimensional
Hilbert space a new entanglement magnitude is introduced for its pure and mixed
states: robustness. It corresponds to the minimal amount of mixing with locally
prepared states which washes out all entanglement. It quantifies in a sense the
endurence of entanglement against noise and jamming. Its properties are studied
comprehensively. Analytical expressions for the robustness are given for pure
states of binary systems, and analytical bounds for mixed states of binary
systems. Specific results are obtained mainly for the qubit-qubit system. As
byproducts local pseudomixtures are generalized, a lower bound for the relative
volume of separable states is deduced and arguments for considering convexity a
necessary condition of any entanglement magnitude are put forward.


title: Simulating quantum operations with mixed environments

abstract:
  We study the physical resources required to implement general quantum
operations, and provide new bounds on the minimum possible size which an
environment must be in order to perform certain quantum operations. We prove
that contrary to a previous conjecture, not all quantum operations on a
single-qubit can be implemented with a single-qubit environment, even if that
environment is initially prepared in a mixed state. We show that a mixed
single-qutrit environment is sufficient to implement a special class of
operations, the generalized depolarizing channels.


title:
One-Parameter Squeezed Gaussian States of Time-Dependent Harmonic
  Oscillator and Selection Rule for Vacuum States

abstract:
  By using the invariant method we find one-parameter squeezed Gaussian states
for both time-independent and time-dependent oscillators. The squeezing
parameter is expressed in terms of energy expectation value for
time-independent case and represents the degree of mixing positive and negative
frequency solutions for time-dependent case. A {\it minimum uncertainty
proposal} is advanced to select uniquely vacuum states at each moment of time.
We show that the Gaussian states with minimum uncertainty coincide with the
true vacuum state for time-independent oscillator and the Bunch-Davies vacuum
for a massive scalar field in a de Sitter spacetime.


title: Quantum Localisation Observables and Accelerated Frames

abstract:
  We define quantum observables associated with Einstein localisation in
space-time. These observables are built on Poincare' and dilatation generators.
Their commutators are given by spin observables defined from the same symmetry
generators. Their shifts under transformations to uniformly accelerated frames
are evaluated through algebraic computations in conformal algebra. Spin number
is found to vary under such transformations with a variation involving further
observables introduced as irreducible quadrupole momenta. Quadrupole
observables may be dealt with as non commutative polarisations which allow one
to define step operators increasing or decreasing the spin number by unity.


title: Quantum state engineering via unitary transformations

abstract:
  We construct a Hamiltonian for the generation of arbitrary pure states of the
quantized electromagnetic field. The proposition is based upon the fact that a
unitary transformation for the generation of number states has been already
found. The general unitary transformation here obtained, would allow the use of
nonlinear interactions for the production of pure states. We discuss the
applicability of this method by giving examples of generation of simple
superposition states. We also compare our Hamiltonian with the one resulting
from the interaction of trapped ions with two laser fields.


title:
Quantum Mechanics without Waves: a Generalization of Classical
  Statistical Mechanics

abstract:
  We generalize classical statistical mechanics to describe the kinematics and
the dynamics of systems whose variables are constrained by a single quantum
postulate (discreteness of the spectrum of values of at least one variable of
the theory). This is possible provided we adopt Feynman's suggestion of
dropping the assumption that the probability for an event must always be a
positive number. This approach has the advantage of allowing a reformulation of
quantum theory in phase space without introducing the unphysical concept of
probability amplitudes, together with all the problems concerning their
ambiguous properties.

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


title:
Time-Dependent Diffeomorphisms as Quantum Canonical Transformations and
  the Time-Dependent Harmonic Oscillator

abstract:
  Quantum canonical transformations corresponding to time-dependent
diffeomorphisms of the configuration space are studied. A special class of
these transformations which correspond to time-dependent dilatations is used to
identify a previously unknown class of exactly solvable time-dependent harmonic
oscillators. The Caldirola-Kanai oscillator belongs to this class. For a
general time-dependent harmonic oscillator, it is shown that choosing the
dilatation parameter to satisfy the classical equation of motion, one obtains
the solution of the Schr\"odinger equation. A simple generalization of this
result leads to the reduction of the Schr\"odinger equation to a second order
ordinary differential equation whose special case is the auxiliary equation of
the Lewis-Riesenfeld invariant theory. Time-evolution operator is expressed in
terms of a positive real solution of this equation in a closed form, and the
time-dependent position and momentum operators are calculated.


title: Relativistic Adiabatic Approximation and Geometric Phase

abstract:
  A relativistic analogue of the quantum adiabatic approximation is developed
for Klein-Gordon fields minimally coupled to electromagnetism, gravity and an
arbitrary scalar potential. The corresponding adiabatic dynamical and
geometrical phases are calculated. The method introduced in this paper avoids
the use of an inner product on the space of solutions of the Klein-Gordon
equation. Its practical advantages are demonstrated in the analysis of the
relativistic Landau level problem and the rotating cosmic string.


title: Decoherence Free Subspaces for Quantum Computation

abstract:
  Decoherence in quantum computers is formulated within the Semigroup approach.
The error generators are identified with the generators of a Lie algebra. This
allows for a comprehensive description which includes as a special case the
frequently assumed spin-boson model. A generic condition is presented for
error-less quantum computation: decoherence-free subspaces are spanned by those
states which are annihilated by all the generators. It is shown that these
subspaces are stable to perturbations and moreover, that universal quantum
computation is possible within them.


title: A Note on (Spin-) Coherent-State Path Integral

abstract:
  It is pointed out that there are some fundamental difficulties with the
frequently used continuous-time formalism of the spin-coherent-state path
integral. They arise already in a single-spin system and at the level of the
"classical action" not to speak of fluctuations around the "classical path".
Similar difficulties turn out to be present in the case of the
(boson-)coherent-state path integral as well; although partially circumventable
by an ingenious trick (Klauder's $\epsilon$-prescription) at the "classical
level", they manifest themselves at the level of fluctuations. Detailed
analysis of the origin of these difficulties makes it clear that the only way
of avoiding them is to work with the proper discrete-time formalism. The thesis
is explicitly illustrated with a harmonic oscillator and a spin under a
constant magnetic field.


title: The Heisenberg Representation of Quantum Computers

abstract:
  Since Shor's discovery of an algorithm to factor numbers on a quantum
computer in polynomial time, quantum computation has become a subject of
immense interest. Unfortunately, one of the key features of quantum computers -
the difficulty of describing them on classical computers - also makes it
difficult to describe and understand precisely what can be done with them. A
formalism describing the evolution of operators rather than states has proven
extremely fruitful in understanding an important class of quantum operations.
States used in error correction and certain communication protocols can be
described by their stabilizer, a group of tensor products of Pauli matrices.
Even this simple group structure is sufficient to allow a rich range of quantum
effects, although it falls short of the full power of quantum computation.


title:
Algorithmic randomness, physical entropy, measurements, and the Demon of
  Choice

abstract:
  Measurements --- interactions which establish correlations between a system
and a recording device --- can be made thermodynamically reversible. One might
be concerned that such reversibility will make the second law of thermodynamics
vulnerable to the designs of the demon of choice, a selective version of
Maxwell's demon. The strategy of the demon of choice is to take advantage of
rare fluctuations to extract useful work, and to reversibly undo measurements
which do not lead to such a favorable but unlikely outcomes. I show that this
threat does not arise as the demon of choice cannot operate without recording
(explicitely or implicitely) whether its measurement was a success (or a
failure). Thermodynamic cost associated with such a record cannot be, on the
average, made smaller than the gain of useful work derived from the
fluctuations.


title: Languages of Quantum Information Theory

abstract:
  This note will introduce some notation and definitions for information
theoretic quantities in the context of quantum systems, such as (conditional)
entropy and (conditional) mutual information. We will employ the natural
C*-algebra formalism, and it turns out that one has an allover dualism of
language: we can define everything for (compatible) observables, but also for
(compatible) C*-subalgebras. The two approaches are unified in the formalism of
quantum operations, and they are connected by a very satisfying inequality,
generalizing the well known Holevo bound. Then we turn to communication via
(discrete memoryless) quantum channels: we formulate the Fano inequality, bound
the capacity region of quantum multiway channels, and comment on the quantum
broadcast channel.


title:
Calculating the Thermal Rate Constant with Exponential Speed-Up on a
  Quantum Computer

abstract:
  It is shown how to formulate the ubiquitous quantum chemistry problem of
calculating the thermal rate constant on a quantum computer. The resulting
exact algorithm scales exponentially faster with the dimensionality of the
system than all known ``classical'' algorithms for this problem.


title: Optimal Cloning of Pure States, Judging Single Clones

abstract:
  We consider quantum devices for turning a finite number N of d-level quantum
systems in the same unknown pure state \sigma into M>N systems of the same
kind, in an approximation of the M-fold tensor product of the state \sigma. In
a previous paper it was shown that this problem has a unique optimal solution,
when the quality of the output is judged by arbitrary measurements, involving
also the correlations between the clones. We show in this paper, that if the
quality judgement is based solely on measurements of single output clones,
there is again a unique optimal cloning device, which coincides with the one
found previously.


title:
Entanglement Induced Radiation Processes Which are First Order in Weak
  Field

abstract:
  Nonlinear processes of light scattering on a two-level system near resonance
are considered. The problem is reduced to the emission and absorption of an
entangled system, formed by a strong resonant field and a two-level system,
having a non-factorizing wave function.


title: Deutsch-Jozsa algorithm as a test of quantum computation

abstract:
  A redundancy in the existing Deutsch-Jozsa quantum algorithm is removed and a
refined algorithm, which reduces the size of the register and simplifies the
function evaluation, is proposed. The refined version allows a simpler analysis
of the use of entanglement between the qubits in the algorithm and provides
criteria for deciding when the Deutsch-Jozsa algorithm constitutes a meaningful
test of quantum computation.


title: Experimental scheme for quantum teleportation of a single-photon packet

abstract:
  Both complete protocol and optical setup for experimental realization of
quantum teleportation of unknown single-photon wave packet are proposed.


title:
Absorption with inversion and amplification without inversion in a
  coherently prepared V - system: a dressed state approach

abstract:
  Light induced absorption with population inversion and amplification without
population inversion (LWI) in a coherently prepared closed three level V - type
system are investigated. This study is performed from the point of view of a
two color dressed state basis. Both of these processes are possible due to
atomic coherence and quantum interference contrary to simple intuitive
predictions. Merely on physical basis, one would expect a complementary process
to the amplification without inversion. We believe that absorption in the
presence of population inversion found in the dressed state picture utilized in
this study, constitutes such a process.
  Novel approximate analytic time dependent solutions, for coherences and
populations are obtained, and are compared with full numerical solutions
exhibiting excellent agreement. Steady state quantities are also calculated,
and the conditions under which the system exhibits absorption and gain with and
without inversion, in the dressed state representation are derived. It is found
that for a weak probe laser field absorption with inversion and amplification
without inversion may occur, for a range of system parameters.


title:
Closing a Loophole in the Case Against the Counterfactual Usage of the
  ABL Rule

abstract:
  A currently discussed interpretation of quantum theory, Time-Symmetrized
Quantum Theory, makes certain claims about the properties of systems between
pre- and post- selection measurements. These claims are based on a
counterfactual usage of the Aharonov-Bergmann-Lebowitz (ABL) rule for
calculating the probabilities of measurement outcomes between such
measurements. It has been argued by several authors that the counterfactual
usage of the ABL rule is, in general, incorrect. This paper examines what might
appear to be a loophole in those arguments and shows that this apparent
loophole cannot be used to support a counterfactual interpretation of the ABL
rule. It is noted that the invalidity of the counterfactual usage of the ABL
rule implies that the characterization of those outcomes receiving probability
1 in a counterfactual application of the rule as `elements of reality' is, in
general, unfounded.


title: Spin in a variable magnetic field: the adiabatic approximation

abstract:
  The problem of spin precession in a time-dependent magnetic field is
considered in the adiabatic approximation where the field direction or the
angular velocity of its rotation is changing slowly. The precession angles are
given by integrals in a way similar to the semi-classical approximation for the
Schr\"{o}dinger equation.


title: All the Bell inequalities

abstract:
  Bell inequalities are derived for any number of observers, any number of
alternative setups for each one of them, and any number of distinct outcomes
for each experiment. It is shown that if a physical system consists of several
distant subsystems, and if the results of tests performed on the latter are
determined by local variables with objective values, then the joint
probabilities for triggering any given set of distant detectors are convex
combinations of a finite number of Boolean arrays, whose components are either
0 or 1 according to a simple rule. This convexity property is both necessary
and sufficient for the existence of local objective variables. It leads to a
simple graphical method which produces a large number of generalized Clauser-
Horne inequalities corresponding to the faces of a convex polytope. It is
plausible that quantum systems whose density matrix has a positive partial
transposition satisfy all these inequalities, and therefore are compatible with
local objective variables, even if their quantum properties are essentially
nonlocal.


title: Retroactive quantum jumps in a strongly-coupled atom-field system

abstract:
  We investigate a novel type of conditional dynamic that occurs in the
strongly-driven Jaynes-Cummings model with dissipation. Extending the work of
Alsing and Carmichael [Quantum Opt. {\bf 3}, 13 (1991)], we present a combined
numerical and analytic study of the Stochastic Master Equation that describes
the system's conditional evolution when the cavity output is continuously
observed via homodyne detection, but atomic spontaneous emission is not
monitored at all. We find that quantum jumps of the atomic state are induced by
its dynamical coupling to the optical field, in order retroactively to justify
atypical fluctuations in ocurring in the homodyne photocurrent.


title: The Capacity of the Quantum Multiple Access Channel

abstract:
  We define classical-quantum multiway channels for transmission of classical
information, after recent work by Allahverdyan and Saakian. Bounds on the
capacity region are derived in a uniform way, which are analogous to the
classically known ones, simply replacing Shannon entropy with von Neumann
entropy. For the single receiver case (multiple access channel) the exact
capacity region is determined. These results are applied to the case of noisy
channels, with arbitrary input signal states. A second issue of this work is
the presentation of a calculus of quantum information quantities, based on the
algebraic formulation of quantum theory.


title: How to Teleport Superpositions of Chiral Amplitudes

abstract:
  Chiral molecules may exist in superpositions of left- and right-handed
states. We show how the amplitudes of such superpositions may be teleported to
the polarization degrees of freedom of a photon and thus measured. Two
experimental schemes are proposed, one leading to perfect, the other to
state-dependent teleportation. Both methods yield complete information about
the amplitudes.


title:
Electron-radiation interaction in a Penning trap: beyond the dipole
  approximation

abstract:
  We investigate the physics of a single trapped electron interacting with a
radiation field without the dipole approximation. This gives new physical
insights in the so-called geonium theory.


title: Unambiguous Discrimination Between Linearly-Independent Quantum States

abstract:
  The theory of generalised measurements is used to examine the problem of
discriminating unambiguously between non-orthogonal pure quantum states.
Measurements of this type never give erroneous results, although, in general,
there will be a non-zero probability of a result being inconclusive. It is
shown that only linearly-independent states can be unambiguously discriminated.
In addition to examining the general properties of such measurements, we
discuss their application to entanglement concentration.


title:
Optimum Unambiguous Discrimination Between Linearly Independent
  Symmetric States

abstract:
  The quantum formalism permits one to discriminate sometimes between any set
of linearly-independent pure states with certainty. We obtain the maximum
probability with which a set of equally-likely, symmetric, linearly-independent
states can be discriminated. The form of this bound is examined for symmetric
coherent states of a harmonic oscillator or field mode.


title: Unraveling quantum dissipation in the frequency domain

abstract:
  We present a quantum Monte Carlo method for solving the evolution of an open
quantum system. In our approach, the density operator evolution is unraveled in
the frequency domain. Significant advantages of this approach arise when the
frequency of each dissipative event conveys information about the state of the
system.


title: Quasi-Exactly Solvable Potentials with Three Known Eigenstates

abstract:
  We propose a new SUSY method for construction of the quasi-exactly solvable
(QES) potentials with three known eigenstates. New QES potentials and
corresponding energy levels and wave functions of the ground state and two
lowest excited state are obtained. The proposed scheme allows also to construct
families of exactly solvable non-singular potentials which are SUSY partners of
the well-known ones.


title: Simulation of finite state machines in a quantum computer

abstract:
  A construction is given for simulating any deterministic finite state machine
(FSM) on a quantum computer in a space-efficient manner. By constructing a
superposition of input strings of lengths K or less, questions can be asked
about the FSM, such as the inputs that reach particular nodes, and the answers
can be found using a search algorithm such as Grover's. This has implications
for the eventual utility of quantum computers for software validation.


title:
Grover's Quantum Search Algorithm for an Arbitrary Initial Amplitude
  Distribution

abstract:
  Grover's algorithm for quantum searching is generalized to deal with
arbitrary initial complex amplitude distributions. First order linear
difference equations are found for the time evolution of the amplitudes of the
marked and unmarked states. These equations are solved exactly. New expressions
are derived for the optimal time of measurement and the maximal probability of
success. They are found to depend on the averages and variances of the initial
amplitude distributions of the marked and unmarked states, but not on higher
moments. Our results imply that Grover's algorithm is robust against modest
noise in the amplitude initialization procedure.


title: Non-Markovian quantum trajectories for spectral detection

abstract:
  We present a formulation of non-Markovian quantum trajectories for open
systems from a measurement theory perspective. In our treatment there are three
distinct ways in which non-Markovian behavior can arise; a mode dependent
coupling between bath (reservoir) and system, a dispersive bath, and by
spectral detection of the output into the bath. In the first two cases the
non-Markovian behavior is intrinsic to the interaction, in the third case the
non-Markovian behavior arises from the method of detection. We focus in detail
on the trajectories which simulate real-time spectral detection of the light
emitted from a localized system. In this case, the non-Markovian behavior
arises from the uncertainty in the time of emission of particles that are later
detected. The results of computer simulations of the spectral detection of the
spontaneous emission from a strongly driven two-level atom are presented.


title: On Quantum Algorithms for Noncommutative Hidden Subgroups

abstract:
  Quantum algorithms for factoring and discrete logarithm have previously been
generalized to finding hidden subgroups of finite Abelian groups. This paper
explores the possibility of extending this general viewpoint to finding hidden
subgroups of noncommutative groups. We present a quantum algorithm for the
special case of dihedral groups which determines the hidden subgroup in a
linear number of calls to the input function. We also explore the difficulties
of developing an algorithm to process the data to explicitly calculate a
generating set for the subgroup. A general framework for the noncommutative
hidden subgroup problem is discussed and we indicate future research
directions.


title:
"Interaction--free'' interaction: entangling evolution via quantum Zeno
  effect

abstract:
  The effect of entangling evolution induced by frequently repeated quantum
measurement is presented. The interesting possibility of conditional freezing
the system in maximally entangled state out of Zeno effect regime is also
revealed. The illustration of the phenomena in terms of dynamical version of
``interaction free'' measurement is presented. Some general conclusions are
provided.


title: Tomography of Quantum Spinor States

abstract:
  A possibility of describing two-level atom states in terms of positive
probability distributions (analog to the symplectic tomography scheme) is
considered. As a result the basis of the irreducible representation of a
rotation group can be realized by a family of the probability distributions of
the spin projection parametrized by points on the sphere. Furthermore the
tomography of rotational states of molecules and nuclei which can be described
by the model of a symmetric top is discussed.


title: Quantum Robots Plus Environments

abstract:
  A quantum robot is a mobile quantum system including an on bord quantum
computer and ancillary systems, that interact with an environment of quantum
systems. Quantum robots carry out tasks whose goals include carrying out
measurements and physical experiments on the environment. Environments
considered so far in the literature: oracles, data bases, and quantum
registers, are shown to be special cases of environments considered here. It is
noted that quantum robots should include a quantum computer and cannot be
simply a multistate head. A model is discussed in which each task, as a
sequence of computation and action phases, is described by a unitary step
operator. Overall system dynamics is described in terms of a Feynman sum over
paths of completed computation and action phases. A simple task example,
measuring the distance between the quantum robot and a particle on a 1D space
lattice, with quantum phase path and time duration dispersion present, is
analyzed.


title: The Continuum Limit and Integral Vacuum Charge

abstract:
  We investigate a commonly used formula which seems to give non-integral
vacuum charge in the continuum limit. We show that the limit is subtle and care
must be taken to get correct results.


title: A comparison of entanglement measures

abstract:
  We compare the entanglement of formation with a measure defined as the
modulus of the negative eigenvalue of the partial transpose. In particular, we
investigate whether both measures give the same ordering of density operators
with respect to the amount of entanglement.


title: What is in One: Uncertainty quantum and Continuum Hypothesis

abstract:
  The concept of measurement is discussed. It is argued that counting process
in mathematics is also measurement which requires a basic unit. The idea of
scale is put forward. The basic unit itself, which are composed of the
infinitesimal of uncertainty quantum, can be regarded as infinite in another
scale. Thus infinite, infinitesimal and integer " 1 " are unified. It is
proposed that multiplication changes to summation when it is transformed to a
larger scale. The Continuum Hypothesis is proved to be correct after a scale
transformation.


title: Momentum distribution of confined bosons: temperature dependence

abstract:
  The momentum distribution function of a parabolically confined gas of bosons
with harmonic interparticle interactions is derived. In the Bose-Einstein
condensation region, this momentum distribution substantially deviates from a
Maxwell-Boltzmann distribution. It is argued that the determination of the
temperature of the boson gas from the Bose-Einstein momentum distribution
function is more appropriate than the currently used fitting to the high
momentum tail of the Maxwell-Boltzmann distribution.