title:
Displacement-Operator Squeezed States. II. Examples of Time-Dependent
  Systems Having Isomorphic Symmetry Algebras

abstract:
  In this article, results from the previous paper (I) are applied to
calculations of squeezed states for such well-known systems as the harmonic
oscillator, free particle, linear potential, oscillator with a uniform driving
force, and repulsive oscillator. For each example, expressions for the
expectation values of position and momentum are derived in terms of the initial
position and momentum, as well as in the $(\alpha,z)$- and in the
$(z,\alpha)$-representations described in I. The dependence of the
squeezed-state uncertainty products on the time and on the squeezing parameters
are determined for each system.


title: Decoherence and Efficiency of Quantum Error Correction

abstract:
  Certain physical aspects of quantum error correction are discussed for a
quantum computer (n-qubit register) in contact with a decohering environment.
Under rather plausible assumptions upon the form of the computer-environment
interaction, the efficiency of a general correcting procedure is evaluated as a
function of the spontaneous-decay duration and the rank of errors covered by
the procedure. It is proved that the probability of errors can be made
arbitrarily small by enhancing the correction method, provided the decohering
interaction is represented by a bounded operator.


title: The Ion Trap Quantum Information Processor

abstract:
  An introductory review of the linear ion trap is given, with particular
regard to its use for quantum information processing. The discussion aims to
bring together ideas from information theory and experimental ion trapping, to
provide a resource to workers unfamiliar with one or the other of these
subjects. It is shown that information theory provides valuable concepts for
the experimental use of ion traps, especially error correction, and conversely
the ion trap provides a valuable link between information theory and physics,
with attendant physical insights. Example parameters are given for the case of
calcium ions. Passive stabilisation will allow about 200 computing operations
on 10 ions; with error correction this can be greatly extended.


title: Concatenated Quantum Codes

abstract:
  One of the main problems for the future of practical quantum computing is to
stabilize the computation against unwanted interactions with the environment
and imperfections in the applied operations. Existing proposals for quantum
memories and quantum channels require gates with asymptotically zero error to
store or transmit an input quantum state for arbitrarily long times or
distances with fixed error. In this report a method is given which has the
property that to store or transmit a qubit with maximum error $\epsilon$
requires gates with error at most $c\epsilon$ and storage or channel elements
with error at most $\epsilon$, independent of how long we wish to store the
state or how far we wish to transmit it. The method relies on using
concatenated quantum codes with hierarchically implemented recovery operations.
The overhead of the method is polynomial in the time of storage or the distance
of the transmission. Rigorous and heuristic lower bounds for the constant $c$
are given.


title: Time-of-arrival formalism for the relativistic particle

abstract:
  A suitable operator for the time-of-arrival at a detector is defined for the
free relativistic particle in 3+1 dimensions. For each detector position, there
exists a subspace of detected states in the Hilbert space of solutions to the
Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of
the time-of-arrival operator apply inside this subspace, opening up a standard
probabilistic interpretation.


title:
Extra-symmetric Born--Infeld theory of electroweak and gravitational
  fields

abstract:
  This paper suggests a generalization of the Born--Infeld action (1932) for
the case of electroweak and gravitational fields. Basic notions one deals with
are Dirac matrices, $\gamma_{a}$, and dimensionless covariant derivatives,
$\pi_{a} = - i\ell \nabla_{a}$, given in spinorial and scalar representations.
The action contains a characteristic length $\ell$ (which is of order of
magnitude of Planck's length), as a parameter and possesses an extra symmetry
with respect to transformations of the Lorentz group imposed on pairs
($\gamma_{a}$, $\pi_{a}$). It's shown that parameter of the Lorentz group is
associated with a constant value of the electroweak potential at spatial
infinity.


title: Instantonic approach to triple well potential

abstract:
  By using a usual instanton method we obtain the energy splitting due to
quantum tunneling through the triple well barrier. It is shown that the term
related to the midpoint of the energy splitting in propagator is quite
different from that of double well case, in that it is proportional to the
algebraic average of the frequencies of the left and central wells.


title:
$sl(2)$ variational schemes for solving one class of quantum nonlinear
  models

abstract:
  Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum
models, including multiboson and frequency conversion ones, are expressed as
non-linear functions of $sl(2)$ generators. It enables us to use standard
variational schemes, based on $sl(2)$ generalized coherent states as trial
functions, for solving both spectral and evolution tasks. In such a manner a
new analytical expression is found for energy spectra in a mean-field
approximation which is beyond quasi-equidistant ones obtained earlier.


title: Comment on quant-ph/9509008 by Kumar and Khare

abstract: One can find some comments related to the isospectral issue


title: Path Integral in Holomorphic Representation without Gauge Fixation

abstract:
  A method of path integral construction without gauge fixing in the
holomorphic representation is proposed for finite-dimensional gauge models.
This path integral determines a manifestly gauge-invariant kernel of the
evolution operator.


title: Comment on ``Hidden quantum nonlocality revealed by local filters''

abstract:
  In Section 3 of his paper (N. Gisin, Phys. Lett. A 210 (1996) 151), Gisin
argues that a ``careless application of generalized quantum measurements can
violate Bell's inequality even for mixtures of product states.'' However, the
observed violation of the CHSH inequality is not in fact due to the application
of generalized quantum measurements, but rather to a misapplication of the
inequality itself -- to conditional expectations in which the conditioning
depends upon the measurements under consideration.


title: Dynamical identification of open quantum systems

abstract:
  I propose a quantum trajectories approach to parametric identification of the
effective Hamiltonian for a Markovian open quantum system, and discuss an
application motivated by recent experiments in cavity quantum electrodynamics.
This example illustrates a strategy for quantum parameter estimation that
efficiently utilizes the information carried by correlations between
measurements distributed in time.


title: Nonclassical interferometry with intelligent light

abstract:
  We study the phase sensitivity of SU(2) and SU(1,1) interferometers fed by
two-mode field states which are intelligent states for Hermitian generators of
the SU(2) and SU(1,1) groups, respectively. Intelligent states minimize
uncertainty relations and this makes possible an essential reduction of the
quantum noise in interferometers. Exact closed expressions for the minimum
detectable phase shift are obtained in terms of the Jacobi polynomials. These
expressions are compared with results for some conventional input states, and
some known results for the squeezed input states are reviewed. It is shown that
the phase sensitivity for an interferometer that employs squeezing-producing
active devices (such as four-wave mixers) should be analyzed in two regimes:
(i) fixed input state and variable interferometer, and (ii) fixed
interferometer and variable input state. The behavior of the phase sensitivity
is essentially different in these two regimes. The use of the SU(2) intelligent
states allows us to achieve a phase sensitivity of order $1/\bar{N}$ (where
$\bar{N}$ is the total number of photons passing through the phase shifters of
the interferometer) without adding four-wave mixers. This avoids the duality in
the behavior of the phase sensitivity that occurs for the squeezed input. On
the other hand, the SU(1,1) intelligent states have the property of achieving
the phase sensitivity of order $1/\bar{N}$ in both regimes.


title: Coherent states for quantum systems with a trilinear boson Hamiltonian

abstract:
  We introduce a set of coherent states which are associated with quantum
systems governed by a trilinear boson Hamiltonian. These states are produced by
the action of a nonunitary displacement operator on a reference state and can
be equivalently defined by some eigenvalue equations. The system prepared
initially in the reference state will evolve into the coherent state during the
first instants of the interaction process. Some properties of the coherent
states are discussed. In particular, the resolution of the identity is derived
and the related analytic representation in the complex plane is developed. It
is shown that this analytic representation coincides with a double
representation based on the Glauber coherent states of the pump mode and on the
SU(1,1) Perelomov coherent states of the signal-idler system. Entanglement
between the field modes and photon statistics of the coherent states are
studied. Connections between the coherent states and the long-time evolution
induced by the trilinear Hamiltonian are considered.


title: Beneath Gauge

abstract:
  Seeking a relativistic quantum infrastructure for gauge physics, we analyze
spacetime into three levels of quantum aggregation analogous to atoms, bonds
and crystals. Quantum spacetime points with no extension make up more complex
link units with microscopic extension, which make up networks with macroscopic
extension. Such a multilevel quantum theory implies parastatistics for the
lowest level entities without additional physical assumptions. Any hypercubical
vacuum mode with off-diagonal long-range order that is covariant under
$\POINCARE$ also has bonus internal symmetries somewhat like those of the
standard model. A vacuum made with the dipole link proposed earlier has too
much symmetry. A quadrupole link solves this problem.


title: Hypercrystalline vacua

abstract:
  Let a quantum network be a Fermi-Dirac assembly of Fermi-Dirac assemblies of
...of quantum points, interpreted topologically. The simplest quantum-network
vacuum modes with exact conservation of relativistic energy-momentum and
angular momentum also support the local non-Abelian groups of the standard
model, torsion and gravity. The spacetime points of these models naturally obey
parastatistics. We construct a left-handed vacuum network among others.


title: Reducing Quantum Errors and Improving Large Scale Quantum Cryptography

abstract:
  Noise causes severe difficulties in implementing quantum computing and
quantum cryptography. Several schemes have been suggested to reduce this
problem, mainly focusing on quantum computation. Motivated by quantum
cryptography, we suggest a coding which uses $N$ quantum bits ($N=n^2$) to
encode one quantum bit, and reduces the error exponentially with $n$. Our
result suggests the possibility of distributing a secure key over very long
distances, and maintaining quantum states for very long times. It also provides
a new quantum privacy amplification against a strong adversary.


title: Quantum Reed-Muller Codes

abstract:
  A set of quantum error correcting codes based on classical Reed-Muller codes
is described. The codes have parameters [[n,k,d]] = [[2^r, 2^r - C(r,t) - 2
sum_{i=0}^{t-1} C(r,i), 2^t + 2^{t-1} ]].


title: On a Generalized Oscillator System: Interbasis Expansions

abstract:
  This article deals with a nonrelativistic quantum mechanical study of a
dynamical system which generalizes the isotropic harmonic oscillator system in
three dimensions. The problem of interbasis expansions of the wavefunctions is
completely solved. A connection between the generalized oscillator system
(projected on the z-line) and the Morse system (in one dimension) is discussed.


title:
Conditional generation of error syndromes in fault-tolerant error
  correction

abstract:
  In this paper we show how the fault--tolerant error correction scheme
recently proposed by DiVincenzo and Shor may be improved. Our scheme, unlike
the earlier one, can also deal with a single error that might occur {\em
during} the gate operations that are required for the implementation of the
error correction and not only in--between the gates and hence presents an
improvement towards enabling error correction and with it the practical
possibility of some more involved quantum computations, such as e.g.
factorization of large numbers.


title: Design of gates for quantum computation: the NOT gate

abstract:
  We offer an alternative to the conventional network formulation of quantum
computing. We advance the analog approach to quantum logic gate/circuit
construction. As an illustration, we consider the spatially extended NOT gate
as the first step in the development of this approach. We derive an explicit
form of the interaction Hamiltonian corresponding to this gate and analyze its
properties. We also discuss general extensions to the case of certain
time-dependent interactions which may be useful for practical realization of
quantum logic gates.


title: Quantum Correlations, Local Interactions and Error Correction

abstract:
  We consider the effects of local interactions upon quantum mechanically
entangled systems. In particular we demonstrate that non-local correlations
cannot increase through local operations on any of the subsystems, but that
through the use of quantum error correction methods, correlations can be
maintained. We provide two mathematical proofs that local general measurements
cannot increase correlations, and also derive general conditions for quantum
error correcting codes. Using these we show that local quantum error correction
can preserve nonlocal features of entangled quantum systems. We also
demonstrate these results by use of specific examples employing correlated
optical cavities interacting locally with resonant atoms. By way of counter
example, we also describe a mechanism by which correlations can be increased,
which demonstrates the need for it non-local interactions.


title:
Non-Abelian Geometrical Phase for General Three-Dimensional Quantum
  Systems

abstract:
  Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems
with a three-dimensional Hilbert space. Necessary and sufficient conditions for
the occurrence of the non-Abelian geometrical phases are obtained without
actually solving the full eigenvalue problem for the instantaneous Hamiltonian.
The parameter space of such systems which has the structure of $\xC P^2$ is
explicitly constructed. The results of this article are applicable for
arbitrary multipole interaction Hamiltonians $H=Q^{i_1,\cdots i_n}J_{i_1}\cdots
J_{i_n}$ and their linear combinations for spin $j=1$ systems. In particular it
is shown that the nuclear quadrupole Hamiltonian $H=Q^{ij}J_iJ_j$ does actually
lead to non-Abelian geometric phases for $j=1$. This system, being bosonic, is
time-reversal-invariant. Therefore it cannot support Abelian adiabatic
geometrical phases.


title:
Scattering in one dimension: The coupled Schroedinger equation,
  threshold behaviour and Levinson's theorem

abstract:
  We formulate scattering in one dimension due to the coupled Schr\"{o}dinger
equation in terms of the $S$ matrix, the unitarity of which leads to
constraints on the scattering amplitudes. Levinson's theorem is seen to have
the form $\eta(0) = \pi (n_b + 1/2 n - 1/2 N)$, where $\eta(0)$ is the phase of
the $S$ matrix at zero energy, $n_b$ the number of bound states with nonzero
binding energy, $n$ the number of half-bound states, and $N$ the number of
coupled equations. In view of the effects due to the half-bound states, the
threshold behaviour of the scattering amplitudes is investigated in general,
and is also illustrated by means of particular potential models.


title:
A non group theoretic proof of completeness of arbitrary coherent states
  $D(\alpha)\mid f>$

abstract:
  A new proof for the completeness of the coherent states $D(\alpha )\mid f>$
for the Heisenberg Weyl group and the groups $SU(2)$ and $SU(1,1)$ is
presented. Generalizations of these results and their consequences are
disussed.


title:
Eigenstates of linear combinations of two boson creation and
  annihilation operators : An algebraic approach

abstract:
  Eigenstates of the linear combinations $a^2+\beta a^{\dagger2}$ and $ab+\beta
a^\dagger b^\dagger$ of two boson creation and annihilation operators are
presented. The algebraic procedure given here is based on the work of Shanta et
al. [Phys. Rev. Lett. {\bf 72}, 1447, 1994] for constructing eigenstates of
generalized annihilation operators.


title: Generalized quantum measurements and local realism

abstract:
  The structure of a local hidden variable model for experiments involving
sequences of measurements rigorously is analyzed. Constraints imposed by local
realism on the conditional probabilities of the outcomes of such measurement
schemes are explicitly derived. The violation of local realism in the case of
``hidden nonlocality'' is illustrated by an operational example.


title: A direct proof of completeness of squeezed odd-number states

abstract:
  A direct proof of the resolution of the identity in the odd sector of the
Fock space in terms of squeezed number states $D(\xi)|2m+1>; D(\xi) =
\exp(({\xi}a^{\dagger2}-{\xi}^*{a^2})/2)$ is given. The proof entails
evaluation of an integral involving Jacobi polynomials. This is achieved by the
use of Racah identities.


title:
Transformation Properties of Classical and Quantum Laws under Some
  Nonholonomic Spacetime Transformations

abstract:
  Nonrelativistic Newton and Schroedinger equations remain correct not only
under holonomic but also under nonholonomic transformations of the spacetime
coordinates. Here we study the properties of transformations which are
holonomic in the space coordinates while additionally tranforming the time in a
path-dependent way. This makes them nonholonomic in spacetime. The resulting
transformation formulas of physical quantities establish relations between
different physical systems. Furthermore we point out certain
differential-geometric features of these relations.


title: From quantum trajectories to classical orbits

abstract:
  Recently it has been shown that the evolution of open quantum systems may be
``unraveled'' into individual ``trajectories,'' providing powerful numerical
and conceptual tools. In this letter we use quantum trajectories to study
mesoscopic systems and their classical limit. We show that in this limit,
Quantum Jump (QJ) trajectories approach a diffusive limit very similar to the
Quantum State Diffusion (QSD) unraveling. The latter follows classical
trajectories in the classical limit. Hence, both unravelings show the rise of
classical orbits. This is true for both regular and chaotic systems (which
exhibit strange attractors).


title: Subtleties in Quantum Mechanical Metastability

abstract:
  We present a detailed discussion of some features of quantum mechanical
metastability. We analyze the nature of decaying (quasistationary) states and
the regime of validity of the exponencial law, as well as decays at finite
temperature. We resort to very simple systems and elementary techniques to
emphasize subtle aspects of the problem.


title: Revival Structure of Stark Wave Packets

abstract:
  The revival structure of Stark wave packets is considered. These wave packets
have energies depending on two quantum numbers and are characterized by two
sets of classical periods and revival times. The additional time scales result
in revival structures different from those of free Rydberg wave packets. We
show that Stark wave packets can exhibit fractional revivals. We also show that
these wave packets exhibit particular features unique to the Stark effect. For
instance, the wave functions can be separated into distinct sums over even and
odd values of the principal quantum number. These even and odd superpositions
interfere in different ways, which results in unexpected periodicities in the
interferograms of Stark wave packets.


title: Quantum jumps in hydrogen-like systems

abstract:
  In this paper it is shown that the Lyman-$\alpha$ transition of a single
hydrogen-like system driven by a laser exhibits macroscopic dark periods,
provided there exists an additional constant electric field. We describe the
photon-counting process under the condition that the polarization of the laser
coincides with the direction of the constant electric field. The theoretical
results are given for the example of $^4{He}^+$. We show that the emission
behavior depends sensitively on the Lamb shift (W.E. Lamb, R.C. Retherford,
Phys. Rev. 72, 241 (1947)) between the $2s_{1/2}$ and $2p_{1/2}$ energy levels.
A possibly realizable measurement of the mean duration of the dark periods
should give quantitative information about the above energy difference by using
the proposed photon-counting process.


title: Wigner-Weyl-Moyal Formalism on Algebraic Structures

abstract:
  We first introduce the Wigner-Weyl-Moyal formalism for a theory whose
phase-space is an arbitrary Lie algebra. We also generalize to quantum Lie
algebras and to supersymmetric theories. It turns out that the
non-commutativity leads to a deformation of the classical phase-space: instead
of being a vector space it becomes a manifold, the topology of which is given
by the commutator relations. It is shown in fact that the classical
phase-space, for a semi-simple Lie algebra, becomes a homogenous symplectic
manifold. The symplectic product is also deformed. We finally make some
comments on how to generalize to $C^*$-algebras and other operator algebras
too.


title: Wormholes and Time-Machines

abstract:
  It has been proposed that wormholes can be made to function as time-machines.
This opens up the question of whether this can be accomodated within a
self-consistent physics or not. In this contribution we present some quantum
mechanical considerations in this respect.


title: Bose-stimulated scattering off a cold atom trap

abstract:
  The angle and temperature dependence of the photon scattering rate for
Bose-stimulated atom recoil transitions between occupied states is compared to
diffraction and incoherent Rayleigh scattering near the Bose-Einstein
transition for an optically thin trap in the limit of large particle number, N.
Each of these processes has a range of angles and temperatures for which it
dominates over the others by a divergent factor as N->oo.


title:
Emergence of a Wiener process as a result of the quantum mechanical
  interaction with a macroscopic medium

abstract:
  We analyze a modified version of the Coleman-Hepp model, that is able to take
into account energy-exchange processes between the incoming particle and the
linear array made up of $N$ spin-1/2 systems. We bring to light the presence of
a Wiener dissipative process in the weak-coupling, macroscopic ($N \rightarrow
\infty$) limit. In such a limit and in a restricted portion of the total
Hilbert space, the particle undergoes a sort of Brownian motion, while the free
Hamiltonian of the spin array serves as a Wiener process. No assumptions are
made on the spectrum of the Hamiltonian of the spin system, and no partial
trace is computed over its states. The mechanism of appearance of the
stochastic process is discussed and contrasted to other noteworthy examples in
the literature. The links with van Hove's ``$\lambda^2 T$ limits are
emphasized.


title:
The Post-Decoherence Density Matrix Propagator for Quantum Brownian
  Motion

abstract:
  Using the path integral representation of the density matrix propagator of
quantum Brownian motion, we derive its asymptotic form for times greater than
the localization time, $ (\hbar / \gamma k T )^{\half}$, where $\gamma$ is the
dissipation and $T$ the temperature of the thermal environment. The
localization time is typically greater than the decoherence time, but much
shorter than the relaxation time, $\gamma^{-1}$. We use this result to show
that the reduced density operator rapidly evolves into a state which is
approximately diagonal in a set of generalized coherent states. We thus
reproduce, using a completely different method, a result we previously obtained
using the quantum state diffusion picture (Phys.Rev. D52, 7294 (1995)). We also
go beyond this earlier result, in that we derive an explicit expression for the
weighting of each phase space localized state in the approximately diagonal
density matrix, as a function of the initial state. For sufficiently long times
it is equal to the Wigner function, and we confirm that the Wigner function is
positive for times greater than the localization time (multiplied by a number
of order 1).


title: Entropic Bell Inequalities

abstract:
  We derive entropic Bell inequalities from considering entropy Venn diagrams.
These entropic inequalities, akin to the Braunstein-Caves inequalities, are
violated for a quantum mechanical Einstein-Podolsky-Rosen pair, which implies
that the conditional entropies of Bell variables must be negative in this case.
This suggests that the satisfaction of entropic Bell inequalities is equivalent
to the non-negativity of conditional entropies as a necessary condition for
separability.


title: Non-binary Unitary Error Bases and Quantum Codes

abstract:
  Error operator bases for systems of any dimension are defined and natural
generalizations of the bit/sign flip error basis for qubits are given. These
bases allow generalizing the construction of quantum codes based on eigenspaces
of Abelian groups. As a consequence, quantum codes can be constructed from
linear codes over $\ints_n$ for any $n$. The generalization of the punctured
code construction leads to many codes which permit transversal (i.e. fault
tolerant) implementations of certain operations compatible with the error
basis.


title: Group Representations, Error Bases and Quantum Codes

abstract:
  This report continues the discussion of unitary error bases and quantum codes
begun in "Non-binary Unitary Error Bases and Quantum Codes". Nice error bases
are characterized in terms of the existence of certain characters in a group. A
general construction for error bases which are non-abelian over the center is
given. The method for obtaining codes due to Calderbank et al. is generalized
and expressed purely in representation theoretic terms. The significance of the
inertia subgroup both for constructing codes and obtaining the set of
transversally implementable operations is demonstrated.


title: Algebraic Coherent States and Squeezing

abstract:
  Eigenstates of general complex linear combination of SU(1,1) generators
(su^c(1,1) algebraic coherent states (ACS)) are constructed and discussed. In
case of quadratic boson representation ACS can exhibit strong both linear and
quadratic amplitude squeezing. ACS for a given Lie group algebra contain the
corresponding Perelomov CS with maximal symmetry.


title: Relational Quantum Mechanics

abstract:
  I suggest that the common unease with taking quantum mechanics as a
fundamental description of nature (the "measurement problem") could derive from
the use of an incorrect notion, as the unease with the Lorentz transformations
before Einstein derived from the notion of observer-independent time. I suggest
that this incorrect notion is the notion of observer-independent state of a
system (or observer-independent values of physical quantities). I reformulate
the problem of the "interpretation of quantum mechanics" as the problem of
deriving the formalism from a few simple physical postulates. I consider a
reformulation of quantum mechanics in terms of information theory. All systems
are assumed to be equivalent, there is no observer-observed distinction, and
the theory describes only the information that systems have about each other;
nevertheless, the theory is complete.


title: Quantum Mechanics as a Classical Theory XIII: The Tunnel Effect

abstract:
  In this continuation paper we will address the problem of tunneling. We will
show how to settle this phenomenon within our classical interpretation. It will
be shown that, rigorously speaking, there is no tunnel effect at all.


title: Dynamics as Shadow of Phase Space Geometry

abstract:
  Starting with the generally well accepted opinion that quantizing an
arbitrary Hamiltonian system involves picking out some additional structure on
the classical phase space (the {\sl shadow} of quantum mechanics in the
classical theory), we describe classical as well as quantum dynamics as a
purely geometrical effect by introducing a {\sl phase space metric structure}.
This produces an ${\cal O}(\hbar)$ modification of the classical equations of
motion reducing at the same time the quantization of an arbitrary Hamiltonian
system to standard procedures. Our analysis is carried out in analogy with the
adiabatic motion of a charged particle in a curved background (the additional
metric structure) under the influence of a universal magnetic field (the
classical symplectic structure). This allows one to picture dynamics in an
unusual way, and reveals a dynamical mechanism that produces the selection of
the right set of physical quantum states.


title: Locality and Causality in Hidden Variables Models of Quantum Theory

abstract:
  Motivated by Popescu's example of hidden nonlocality, we elaborate on the
conjecture that quantum states that are intuitively nonlocal, i.e., entangled,
do not admit a local causal hidden variables model. We exhibit quantum states
which either (i) are nontrivial counterexamples to this conjecture or (ii)
possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we
propose a nonlocality complexity classification scheme suggested by the latter
possibility. Furthermore, we show that Werner's (and similar) hidden variables
models can be extended to an important class of generalized observables.
Finally a result of Fine on the equivalence of stochastic and deterministic
hidden variables is generalized to causal models.


title:
On Schizophrenic Experiences of the Neutron or Why We Should Believe in
  the Many-Worlds Interpretation of Quantum Theory

abstract:
  This is a philosophical paper in favor of the Many-Worlds Interpretation
(MWI) of quantum theory. The concept of the ``measure of existence of a world''
is introduced and some difficulties with the issue of probability in the
framework of the MWI are resolved. Brief comparative analyses of the Bohm
theory and the Many-Minds Interpretation are given.


title: Defending Time-Symmetrized Quantum Theory

abstract:
  Recently, several authors have criticized time-symmetrized quantum theory
originated by the work of Aharonov et al. (1964). The core of this criticism
was the proof, which appeared in various forms, showing that counterfactual
interpretation of time-symmetrized quantum theory cannot be reconciled with the
standard quantum theory. I argue here that the apparent contradiction appears
due to inappropriate usage of traditional time asymmetric approach to
counterfactuals, and that the contradiction disappears when the problem is
analyzed in terms of time-symmetric counterfactuals. I analyze various aspects
of time-symmetry of quantum theory and defend the time-symmetrized formalism.


title:
Effect of Anharmonicity on the WKB Energy Splitting in a Double Well
  Potential

abstract:
  We investigate the effect of anharmonicity on the WKB approximation in a
double well potential. By incorporating the anharmonic perturbation into the
WKB energy splitting formula we show that the WKB approximation can be greatly
improved in the region over which the tunneling is appreciable. We also observe
that the usual WKB results can be obtained from our formalism as a limiting
case in which the two potential minima are far apart.


title: SUSUSY quantum mechanics

abstract:
  The exactly solvable eigenproblems in Schr\"odinger quantum mechanics
typically involve the differential "shift operators". In the standard
supersymmetric (SUSY) case, the shift operator turns out to be of first order.
In this work, I discuss a technique to generate exactly solvable eigenproblems
by using second order shift operators. The links between this method and SUSY
are analysed. As an example, we show the existence of a two-parametric family
of exactly solvable Hamiltonians, which contains the Abraham-Moses potentials
as a particular case.


title: Quantum signal splitting that avoids initialization of the targets

abstract:
  The classical signal splitting and copying are not possible in quantum
mechanics. Specifically, one cannot copy the basis up and down states of the
input (I) two-state system (qubit, spin) into the copy (C) and duplicate-copy
(D) two-state systems if the latter systems are initially in an arbitrary
state. We consider instead a quantum evolution in which the basis states of I
at time t are duplicated in at least two of the systems I, C, D, at time t +
Delta t. In essence, the restriction on the initial target states is exchanged
for uncertainty as to which two of the three qubits retain copies of the
initial source state.


title: On the Influence of Pulse Shapes on Ionization Probability

abstract:
  We investigate analytical expressions for the upper and lower bounds for the
ionization probability through ultra-intense shortly pulsed laser radiation. We
take several different pulse shapes into account, including in particular those
with a smooth adiabatic turn-on and turn-off. For all situations for which our
bounds are applicable we do not find any evidence for bound-state
stabilization.


title: Quantum state estimation

abstract:
  New algorithm for quantum state estimation based on the maximum likelihood
estimation is proposed. Existing techniques for state reconstruction based on
the inversion of measured data are shown to be overestimated since they do not
guarantee the positive definiteness of the reconstructed density matrix.


title: The Ithaca Interpretation of Quantum Mechanics

abstract:
  I list several strong requirements for what I would consider a sensible
interpretation of quantum mechanics and I discuss two simple theorems. One, as
far as I know, is new; the other was only noted a few years ago. Both have
important implications for such a sensible interpretation. My talk will not
clear everything up; indeed, you may conclude that it has not cleared anything
up. But I hope it will provide a different perspective from which to view some
old and vexing puzzles (or, if you believe nothing needs to be cleared up, some
ancient verities.)


title: Structure and Function

abstract:
  I discuss the role of quantum dynamics in brain and living matter physics.
The paper is presented in the form of a letter to Patricia S. Churchland.


title: Unitary dynamics for quantum codewords

abstract:
  A quantum codeword is a redundant representation of a logical qubit by means
of several physical qubits. It is constructed in such a way that if one of the
physical qubits is perturbed, for example if it gets entangled with an unknown
environment, there still is enough information encoded in the other physical
qubits to restore the logical qubit, and disentangle it from the environment.
The recovery procedure may consist of the detection of an error syndrome,
followed by the correction of the error, as in the classical case. However, it
can also be performed by means of unitary operations, without having to know
the error syndrome. Since quantum codewords span only a restricted subspace of
the complete physical Hilbert space, the unitary operations that generate
quantum dynamics (that is, the computational process) are subject to
considerable arbitrariness, similar to the gauge freedom in quantum field
theory. Quantum codewords can thus serve as a toy model for investigating the
quantization of constrained dynamical systems.


title: Quantum nonlocality and inseparability

abstract:
  A quantum system consisting of two subsystems is separable if its density
matrix can be written as $\rho=\sum w_K \rho_K'\otimes \rho_K''$, where
$\rho_K'$ and $\rho_K''$ are density matrices for the two subsytems, and the
positive weights $w_K$ satisfy $\sum w_K=1$. A necessary condition for
separability is derived and is shown to be more sensitive than Bell's
inequality for detecting quantum inseparability. Moreover, collective tests of
Bell's inequality (namely, tests that involve several composite systems
simultaneously) may sometimes lead to a violation of Bell's inequality, even if
the latter is satisfied when each composite system is tested separately.


title:
Schr\"{o}dinger Intelligent States and Linear and Quadratic Amplitude
  Squeezing

abstract:
  A complete set of solutions |z,u,v>_{sa} of the eigenvalue equation
(ua^2+va^{dagger 2})|z,u,v> = z|z,u,v> ([a,a^{dagger}]=1) are constructed and
discussed. These and only these states minimize the Schr\"{o}dinger uncertainty
inequality for the squared amplitude (s.a.) quadratures. Some general
properties of Schr\"{o}dinger intelligent states (SIS) |z,u,v> for any two
observables X, Y are discussed, the sets of even and odd s.a. SIS |z,u,v;+,->
being studied in greater detail. The set of s.a. SIS contain all even and odd
coherent states (CS) of Dodonov, Malkin and Man'ko, the Perelomov SU(1,1) CS
and the squeezed Hermite polynomial states of Bergou, Hillery and Yu. The even
and odd SIS can exhibit very strong both linear and quadratic squeezing (even
simultaneously) and super- and subpoissonian statistics as well. A simple
sufficient condition for superpoissonian statistics is obtained and the
diagonalization of the amplitude and s.a. uncertainty matrices in any pure or
mixed state by linear canonical transformations is proven.


title: A Hamiltonian for quantum copying

abstract:
  We derive an explicit Hamiltonian for copying the basis up and down states of
a quantum two-state system - a qubit - onto n "copy" qubits initially all
prepared in the down state. In terms of spin components, for spin-1/2 particle
spin states, the resulting Hamiltonian involves n- and (n+1)-spin interactions.
The case n=1 also corresponds to a quantum-computing controlled-NOT gate.


title:
Operator Transformations Between Exactly Solvable Potentials and Their
  Lie Group Generators

abstract:
  One may obtain, using operator transformations, algebraic relations between
the Fourier transforms of the causal propagators of different exactly solvable
potentials. These relations are derived for the shape invariant potentials.
Also, potentials related by real transformation functions are shown to have the
same spectrum generating algebra with Hermitian generators related by this
operator transformation.


title: Wave-Packet Revivals for Quantum Systems with Nondegenerate Energies

abstract:
  The revival structure of wave packets is examined for quantum systems having
energies that depend on two nondegenerate quantum numbers. For such systems,
the evolution of the wave packet is controlled by two classical periods and
three revival times. These wave packets exhibit quantum beats in the initial
motion as well as new types of long-term revivals. The issue of whether
fractional revivals can form is addressed. We present an analytical proof
showing that at certain times equal to rational fractions of the revival times
the wave packet can reform as a sum of subsidiary waves and that both
conventional and new types of fractional revivals can occur.


title: A Gravitational Explanation for Quantum Mechanics

abstract:
  It is shown that certain structures in classical General Relativity can give
rise to non-classical logic, normally associated with Quantum Mechanics. A
4-geon model of an elementary particle is proposed which is asymptotically
flat, particle-like and has a non-trivial causal structure. The usual Cauchy
data are no longer sufficient to determine a unique evolution. The measurement
apparatus itself can impose non-redundant boundary conditions. Measurements of
such an object would fail to satisfy the distributive law of classical physics.
This model reconciles General Relativity and Quantum Mechanics without the need
for Quantum Gravity. The equations of Quantum Mechanics are unmodified but it
is not universal; classical particles and waves could exist and there is no
graviton.


title:
Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive
  particles

abstract:
  The EPRB experiment with massive partcles can be formulated if one defines
spin in a relativistic way. Two versions are discussed: The one using the spin
operator defined via the relativistic center-of-mass operator, and the one
using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction
for the EPRB experiment: The degree of violation of the Bell inequality
DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The
phenomenon can be physically understood as a combined effect of the Lorentz
contraction and the Moller shift of the relativistic center of mass. The effect
is therefore stronger than standard relativistic phenomena such as the Lorentz
contraction or time dilatation. The fact that the Bell inequality is in general
less violated than in the nonrelativistic case will have to be taken into
account in tests for eavesdropping if massive particles will be used for a key
transfer.


title:
Quantum Mechanics as a Classical Theory XIV: Connection with Stochastic
  Processes

abstract:
  In this paper we are interested in unraveling the mathematical connections
between the stochastic derivation of Schr\"odinger equation and ours. It will
be shown that these connections are given by means of the time-energy
dispersion relation and will allow us to interpret this relation on more
sounded grounds. We also discuss the underlying epistemology.


title: On the von Neumann capacity of noisy quantum channels

abstract:
  We discuss the capacity of quantum channels for information transmission and
storage. Quantum channels have dual uses: they can be used to transmit known
quantum states which code for classical information, and they can be used in a
purely quantum manner, for transmitting or storing quantum entanglement. We
propose here a definition of the von Neumann capacity of quantum channels,
which is a quantum mechanical extension of the Shannon capacity and reverts to
it in the classical limit. As such, the von Neumann capacity assumes the role
of a classical or quantum capacity depending on the usage of the channel. In
analogy to the classical construction, this capacity is defined as the maximum
von Neumann mutual entropy processed by the channel, a measure which reduces to
the capacity for classical information transmission through quantum channels
(the "Kholevo capacity") when known quantum states are sent. The quantum mutual
entropy fulfills all basic requirements for a measure of information, and
observes quantum data-processing inequalities. We also derive a quantum Fano
inequality relating the quantum loss of the channel to the fidelity of the
quantum code. The quantities introduced are calculated explicitly for the
quantum "depolarizing" channel. The von Neumann capacity is interpreted within
the context of superdense coding, and an "extended" Hamming bound is derived
that is consistent with that capacity.


title: On Quantizing $T^*S^1$

abstract:
  In this paper we continue our study of Groenewold-Van Hove obstructions to
quantization. We show that there exists such an obstruction to quantizing the
cylinder $T^*S^1.$ More precisely, we prove that there is no quantization of
the Poisson algebra of $T^*S^1$ which is irreducible on a naturally defined
$e(2) \times R$ subalgebra. Furthermore, we determine the maximal
``polynomial'' subalgebras that can be consistently quantized, and completely
characterize the quantizations thereof. This example provides support for one
of the conjectures in Gotay et al 1996, but disproves part of another. Passing
to coverings, we also derive a no-go result for $R^2$ which is comparatively
stronger than those originally found by Groenewold and Van Hove.


title:
Classical-Like Description of Quantum Dynamics by Means of Symplectic
  Tomography

abstract:
  The dynamical equation of quantum mechanics are rewritten in form of
dynamical equations for the measurable, positive marginal distribution of the
shifted, rotated and squeezed quadrature introduced in the so called
"symplectic tomography". Then the possibility of a purely classical description
of a quantum system as well as a reinterpretation of the quantum measurement
theory is discussed and a comparision with the well known quasi-probabilities
approach is given. Furthermore, an analysis of the properties of this marginal
distribution, which contains all the quantum information, is performed in the
framework of classical probability theory. Finally examples of harmonic
oscillator's states dynamics are treated.


title: Convergence Behavior of Variational Perturbation Expansions

abstract:
  Variational weak-coupling perturbation theory yields converging
approximations, uniformly in the coupling strength. This allows us to calculate
directly the coefficients of `strong-coupling' expansions. For the anharmonic
oscillator we explain the physical origin of the empirically observed
convergence behavior which is exponentially fast with superimposed
oscillations.


title:
Prescription for experimental determination of the dynamics of a quantum
  black box

abstract:
  We give an explicit prescription for experimentally determining the evolution
operators which completely describe the dynamics of a quantum mechanical black
box -- an arbitrary open quantum system. We show necessary and sufficient
conditions for this to be possible, and illustrate the general theory by
considering specifically one and two quantum bit systems. These procedures may
be useful in the comparative evaluation of experimental quantum measurement,
communication, and computation systems.


title:
Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact
  Case and Classical theories Revisited''

abstract:
  We show that the WKB approximation gives the exact result in the trace
formula of ``$CQ^N$'', which is the non-compact counterpart of $CP^N$, in terms
of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on
$CP^N$ and $CQ^N$ and, especially, construct that on $CQ^N$ with the unitary
form. We also revisit the exact calculation of the classical patition functions
of them.


title: Atomic Quantum Zeno Effect for Ensembles and Single Systems

abstract:
  The so-called quantum Zeno effect is essentially a consequence of the
projection postulate for ideal measurements. To test the effect Itano et al.
have performed an experiment on an ensemble of atoms where rapidly repeated
level measurements were realized by means of short laser pulses. Using
dynamical considerations we give an explanation why the projection postulate
can be applied in good approximation to such measurements. Corrections to ideal
measurements are determined explicitly. This is used to discuss in how far the
experiment of Itano et al. can be considered as a test of the quantum Zeno
effect. We also analyze a new possible experiment on a single atom where
stochastic light and dark periods can be interpreted as manifestation of the
quantum Zeno effect. We show that the measurement point of view gives a quick
and intuitive understanding of experiments of the above type, although a finer
analysis has to take the corrections into account.


title: Mass as a Relativistic Quantum Observable

abstract:
  A field state containing photons propagating in different directions has a
non vanishing mass which is a quantum observable. We interpret the shift of
this mass under transformations to accelerated frames as defining space-time
observables canonically conjugated to energy-momentum observables. Shifts of
quantum observables differ from the predictions of classical relativity theory
in the presence of a non vanishing spin. In particular, quantum redshift of
energy-momentum is affected by spin. Shifts of position and energy-momentum
observables however obey simple universal rules derived from invariance of
canonical commutators.


title: Negative entropy in quantum information theory

abstract:
  We present a quantum information theory that allows for the consistent
description of quantum entanglement. It parallels classical (Shannon)
information theory but is based entirely on density matrices, rather than
probability distributions, for the description of quantum ensembles. We find
that, unlike in Shannon theory, conditional entropies can be negative when
considering quantum entangled systems such as an Einstein-Podolsky-Rosen pair,
which leads to a violation of well-known bounds of classical information
theory. Negative quantum entropy can be traced back to ``conditional'' density
matrices which admit eigenvalues larger than unity. A straightforward
definition of mutual quantum entropy, or ``mutual entanglement'', can also be
constructed using a ``mutual'' density matrix. Such a unified
information-theoretic description of classical correlation and quantum
entanglement clarifies the link between them: the latter can be viewed as
``super-correlation'' which can induce classical correlation when considering a
ternary or larger system.


title: Galilean non-invariance of geometric phase

abstract:
  It is shown that geometric phase in non-relativistic quantum mechanics is not
Galilean invariant.


title: Integrability and Computability in Simulating Quantum Systems

abstract:
  An impossibility theorem on approximately simulating quantum non-integrable
Hamiltonian systems is presented here. This result shows that there is a
trade-off between the unitary property and the energy expectation conservation
law in time-descretization of quantum non-integrable systems, whose classical
counterpart is Ge-Marsden's impossibility result about simulating classically
non-integrable Hamiltonian systems using integration schemes preserving
symplectic (Lie-Poisson) property.


title: Extended Quantum XOR Gate in Terms of Two-Spin Interactions

abstract:
  Considerations of feasibility of quantum computing lead to the study of
multispin quantum gates in which the input and output two-state systems (spins)
are not identical. We provide a general discussion of this approach and then
propose an explicit two-spin interaction Hamiltonian which accomplishes the
quantum XOR gate function for a system of three spins: two input and one
output.


title: Experimental status of quaternionic quantum mechanics

abstract:
  Analysis of the logical foundations of quantum mechanics indicates the
possibility of constructing a theory using quaternionic Hilbert spaces. Whether
this mathematical structure reflects reality is a matter for experiment to
decide. We review the only direct search for quaternionic quantum mechanics yet
carried out and outline a recent proposal by the present authors to look for
quaternionic effects in correlated multi-particle systems. We set out how such
experiments might distinguish between the several quaternionic models proposed
in the literature.


title:
A Collection of Probabilistic Hidden-Variable Theorems and
  Counterexamples

abstract:
  The purpose of this article is to formulate a number of probabilistic
hidden-variable theorems, to provide proofs in some cases, and counterexamples
to some conjectured relationships. The first theorem is the fundamental one. It
asserts the general equivalence of the existence of a hidden variable and the
existence of a joint probability distribution of the observed quatities,
whether finite or continuous.


title: Threshold Accuracy for Quantum Computation

abstract:
  We have previously (quant-ph/9608012) shown that for quantum memories and
quantum communication, a state can be transmitted over arbitrary distances with
error $\epsilon$ provided each gate has error at most $c\epsilon$. We discuss a
similar concatenation technique which can be used with fault tolerant networks
to achieve any desired accuracy when computing with classical initial states,
provided a minimum gate accuracy can be achieved. The technique works under
realistic assumptions on operational errors. These assumptions are more general
than the stochastic error heuristic used in other work. Methods are proposed to
account for leakage errors, a problem not previously recognized.


title: Quantum Randomness and Nondeterminism

abstract:
  Does the notion of a quantum randomized or nondeterministic algorithm make
sense, and if so, does quantum randomness or nondeterminism add power? Although
reasonable quantum random sources do not add computational power, the
discussion of quantum randomness naturally leads to several definitions of the
complexity of quantum states. Unlike classical string complexity, both
deterministic and nondeterministic quantum state complexities are interesting.
A notion of \emph{total quantum nondeterminism} is introduced for decision
problems. This notion may be a proper extension of classical nondeterminism.


title: Chaos in Time Dependent Variational Approximations to Quantum Dynamics

abstract:
  Dynamical chaos has recently been shown to exist in the Gaussian
approximation in quantum mechanics and in the self-consistent mean field
approach to studying the dynamics of quantum fields. In this study, we first
show that any variational approximation to the dynamics of a quantum system
based on the Dirac action principle leads to a classical Hamiltonian dynamics
for the variational parameters. Since this Hamiltonian is generically nonlinear
and nonintegrable, the dynamics thus generated can be chaotic, in distinction
to the exact quantum evolution. We then restrict attention to a system of two
biquadratically coupled quantum oscillators and study two variational schemes,
the leading order large N (four canonical variables) and Hartree (six canonical
variables) approximations. The chaos seen in the approximate dynamics is an
artifact of the approximations: this is demonstrated by the fact that its onset
occurs on the same characteristic time scale as the breakdown of the
approximations when compared to numerical solutions of the time-dependent
Schrodinger equation.


title: What is achieved by decoherence?

abstract:
  A short critical review of the concept of decoherence, its consequences, and
its possible implications for the interpretation of quantum theory is given.


title: Decoherence limits to quantum computation using trapped ions

abstract:
  We investigate the problem of factorization of large numbers on a quantum
computer which we imagine to be realized within a linear ion trap. We derive
upper bounds on the size of the numbers that can be factorized on such a
quantum computer. These upper bounds are independent of the power of the
applied laser. We investigate two possible ways to implement qubits, in
metastable optical transitions and in Zeeman sublevels of a stable ground
state, and show that in both cases the numbers that can be factorized are not
large enough to be of practical interest. We also investigate the effect of
quantum error correction on our estimates and show that in realistic systems
the impact of quantum error correction is much smaller than expected. Again no
number of practical interest can be factorized.


title: Mixing Quantum and Classical Mechanics

abstract:
  Using a group theoretical approach we derive an equation of motion for a
mixed quantum-classical system. The quantum-classical bracket entering the
equation preserves the Lie algebra structure of quantum and classical
mechanics: The bracket is antisymmetric and satisfies the Jacobi identity, and,
therefore, leads to a natural description of interaction between quantum and
classical degrees of freedom. We apply the formalism to coupled quantum and
classical oscillators and show how various approximations, such as the
mean-field and the multiconfiguration mean-field approaches, can be obtained
from the quantum-classical equation of motion.


title: Dichotomic Functions and Bell's Theorems

abstract:
  It is shown that correlations of dichotomic functions can not conform to
results from Quantum Mechanics. Also, it is seen that the assumptions attendant
to optical tests of Bell's Inequalities actually are consistent with classical
physics so that in conclusion, Bell's Theorems do not preclude hidden variable
interpretations of Quantum Mechanics.


title: Wavelets and Information-preserving Transformations

abstract:
  The underlying mathematics of the wavelet formalism is a representation of
the inhomogeneous Lorentz group or the affine group. Within the framework of
wavelets, it is possible to define the ``window'' which allows us to introduce
a Lorentz-covariant cut-off procedure. The window plays the central role in
tackling the problem of photon localization. It is possible to make a
transition from light waves to photons through the window. On the other hand,
the windowed wave function loses analyticity. This loss of analyticity can be
measured in terms of entropy difference. It is shown that this entropy
difference can be defined in a Lorentz-invariant manner within the framework of
the wavelet formalism.


title:
Quantum dynamics with intermediate measurements in agreement with the
  classical dynamics

abstract:
  The effect of repetitive measurement for quantum dynamics of driven by an
intensive external force of the simple few-level systems as well as of the
multilevel systems that exhibit the quantum localisation of classical chaos is
investigated. Frequent measurement of the simple system yields to the quantum
Zeno effect while that of the suppressed quantum system, which classical
counterpart exhibits chaos, results in the delocalisation of the quantum
suppression. From the analysis we may conclude that continuously observable
quasiclassical system evolves essentially classically-like.


title:
Quantum Corrections to the Classical Dynamics: Application to the SU(2)
  Lipkin Model

abstract:
  We show how nonrelativistic many body techniques can be used to study quantum
corrections to the classical limit, in particular of the $SU(2)$ Lipkin Model.
We show that the quantum corrections are essentially of two types: unitary and
nonunitary. In this work we perform a detailed study of the unitary
corrections. They can be cast in Hamiltonian form and are shown to double the
number of degrees of freedom. As a consequence chaotic behavior emerges. We
show that this semiquantal chaos is the mechanism trough which tunneling is
effected. We also show that these corrections systematically improve the
classical results and propose some quantitative measure of this improvement.


title: Hypergeometric States and Their Nonclassical Properties

abstract:
  `Hypergeometric states', which are a one-parameter generalization of binomial
states of the single-mode quantized radiation field, are introduced and their
nonclassical properties are investigated. Their limits to the binomial states
and to the coherent and number states are studied. The ladder operator
formulation of the hypergeometric states is found and the algebra involved
turns out to be a one-parameter deformation of $su(2)$ algebra. These states
exhibit highly nonclassical properties, like sub-Poissonian character,
antibunching and squeezing effects. The quasiprobability distributions in phase
space, namely the $Q$ and the Wigner functions are studied in detail. These
remarkable properties seem to suggest that the hypergeometric states deserve
further attention from theoretical and applicational sides of quantum optics.


title:
Negative Binomial and Multinomial States: probability distributions and
  coherent states

abstract:
  Following the relationship between probability distribution and coherent
states, for example the well known Poisson distribution and the ordinary
coherent states and relatively less known one of the binomial distribution and
the $su(2)$ coherent states, we propose ``interpretation'' of $su(1,1)$ and
$su(r,1)$ coherent states ``in terms of probability theory''. They will be
called the ``negative binomial'' (``multinomial'') ``states'' which correspond
to the ``negative'' binomial (multinomial) distribution, the non-compact
counterpart of the well known binomial (multinomial) distribution. Explicit
forms of the negative binomial (multinomial) states are given in terms of
various boson representations which are naturally related to the probability
theory interpretation. Here we show fruitful interplay of probability theory,
group theory and quantum theory.


title: Correcting Quantum Errors In Higher Spin Systems

abstract:
  I consider the theory of quantum error correcting code (QECC) where each
quantum particle has more than two possible eigenstates. In this higher spin
system, I report an explicit QECC that is related to the symmetry group ${\Bbb
Z}_2^{\otimes (N-1)} \otimes S_N$. This QECC, which generalizes Shor's simple
majority vote code, is able to correct errors arising from exactly one quantum
particle. I also provide a simple encoding algorithm.


title: Negative Binomial States of Quantized Radiation Fields

abstract:
  We introduce the negative binomial states with negative binomial distribution
as their photon number distribution. They reduce to the ordinary coherent
states and Susskind-Glogower phase states in different limits. The ladder and
displacement operator formalisms are found and they are essentially the
Perelomov's su(1,1) coherent states via its Holstein-Primakoff realisation.
These states exhibit strong squeezing effect and they obey the super-Poissonian
statistics. A method to generate these states is proposed.


title: Lax-Phillips Theory and Quantum Evolution

abstract:
  The scattering theory of Lax and Phillips, designed primarily for hyperbolic
systems, such as electromagnetic or acoustic waves, is described. This theory
provides a realization of the theorem of Foias and Nagy; there is a subspace of
the Hilbert space in which the unitary evolution of the system, restricted to
this subspace, is realized as a semigroup. The embedding of the quantum theory
into this structure, carried out by Flesia and Piron, is reviewed. We show how
the density matrix for an effectively pure state can evolve to an effectively
mixed state (decoherence) in this framework. Necessary conditions are given for
the realization of the relation between the spectrum of the generator of the
semigroup and the singularities of the $S$-matrix (in energy representation).
It is shown that these conditions may be met in the Liouville space formulation
of quantum evolution, and in the Hilbert space of relativistic quantum theory.


title: Tight Binding Hamiltonians and Quantum Turing Machines

abstract:
  This paper extends work done to date on quantum computation by associating
potentials with different types of computation steps. Quantum Turing machine
Hamiltonians, generalized to include potentials, correspond to sums over tight
binding Hamiltonians each with a different potential distribution. Which
distribution applies is determined by the initial state. An example, which
enumerates the integers in succession as binary strings, is analyzed. It is
seen that for some initial states the potential distributions have
quasicrystalline properties and are similar to a substitution sequence.


title: WKB to all orders and the accuracy of the semiclassical quantization

abstract:
  We perform a systematic WKB expansion to all orders for a one-dimensional
system with potential $V(x)=U_0/\cos^2{(\alpha x)}$. We are able to sum the
series to the exact energy spectrum. Then we show that at any finite order the
error of the WKB approximation measured in the natural units of the mean energy
level spacing does not go to zero when the quantum number goes to infinity.
Therefore we make the general conclusion that the semiclassical approximations
fail to predict the individual energy levels within a vanishing fraction of the
mean energy level spacing.


title: Relativistic Quantum Events

abstract:
  We extend the ideas of L.P. Horwitz and C. Piron and we propose a
relativistic version of Event Enhanced Quantum Theory, with an event generating
algorithm for spin one-half particle detectors. The algorithm is based on
proper time formulation of the relativistic quantum theory. Although we use
indefinite metric, all the probabilities controlling the random process of the
detector clicks are non--negative.


title: Note on the Demkov-Ostrovsky nodeless sector

abstract:
  We briefly tackle the following concepts in the Demkov-Ostrovsky (DO)
nodeless sector: (i) orbital impedance, (ii) orbital capacity, (iii) closeness
to reflectionlessness. Moreover, using previous supersymmetric results for the
DO problem, a strictly isospectral effect in the DO orbital impedances is
discussed and explicit plots are displayed for the Maxwell fisheye lens. This
effect, though rather small, is general, that is, it may apply to any focusing
structure.


title: Superrelativity as a unification of quantum theory and relativity

abstract:
  Principle of ``Superrelativity'' has been proposed in order to avoid the
contradiction between principle of relativity and foundations of quantum
theory. Solutions of a newly derived non-linear Klein-Gordon equation
presumably may be treated as primordial nonlocal elements of quantum theory. It
is shown that in the framework of CP(N-1) model supplementary elements which
are non-local in spacetime but local in the projective Hilbert space permit us
to avoid at least one of the main difficulties of quantum theory-the necessity
to relate the ``reality'' of a quantum state with a measuring process. In the
framework of superrelativity the geometry of the projective Hilbert space
(Fubini-Study metric and connection) together with the non-linear wave equation
are full and closed quantum scheme.


title: Correcting the effects of spontaneous emission on cold trapped ions

abstract:
  We propose two quantum error correction schemes which increase the maximum
storage time for qubits in a system of cold trapped ions, using a minimal
number of ancillary qubits. Both schemes consider only the errors introduced by
the decoherence due to spontaneous emission from the upper levels of the ions.
Continuous monitoring of the ion fluorescence is used in conjunction with
selective coherent feedback to eliminate these errors immediately following
spontaneous emission events, and the conditional time evolution between quantum
jumps is removed by symmetrizing the quantum codewords.


title: Scattering Wave Functions at Bound State Poles

abstract:
  The normalisation relation between the bound and scattering S-state wave
functions, extrapolated to the bound state pole, is derived from the
Schroedinger equation. It is shown that, unlike previous work, the result does
not depend on the details of the potential through the corresponding Jost
function but is given uniquely in terms of the binding energy. The
generalisations to higher partial waves and one-dimensional scattering are
given.


title: Interaction-Free Measurements

abstract:
  A brief review of interaction-free measurements (IFM) is presented. The IFM
is a solution of a quantum puzzle: How to test a bomb which explodes on every
test without exploding it? This paper was given in the Oxford conference in
honor of Roger Penrose.


title: Sonoluminescence as Quantum Vacuum Radiation, Reply to Comments

abstract:
  Reply to Comments by Lambrecht, Jaekel, and Reynaud, and by Garcia and
Levanyuk, submitted to Physical Review Letters.


title: Linear quantum state diffusion for non-Markovian open quantum systems

abstract:
  We demonstrate the relevance of complex Gaussian stochastic processes to the
stochastic state vector description of non-Markovian open quantum systems.
These processes express the general Feynman-Vernon path integral propagator for
open quantum systems as the classical ensemble average over stochastic pure
state propagators in a natural way. They are the coloured generalization of
complex Wiener processes in quantum state diffusion stochastic Schrodinger
equations.


title: Time Symmetry in Microphysics

abstract:
  Physics takes for granted that interacting physical systems with no common
history are independent, before their interaction. This principle is
time-asymmetric, for no such restriction applies to systems with no common
future, after an interaction. The time-asymmetry is normally attributed to
boundary conditions. I argue that there are two distinct independence
principles of this kind at work in contemporary physics, one of which cannot be
attributed to boundary conditions, and therefore conflicts with the assumed T
(or CPT) symmetry of microphysics. I note that this may have interesting
ramifications in quantum mechanics.


title: Coherent States and the Measurement Problem

abstract:
  The convenience of coherent state representation is discussed from the
viewpoint of what is in a broad sense called the measurement problem in quantum
mechanics. Standard quantum theory in coherent state representation is
intrinsically related to a number of earlier concepts conciliating quantum and
classical processes. From a natural statistical interpretation, free of
collapses or measurements, the usual von Neumann-L\"uders collapse as well as
its quantum state diffusion interpretation follow. In particular, a theory of
coupled quantum and classical dynamics arises, containing the fluctuation
corrections versus the fenomenological mean-field theories.


title: Quantum Control of Chaos inside a Cavity

abstract:
  By sending many two-level atoms through a cavity resonant with the atomic
transition, and letting the interaction times between the atoms and the cavity
be randomly distributed, we end up with a predetermined Fock state of the
electromagnetic field inside the cavity if we perform after the interaction
with the cavity a conditional measurement of the internal state of each atom in
a coherent superposition of its ground and excited states. Differently from
previous schemes, this procedure turns out to be very stable under fluctuations
in the interaction times.


title: A New Time-Scale for Tunneling

abstract:
  We study the tunneling through an oscillating delta barrier. Using time
periodicity of the model, the time-dependent Schr\"odinger equation is reduced
to a simple but infinite matrix equation. Employing Toeplitz matrices methods,
the infinite matrix is replaces by a $3\times 3$ matrix, allowing an analytical
solution. Looking at the frequency dependence of the transmissionamplitudes,
one observes a new time scale which dominates the tunneling dynamics. This time
scale differs from the one previously introduced by B\"uttiker and Landauer.
The relation between these two is discussed.


title: Quantum MacWilliams Identities

abstract:
  We derive a relationship between two different notions of fidelity
(entanglement fidelity and average fidelity) for a completely depolarizing
quantum channel. This relationship gives rise to a quantum analog of the
MacWilliams identities in classical coding theory. These identities relate the
weight enumerator of a code to the one of its dual and, with linear programming
techniques, provided a powerful tool to investigate the possible existence of
codes. The same techniques can be adapted to the quantum case. We give examples
of their power.


title: Dynamical peculiarities of the nonlinear quasiclassical systems

abstract:
  The quantum-classical correspondence for dynamics of the nonlinear
classically chaotic systems is analysed. The problem of quantum chaos consists
of two parts: the quasiclassical quantisation of the chaotic systems and
attempts to understand the classical chaos in terms of quantum mechanics. The
first question has been partially solved by the Gutzwiller semiclassical trace
formula for the eigenvalues of chaotic systems, while the classical chaos may
be derived from quantum equations only introducing the decoherence process due
to interaction with system's environment or intermediate frequent measurement.
We may conclude that continuously observable quasiclassical system evolves
essentially classically-like.


title: Codes for the Quantum Erasure Channel

abstract:
  The quantum erasure channel (QEC) is considered. Codes for the QEC have to
correct for erasures, i. e., arbitrary errors at known positions. We show that
four qubits are necessary and sufficient to encode one qubit and correct one
erasure, in contrast to five qubits for unknown positions. Moreover, a family
of quantum codes for the QEC, the quantum BCH codes, that can be efficiently
decoded is introduced.


title: Bosonic Quantum Codes for Amplitude Damping

abstract:
  Traditional quantum error correction involves the redundant encoding of k
quantum bits using n quantum bits to allow the detection and correction of any
t bit error. The smallest general t=1 code requires n=5 for k=1. However, the
dominant error process in a physical system is often well known, thus inviting
the question: given a specific error model, can more efficient codes be
devised? We demonstrate new codes which correct just amplitude damping errors
which allow, for example, a t=1, k=1 code using effectively n=4.6. Our scheme
is based on using bosonic states of photons in a finite number of optical
modes. We present necessary and sufficient conditions for the codes, and
describe construction algorithms, physical implementation, and performance
bounds.


title: Thermodynamics and the Measure of Entanglement

abstract:
  We point out formal correspondences between thermodynamics and entanglement.
By applying them to previous work, we show that entropy of entanglement is the
unique measure of entanglement for pure states.


title: On the EPR Phenomenon

abstract:
  The origin of the nonlocal nature of quantum mechanics is investigated in the
context of Everett's formulation of quantum mechanics. EPR phenomenon can fully
be explained without introducing any kind of decoherence.


title:
Quantum nondemolition measurements on two-level atomic systems and
  temporal Bell inequalities

abstract:
  The evolution of a two-level system subjected to stimulated transitions which
is undergoing a sequence of measurements of the level occupation probability is
evaluated. Its time correlation function is compared to the one obtained
through the pure Schroedinger evolution. Systems of this kind have been
recently proposed for testing the quantum mechanical predictions against those
of macrorealistic theories, by means of temporal Bell inequalities. The
classical requirement of noninvasivity, needed to define correlation functions
in the realistic case, finds a quantum counterpart in the quantum nondemolition
condition. The consequences on the observability of quantum mechanically
predicted violations to temporal Bell inequalities are drawn and compared to
the already dealt case of the rf-SQUID dynamics.


title: Quantum shadow enumerators

abstract:
  In a recent paper [quant-ph/9610040], Shor and Laflamme define two ``weight
enumerators'' for quantum error correcting codes, connected by a MacWilliams
transform, and use them to give a linear-programming bound for quantum codes.
We extend their work by introducing another enumerator, based on the classical
theory of shadow codes, that tightens their bounds significantly. In
particular, nearly all of the codes known to be optimal among additive quantum
codes (codes derived from orthogonal geometry ([quant-ph/9608006])) can be
shown to be optimal among all quantum codes. We also use the shadow machinery
to extend a bound on additive codes (E. M. Rains, manuscript in preparation) to
general codes, obtaining as a consequence that any code of length n can correct
at most floor((n+1)/6) errors.


title: From Quantum to Classical: the Quantum State Diffusion Model

abstract:
  Quantum mechanics is nonlocal. Classical mechanics is local. Consequently
classical mechanics can not explain all quantum phenomena. Conversely, it is
cumbersome to use quantum mechanics to describe classical phenomena. Not only
are the computations more complex, but - and this is the main point - it is
conceptually more difficult: one has to argue that nonlocality, entanglement
and the principle of superposition can be set aside when crossing the "quantum
$\rightarrow$ classical" border. Clearly, nonlocality, entanglement and the
principle of superposition should become irrelevant in the classical limit. But
why should one argue? Shouldn't it just come out of the equations? Does it come
out of the equations? This contribution is about the last question. And the
answer is: "it depends on which equation".


title:
Generally Deformed Oscillator, Isospectral Oscillator System and
  Hermitian Phase Operator

abstract:
  The generally deformed oscillator (GDO) and its multiphoton realization as
well as the coherent and squeezed vacuum states are studied. We discuss, in
particular, the GDO depending on a complex parameter q (therefore we call it
q-GDO) together with the finite dimensional cyclic representations. As a
realistic physical system of GDO the isospectral oscillator system is studied
and it is found that its coherent and squeezed vacuum states are closely
related to those of the oscillator. It is pointed out that starting from the
q-GDO with q root of unity one can define the hermitian phase operators in
quantum optics consistently and algebraically. The new creation and
annihilation operators of the Pegg-Barnett type phase operator theory are
defined by using the cyclic representations and these operators degenerate to
those of the ordinary oscillator in the classical limit q->1.


title: A Framework for Quantum Search Heuristics

abstract:
  A quantum algorithm for combinatorial search is presented that provides a
simple framework for utilizing search heuristics. The algorithm is evaluated in
a new case that is an unstructured version of the graph coloring problem. It
performs significantly better than the direct use of quantum parallelism, on
average, in cases corresponding to previously identified phase transitions in
search difficulty. The conditions underlying this improvement are described.
Much of the algorithm is independent of particular problem instances, making it
suitable for implementation as a special purpose device.


title:
Quantum mechanics of lattice gas automata. I. One particle plane waves
  and potentials

abstract:
  Classical lattice gas automata effectively simulate physical processes such
as diffusion and fluid flow (in certain parameter regimes) despite their
simplicity at the microscale. Motivated by current interest in quantum
computation we recently defined quantum lattice gas automata; in this paper we
initiate a project to analyze which physical processes these models can
effectively simulate. Studying the single particle sector of a one dimensional
quantum lattice gas we find discrete analogues of plane waves and wave packets,
and then investigate their behaviour in the presence of inhomogeneous
potentials.


title: Entanglement-Enhanced Classical Communication on a Noisy Quantum Channel

abstract:
  We consider the problem of trying to send a single classical bit through a
noisy quantum channel when two transmissions through the channel are available
as a resource. Classically, two transmissions add nothing to the receiver's
capability of inferring the bit. In the quantum world, however, one has the
possible further advantage of entangling the two transmissions. We demonstrate
that, for certain noisy channels, such entangled transmissions enhance the
receiver's capability of a correct inference.


title:
Effects of Inelastic Scattering on Tunneling Time in Generalized
  Nelson's Quantum Mechanics

abstract:
  We analyze the effects of inelastic scattering on the tunneling time
theoretically, using generalized Nelson's quantum mechanics. This
generalization enables us to describe quantum system with optical potential and
channel couplings in a real time stochastic approach, which seems to give us a
new insight into quantum mechanics beyond Copenhagen interpretation.


title: Cold, dilute, trapped bosons as an open quantum system

abstract:
  We present a master equation governing the reduced density operator for a
single trapped mode of a cold, dilute, weakly interacting Bose gas; and we
obtain an operator fluctuation-dissipation relation in which the
Ginzburg-Landau effective potential plays a physically transparent role. We
also identify a decoherence effect that tends to preserve symmetry, even when
the effective potential has a ``Mexican hat'' form.


title: Beyond Uncertainty: the internal structure of electrons and photons

abstract:
  The wave-structure of moving electrons is analyzed on a fundamental level by
employing a modified de Broglie relation. Formalizing the wave-function $\psi$
in real notation yields internal energy components due to mass oscillations.
The wave-features can then be referred to physical waves of discrete frequency
$\nu$ and the classical dispersion relation $\lambda \nu = u $, complying with
the classical wave equation. Including external potentials yields the
Schr\"odinger equation, which, in this context, is arbitrary due to the
internal energy components. It can be established that the uncertainty
relations are an expression of this, fundamental, arbitrariness. Electrons and
photons can be described by an identical formalism, providing formulations
equivalent to the Maxwell equations. The wave equations of intrinsic particle
properties are Lorentz invariant considering total energy of particles,
although transformations into a moving reference frame lead to an increase of
intrinsic potentials. Interactions of photons and electrons are treated
extensively, the results achieved are equivalent to the results in quantum
theory. Electrostatic interactions provide, a posteriori, a justification for
the initial assumption of electron-wave stability: the stability of electron
waves can be referred to vanishing intrinsic fields of interaction. The concept
finally allows the conclusion that a significant correlation for a pair of spin
particles in EPR--like measurements is likely to violate the uncertainty
relations.


title: Information Gain vs. State Disturbance in Quantum Theory

abstract:
  The engine that powers quantum cryptography is the principle that there are
no physical means for gathering information about the identity of a quantum
system's state (when it is known to be prepared in one of a set of
nonorthogonal states) without disturbing the system in a statistically
detectable way. This situation is often mistakenly described as a consequence
of the ``Heisenberg uncertainty principle.'' A more accurate account is that it
is a unique feature of quantum phenomena that rests ultimately on the Hilbert
space structure of the theory along with the fact that time evolutions for
isolated systems are unitary. In this paper we shall explore several aspects of
the information--disturbance principle in an attempt to make it firmly
quantitative and flesh out its significance for quantum theory as a whole.


title: Quantum codewords contradict local realism

abstract:
  Quantum codewords are highly entangled combinations of two-state systems. The
standard assumptions of local realism lead to logical contradictions similar to
those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and
Mermin. The new contradictions have some noteworthy features that did not
appear in the older ones.


title: New features in supersymmetry breakdown in quantum mechanics

abstract:
  The supersymmetric quantum mechanical model based on higher-derivative
supercharge operators possessing unbroken supersymmetry and discrete energies
below the vacuum state energy is described. As an example harmonic oscillator
potential is considered.


title: Complete Characterization of a Quantum Process: the Two-Bit Quantum Gate

abstract:
  We show how to fully characterize a quantum process in an open quantum
system. We particularize the procedure to the case of a universal two-qubit
gate in a quantum computer. We illustrate the method with a numerical
simulation of a quantum gate in the ion trap quantum computer.


title:
Gaussian Wigner distributions and hierarchies of nonclassical states in
  quantum optics-The single mode case

abstract:
  A recently introduced hierarchy of states of a single mode quantised
radiation field is examined for the case of centered Guassian Wigner
distributions. It is found that the onset of squeezing among such states
signals the transition to the strongly nonclassical regime. Interesting
consequences for the photon number distribution, and explicit representations
for them, are presented.


title: Positive-Operator-Valued Time Observable in Quantum Mechanics

abstract:
  We examine the longstanding problem of introducing a time observable in
Quantum Mechanics; using the formalism of positive-operator-valued measures we
show how to define such an observable in a natural way and we discuss some
consequences.


title:
A Dynamical Reduction Theory of Einstein-Podolsky-Rosen Correlations and
  a Possible Origin of CP Violations

abstract:
  We show that there is essentially only one way to construct a stochastic
Schrodinger equation that gives a dynamical account of the transformation of
entangled into factorized states and is consistent both with quantum mechanics
and required symmetries. The noisy, non-linear term is a unimodular scalar
multiple of the time reversal operator that must be present whenever a
Hamiltonian term in the Schrodinger equation can distinguish the factorized
constituents of an entangled state. The dynamical mechanism involved in the
transformation of entangled into factorized states provides an explanation for
the fact that Einstein-Podolsky-Rosen correlations appear in a time determined
by the response of the measuring device and independent of the distance between
the particles. The dependence on the response time of the measuring device may
be testable through a delay in observing the collapse of mesoscopic
``Schrodinger cat" states in ion traps. It is further shown that there are
situations where a two-particle interaction can induce a non-linear term by
virtue of coupling to decay modes that distinguish factorized constituents of
an entangled state. We show that this should happen in the neutral K-meson
system where the entangled $K_L$ state is pushed slightly in the direction of a
factorized constituent ($K_o$ or $\overline{K_o}$) as a consequence of the fact
that these can be distinguished via the sign of the charged lepton in a
semi-leptonic decay mode. The result is a CP violation that is within 20% of
the experimental value.


title:
Quantum state transfer and entanglement distribution among distant nodes
  in a quantum network

abstract:
  We propose a scheme to utilize photons for ideal quantum transmission between
atoms located at spatially-separated nodes of a quantum network. The
transmission protocol employs special laser pulses which excite an atom inside
an optical cavity at the sending node so that its state is mapped into a
time-symmetric photon wavepacket that will enter a cavity at the receiving node
and be absorbed by an atom there with unit probability. Implementation of our
scheme would enable reliable transfer or sharing of entanglement among
spatially distant atoms.


title: Weak measurement and the traversal time problem

abstract:
  The theory of weak measurement, proposed by Aharonov and coworkers, has been
applied by Steinberg to the long-discussed traversal time problem. The
uncertainty and ambiguity that characterize this concept from the perspective
of von Neumann measurement theory apparently vanish, and joint probabilities
and conditional averages become meaningful concepts. We express the Larmor
clock and some other well-known methods in the weak measurement formalism. We
also propose a method to determine higher moments of the traversal time
distribution in terms of the outcome of a gedanken experiment, by introducing
an appropriate operator. Since the weak measurement approach can sometimes lead
to unphysical results, for example average negative reflection times and higher
moments, the interpretation of the results obtained remains an open problem.


title: Time-dependent parasupersymmetry in quantum mechanics

abstract:
  Parasupersymmetry of the one dimensional time-dependent Schr\"odinger
equation is established. It is intimately connected with a chain of the
time-dependent Darboux transformations. As an example a parasupersymmetric
model of nonrelativistic free particle with threefold degenerate discrete
spectrum of an integral of motion is constructed.


title: Quantum Zeno Effect and Light-Dark Periods for a Single Atom

abstract:
  The quantum Zeno effect (QZE) predicts a slow-down of the time development of
a system under rapidly repeated ideal measurements, and experimentally this was
tested for an ensemble of atoms using short laser pulses for non-selective
state measurements. Here we consider such pulses for selective measurements on
a single system. Each probe pulse will cause a burst of fluorescence or no
fluorescence. If the probe pulses were strictly ideal measurements, the QZE
would predict periods of fluorescence bursts alternating with periods of no
fluorescence (light and dark periods) which would become longer and longer with
increasing frequency of the measurements. The non-ideal character of the
measurements is taken into account by incorporating the laser pulses in the
interaction, and this is used to determine the corrections to the ideal case.
In the limit, when the time between the laser pulses goes to zero, no freezing
occurs but instead we show convergence to the familiar macroscopic light and
dark periods of the continuously driven Dehmelt system. An experiment of this
type should be feasible for a single atom or ion in a trap


title: Quantum Smart Matter

abstract:
  The development of small-scale sensors and actuators enables the construction
of smart matter in which physical properties of materials are controlled in a
distributed manner. In this paper, we describe how quantum computers could
provide an additional capability, programmable control over some quantum
behaviors of such materials. This emphasizes the need for spatial coherence, in
contrast to the more commonly discussed issue of temporal coherence for quantum
computing. We also discuss some possible applications and engineering issues
involved in exploiting this possibility.


title: Quantum signatures of chaos in the dynamics of a trapped ion

abstract:
  We show how a nonlinear chaotic system, the parametrically kicked nonlinear
oscillator, may be realised in the dynamics of a trapped, laser-cooled ion,
interacting with a sequence of standing wave pulses. Unlike the original
optical scheme [G.J.Milburn and C.A.Holmes, Phys. Rev A, 44, p4704, (1991)],
the trapped ion enables strongly quantum dynamics with minimal dissipation.
This should permit an experimental test of one of the quantum signatures of
chaos; irregular collapse and revival dynamics of the average vibrational
energy.


title: The Capacity of Quantum Channel with General Signal States

abstract:
  It is shown that the capacity of a classical-quantum channel with arbitrary
(possibly mixed) states equals to the maximum of the entropy bound with respect
to all apriori distributions. This completes the recent result of Hausladen,
Jozsa, Schumacher, Westmoreland and Wooters, who proved the equality for the
pure state channel.


title:
Realistic experiments for measuring the wave function of a single
  particle

abstract:
  We suggest scattering experiments which implement the concept of ``protective
measurements'' allowing the measurement of the complete wave function even when
only one quantum system (rather than an ensemble) is available. Such scattering
experiments require massive, slow, projectiles with kinetic energies lower than
the first excitation of the system in question. The results of such experiments
can have a (probabilistic) distribution (as is the case when the Born
approximation for the scattering is valid) or be deterministic (in a
semi-classical limit).


title: Fault Tolerant Quantum Computation with Constant Error

abstract:
  Recently Shor showed how to perform fault tolerant quantum computation when
the error probability is logarithmically small. We improve this bound and
describe fault tolerant quantum computation when the error probability is
smaller than some constant threshold. The cost is polylogarithmic in time and
space, and no measurements are used during the quantum computation. The result
holds also for quantum circuits which operate on nearest neighbors only. To
achieve this noise resistance, we use concatenated quantum error correcting
codes. The scheme presented is general, and works with all quantum codes that
satisfy some restrictions, namely that the code is ``proper''.
  We present two explicit classes of proper quantum codes. The first example of
proper quantum codes generalizes classical secret sharing with polynomials. The
second uses a known class of quantum codes and converts it to a proper code.
This class is defined over a field with p elements, so the elementary quantum
particle is not a qubit but a ``qupit''. With our codes, the threshold is about
10^(-6). Hopefully, this paper motivates a search for proper quantum codes with
higher thresholds, at which point quantum computation becomes practical.


title: Coherent State Approach to Time Reparameterization Invariant Systems

abstract:
  For many years coherent states have been a useful tool for understanding
fundamental questions in quantum mechanics. Recently, there has been work on
developing a consistent way of including constraints into the phase space path
integral that naturally arises in coherent state quantization. This new
approach has many advantages over other approaches, including the lack of any
Gribov problems, the independence of gauge fixing, and the ability to handle
second-class constraints without any ambiguous determinants. In this paper, I
use this new approach to study some examples of time reparameterization
invariant systems, which are of special interest in the field of quantum
gravity.


title: Active stabilisation, quantum computation and quantum state synthesis

abstract:
  Active stabilisation of a quantum system is the active suppression of noise
(such as decoherence) in the system, without disrupting its unitary evolution.
Quantum error correction suggests the possibility of achieving this, but only
if the recovery network can suppress more noise than it introduces. A general
method of constructing such networks is proposed, which gives a substantial
improvement over previous fault tolerant designs. The construction permits
quantum error correction to be understood as essentially quantum state
synthesis. An approximate analysis implies that algorithms involving very many
computational steps on a quantum computer can thus be made possible.


title: Limitations of Noisy Reversible Computation

abstract:
  Noisy computation and reversible computation have been studied separately,
and it is known that they are as powerful as unrestricted computation. We study
the case where both noise and reversibility are combined and show that the
combined model is weaker than unrestricted computation. In our noisy reversible
circuits, each wire is flipped with probability p each time step, and all the
inputs to the circuit are present in time 0. We prove that any noisy reversible
circuit must have size exponential in its depth in order to compute a function
with high probability. This is tight as we show that any circuit can be
converted into a noise-resistant reversible one with a blow up in size which is
exponential in the depth. This establishes that noisy reversible computation
has the power of the complexity class NC^1.
  We extend this to quantum circuits(QC). We prove that any noisy QC which is
not worthless, and for which all inputs are present at time 0, must have size
exponential in its depth. (This high-lights the fact that fault tolerant QC
must use a constant supply of inputs all the time.) For the lower bound, we
show that quasi-polynomial noisy QC are at least powerful as logarithmic depth
QC, (or QNC^1). Making these bounds tight is left open in the quantum case.


title: Polynomial Simulations of Decohered Quantum Computers

abstract:
  We define formally decohered quantum computers (using density matrices), and
present a simulation of them by a probabalistic classical Turing Machine. We
study the slowdown of the simulation for two cases: (1) sequential quantum
computers, or quantum Turing machines(QTM), and (2) parallel quantum computers,
or quantum circuits. This paper shows that the computational power of decohered
quantum computers depends strongly on the amount of parallelism in the
computation.
  The expected slowdown of the simulation of a QTM is polynomial in time and
space of the quantum computation, for any non zero decoherence rate. This means
that a QTM subjected to any amount of noise is worthless. For decohered quantum
circuits, the situation is more subtle and depends on the decoherence rate,
eta. We find that our simulation is efficient for circuits with decoherence
rate higher than some constant, but exponential for general circuits with
decoherence rate lower than some other constant. Using computer experiments, we
show that the transition from exponential cost to polynomial cost happens in a
short range of decoherence rates, and exhibit the phase transitions in various
quantum circuits.


title: Accuracy of Semiclassical Methods for Shape Invariant Potentials

abstract:
  We study the accuracy of several alternative semiclassical methods by
computing analytically the energy levels for many large classes of exactly
solvable shape invariant potentials. For these potentials, the ground state
energies computed via the WKB method typically deviate from the exact results
by about 10%, a recently suggested modification using nonintegral Maslov
indices is substantially better, and the supersymmetric WKB quantization method
gives exact answers for all energy levels.