title: Quantum Noise in Quantum Optics: the Stochastic Schr\"odinger Equation

abstract:
  Lecture Notes for the Les Houches Summer School LXIII on Quantum Fluctuations
in July 1995 to appear in Elsevier Science Publishers B.V. 1997, edited by E.
Giacobino and S. Reynaud.


title: Information-theoretic interpretation of quantum error-correcting codes

abstract:
  Quantum error-correcting codes are analyzed from an information-theoretic
perspective centered on quantum conditional and mutual entropies. This approach
parallels the description of classical error correction in Shannon theory,
while clarifying the differences between classical and quantum codes. More
specifically, it is shown how quantum information theory accounts for the fact
that "redundant" information can be distributed over quantum bits even though
this does not violate the quantum "no-cloning" theorem. Such a remarkable
feature, which has no counterpart for classical codes, is related to the
property that the ternary mutual entropy vanishes for a tripartite system in a
pure state. This information-theoretic description of quantum coding is used to
derive the quantum analogue of the Singleton bound on the number of logical
bits that can be preserved by a code of fixed length which can recover a given
number of errors.


title: Non-classical interference between independent sources

abstract:
  When a one-photon state is mixed with a (separate) weak coherent state at a
beamsplitter the probability for detecting one photon in each beamsplitter
output approaches zero due to destructive interference. We demonstrate this
non-classical interference effect using pulse-gated single photons and weak
mode-locked laser pulses.


title: Five Quantum Register Error Correction Code For Higher Spin Systems

abstract:
  I construct a quantum error correction code (QECC) in higher spin systems
using the idea of multiplicative group character. Each $N$ state quantum
particle is encoded as five $N$ state quantum registers. By doing so, this code
can correct any quantum error arising from any one of the five quantum
registers. This code generalizes the well-known five qubit perfect code in
spin-1/2 systems and is shown to be optimal for higher spin systems. I also
report a simple algorithm for encoding. The importance of multiplicative group
character in constructing QECCs will be addressed.


title: Converse coding theorems for quantums source and noisy channel

abstract:
  The weak converse coding theorems have been proved for the quantum source and
channel. The results give the lower bound for capacity of source and the upper
bound for capacity of channel. The monotonicity of mutual quantum information
have also been proved. PACS numbers: 03.65.Bz


title:
Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position
  Operator

abstract:
  For Dirac equation, operator-invariants containing explicit time-dependence
in parallel to known time-dependent invariants of nonrelativistic Schr\"odinger
equation are introduced and discussed. As an example, a free Dirac particle is
considered and new invariants are constructed for it. The integral of motion,
which is initial Newton-Wigner position operator, is obtained explicitly for a
free Dirac particle. For such particle with kick modeled by delta-function of
time, the time-depending integral, which has physical meaning of initial
momentum, is found.


title:
Ideal Quantum Communication over Noisy Channels: a Quantum Optical
  Implementation

abstract:
  We consider transmission of an (unknown) quantum state between two distant
atoms via photons. Based on a quantum-optical realistic model, we define a
noisy quantum channel which includes systematic errors as well as errors due to
coupling to the environment. We present a protocol that allows one to
accomplish ideal transmission by repeating the transfer operation as many times
as needed.


title:
The quantum cryptography and the unambiguous measurement of quantum
  nonorthogonal states

abstract:
  We discuss the unambiguous measurement of quantum nonorthogonal states in
connection with the quantum cryptography. We show that checking a ratio of null
one to signal is essential in detecting a certain kind of eavesdropping in the
case of two nonorthogonal states quantum cryptography. We prove that it is not
needed in the case of the four states quantum cryptography.


title: Quantum harmonic oscillator state synthesis and analysis

abstract:
  Experiments are described in which a single, harmonically bound, beryllium
ion in a Paul trap is put into Fock, thermal, coherent, squeezed, and
Schroedinger cat states. Experimental determinations of the density matrix and
the Wigner function are described. A simple calculation of the decoherence of a
superposition of coherent states due to an external electric field is given.


title: Tailoring Many-Body Interactions to Solve Hard Combinatorial Problems

abstract:
  A quantum machine consisting of interacting linear clusters of atoms is
proposed for the 3SAT problem. Each cluster with two relevant states of
collective motion can be used to register a Boolean variable. Given any 3SAT
Boolean formula the interactions among the clusters can be so tailored that the
ground state(s) (possibly degenerate) of the whole system encodes the
satisfying truth assignment(s) for it. This relates the 3SAT problem to the
dynamics of the properly designed glass system.


title: Theory of controlled quantum dynamics

abstract:
  We introduce a general formalism, based on the stochastic formulation of
quantum mechanics, to obtain localized quasi-classical wave packets as
dynamically controlled systems, for arbitrary anharmonic potentials. The
control is in general linear, and it amounts to introduce additional quadratic
and linear time-dependent terms to the given potential. In this way one can
construct for general systems either coherent packets moving with constant
dispersion, or dynamically squeezed packets whose spreading remains bounded for
all times. In the standard operatorial framework our scheme corresponds to a
suitable generalization of the displacement and scaling operators that generate
the coherent and squeezed states of the harmonic oscillator.


title: Superconductive Static Quantum Logic

abstract:
  Superconducting rings with exactly $\Phi _0/2$ magnetic flux threading are
analogous of Ising spins having two degenerate states which can be used to
store binary information. When brought close these rings interact by means of
magnetic coupling. If the interactions are properly tailored, a system of such
superconducting rings can accomplish static quantum logic in the sense that the
states of the rings interpreted as Boolean variables satisfy the desired logic
relations when and only when the whole system is in the ground state. Such
static logic is essential to carry out the static quantum computation [1,2].


title: On Scale Invariance and Anomalies in Quantum Mechanics

abstract:
  We re-consider the quantum mechanics of scale invariant potentials in two
dimensions. The breaking of scale invariance by quantum effects is analyzed by
the explicit evaluation of the phase shift and the self-adjoint extension
method. We argue that the breaking of scale invariance reported in the
literature for the $\delta$(r) potential, is an example of explicit and not an
anomaly or quantum mechanical symmetry breaking.


title:
Time dependent partial waves and vortex rings in the dynamics of wave
  packets

abstract:
  We have found a new class of time dependent partial waves which are solutions
of time dependent Schr\"odinger equation for three dimensional harmonic
oscillator. We also showed the decomposition of coherent states of harmonic
oscillator into these partial waves. This decomposition appears perticularly
convenient for a description of the dynamics of a wave packet representing a
particle with spin when the spin--orbit interaction is present in the
hamiltonian. An example of an evolution of a localized wave packet into a torus
and backwards, for a particular initial conditions is analysed in analytical
terms and shown with a computer graphics.


title:
New mechanism of collapse and revival in wave packet dynamics due to
  spin-orbit interaction

abstract:
  The article discusses the properties of time evolution of wave packets in a
few systems. Dynamics of wave packet motion for Rydberg atoms with the
hierarchy of collapses and revivals is briefly reviewed. The main part of the
paper focuses on the new mechanism of quantum reccurrences in wave packet
dynamics. This mechanism can occur (in principle) in any physical system with
strong enough spin-orbit interaction. We discuss here the SPIN_ORBIT PENDULUM
effect that consists in different motions of subpackets possessing different
spin fields and results in oscillations of a fraction of average angular
momentum between spin and ordinary subspaces. The evolution of localized wave
packet into toroidal objects and backwards (for other class of initial
conditions) is also subject to discussion.


title:
Exact Solution Versus Gaussian Approximation for a Non-Ideal Bose Gas in
  One-Dimension

abstract:
  We investigate ground-state and excitation spectrum of a system of
non-relativistic bosons in one-dimension interacting through repulsive,
two-body contact interactions in a self-consistent Gaussian mean-field
approximation. The method consists in writing the variationally determined
density operator as the most general Gaussian functional of the quantized field
operators. There are mainly two advantages in working with one-dimension.
First, the existence of an exact solution for the ground-state and excitation
energies. Second, neither in the perturbative results nor in the Gaussian
approximation itself we do not have to deal with the three-dimensional
patologies of the contact interaction . So that this scheme provides a clear
comparison between these three different results.


title: Static Quantum Computation

abstract:
  Tailoring many-body interactions among a proper quantum system endows it with
computing ability by means of static quantum computation in the sense that some
of the physical degrees of freedom can be used to store binary information and
the corresponding binary variables satisfy some given logic relations if and
only if the system is in the ground state. Two theorems are proved showing that
the universal static quantum computer can encode the solutions for any P and NP
problem into its ground state using only polynomial number (in the problem
input size) of logic gates. The second step is to read out the solutions by
relaxing the system. The time complexity is relevant when one tries to read out
the solution by relaxing the system, therefore our model of static quantum
computation provides a new connection between the computational complexity and
the dynamics of a complex system.


title: Multiple Quantization and the Concept of Information

abstract:
  The understanding of the meaning of quantization seems to be the main problem
in understanding quantum structures. In this paper first the difference between
quantized particle vs. radiation fields in the formalism of canonical
quantization is discussed. Next von Weizsaecker's concept of ''multiple
quantization'' which leads to an understanding of quantization as an iteration
of probability theory is explained. Finally a connection between quantization
and the idea of a ''general theory of information'' is considered. This brings
together semantic information with the different levels of quantization and
expresses the philosophical attitude of this paper concerning the
interpretation of quantum theory.


title: On the Aharonov-Bohm Effect

abstract:
  Using the theory of self-adjoint extensions, we construct all the possible
hamiltonians describing the non relativistic Aharonov-Bohm effect. In general
the resulting hamiltonians are not rotationally invariant so that the angular
momentum is not a constant of motion. Using an explicit formula for the
resolvent, we describe the spectrum and compute the generalized eigenfunctions
and the scattering amplitude.


title: Information transmission through a noisy quantum channel

abstract:
  Noisy quantum channels may be used in many information carrying applications.
We show that different applications may result in different channel capacities.
Upper bounds on several of these capacities are proved. These bounds are based
on the coherent information, which plays a role in quantum information theory
analogous to that played by the mutual information in classical information
theory. Many new properties of the coherent information and entanglement
fidelity are proved. Two non-classical features of the coherent information are
demonstrated: the failure of subadditivity, and the failure of the pipelining
inequality. Both properties arise as a consequence of quantum entanglement, and
give quantum information new features not found in classical information
theory. The problem of a noisy quantum channel with a classical observer
measuring the environment is introduced, and bounds on the corresponding
channel capacity proved. These bounds are always greater than for the
unobserved channel. We conclude with a summary of open problems.


title: Quantum Isomorphic Simulation

abstract:
  A new type of quantum simulator is proposed which can simulate any quantum
many-body system in an isomorphic manner. It can actually synthesize a
duplicate of the system to be simulated. The isomorphic simulation has the
great advantage that the inevitable coupling of the simulator to the
environment can be fully exploited in simulating thermodynamic processes.


title:
Dynamical Semigroup Description of Coherent and Incoherent
  Particle-Matter Interaction

abstract:
  The meaning of statistical experiments with single microsystems in quantum
mechanics is discussed and a general model in the framework of non-relativistic
quantum field theory is proposed, to describe both coherent and incoherent
interaction of a single microsystem with matter. Compactly developing the
calculations with superoperators, it is shown that the introduction of a time
scale, linked to irreversibility of the reduced dynamics, directly leads to a
dynamical semigroup expressed in terms of quantities typical of scattering
theory. Its generator consists of two terms, the first linked to a coherent
wavelike behaviour, the second related to an interaction having a measuring
character, possibly connected to events the microsystem produces propagating
inside matter. In case these events breed a measurement, an explicit
realization of some concepts of modern quantum mechanics ("effects" and
"operations") arises. The relevance of this description to a recent debate
questioning the validity of ordinary quantum mechanics to account for such
experimental situations as, e.g., neutron-interferometry, is briefly discussed.


title: Perturbation of an Eigen-Value from a Dense Point Spectrum : An Example

abstract:
  We study a perturbed Floquet Hamiltonian $K+\beta V$ depending on a coupling
constant $\beta$. The spectrum $\sigma(K)$ is assumed to be pure point and
dense. We pick up an eigen-value, namely $0\in\sigma(K)$, and show the
existence of a function $\lambda(\beta)$ defined on $I\subset\R$ such that
$\lambda(\beta) \in \sigma(K+\beta V)$ for all $\beta\in I$, 0 is a point of
density for the set $I$, and the Rayleigh-Schr\"odinger perturbation series
represents an asymptotic series for the function $\lambda(\beta)$. All ideas
are developed and demonstrated when treating an explicit example but some of
them are expected to have an essentially wider range of application.


title:
Quantum dynamics of cold trapped ions, with application to quantum
  computation

abstract:
  The theory of interactions between lasers and cold trapped ions as it
pertains to the design of Cirac-Zoller quantum computers is discussed. The mean
positions of the trapped ions, the eigenvalues and eigenmodes of the ions'
oscillations, the magnitude of the Rabi frequencies for both allowed and
forbidden internal transitions of the ions and the validity criterion for the
required Hamiltonian are calculated. Energy level data for a variety of ion
species is also presented.


title:
Uncertainty Relations for Two Dimensional Quantized Electromagnetic
  Potential

abstract:
  The canonical quantization of flux is performed. It is shown that according
to the canonical flux quantization there must be a new uncertainty relation: $e
\Delta A_m . \Delta x_m \geq \hbar$ where $A_m$ and $\Delta x_m \geq l_B$ are
the electromagnetic gauge potential, the position uncertainty and the magnetic
length, respectively. Other arguments in favour of this uncertainty relation
are also discussed.


title: Bringing Up a Quantum Baby

abstract:
  Any two infinite-dimensional (separable) Hilbert spaces are unitarily
isomorphic. The sets of all their self-adjoint operators are also therefore
unitarily equivalent. Thus if all self-adjoint operators can be observed, and
if there is no further major axiom in quantum physics than those formulated for
example in Dirac's `Quantum Mechanics', then a quantum physicist would not be
able to tell a torus from a hole in the ground. We argue that there are indeed
such axioms involving vectors in the domain of the Hamiltonian: The
``probability densities'' (hermitean forms) \psi^\dagger \chi for \psi,\chi in
this domain generate an algebra from which the classical configuration space
with its topology (and with further refinements of the axiom, its C^K and
C^infinity structures) can be reconstructed using Gel'fand - Naimark theory.
Classical topology is an attribute of only certain quantum states for these
axioms, the configuration space emergent from quantum physics getting
progressively less differentiable with increasingly higher excitations of
energy and eventually altogether ceasing to exist. After formulating these
axioms, we apply them to show the possibility of topology change and to discuss
quantized fuzzy topologies. Fundamental issues concerning the role of time in
quantum physics are also addressed.


title: More on Static Quantum Computation

abstract:
  The construction of a universal static quantum computer actually provides
another proof of the NP-hardness of spin-glass problems.


title: The lambda-q calculus can efficiently simulate quantum computers

abstract:
  We show that the lambda-q calculus can efficiently simulate quantum Turing
machines by showing how the lambda-q calculus can efficiently simulate a class
of quantum cellular automaton that are equivalent to quantum Turing machines.
We conclude by noting that the lambda-q calculus may be strictly stronger than
quantum computers because NP-complete problems such as satisfiability are
efficiently solvable in the lambda-q calculus but there is a widespread doubt
that they are efficiently solvable by quantum computers.


title: Resilient Quantum Computation: Error Models and Thresholds

abstract:
  Recent research has demonstrated that quantum computers can solve certain
types of problems substantially faster than the known classical algorithms.
These problems include factoring integers and certain physics simulations.
Practical quantum computation requires overcoming the problems of environmental
noise and operational errors, problems which appear to be much more severe than
in classical computation due to the inherent fragility of quantum
superpositions involving many degrees of freedom. Here we show that arbitrarily
accurate quantum computations are possible provided that the error per
operation is below a threshold value. The result is obtained by combining
quantum error-correction, fault tolerant state recovery, fault tolerant
encoding of operations and concatenation. It holds under physically realistic
assumptions on the errors.


title: States prepared by decay

abstract:
  We consider the time evolution of a discrete state embedded in a continuum.
Results from scattering theory can be utilized to solve the initial value
problem and discuss the system as a model of wave packet preparation. Extensive
use is made of the analytic properties of the propagators, and simple model
systems are evaluated to illustrate the argument. We verify the exponential
appearence of the continuum state and its propagation as a localized wave
packet.


title: On the Quantum Space-Time Coordinates of an Event

abstract:
  This paper gives a representation of the most general positive operator
valued measure in Minkowski space-time, covariant with respect to the Poincare'
group. It provides the correct mathematical description of the space-time
coordinates of a quantum event, described by a quantum object with suitable
properties. It is known that these coordinates cannot be represented by
self-adjoint operators or by the corresponding projection valued measure.


title:
Quantum stochastic differential equation is unitary equivalent to a
  symmetric boundary value problem in Fock space

abstract:
  We show a new remarkable connection between the symmetric form of a quantum
stochastic differential equation (QSDE) and the strong resolvent limit of
Schr\"odinger equations in Fock space: the strong resolvent limit is unitary
equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitary
equivalent to the symmetric (or Stratonovich) form of QSDE.
  We prove that QSDE is unitary equivalent to a symmetric boundary value
problem for the Schr\"odinger equation in Fock space. The boundary condition
describes standard jumps of the phase and amplitude of components of Fock
vectors belonging to the range of the resolvent. The corresponding Markov
evolution equation (the Lindblad or Markov master equation) is derived from the
boundary value problem for the Schr\"odinger equation.}


title: On the validity of the Aharonov-Bergmann-Lebowitz rule

abstract:
  It is argued that the proof of Cohen [Phys. Rev. A 51, 4373 (1995)] which
shows that an application of the Aharonov-Bergmann-Lebowitz (ABL) rule leads to
contradiction with predictions of quantum theory is erroneous. A generalization
of the ABL rule for the case of an incomplete final measurement (which is
needed for the analysis of Cohen's proof) is presented.


title: A nonadditive quantum code

abstract:
  Up to now every good quantum error-correcting code discovered has had the
structure of an eigenspace of an Abelian group generated by tensor products of
Pauli matrices; such codes are known as stabilizer or additive codes. In this
letter we present the first example of a code that is better than any code of
this type. It encodes six states in five qubits and can correct the erasure of
any single qubit.


title:
Subdynamics through Time Scales and Scattering Maps in Quantum Field
  Theory

abstract:
  It is argued that the dynamics of an isolated system, due to the concrete
procedure by which it is separated from the environment, has a non-Hamiltonian
contribution. By a unified quantum field theoretical treatment of typical
subdynamics, e.g., hydrodynamics, kinetic theory, master equation for a
particle interacting with matter, we look for the structure of this more
general dynamics.


title:
Separability criterion and inseparable mixed states with positive
  partial transposition

abstract:
  It is shown that any separable state on Hilbert space ${\cal H}={\cal
H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure
product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion
for mixed states in terms of range of density matrix is obtained. It is used in
construction of inseparable mixed states with positive partial transposition in
the case of $3\times 3$ and $2\times 4$ systems. The states represent an
entanglement which is hidden in a more subtle way than it has been known so
far.


title:
A particle-number-conserving Bogoliubov method which demonstrates the
  validity of the time-dependent Gross-Pitaevskii equation for a highly
  condensed Bose gas

abstract:
  The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number $ N$ of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator $A$ for the total number
of particles and the sum of a ``condensate wavefunction'' $\xi(x)$ and a phonon
field operator $\chi(x)$ in the form $\psi(x) \approx A\{\xi(x) +
\chi(x)/\sqrt{N}\}$ when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of $\sqrt{N}$,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.


title: Quantum Mechanics as a Classical Theory XV: Thermodynamical Derivation

abstract:
  We present in this continuation paper a new axiomatic derivation of the
Schr\"odinger equation from three basic postulates. This new derivation sheds
some light on the thermodynamic character of the quantum formalism. We also
show the formal connection between this derivation and the one previously done
by other means. Some considerations about metaestability are also drawn. We
return to an example previously developed to show how the connection between
both derivations works.


title:
The quantum potential: the breakdown of classical symplectic symmetry
  and the energy of localisation and dispersion

abstract:
  The composition of the quantum potential and its role in the breakdown of
classical symplectic symmetry in quantum mechanics is investigated. General
expressions are derived for the quantum potential in both configuration space
and momentum space representations. By comparing the configuration space and
momentum space representations of the causal interpretation of quantum
mechanics, the quantum potential is shown to break the symplectic symmetry that
exists between these two representations in classical mechanics. In addition,
it is shown that the quantum potential in configuration space may be expressed
as the sum of a momentum dispersion energy and a spatial localisation energy; a
complementary expression for the quantum potential being found in the momentum
representation. The composition and role of the quantum potential in both
representations is analysed for a particle in a linear potential and for two
eigenstates of the quantum harmonic oscillator.


title: On Many-Minds Interpretations of Quantum Theory

abstract:
  This paper is a response to some recent discussions of many-minds
interpretations in the philosophical literature. After an introduction to the
many-minds idea, the complexity of quantum states for macroscopic objects is
stressed. Then it is proposed that a characterization of the physical structure
of observers is a proper goal for physical theory. It is argued that an
observer cannot be defined merely by the instantaneous structure of a brain,
but that the history of the brain's functioning must also be taken into
account. Next the nature of probability in many-minds interpretations is
discussed and it is suggested that only discrete probability models are needed.
The paper concludes with brief comments on issues of actuality and identity
over time.


title: Reversible Simulation of Irreversible Computation by Pebble Games

abstract:
  Reversible simulation of irreversible algorithms is analyzed in the stylized
form of a `reversible' pebble game. While such simulations incur little
overhead in additional computation time, they use a large amount of additional
memory space during the computation. The reacheable reversible simulation
instantaneous descriptions (pebble configurations) are characterized
completely. As a corollary we obtain the reversible simulation by Bennett and
that among all simulations that can be modelled by the pebble game, Bennett's
simulation is optimal in that it uses the least auxiliary space for the
greatest number of simulated steps. One can reduce the auxiliary storage
overhead incurred by the reversible simulation at the cost of allowing limited
erasing leading to an irreversibility-space tradeoff. We show that in this
resource-bounded setting the limited erasing needs to be performed at precise
instants during the simulation. We show that the reversible simulation can be
modified so that it is applicable also when the simulated computation time is
unknown.


title: Quantum Computations and Images Recognition

abstract:
  The using of quantum parallelism is often connected with consideration of
quantum system with huge dimension of space of states. The n-qubit register can
be described by complex vector with 2^n components (it belongs to n'th tensor
power of qubit spaces). For example, for algorithm of factorization of numbers
by quantum computer n can be about a few hundreds for some realistic
applications for cryptography. The applications described further are used some
other properties of quantum systems and they do not demand such huge number of
states.
  The term "images recognition" is used here for some broad class of problems.
For example, we have a set of some objects V_i and function of "likelihood":
  F(V,W) < F(V,V) = 1
  If we have some "noisy" or "distorted" image W, we can say that recognition
of W is V_i, if F(W,V_i) is near 1 for some V_i.


title: Weisskopf-Wigner model for wave packet excitation

abstract:
  We consider a laser induced molecular excitation process as a decay of a
single energy state into a continuum. The analytic results based on
Weisskopf-Wigner approach and perturbation calculations are compared with
numerical wave packet results. We find that the decay model describes the
excitation process well within the expected parameter region.


title:
Comparative Noninformativities of Quantum Priors Based on Monotone
  Metrics

abstract:
  We consider a family of prior probability distributions of particular
interest, all being defined on the three-dimensional convex set of two-level
quantum systems. Each distribution is, following recent work of Petz and Sudar,
taken to be proportional to the volume element of a monotone metric on that
Riemannian manifold. We apply an entropy-based test (a variant of one recently
developed by Clarke) to determine which of two priors is more noninformative in
nature. This involves converting them to posterior probability distributions
based on some set of hypothesized outcomes of measurements of the quantum
system in question. It is, then, ascertained whether or not the original
relative entropy (Kullback-Leibler distance) between a pair of priors increases
or decreases when one of them is exchanged with its corresponding posterior.
The findings lead us to assert that the maximal monotone metric yields the most
noninformative (prior) distribution and the minimal monotone (that is, the
Bures) metric, the least. Our conclusions both agree and disagree, in certain
respects, with ones recently reached by Hall, who relied upon a less specific
test criterion than our entropy-based one.


title: On Reliability Function of Quantum Communication Channel

abstract:
  The reliability function gives the rate of exponential convergence to zero of
the error probability in a communication channel. In this paper bounds for the
reliability function of a quantum pure state channel are given, reminiscent of
the corresponding classical bounds. This in particular suggests an alternative
proof of the coding theorem for quantum noiseless channel, which would make no
use of the notion of typical subspace. Example of binary quantum channel is
considered in some detail.


title: Reconstruction of the joint state of a two-mode Bose-Einstein condensate

abstract:
  We propose a scheme to reconstruct the state of a two-mode Bose-Einstein
condensate, with a given total number of atoms, using an atom interferometer
that requires beam splitter, phase shift and non-ideal atom counting
operations. The density matrix in the number-state basis can be computed
directly from the probabilities of different counts for various phase shifts
between the original modes, unless the beamsplitter is exactly balanced.
Simulated noisy data from a two-mode coherent state is produced and the state
is reconstructed, for 49 atoms. The error can be estimated from the singular
values of the transformation matrix between state and probability data.


title: The Effective Action for a Relativistic Jaynes-Cummings Model

abstract:
  We describe an effective field theory for atomic lasers which reduces to the
Jaynes-Cummings model in the non-relativistic, single mode limit. Our action
describes a multi-mode system, with general polarizations and Lorentz
invariance and can therefore be used in all contexts from the astrophysical to
the laboratory. We show how to compute the effective action for this model and
perform the calculation explicitly at the one loop level. Our model provides a
way of analyzing a many-particle, two-state model with arbitrary boundary
conditions.


title: A Note on Non-Additive Quantum Codes

abstract:
  A method to combine two quantum error-correcting codes is presented. Even
when starting with additive codes, the resulting code might be non-additive.
Furthermore, the notion of the erasure space is introduced which gives a full
characterisation of the erasure-correcting capabilities of the codes. For the
special case that the two codes are unitary images of each other, the erasure
space and the pure erasure space of the resulting code can be calculated.


title: Generalized Quantum Mechanics and Nonlinear Gauge Transformations

abstract:
  Motivated by the problems of interpretation of a nonlinear evolution equation
in quantum mechanics we discuss in this contribution the concept of nonlinear
gauge transformations, that has recently been introduced in joint work with
Doebner and Goldin, in the framework of Mielnik's Generalized Quantum
Mechanics. Using these gauge transformations we construct linear quantum
systems in a ``nonlinear disguise'', and a gauge generalization of these (in
analogy to the minimal coupling of orthodox quantum mechanics) leads to a
unification of Bialynicki-Birula--Mycielski and Doebner--Goldin evolution
equations for the quantum system. The notion of nonlinear observables
introduced by L\"ucke is finally discussed in the same framework.


title: The analysis of Hardy's experiment revisited

abstract:
  Cohen and Hiley [Phys. Rev. A 52, 76 (1995)] have criticized the analysis of
Hardy's gedanken experiment according to which the contradiction with quantum
theory in Hardy's experiment arises due the failure of the "product rule" for
the elements of reality of pre- and post-selected systems. It is argued that
the criticism of Cohen and Hiley is not sound.


title: Radiative Corrections to the Casimir Energy

abstract:
  The lowest radiative correction to the Casimir energy density between two
parallel plates is calculated using effective field theory. Since the
correlators of the electromagnetic field diverge near the plates, the
regularized energy density is also divergent. However, the regularized integral
of the energy density is finite and varies with the plate separation L as
1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but
more transparent theory of a massless scalar field in 1+1 dimensions confined
to a line element of length L and satisfying Dirichlet boundary conditions.


title: Deformations and Nonlinear Systems

abstract:
  The q-deformation of harmonic oscillators is shown to lead to q-nonlinear
vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger
equation are considered. The procedure is generalized to broader class of
nonlinearities related to other types of deformations. The nonlinear
noncanonical transforms used in the deformation procedure are shown to preserve
in some cases the linear dynamical equations, for instance, for the harmonic
oscillators. The nonlinear coherent states and some physical aspects of the
deformations are reviewed.


title: Quantum reference systems: a new framework for quantum mechanics

abstract:
  A new interpretation of nonrelativistic quantum mechanics is presented. It
explains the violation of Bell's inequality by maintaining realism and the
principle of locality. Schrodinger's cat paradox and the
Einstein-Podolsky-Rosen paradox are solved, too. The new approach assumes the
universal validity of the Schrodinger equation, while von Neumann's postulates
about the measurement process are replaced with a new, consistent set of
postulates. The underlying idea is that quantum states depend on quantum
reference systems in a fundamental way. Quantum reference systems (a new
concept, first introduced in this paper) are themselves physical systems which
contain the system to be described.


title:
Reversibility and Adiabatic Computation: Trading Time and Space for
  Energy

abstract:
  Future miniaturization and mobilization of computing devices requires energy
parsimonious `adiabatic' computation. This is contingent on logical
reversibility of computation. An example is the idea of quantum computations
which are reversible except for the irreversible observation steps. We propose
to study quantitatively the exchange of computational resources like time and
space for irreversibility in computations. Reversible simulations of
irreversible computations are memory intensive. Such (polynomial time)
simulations are analysed here in terms of `reversible' pebble games. We show
that Bennett's pebbling strategy uses least additional space for the greatest
number of simulated steps. We derive a trade-off for storage space versus
irreversible erasure. Next we consider reversible computation itself. An
alternative proof is provided for the precise expression of the ultimate
irreversibility cost of an otherwise reversible computation without
restrictions on time and space use. A time-irreversibility trade-off hierarchy
in the exponential time region is exhibited. Finally, extreme
time-irreversibility trade-offs for reversible computations in the thoroughly
unrealistic range of computable versus noncomputable time-bounds are given.


title:
Non-local two-photon correlations using interferometers physically
  separated by 35 meters

abstract:
  An experimental demonstration of quantum correlations is presented. Energy
and time entangled photons at wavelengths of 704 and 1310 nm are produced by
parametric downconversion in KNbO3 and are sent through optical fibers into a
bulk-optical (704 nm) and an all-fiber Michelson-interferometer (1310 nm),
respectively. The two interferometers are located 35 meters aside from one
another. Using Faraday-mirrors in the fiber-interferometer, all birefringence
effects in the fibers are automatically compensated. We obtained two-photon
fringe visibilities of up to 95 % from which one can project a violation of
Bell's inequality by 8 standard deviations. The good performance and the
auto-aligning feature of Faraday-mirror interferometers show their potential
for a future test of Bell's inequalities in order to examine
quantum-correlations over long distances.


title: Interferometry with Faraday mirrors for quantum cryptography

abstract:
  Quantum Cryptography over 23km of installed Telecom fiber using a novel
interferometer with Faraday mirrors is presented. The interferometer needs no
alignment nor polarization control and features 99.8% fringe visibility. A
secret key of 20kbit length with a error rate of 1.35% for 0.1 photon per pulse
was produced.


title:
Statistical Inference, Distinguishability of Quantum States, And Quantum
  Entanglement

abstract:
  We argue from the point of view of statistical inference that the quantum
relative entropy is a good measure for distinguishing between two quantum
states (or two classes of quantum states) described by density matrices. We
extend this notion to describe the amount of entanglement between two quantum
systems from a statistical point of view. Our measure is independent of the
number of entangled systems and their dimensionality.


title: Least-squares inversion for density-matrix reconstruction

abstract:
  We propose a method for reconstruction of the density matrix from measurable
time-dependent (probability) distributions of physical quantities. The
applicability of the method based on least-squares inversion is - compared with
other methods - very universal. It can be used to reconstruct quantum states of
various systems, such as harmonic and and anharmonic oscillators including
molecular vibrations in vibronic transitions and damped motion. It also enables
one to take into account various specific features of experiments, such as
limited sets of data and data smearing owing to limited resolution. To
illustrate the method, we consider a Morse oscillator and give a comparison
with other state-reconstruction methods suggested recently.


title: Quantum lattice gases and their invariants

abstract:
  The one particle sector of the simplest one dimensional quantum lattice gas
automaton has been observed to simulate both the (relativistic) Dirac and
(nonrelativistic) Schroedinger equations, in different continuum limits. By
analyzing the discrete analogues of plane waves in this sector we find
conserved quantities corresponding to energy and momentum. We show that the
Klein paradox obtains so that in some regimes the model must be considered to
be relativistic and the negative energy modes interpreted as positive energy
modes of antiparticles. With a formally similar approach--the Bethe ansatz--we
find the evolution eigenfunctions in the two particle sector of the quantum
lattice gas automaton and conclude by discussing consequences of these
calculations and their extension to more particles, additional velocities, and
higher dimensions.

categories: quant-ph comp-gas cond-mat.stat-mech nlin.CG


title: Quantum Space-Time and Tetrads

abstract:
  The description of space-time in a quantum theoretical framework must be
considered as a fundamental problem in physics. Most attempts start with an
already given classical space-time - then the quantization is done. In contrast
to this the central assumption in this paper is not to start with space-time,
but to derive it from some more abstract presuppositions like this is done in
von Weizsaecker's "quantum theory of ur-alternatives". Mathematically the
transition from a manifold with spin structure to a manifold with four real
space-time coordinates has to be considered. The suggestion is made that this
transition can be well described by using a tetradial formalism which appears
to be the most natural connection between ur-spinors and real four-vectors.


title: Coherent State Approach to Quantum Clocks

abstract:
  The ``problem of time'' has been a pressing issue in quantum gravity for some
time. To help understand this problem, Rovelli proposed a model of a two
harmonic oscillators system where one of the oscillators can be thought of as a
``clock'' for the other oscillator thus giving a natural time reference frame
for the system. Recently, the author has constructed an explicit form for the
coherent states on the reduced phase space of this system in terms of Klauder's
projection operator approach. In this paper, by using coherent state
representations and other tools from coherent state quantization, I investigate
the construction of gauge invariant operators on this reduced phase space, and
the ability to use a quantum oscillator as a ``clock.''


title: Comment on ``Nonlocality of a Single Photon Revisited''

abstract:
  This paper has been withdrawn. A significantly revised version will be posted
in the near future.


title:
Wiener Integration for Quantum Systems: A Unified Approach to the
  Feynman-Kac formula

abstract:
  A generalized Feynman-Kac formula based on the Wiener measure is presented.
Within the setting of a quantum particle in an electromagnetic field it yields
the standard Feynman-Kac formula for the corresponding Schr\"odinger semigroup.
In this case rigorous criteria for its validity are compiled. Finally,
phase-space path-integral representations for more general quantum Hamiltonians
are derived. These representations rely on a generalized Lie-Trotter formula
which takes care of the operator-ordering multiplicity, but in general is not
related to a path measure.


title: Programmable quantum gate arrays

abstract:
  We show how to construct quantum gate arrays that can be programmed to
perform different unitary operations on a data register, depending on the input
to some program register. It is shown that a universal quantum gate array - a
gate array which can be programmed to perform any unitary operation - exists
only if one allows the gate array to operate in a probabilistic fashion. The
universal quantum gate array we construct requires an exponentially smaller
number of gates than a classical universal gate array.


title: Pumping of twin-trap Bose-Einstein condensates

abstract:
  We consider extensions of the twin-trap Bose-Einstein condensate system of
Javaneinen and Yoo [Phys. Rev. Lett., 76, 161--164 (1996)] to include pumping
and output couplers. Such a system permits a continual outflow of two beams of
atoms with a relative phase coherence maintained by the detection process. We
study this system for two forms of thermal pumping, both with and without the
influence of inter-atomic collisions. We also examine the effects of pumping on
the phenomenon of collapses and revivals of the relative phase between the
condensates.


title:
Quantum Noise and Polarization Fluctuations in Vertical Cavity Surface
  Emitting Lasers

abstract:
  We investigate the polarization fluctuations caused by quantum noise in
quantum well vertical cavity surface emitting lasers (VCSELs). Langevin
equations are derived on the basis of a generalized rate equation model in
which the influence of competing gain-loss and frequency anisotropies is
included. This reveals how the anisotropies and the quantum well confinement
effects shape the correlations and the magnitude of fluctuations in ellipticity
and in polarization direction. According to our results all parameters used in
the rate equations may be obtained experimentally from precise time resolved
measurements of the intensity and polarization fluctuations in the emitted
laser light. To clarify the effects of anisotropies and of quantum well
confinement on the laser process in VCSELs we therefore propose time resolved
measurements of the polarization fluctuations in the laser light. In
particular, such measurements allow to distinguish the effects of frequency
anisotropy and of gain-loss anisotropy and would provide data on the spin
relaxation rate in the quantum well structure during cw operation as well as
representing a new way of experimentally determinig the linewidth enhancement
factor alpha.

categories: quant-ph adap-org cond-mat nlin.AO physics.optics


title: From quantum-codemaking to quantum code-breaking

abstract:
  This is a semi-popular overview of quantum entanglement as an important
physical resource in the field of data security and quantum computing. After a
brief outline of entanglement's key role in philosophical debates about the
meaning of quantum mechanics I describe its current impact on both cryptography
and cryptanalysis. The paper is based on the lecture given at the conference
"Geometric Issues in the Foundations of Science" (Oxford, June 1996) in honor
of Roger Penrose.


title: Decoherence of quantum registers

abstract:
  We consider decoherence of quantum registers, which consist of the qubits
sited approximately periodically in space. The sites of the qubits are
permitted to have a small random variance. We derive the explicit conditions
under which the qubits can be assumed decohering independently. In other
circumstances, the qubits are decohered cooperatively. We describe two kinds of
collective decoherence. In each case, a scheme is proposed for reducing the
collective decoherence. The schemes operate by encoding the input states of the
qubits into some ''subdecoherent'' states.


title:
Zero-energy states for a class of quasi-exactly solvable rational
  potentials

abstract:
  Quasi-exactly solvable rational potentials with known zero-energy solutions
of the Schro\" odinger equation are constructed by starting from exactly
solvable potentials for which the Schr\" odinger equation admits an so(2,1)
potential algebra. For some of them, the zero-energy wave function is shown to
be normalizable and to describe a bound state.


title: Measurement in Quantum Physics

abstract:
  The conceptual problems in quantum mechanics -- related to the collapse of
the wave function, the particle-wave duality, the meaning of measurement --
arise from the need to ascribe particle character to the wave function. As will
be shown, all these problems dissolve when working instead with quantum fields,
which have both wave and particle character. Otherwise the predictions of
quantum physics, including Bell's inequalities, coincide with those of the
standard treatments. The transfer of the results of the quantum measurement to
the classical realm is also discussed.


title:
Photon-added state preparation via conditional measurement on a beam
  splitter

abstract:
  We show that conditional output measurement on a beam splitter may be used to
produce photon-added states for a large class of signal-mode quantum states,
such as thermal states, coherent states, squeezed states, displaced
photon-number states, and coherent phase states. Combining a mode prepared in
such a state and a mode prepared in a photon-number state, the state of the
mode in one of the output channels of the beam splitter ``collapses'' to a
photon-added state, provided that no photons are detected in the other output
channel. We present analytical and numerical results, with special emphasis on
photon-added coherent and squeezed vacuum states. In particular, we show that
adding photons to a squeezed vacuum yields superpositions of quantum states
which show all the typical features of Schr\"{o}dinger-cat-like states.


title: Preserving coherence in quantum computation by pairing quantum bits

abstract:
  A scheme is proposed for protecting quantum states from both independent
decoherence and cooperative decoherence. The scheme operates by pairing each
qubit (two-state quantum system) with an ancilla qubit and by encoding the
states of the qubits into the corresponding coherence-preserving states of the
qubit-pairs. In this scheme, the amplitude damping (loss of energy) is
prevented as well as the phase damping (dephasing) by a strategy called the
free-Hamiltonian-elimination We further extend the scheme to include quantum
gate operations and show that loss and decoherence during the gate operations
can also be prevented.


title: Entanglement of a Pair of Quantum Bits

abstract:
  The ``entanglement of formation'' of a mixed state of a bipartite quantum
system can be defined in terms of the number of pure singlets needed to create
the state with no further transfer of quantum information. We find an exact
formula for the entanglement of formation for all mixed states of two qubits
having no more than two non-zero eigenvalues, and we report evidence suggesting
that the formula is valid for all states of this system.


title: Quantum controllers for quantum systems

abstract:
  This paper discusses fully coherent quantum feedback control, in which the
sensors, controller, and actuators are quantum systems and interact coherently
with the system to be controlled: as a result, the entire feedback loop is
coherent. Unlike conventional semiclassical feedback control of quantum
systems, feedback control by quantum controllers is not stochastic, preserves
the initial state of the controlled system, and can control quantum systems in
ways that are not possible using conventional, incoherent feedback control. In
particular, the target state to which the quantum controller drives the system
can be entangled with another quantum system. This paper investigates quantum
controllers and states necessary and sufficient conditions for a Hamiltonian
quantum system to be observable and controllable by a quantum controller.


title: Nonorthogonal Quantum States Maximize Classical Information Capacity

abstract:
  I demonstrate that, rather unexpectedly, there exist noisy quantum channels
for which the optimal classical information transmission rate is achieved only
by signaling alphabets consisting of nonorthogonal quantum states.


title: The Associated Metric for a Particle in a Quantum Energy Level

abstract:
  We show that the probabilistic distribution over the space in the spectator
world, can be associated via noncommutative geometry (with some modifications)
to a metric in which the particle lives. According to this geometrical view,
the metric in the particle world is ``contracted'' or ``stretched'' in an
inverse proportion to the probability distribution.


title: Quantum Reed-Muller Codes

abstract:
  This paper presents a set of quantum Reed-Muller codes which are typically
100 times more effective than existing quantum Reed-Muller codes.


title: Quantum copying: A network

abstract:
  We present a network consisting of quantum gates which produces two imperfect
copies of an arbitrary qubit. The quality of the copies does not depend on the
input qubit. We also show that for a restricted class of inputs it is possible
to use a very similar network to produce three copies instead of two. For
qubits in this class, the copy quality is again independent of the input and is
the same as the quality of the copies produced by the two-copy network.


title: On the Nature of Charge Conjugation in Quantum Theory

abstract:
  On the basis of the invariance of Dirac equation Lu(x,c)=0 with respect to
the inversion of the speed of light Q:(x,c)=(x,-c), it is shown that the
relationship [C,PTQ]u(x,c)=0 between the transformations of the charge
conjugation C, the space inversion P, the time reversal T and the inversion of
the speed of light Q is true. The charge conjugation in quantum theory may be
interpreted as the consequence of the discrete symmetries reflecting the
fundamental properties of space, time and speed of light.


title: Nonbinary quantum codes

abstract:
  We present several results on quantum codes over general alphabets (that is,
in which the fundamental units may have more than 2 states). In particular, we
consider codes derived from finite symplectic geometry assumed to have
additional global symmetries. From this standpoint, the analogues of
Calderbank-Shor-Steane codes and of GF(4)-linear codes turn out to be special
cases of the same construction. This allows us to construct families of quantum
codes from certain codes over number fields; in particular, we get analogues of
quadratic residue codes, including a single-error correcting code encoding one
letter in five, for any alphabet size. We also consider the problem of
fault-tolerant computation through such codes, generalizing ideas of Gottesman.


title: Continuous Fuzzy Measurement of Energy for a Two-Level System

abstract:
  A continuous measurement of energy which is sharp (perfect) leads to the
quantum Zeno effect (freezing of the state). Only if the quantum measurement is
fuzzy, continuous monitoring gives a readout E(t) from which information about
the dynamical development of the state vector of the system may be obtained in
certain cases. This is studied in detail. Fuzziness is thereby introduced with
the help of restricted path integrals equivalent to non-Hermitian Hamiltonians.
For an otherwise undisturbed multilevel system it is shown that this
measurement represents a model of decoherence. If it lasts long enough, the
measurement readout discriminates between the energy levels and the von Neumann
state reduction is obtained. For a two-level system under resonance influence
(which undergoes in absence of measurement Rabi oscillations between the
levels) different regimes of measurement are specified depending on its
duration and fuzziness: 1) the Zeno regime where the measurement results in a
freezing of the transitions between the levels and 2) the Rabi regime when the
transitions maintain. It is shown that in the Rabi regime at the border to the
Zeno regime a correlation exists between the time dependent measurement readout
and the modified Rabi oscillations of the state of the measured system.
Possible realizations of continuous fuzzy measurements of energy are sketched.


title: Monte Carlo Simulation of Quantum Computation

abstract:
  The many-body dynamics of a quantum computer can be reduced to the time
evolution of non-interacting quantum bits in auxiliary fields by use of the
Hubbard-Stratonovich representation of two-bit quantum gates in terms of
one-bit gates. This makes it possible to perform the stochastic simulation of a
quantum algorithm, based on the Monte Carlo evaluation of an integral of
dimension polynomial in the number of quantum bits. As an example, the
simulation of the quantum circuit for the Fast Fourier Transform is discussed.


abstract:
  The Bures distance between two displaced thermal states and the corresponding
geometric quantities (statistical metric, volume element, scalar curvature) are
computed. Under nonunitary (dissipative) dynamics, the statistical distance
shows the same general features previously reported in the literature by
Braunstein and Milburn for two--state systems. The scalar curvature turns out
to have new interesting properties when compared to the curvature associated
with squeezed thermal states.


title: Macroscopic quantum damping in SQUID rings

abstract:
  The measurement process is introduced in the dynamics of Josephson devices
exhibiting quantum behaviour in a macroscopic degree of freedom. The
measurement is shown to give rise to a dynamical damping mechanism whose
experimental observability could be relevant to understand decoherence in
macroscopic quantum systems.


title: Can single-photon states violate causality?

abstract: This paper has been withdrawn.


title: Simulation of Many-Body Fermi Systems on a Universal Quantum Computer

abstract:
  We provide fast algorithms for simulating many body Fermi systems on a
universal quantum computer. Both first and second quantized descriptions are
considered, and the relative computational complexities are determined in each
case. In order to accommodate fermions using a first quantized Hamiltonian, an
efficient quantum algorithm for anti-symmetrization is given. Finally, a
simulation of the Hubbard model is discussed in detail.


title: Notes on free fall of a particle and bouncing on a reflecting surface

abstract:
  Considerable progress has recently been made in controling the motion of free
atomic particles by means of light pressure exerted by laser radiation. The
free fall of atoms and bouncing on a reflecting surface made from evanescent
wave formed by internal reflection of a quasiresonant laser beam at a curved
glass surface in the presence of homogeneous gravitational field has been
observed. In this paper we present the energy quantization of this system by
making use the asymptotic expansion method. It is shown that for large $n$ the
levels go like $n^{2/3}$ which may be compared with $n^2$ for the infinite
square well.


title: Measurability in Linear and Non-Linear Quantum Mechanical Systems

abstract:
  The measurability by means of continuous measurements, of an observable
$\A(t_0)$, at an instant, and of a time averaged observable, $\bar \A=1/T\int
\A(t')dt'$, is examined for linear and in particular for non-linear quantum
mechanical systems. We argue that only when the exact (non-perturbative)
solution is known, an exact measurement may be possible. A perturbative
approach is shown to fail in the non-linear case for measurements with accuracy
$\Delta \bar \A < \Delta \bar \A_{min}(T)$, giving rise to a restriction on the
accuracy. Thus, in order to prepare an initial pure state of a non-linear
system, by means of a continuous measurement, the exact non-perturbative
solution must be known.


title: Approximate quantum error correction can lead to better codes

abstract:
  We present relaxed criteria for quantum error correction which are useful
when the specific dominant noise process is known. These criteria have no
classical analogue. As an example, we provide a four-bit code which corrects
for a single amplitude damping error. This code violates the usual Hamming
bound calculated for a Pauli description of the error process, and does not fit
into the GF(4) classification.


title: Quantum computation with phase drift errors

abstract:
  We present results of numerical simulations of the evolution of an ion trap
quantum computer made out of 18 ions which are subject to a sequence of nearly
15000 laser pulses in order to find the prime factors of N=15. We analyze the
effect of random and systematic phase drift errors arising from inaccuracies in
the laser pulses which induce over (under) rotation of the quantum state.
Simple analytic estimates of the tolerance for the quality of driving pulses
are presented. We examine the use of watchdog stabilization to partially
correct phase drift errors concluding that, in the regime investigated, it is
rather inefficient.


title: Quantum Mechanics as a Classical Theory XVI: Positive-Definite Densities

abstract:
  In this paper we will turn our attention to the problem of obtaining
phase-space probability density functions. We will show that it is possible to
obtain functions which assume only positive values over all its domain of
definition.


title: O(3,3)-like Symmetries of Coupled Harmonic Oscillators

abstract:
  In classical mechanics, the system of two coupled harmonic oscillators is
shown to possess the symmetry of the Lorentz group O(3,3) applicable to a
six-dimensional space consisting of three space-like and three time-like
coordinates, or SL(4,r) in the four-dimensional phase space consisting of two
position and two momentum variables. In quantum mechanics, the symmetry is
reduced to that of O(3,2) or Sp(4), which is a subgroup of O(3,3) or SL(4,r)
respectively. It is shown that among the six Sp(4)-like subgroups, only one
possesses the symmetry which can be translated into the group of unitary
transformations in quantum mechanics. In quantum mechanics, there is the lower
bound in the size of phase space for each mode determined by the uncertainty
principle while there are no restriction on the phase-space size in classical
mechanics. This is the reason why the symmetry is smaller in quantum mechanics.


title:
Measurement processes in quantum physics: a new theory of measurements
  in terms of statistical ensembles

abstract:
  Considering the recently established arbitrariness the Schroedinger equation
has to be interpreted as an equation of motion for a statistical ensemble of
particles. The statistical qualities of individual particles derive from the
unknown intrinsic energy components, they depend on the physical environment by
way of external potentials. Due to these statistical qualities and wave
function normalization, non-locality is inherent to the fundamental relations
of Planck, de Broglie and Schroedinger. A local formulation of these statements
is introduced and briefly assessed, the modified and local Schroedinger
equation is non-linear. Quantum measurements are analyzed in detail, the exact
interplay between causal and statistical reasons in a measurement process can
be accounted for. Examples of individual measurement effects in quantum theory
are given, the treatment of diffraction experiments, neutron interferences,
quantum erasers, the quantum Zeno effect, and interaction-free measurements can
be described consistent with the suggested framework. The paper additionally
provides a strictly local and deterministic calculation of interactions in a
magnetic field. The results suggest that quantum theory is a statistical
formalism which derives its validity in measurements from considering every
possible measurement of a given system. It can equally be established, that the
framework of quantum physics is theoretically incomplete, because a
justification of ensemble qualities is not provided.


title:
Hyperfinite-operational Approach to the Problem of Time Reversibility of
  Quantum Mechanics

abstract:
  This paper outlines a mathematical framework of quantum probability in which
the time asymmetry in describing measuring processes is avoided. The main
objects of the framework are hyperfinite operations, which are constructed by
using nonstandard analysis and the operational approach by Davies and Lewis.
Then the notions of Bayesian conditional probability are defined, and
Bayes-type theorems in terms of the probability are showed.


title:
Dissipative Quantum Tunneling from Quantum Potential Approach -- Back
  Reaction of Particle Creation --

abstract:
  Back reaction of the particle creation on the quantum tunneling process is
analyzed in real time formalism. We use quantum potential method in which whole
quantum dynamics is exactly projected to a classical Hamilton-Jacobi equation
with quantum corrections. We derive the reduction of the tunneling rate due to
this particle creation effect.


title:
Comments to On the Accuracy of Lamb Shift Measurements in Hydrogen
  (Physica Scripta, 55 (1997) 33-40) by V. G. Pal'chikov, Yu. L. Sokolov, and
  V. P. Yakovlev

abstract:
  The work is a comments on the article of V. G. Pal'chikov, Yu. L. Sokolov,
and V. P. Yakovlev, devoted to the measurement of the Lamb shift in the
hydrogen atom and published in Physica Scripta, 55 (1997) 33-40.


title: Arrival time in quantum mechanics

abstract:
  A self-adjoint operator with dimensions of time is explicitly constructed,
and it is shown that its complete and orthonormal set of eigenstates can be
used to define consistently a probability distribution of the time of arrival
at a spatial point.


title: Extension of the Barut-Girardello Coherent State and Path Integral

abstract:
  We extend the Barut-Girardello coherent state for the representation of
$SU(1,1)$ to the coherent state for a representation of $U(N,1)$ and construct
the measure. We also construct a path integral formula for some Hamiltonian.


title: Quantum Telecomputation

abstract:
  Quantum mechanics permits certain kinds of non-local effects. This paper
demonstrates how these can be used for distributed computation with minimal
communication between various processors. The problem considered is that of
estimating the mean of N items to a certain precision. First a serial quantum
mechanical algorithm for this is presented that is faster than any classical
algorithm. Next it is shown how this can be efficiently parallelized with
quantum mechanical processors that are remotely located. These processors
consist of coupled EPR particles. Each processor has just to communicate one
bit of classical information to a central location at the end of its local
computation.


title: A Greenberger-Horne-Zeilinger experiment for mixed states

abstract:
  This paper shows how the Greenberger-Horne-Zeilinger experiment, which
demonstrates the nonlocal nature of quantum mechanics, can be performed using
nuclear magnetic resonance on spins in molecules at finite temperature. The use
of nuclear magnetic resonance techniques allows the experiment to uncover the
nonlocality not just of special GHZ states, but of arbitrary three particle
states.


title:
A complementary group technique for a resolution of the outer
  multiplicity problem of SU(n): (I) Littlewood rule and a complementary group
  of SU(n)

abstract:
  A complementary group to SU(n) is found that realizes all features of the
Littlewood rule for Kronecker products of SU(n) representations. This is
accomplished by considering a state of SU(n) to be a special Gel'fand state of
the complementary group {\cal U}(2n-2). The labels of {\cal U}(2n-2) can be
used as the outer multiplicity labels needed to distinguish multiple
occurrences of irreducible representations (irreps) in the SU(n)\times
SU(n)\downarrow SU(n) decomposition that is obtained from the Littlewood rule.
Furthermore, this realization can be used to determine SU(n)\supset
SU(n-1)\times U(1) Reduced Wigner Coefficients (RWCs) and Clebsch-Gordan
Coefficients (CGCs) of SU(n), using algebraic or numeric methods, in either the
canonical or a noncanonical basis. The method is recursive in that it uses
simpler RWCs or CGCs with one symmetric irrep in conjunction with standard
recoupling procedures. New explicit formulae for the multiplicity for SU(3) and
SU(4) are used to illustrate the theory.


title:
A complementary group technique for the resolution of the outer
  multiplicity problem of SU(n): (II) A recoupling approach to the solution of
  SU(3)\supset U(2) reduced Wigner coefficients

abstract:
  A general procedure for the derivation of SU(3)\supset U(2) reduced Wigner
coefficients for the coupling (\lambda_{1}\mu_{1})\times
(\lambda_{2}\mu_{2})\downarrow (\lambda\mu)^{\eta}, where \eta is the outer
multiplicity label needed in the decomposition, is proposed based on a
recoupling approach according to the complementary group technique given in
(I). It is proved that the non-multiplicity-free reduced Wigner coefficients of
SU(n) are not unique with respect to canonical outer multiplicity labels, and
can be transformed from one set of outer multiplicity labels to another. The
transformation matrices are elements of SO(m), where m is the number of
occurrence of the corresponding irrep (\lambda\mu) in the decomposition
(\lambda_{1}\mu_{1})\times (\lambda_{2}\mu_{2})\downarrow (\lambda\mu). Thus, a
kind of the reduced Wigner coefficients with multiplicity is obtained after a
special SO(m) transformation. New features of this kind of reduced Wigner
coefficients and the differences from the reduced Wigner coefficients with
other choice of the multiplicity label given previously are discussed. The
method can also be applied to the derivation of general SU(n) Wigner or reduced
Wigner coefficients with multiplicity. Algebraic expression of another kind of
reduced Wigner coefficients, the so-called reduced auxiliary Wigner
coefficients for SU(3)\supset U(2), are also obtained.


title: Measured Quantum Dynamics of a Trapped Ion

abstract:
  The measurement process is taken into account in the dynamics of trapped ions
prepared in nonclassical motional states. The induced decoherence is shown to
manifest itself both in the inhibition of the internal population dynamics and
in a damping of the vibrational motion without classical counterpart.
Quantitative comparison with present experimental capabilities is discussed,
leading to a proposal for the verification of the predicted effects.


title:
Entropy and optimal decompositions of states relative to a maximal
  commutative subalgebra

abstract:
  To calculate the entropy of a subalgebra or of a channel with respect to a
state, one has to solve an intriguing optimalization problem. The latter is
also the key part in the entanglement of formation concept, in which case the
subalgebra is a subfactor. I consider some general properties, valid for these
definitions in finite dimensions, and apply them to a maximal commutative
subalgebra of a full matrix algebra. The main method is an interplay between
convexity and symmetry. A collection of helpful tools from convex analysis for
the problems in question is collected in an appendix.


title:
Polynomial Lie Algebras and Associated Pseudogroup Structures in
  Composite Quantum Models

abstract:
  Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant
polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having
invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure
functions in commutation relations, are related to pseudogroup structures $\exp
V, V\in g_{pd}$ and describe dynamic symmetry of models under study. Physical
applications of algebras $g_{pd}$ in quantum optics and in composite field
theories are briefly discussed.


title: Spatially Correlated Qubit Errors and Burst-Correcting Quantum Codes

abstract:
  We explore the design of quantum error-correcting codes for cases where the
decoherence events of qubits are correlated. In particular, we consider the
case where only spatially contiguous qubits decohere, which is analogous to the
case of burst errors in classical coding theory. We present several different
efficient schemes for constructing families of such codes. For example, one can
find one-dimensional quantum codes of length n=13 and 15 that correct burst
errors of width b < 4; as a comparison, a random-error correcting quantum code
that corrects t=3 errors must have length n > 18. In general, we show that it
is possible to build quantum burst-correcting codes that have near optimal
dimension. For example, we show that for any constant b, there exist
b-burst-correcting quantum codes with length n, and dimension k=n-log n -O(b);
as a comparison, the Hamming bound for the case with t (constant) random errors
yields k < n - t log n - O(1) .


title: Two non-orthogonal states can be cloned by a unitary-reduction process

abstract:
  We show that, there are physical means for cloning two non-orthogonal pure
states which are secretly chosen from a certain set $% \$={ | \Psi_0 > , |
\Psi_1 > }$. The states are cloned through a unitary evolution together with a
measurement. The cloning efficiency can not attain 100%. With some negative
measurement results, the cloning fails.


title: Bohmian Mechanics Revisited

abstract:
  We consider the problem of whether there are deterministic theories
describing the evolution of an individual physical system in terms of the
definite trajectories of its constituent particles and which stay in the same
relation to Quantum Mechanics as Bohmian Mechanics but which differ from the
latter for what concerns the trajectories followed by the particles. Obviously,
one has to impose on the hypothetical alternative theory precise physical
requirements. We analyse various such constraints and we show step by step how
to meet them. This way of attacking the problem allows to recall and focus on
some relevant features of Bohm's theory. One of the central requirements we
impose on the models we are going to analyse has to do with their
transformation properties under the transformations of the extended Galilei
group. In a context like the one we are interested in one can put forward
various requests that we refer to as physical and genuine covariance and
invariance. Other fundamental requests are that the theory allows the
description of isolated physical systems as well as that it leads to a solution
(in the same sense as Bohmian Mechanics) of the measurement problem. We show
that there are infinitely many inequivalent (from the point of view of the
trajectories) bohmian-like theories reproducing the predictions of Quantum
Mechanics.


title:
On the Torus Quantization of Two Anyons with Coulomb Interaction in a
  Magnetic Field

abstract:
  We study two anyons with Coulomb interaction in a uniform magnetic field $B$.
By using the torus quantization we obtain the modified Landau and Zeeman
formulas for the two anyons. Then we derive a simple algebraic equation for the
full spectral problem up to the second order in $B$.

categories: quant-ph chao-dyn cond-mat hep-th nlin.CD


title:
Comment on ``Resonant Spectra and the Time Evolution of the Survival and
  Nonescape Probabilities''

abstract:
  In [G. Garcia-Calderon, J. L. Mateos, and M. Moshinsky, Phys. Rev. Lett. 74,
337 (1995)], the time evolution of the quantum decay of a state initially
located within an interaction region of finite range was investigated. In
particular, it was shown that the survival and nonescape probabilities behave
differently at very large times. The purpose of this Comment is to show that
they have the same asymptotic behavior.


title:
Demonstration of the quantum mechanics applicability limits in time
  reversion experiments in spin macrosystems

abstract:
  An experimental study of the applicability of mechanics equations to
describing the process of equilibrium establishing in an isolated spin system
was performed. The time-reversion effects were used at the experiments. It was
demonstrated, that the equations of mechanics do not describe the spin
macrosystem transition to the equilibrium. The experimental results correspond
to the theory which is based on the non-equilibrium thermodynamics methods and
takes into account the quick decay of cross-correlations in the systems.


title: Lorentz-covariant stochastic wave function dynamics?

abstract:
  The e-print is completely withdrawn for it was based on a report which was
not public. The author seriously apologizes because he was unaware.


title: Substituting Quantum Entanglement for Communication

abstract:
  We show that quantum entanglement can be used as a substitute for
communication when the goal is to compute a function whose input data is
distributed among remote parties. Specifically, we show that, for a particular
function among three parties (each of which possesses part of the function's
input), a prior quantum entanglement enables one of them to learn the value of
the function with only two bits of communication occurring among the parties,
whereas, without quantum entanglement, three bits of communication are
necessary. This result contrasts the well-known fact that quantum entanglement
cannot be used to simulate communication among remote parties.


title: An Exact Quantum Polynomial-Time Algorithm for Simon's Problem

abstract:
  We investigate the power of quantum computers when they are required to
return an answer that is guaranteed to be correct after a time that is
upper-bounded by a polynomial in the worst case. We show that a natural
generalization of Simon's problem can be solved in this way, whereas previous
algorithms required quantum polynomial time in the expected sense only, without
upper bounds on the worst-case running time. This is achieved by generalizing
both Simon's and Grover's algorithms and combining them in a novel way. It
follows that there is a decision problem that can be solved in exact quantum
polynomial time, which would require expected exponential time on any classical
bounded-error probabilistic computer if the data is supplied as a black box.


title: Quantum Nondemolition Monitoring of Universal Quantum Computers

abstract:
  The halt scheme for quantum Turing machines, originally proposed by Deutsch,
is reformulated precisely and is proved to work without spoiling the
computation. The ``conflict'' pointed out recently by Myers in the definition
of a universal quantum computer is shown to be only apparent. In the context of
quantum nondemolition (QND) measurement, it is also shown that the output
observable, an observable representing the output of the computation, is a QND
observable and that the halt scheme is equivalent to the QND monitoring of the
output observable.


title: Quantum white noise with singular non-linear interaction

abstract:
  A model of a system driven by quantum white noise with singular quadratic
self--interaction is considered and an exact solution for the evolution
operator is found. It is shown that the renormalized square of the squeezed
classical white noise is equivalent to the quantum Poisson process. We describe
how equations driven by nonlinear functionals of white noise can be derived in
nonlinear quantum optics by using the stochastic approximation.


title: Measurement models for time-resolved spectroscopy: a comment

abstract:
  We present an exactly solvable model for photon emission, which allows us to
examine the evolution of the photon wavefunction in space and time. We apply
this model to coherent phenomena in three-level systems with a special emphasis
on the photon detection process.


title:
The Geometry of Consistency: Decohering Histories in Generalized Quantum
  Theory

abstract:
  The geometry of decoherence in generalized "consistent histories" quantum
theory is explored, revealing properties of the theory that are independent of
any particular application of it. It is shown how the decoherence functional of
a closed quantum system may be regarded as an Hermitian form on the space of
linear operators on the Hilbert space of the system. This identification makes
manifest a number of structural properties of decoherence functionals. For
example, a bound on the maximum number of histories in a consistent set is
determined. When the decoherence functional is positive -- as in conventional
quantum mechanics -- it defines a semi-inner product on the space of history
operators. This shows that consistent sets of histories are just orthogonal
sets in this inner product. It further implies the existence in general of
Cauchy-Schwarz and triangle inequalities for positive decoherence functionals.
The geometrical significance of the ILS theorem classifying all possible
decoherence functionals is illuminated, and a version of the ILS theorem for
decoherence functionals on class operators is given. The class of history
operators consistent according to a given decoherence functional is found, and,
conversely, it is shown how to construct the decoherence functionals according
to which a given set of histories is consistent. More generally, the
"geometric" point of view here developed supplies a powerful unified language
with which to solve problems in generalized quantum theory.


title:
Equivalence between Bell's inequality and a constraint on stochastic
  field theories for EPR states

abstract:
  A generalized form of EPR state is defined, embracing both classical and
nonclassical states. It is shown that for such states, Bell's inequality is
equivalent to a constraint on stochastic field theories. Thus, violation of
Bell's inequality can be observed also for weak violation of stochastic field
theories. The Schrodinger cat state is shown to be an example of this.


title: Equivalence between squeezed-state and twin-beam communication channels

abstract:
  We show the equivalence between two different communication schemes that
employ a couple of modes of the electromagnetic field. One scheme uses
unconventional heterodyne detection, with correlated signal and image-band
modes in a twin-beam state from parametric downconversion. The other scheme is
realized through a complex-number coding over quadrature-squeezed states of two
uncorrelated modes, each detected by ordinary homodyning. This equivalence
concerns all the stages of the communication channel: the encoded state, the
optimal amplifier for the channel, the master equation modeling the loss, and
the output measurement scheme. The unitary transformation that connects the two
communication schemes is realized by a frequency conversion device.


title: Added noise in homodyne measurement of field-observables

abstract:
  Homodyne tomography provides a way for measuring generic field-operators.
Here we analyze the determination of the most relevant quantities: intensity,
field, amplitude and phase. We show that tomographic measurements are affected
by additional noise in comparison with the direct detection of each observable
by itself. The case of of coherent states has been analyzed in details and
earlier estimations of tomographic precision are critically discussed.


title:
Electromagnetic Vacuum Fluctuations and Electron Coherence II: Effects
  of Wavepacket Size

abstract:
  If one analyzes the effects of electromagnetic vacuum fluctuations upon an
electron interference pattern in an approximation in which the electrons follow
classical trajectories, an ultraviolet divergence results. It is shown that
this divergence is an artifact of the classical trajectory approximation, and
is absent when the finite sizes of electron wavepackets are accounted for. It
is shown that the vacuum fluctuation effect has a logarithmic dependence upon
the wavepacket size. However, at least in one model geometry, this dependence
cancels when one includes both vacuum fluctuation and photon emission effects.


title:
Phase preparation by atom counting of Bose-Einstein condensates in mixed
  states

abstract:
  We study the build up of quantum coherence between two Bose-Einstein
condensates which are initially in mixed states. We consider in detail the two
cases where each condensate is initially in a thermal or a Poisson distribution
of atom number. Although initially there is no relative phase between the
condensates, a sequence of spatial atom detections produces an interference
pattern with arbitrary but fixed relative phase. The visibility of this
interference pattern is close to one for the Poisson distribution of two
condensates with equal counting rates but it becomes a stochastic variable in
the thermal case, where the visibility will vary from run to run around an
average visibility of $\pi /4.$ In both cases, the variance of the phase
distribution is inversely proportional to the number of atom detections in the
regime where this number is large compared to one but small compared with the
total number of atoms in the condensates.


title: Number phase uncertainty relations: verification by homodyning

abstract:
  It is shown that fundamental uncertainty relations between photon number and
canonical phase of a single-mode optical field can be verified by means of
balanced homodyne measurement. All the relevant quantities can be sampled
directly from the measured phase-dependent quadrature distribution.


title:
Does entanglement depend on the timing of the impacts at the
  beam-splitters?

abstract:
  A new nonlocality experiment with moving beam-splitters is proposed. The
experiment is analysed according to conventional quantum mechanics, and to an
alternative nonlocal description in which superposition depends not only on
indistinguishability but also on the timing of the impacts at the
beam-splitters.


title:
Stochastically positive structures on Weyl algebras. The case of
  quasi-free states

abstract:
  We consider quasi-free stochastically positive ground and thermal states on
Weyl algebras in Euclidean time formulation. In particular, we obtain a new
derivation of a general form of thermal quasi-free state and give conditions
when such state is stochastically positive i.e. when it defines periodic
stochastic process with respect to Euclidean time, so called thermal process.
Then we show that thermal process completely determines modular structure
canonically associated with quasi-free state on Weyl algebra. We discuss a
variety of examples connected with free field theories on globally hyperbolic
stationary space-times and models of quantum statistical mechanics.


title:
Asymptotics of Quantum Relative Entropy From Representation Theoretical
  Viewpoint

abstract:
  In this paper it was proved that the quantum relative entropy $D(\sigma \|
\rho)$ can be asymptotically attained by Kullback Leibler divergences of
probabilities given by a certain sequence of POVMs. The sequence of POVMs
depends on $\rho$, but is independent of the choice of $\sigma$.


title: Asymptotic estimation theory for a finite dimensional pure state model

abstract:
  The optimization of measurement for n samples of pure sates are studied. The
error of the optimal measurement for n samples is asymptotically compared with
the one of the maximum likelihood estimators from n data given by the optimal
measurement for one sample.


title: Polynomial invariants of quantum codes

abstract:
  The weight enumerators (quant-ph/9610040) of a quantum code are quite
powerful tools for exploring its structure. As the weight enumerators are
quadratic invariants of the code, this suggests the consideration of
higher-degree polynomial invariants. We show that the space of degree k
invariants of a code of length n is spanned by a set of basic invariants in
one-to-one correspondence with S_k^n. We then present a number of equations and
inequalities in these invariants; in particular, we give a higher-order
generalization of the shadow enumerator of a code, and prove that its
coefficients are nonnegative. We also prove that the quartic invariants of a
((4,4,2)) are uniquely determined, an important step in a proof that any
((4,4,2)) is additive ([2]).


title: Quantum codes of minimum distance two

abstract:
  It is reasonable to expect the theory of quantum codes to be simplified in
the case of codes of minimum distance 2; thus, it makes sense to examine such
codes in the hopes that techniques that prove effective there will generalize.
With this in mind, we present a number of results on codes of minimum distance
2. We first compute the linear programming bound on the dimension of such a
code, then show that this bound can only be attained when the code either is of
even length, or is of length 3 or 5. We next consider questions of uniqueness,
showing that the optimal code of length 2 or 4 is unique (implying that the
well-known one-qubit-in-five single-error correcting code is unique), and
presenting nonadditive optimal codes of all greater even lengths. Finally, we
compute the full automorphism group of the more important distance 2 codes,
allowing us to determine the full automorphism group of any GF(4)-linear code.


title:
A Linear Programming Approach to Attainable Cramer-Rao type Bounds and
  Randomness Condition

abstract:
  The author studies the Cramer-Rao type bound by a linear programming
approach. By this approach, he found a necessary and sufficient condition that
the Cramer-Rao type bound is attained by a random measurement. In a spin 1/2
system, this condition is satisfied.


title: Timing and Other Artifacts in EPR Experiments

abstract:
  Re-evaluation of the evidence (some of it unpublished) shows that
experimenters conducting Einstein-Podolsky-Bohm (EPR) experiments may have been
deceived by various pre-conceptions and artifacts. False or unproven
assumptions were made regarding, in some cases, fair sampling, in others
timing, accidental coincidences and enhancement. Realist possibilities,
assuming a purely wave model of light, are presented heuristically, and
suggestions given for fruitful lines of research. Quantum Mechanics can be
proved false, but Bell tests have turned out to be unsuitable for the task.


title:
Rigorous results on Schroedinger operators with certain Gaussian random
  potentials in multi-dimensional continuous space

abstract:
  Schroedinger operators with certain Gaussian random potentials in
multi-dimensional Euclidean space possess almost surely an absolutely
continuous integrated density of states and no absolutely continuous spectrum
at sufficiently low energies.


title: On the squeezed states for n observables

abstract:
  Three basic properties (eigenstate, orbit and intelligence) of the canonical
squeezed states (SS) are extended to the case of arbitrary n observables. The
SS for n observables X_i can be constructed as eigenstates of their linear
complex combinations or as states which minimize the Robertson uncertainty
relation. When X_i close a Lie algebra L the generalized SS could also be
introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N
the three generalizations are equivalent. For the simple su(1,1) the family of
eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a
family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1))
orbit although the SU(1,1) group related coherent states (CS) with symmetry are
contained in it.
  Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the
three generators K_j of SU(1,1) in the representations with Bargman index k =
1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail.
These are ideal SS for K_{1,2,3}. In the case of the one mode realization of
su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature
squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states
|z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.


title: Quantum Algorithm for the Collision Problem

abstract:
  In this note, we give a quantum algorithm that finds collisions in arbitrary
r-to-one functions after only O((N/r)^(1/3)) expected evaluations of the
function. Assuming the function is given by a black box, this is more efficient
than the best possible classical algorithm, even allowing probabilism. We also
give a similar algorithm for finding claws in pairs of functions. Furthermore,
we exhibit a space-time tradeoff for our technique. Our approach uses Grover's
quantum searching algorithm in a novel way.


title: Are there basic laws of quantum information processing?

abstract:
  We prove within the standard quantum formalism without reduction postulate
that the no-cloning theorem and the principle of no-increasing of entanglement
under local actions and one-way classical communication are equivalent. We
argue that the result is a manifestation of more general principles governing
quantum information processing analogous to the thermodynamical laws.


title:
Photon Distribution Function for Stocks Wave for Stimulatted Raman
  Scattering

abstract:
  New time-dependent integrals of motion are found for stimulated Raman
scattering. Explicit formula for the photon-number probability distribution as
a function of the laser-field intensity and the medium parameters is obtained
in terms of Hermite polynomials of two variables.


title:
Effective Theories of Coupled Classical and Quantum Variables from
  Decoherent Histories: A New Approach to the Backreaction Problem

abstract:
  We use the decoherent histories approach to quantum theory to derive the form
of an effective theory describing the coupling of classical and quantum
variables. The derivation is carried out for a system consisting of a large
particle coupled to a small particle with the important additional feature that
the large particle is also coupled to a thermal environment producing the
decoherence necessary for classicality. The effective theory is obtained by
tracing out both the environment and the small particle variables. It consists
of a formula for the probabilities of a set of histories of the large particle,
and depends on the dynamics and initial quantum state of the small particle. It
has the form of an almost classical particle coupled to a stochastic variable
whose probabilities are determined by a formula very similar to that given by
quantum measurement theory for continuous measurements of the small particle's
position. The effective theory gives intuitively sensible answers when the
small particle is in a superposition of localized states.


title: Interaction-Free Measurements, Atom Localisation and Complementarity

abstract:
  We analyse interaction-free measurements on classical and quantum objects. We
show the transition from a classical interaction free measurement to a quantum
non-demolition measurement of atom number, and discuss the mechanism of the
enforcement of complementarity in atom interferometric interaction-free
measurements.


title: Propagator for an Aharonov-Bohm-Coulomb system

abstract:
  The propagator of three-dimensional Aharonov-Bohm-Coulomb system is
calculated by following the Duru-Kleinert method. It is shown that the system
is reduced to two independent two dimensional Aharonov-Bohm plus harmonic
oscillator systems through dimensional extension and Kustaanheimo-Stiefel
transformation. The energy spectrum is deduced.


title:
Coupling Classical and Quantum Variables using Continuous Quantum
  Measurement Theory

abstract:
  We propose a system of equations to describe the interaction of a
quasiclassical variable $X$ with a set of quantum variables $x$ that goes
beyond the usual mean field approximation. The idea is to regard the quantum
system as continuously and imprecisely measured by the classical system. The
effective equations of motion for the classical system therefore consist of
treating the quantum variable $x$ as a stochastic c-number $\x (t) $ the
probability distibution for which is given by the theory of continuous quantum
measurements. The resulting theory is similar to the usual mean field equations
(in which $x$ is replaced by its quantum expectation value) but with two
differences: a noise term, and more importantly, the state of the quantum
subsystem evolves according to the stochastic non-linear Schrodinger equation
of a continuously measured system. In the case in which the quantum system
starts out in a superposition of well-separated localized states, the classical
system goes into a statistical mixture of trajectories, one trajectory for each
individual localized state.


title: Quantum Gates and Circuits

abstract:
  A historical review is given of the emergence of the idea of the quantum
logic gate from the theory of reversible Boolean gates. I highlight the quantum
XOR or controlled NOT as the fundamental two-bit gate for quantum computation.
This gate plays a central role in networks for quantum error correction.


title: Jordan Blocks and Exponentially Decaying Higher Order Gamow States

abstract:
  In the framework of the rigged Hilbert space, unstable quantum systems
associated with first order poles of the analytically continued S-matrix can be
described by Gamow vectors which are generalized vectors with exponential decay
and a Breit-Wigner energy distribution. This mathematical formalism can be
generalized to quasistationary systems associated with higher order poles of
the S-matrix, which leads to a set of Gamow vectors of higher order with a
non-exponential time evolution. One can define a state operator from the set of
higher order Gamow vectors which obeys the exponential decay law. We shall
discuss to what extend the requirement of an exponential time evolution
determines the form of the state operator for a quasistationary microphysical
system associated with a higher order pole of the S-matrix.


title:
Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher
  Order S-Matrix Poles

abstract:
  In analogy to Gamow vectors that are obtained from first order resonance
poles of the S-matrix, one can also define higher order Gamow vectors which are
derived from higher order poles of the S-matrix. An S-matrix pole of r-th order
at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ...
, r-1, which are also Jordan vectors of degree (k+1) with generalized
eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a
generalized complex eigenvector expansion, whose form suggests the definition
of a state operator (density matrix) for the microphysical decaying state of
this higher order pole. This microphysical state is a mixture of non-reducible
components. In spite of the fact that the k-th order Gamow-Jordan vectors has
the polynomial time-dependence which one always associates with higher order
poles, the microphysical state obeys a purely exponential decay law.


title: Resonances from Higher Order S-Matrix Poles with Exponential Decay

abstract:
  In analogy to Gamow vectors describing resonance states from first order
S-matrix poles, one can define Gamow vectors from higher order poles of the
S-matrix. With these vectors we are going to discuss a density operator that
describes exponentially decaying resonances from higher order poles.