title: Insecurity of Quantum Secure Computations

abstract:
  It had been widely claimed that quantum mechanics can protect private
information during public decision in for example the so-called two-party
secure computation. If this were the case, quantum smart-cards could prevent
fake teller machines from learning the PIN (Personal Identification Number)
from the customers' input. Although such optimism has been challenged by the
recent surprising discovery of the insecurity of the so-called quantum bit
commitment, the security of quantum two-party computation itself remains
unaddressed. Here I answer this question directly by showing that all
``one-sided'' two-party computations (which allow only one of the two parties
to learn the result) are necessarily insecure. As corollaries to my results,
quantum one-way oblivious password identification and the so-called quantum
one-out-of-two oblivious transfer are impossible. I also construct a class of
functions that cannot be computed securely in any ``two-sided'' two-party
computation. Nevertheless, quantum cryptography remains useful in key
distribution and can still provide partial security in ``quantum money''
proposed by Wiesner.


title: Accessible information in quantum measurement

abstract:
  The amount of information that can be accessed via measurement of a quantum
system prepared in different states is limited by the Kholevo bound. We present
a simple proof of this theorem and its extension to sequential measurements
based on the properties of quantum conditional and mutual entropies. The proof
relies on a minimal physical model of the measurement which does not assume
environmental decoherence, and has an intuitive diagrammatic representation.


title: What is an atom laser?

abstract:
  An atom laser is a hypothetical device which would produce an atomic field
analogous to the electromagnetic field of a photon laser. Here I argue that for
this analogy to be meaningful it is necessary to have a precise definition of a
laser which applies equally to photon or atom lasers. The definition I propose
is based upon the principle that the output of a laser is well-approximated by
a classical wave of fixed intensity and phase. This principle yields four
quantitative conditions which the output of a device must satisfy in order for
that device to be considered a laser. While explaining these requirements, I
analyse the similarities and differences between atom and photon lasers. I show
how these conditions are satisfied first by an idealized photon laser model,
and then by a more generic model which can apply to atom lasers also. Lastly, I
briefly discuss the current proposals for atom lasers and whether they could be
true lasers.


title: Phase Space Distributions from Three-Port Couplers

abstract:
  A wide class of phase space distributions of a single mode radiation field is
shown to be directly accessible to measurement by linear symmetric three-port
optical couplers.


title: Interferometry as a binary decision problem

abstract:
  Binary decision theory has been applied to the general interferometric
problem. Optimal detection scheme-according to the Neyman-Pearson criterion-has
been considered for different phase-enhanced states of radiation field, and the
corresponding bounds on minimum detectable phase shift has been evaluated. A
general bound on interferometric precision has been also obtained in terms of
photon number fluctuations of the signal mode carrying the phase information.


title: Operational Theory of the Eight-Port Homodyne Detection

abstract:
  The eight-port homodyne detection apparatus is analyzed in the framework of
the operational theory of quantum measurement. For an arbitrary quantum noise
leaking through the unused port of the beam splitter, the positive operator
valued measure and the corresponding operational homodyne observables are
derived. It is shown that such an eight-port homodyne device can be used to
construct the operational quantum trigonometry of an optical field. The quantum
trigonometry and the corresponding phase space Wigner functions are derived for
a signal field probed by a classical local oscillator and a squeezed vacuum in
the unused port.


title: The Chaotic Ball: An Intuitive Analogy for EPR Experiments

abstract:
  Actual realisations of EPR experiments do {\em not} demonstrate non-locality.
A model is presented that should enable non-specialists as well as specialists
to understand how easy it is to find realistic explanations for the
observations. The model also suggests new areas where realistic
(``hidden-variable'') models can give valid predictions whilst quantum
mechanics fails. It offers straightforward explanations for some anomalies that
Aspect was unable to account for, providing perhaps the first experimental
evidence that a hidden-variable theory can be {\em superior} to quantum
mechanics. The apparent success of quantum mechanics in predicting results is
shown to be largely due to the use of unjustifiable and biased analysis of the
data. Data that has been discarded because it did not lead to a valid Bell's
test may give further evidence that hidden variables exist.


title: Simulating Ising Spin Glasses on a Quantum Computer

abstract:
  A linear-time algorithm is presented for the construction of the Gibbs
distribution of configurations in the Ising model, on a quantum computer. The
algorithm is designed so that each run provides one configuration with a
quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be A linear-time algorithm is presented for the construction of
the Gibbs distribution of configurations in the Ising model, on a quantum
computer. The algorithm is designed so that each run provides one configuration
with a quantum probability equal to the corresponding thermodynamic weight. The
partition function is thus approximated efficiently. The algorithm neither
suffers from critical slowing down, nor gets stuck in local minima. The
algorithm can be applied in any dimension, to a class of spin-glass Ising
models with a finite portion of frustrated plaquettes, diluted Ising models,
and models with a magnetic field. applied in any dimension, to a class of
spin-glass Ising models with a finite portion of frustrated plaquettes, diluted
Ising models, and models with a magnetic field.


title: Two-photocurrent devices

abstract:
  Heterodyne, eight-port homodyne and six-port homodyne detectors belong to the
class of two-photocurrent devices. Their full equivalence in probing radiation
field has been proved both for ideal and not fully efficient photodetectors.
The output probability distribution has been also evaluated for a generic probe
mode.


title: The Jacobi principal function in Quantum Mechanics

abstract:
  The canonical functional action in the path integral in phase space is
discretized by linking each pair of consecutive vertebral points --${\bf q}_k$
and ${\bf p}_{k+1}$ or ${\bf p}_k$ and ${\bf q}_{k+1}$-- through the invariant
complete solution of the Hamilton-Jacobi equation associated with the classical
path defined by these extremes. When the measure is chosen to reflect the
geometrical character of the propagator (it must behave as a density of weight
1/2 in both of its arguments), the resulting infinitesimal propagator is cast
in the form of an expansion in a basis of short-time solutions of the wave
equation, associated with the eigenfunctions of the initial momenta canonically
conjugated to a set of normal coordinates. The operator ordering induced by
this prescription is a combination of a symmetrization rule coming from the
phase, and a derivative term coming from the measure.


title: Quantum Cloning, Eavesdropping and Bell's inequality

abstract:
  We analyze various eavesdropping strategies on a quantum cryptographic
channel. We present the optimal strategy for an eavesdropper restricted to a
two-dimensional probe, interacting on-line with each transmitted signal. The
link between safety of the transmission and the violation of Bell's inequality
is discussed. We also use a quantum copying machine for eavesdropping and for
broadcasting quantum information.


title: ``Plug and play'' systems for quantum cryptography

abstract:
  We present a time-multiplexed interferometer based on Faraday mirrors, and
apply it to quantum key distribution. The interfering pulses follow exactly the
same spatial path, ensuring very high stability and self balancing. Use of
Faraday mirrors compensates automatically any birefringence effects and
polarization dependent losses in the transmitting fiber. First experimental
results show a fringe visibility of 0.9984 for a 23km-long interferometer,
based on installed telecom fibers.


title:
Quantum Kinetic Theory I: A Quantum Kinetic Master Equation for
  Condensation of a weakly interacting Bose gas without a trapping potential

abstract:
  A Quantum Kinetic Master Equation (QKME) for bosonic atoms is formulated. It
is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas,
and describes the behavior and formation of Bose condensation. The key
assumption in deriving the QKME is a Markov approximation for the atomic
collision terms. In the present paper the basic structure of the theory is
developed, and approximations are stated and justified to delineate the region
of validity of the theory. Limiting cases of the QKME include the Quantum
Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an
equation analogous to the Gross-Pitaevskii equation.


title:
The Quantum state diffusion model and the driven damped nonlinear
  oscillator

abstract:
  We consider a driven damped anharmonic oscillator which classically leads to
a bistable steady state and to hysteresis. The quantum counterpart for this
system has an exact analytical solution in the steady state which does not
display any bistability or hysteresis. We use quantum state diffusion theory to
describe this system and to provide a new perspective on the lack of hysteresis
in the quantum regime so as to study in detail the quantum to classical
transition. The analysis is also relevant to measurements of a single
periodically driven electron in a Penning trap where hysteresis has been
observed.


title: Deconstructing Decoherence

abstract:
  The study of environmentally induced superselection and of the process of
decoherence was originally motivated by the search for the emergence of
classical behavior out of the quantum substrate, in the macroscopic limit. This
limit, and other simplifying assumptions, have allowed the derivation of
several simple results characterizing the onset of environmentally induced
superselection; but these results are increasingly often regarded as a complete
phenomenological characterization of decoherence in any regime. This is not
necessarily the case: The examples presented in this paper counteract this
impression by violating several of the simple ``rules of thumb''. This is
relevant because decoherence is now beginning to be tested experimentally, and
one may anticipate that, in at least some of the proposed applications (e.g.,
quantum computers), only the basic principle of ``monitoring by the
environment'' will survive. The phenomenology of decoherence may turn out to be
significantly different.


title: Error correction and symmetrization in quantum computers

abstract:
  Errors in quantum computers are of two kinds: sudden perturbations to
isolated qubits, and slow random drifts of all the qubits. The latter may be
reduced, but not eliminated, by means of symmetrization, namely by using many
replicas of the computer, and forcing their joint quantum state to be
completely symmetric. On the other hand, isolated errors can be corrected by
quantum codewords that represent a logical qubit in a redundant way, by several
physical qubits. If one of the physical qubits is perturbed, for example if it
gets entangled with an unknown environment, there still is enough information
encoded in the other physical qubits to restore the logical qubit, and
disentangle it from the environment. The recovery procedure may consist of
unitary operations, without the need of actually identifying the error.


title:
Polya States of Quantized Radiation Fields, their Algebraic
  Characterization and Nonclassical Properties

abstract:
  Polya states of single mode radiation field are proposed and their algebraic
characterization and nonclassical properties are investigated. They degenerate
to the binomial (atomic coherent) and negative binomial (Perelomov's su(1,1)
coherent) states in two different limits and further to the number, the
ordinary coherent and Susskind-Glogower phase states. The algebra involved turn
out to be a two-parameter deformation of both su(2) and su(1,1). Nonclassical
properties are investigated in detail.


title: The Quantum Theory of Ur-Objects as a Theory of Information

abstract:
  The quantum theory of ur-objects proposed by C. F. von Weizsaecker has to be
interpreted as a quantum theory of information. Ur-objects, or urs, are thought
to be the simplest objects in quantum theory. Thus an ur is represented by a
two-dimensional Hilbert space with the universal symmetry group SU(2), and can
only be characterized as ''one bit of potential information''. In this sense it
is not a spatial but an ''information atom''. The physical structure of the ur
theory is reviewed, and the philosophical consequences of its interpretation as
an information theory are demonstrated by means of some important concepts of
physics such as time, space, entropy, energy, and matter, which in ur theory
appear to be directly connected with information as ''the'' fundamental
substance. This hopefully will help to provide a new understanding of the
concept of information.


title: A precision test of decoherence

abstract:
  The motion of a charged particle over a conducting plate is damped by Ohmic
resistance to image currents. This interaction between the particle and the
plate must also produce decoherence, which can be detected by examining
interference patterns made by diffracted particle beams which have passed over
the plate. Because the current densities within the plate decay rapidly with
the height of the particle beam above it, the strength of decoherence should be
adjustable across a wide range, allowing one to probe the full range of quantum
through classical behaviour.


title: Stability of 3D Cubic Fixed Point in Two-Coupling-Constant \phi^4-Theory

abstract:
  For an anisotropic euclidean $\phi^4$-theory with two interactions $[u
(\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4]$ the $\beta$-functions are
calculated from five-loop perturbation expansions in $d=4-\varepsilon$
dimensions, using the knowledge of the large-order behavior and Borel
transformations. For $\varepsilon=1$, an infrared stable cubic fixed point for
$M \geq 3$ is found, implying that the critical exponents in the magnetic phase
transition of real crystals are of the cubic universality class. There were
previous indications of the stability based either on lower-loop expansions or
on less reliable Pad\'{e approximations, but only the evidence presented in
this work seems to be sufficently convincing to draw this conclusion.


title: q-oscillators, (non-)Kaehler manifolds and constrained dynamics

abstract:
  It is shown that q-deformed quantum mechanics (systems with q-deformed
Heisenberg commutation relations) can be interpreted as an ordinary quantum
mechanics on Kaehler manifolds, or as a quantum theory with second (or first)-
class constraints.


title:
Quantum Canonical Transformations and Exact Solution of the Schreodinger
  Equation

abstract:
  Time-dependent unitary transformations are used to study the Schreodinger
equation for explicitly time-dependent Hamiltonians of the form $H(t)=\vec
R(t).\vec J$, where $\vec R$ is an arbitrary real vector-valued function of
time and $\vec J$ is the angular momentum operator. The solution of the
Schreodinger equation for the most general Hamiltonian of this form is shown to
be equivalent to the special case $\vec R=(1,0,\nu(t))$. This corresponds to
the problem of driven two-level atom for the spin half representation of $\vec
J$. It is also shown that by requiring the magnitude of $\vec R$ to depend on
its direction in a particular way, one can solve the Schreodinger equation
exactly. In particular, it is shown that for every Hamiltonian of the form
$H(t)=\vec R(t)\cdot \vec J$ there is another Hamiltonian with the same
eigenstates for which the Schreodinger equation is exactly solved. The
application of the results to the exact solution of the parallel transport
equation and exact holonomy calculation for SU(2) principal bundles (Yang-Mills
gauge theory) is also pointed out.


title:
Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary
  Transformation and a New Class of Exactly Solvable Oscillators

abstract:
  A time-dependent unitary (canonical) transformation is found which maps the
Hamiltonian for a harmonic oscillator with time-dependent real mass and real
frequency to that of a generalized harmonic oscillator with time-dependent real
mass and imaginary frequency. The latter may be reduced to an ordinary harmonic
oscillator by means of another unitary (canonical) transformation. A simple
analysis of the resulting system leads to the identification of a previously
unknown class of exactly solvable time-dependent oscillators. Furthermore, it
is shown how one can apply these results to establish a canonical equivalence
between some real and imaginary frequency oscillators. In particular it is
shown that a harmonic oscillator whose frequency is constant and whose mass
grows linearly in time is canonically equivalent with an oscillator whose
frequency changes from being real to imaginary and vice versa repeatedly.


title: Maximum Information and Quantum Prediction Algorithms

abstract:
  This paper describes an algorithm for selecting a consistent set within the
consistent histories approach to quantum mechanics and investigates its
properties. The algorithm uses a maximum information principle to select from
among the consistent sets formed by projections defined by the Schmidt
decomposition. The algorithm unconditionally predicts the possible events in
closed quantum systems and ascribes probabilities to these events. A simple
spin model is described and a complete classification of all exactly consistent
sets of histories formed from Schmidt projections in the model is proved. This
result is used to show that for this example the algorithm selects a physically
realistic set. Other tentative suggestions in the literature for set selection
algorithms using ideas from information theory are discussed.


title: Moyal Quantization and Group Theory

abstract:
  We deduce a kernel that allows the Moyal quantization of the cylinder (as
phase space) by means of the Stratonovich-Weyl correspondence.


title:
The AC Stark, Stern-Gerlach, and Quantum Zeno Effects in Interferometric
  Qubit Readout

abstract:
  This article describes the AC Stark, Stern-Gerlach, and Quantum Zeno effects
as they are manifested during continuous interferometric measurement of a
two-state quantum system (qubit). A simple yet realistic model of the
interferometric measurement process is presented, and solved to all orders of
perturbation theory in the absence of thermal noise. The statistical properties
of the interferometric Stern-Gerlach effect are described in terms of a
Fokker-Plank equation, and a closed-form expression for the Green's function of
this equation is obtained. Thermal noise is added in the form of a
externally-applied Langevin force, and the combined effects of thermal noise
and measurement are considered. Optical Bloch equations are obtained which
describe the AC Stark and Quantum Zeno effects. Spontaneous qubit transitions
are shown to be observationally equivalent to transitions induced by external
Langevin forces. The effects of delayed choice are discussed. Practical
experiments involving trapped ions are suggested. The results are relevant to
the design of qubit readout systems in quantum computing, and to single-spin
detection in magnetic resonance force microscopy.


title: Borel Quantization: Kinematics and Dynamics

abstract:
  In this contribution we review results on the kinematics of a quantum system
localized on a connected configuration manifold and compatible dynamics for the
quantum system including external fields and leading to non-linear
Schr\"odinger equations for pure states.


title:
Reducing decoherence in quantum computer memory with all quantum bits
  coupling to the same environment

abstract:
  Decoherence in quantum computer memory due to the inevitable coupling to the
external environment is examined. We take the assumption that all quantum bits
(qubits) interact with the same environment rather than the assumption of
separate environments for different qubits. It is found that the qubits are
decohered collectively. For some kinds of entangled input states, no
decoherence occurs at all in the memory even if the qubits are interacting with
the environment. Based on this phenomenon, a scheme is proposed for reducing
the collective decoherence. We also discuss possible implications of this
decoherence model for quantum measurements.


title: Density Matrix From Photon Number Tomography

abstract:
  We provide a simple analytic relation which connects the density operator of
the radiation field with the number probabilities. The problem of
experimentally "sampling" a general matrix elements is studied, and the
deleterious effects of nonunit quantum efficiency in the detection process are
analyzed showing how they can be reduced by using the squeezing technique. The
obtained result is particulary useful for intracavity field reconstruction
states.


title: Ponderomotive Control of Quantum Macroscopic Coherence

abstract:
  It is shown that because of the radiation pressure a Schr\"odinger cat state
can be generated in a resonator with oscillating wall. The optomechanical
control of quantum macroscopic coherence and its detection is taken into
account introducing new cat states. The effects due to the environmental
couplings with this nonlinear system are considered developing an operator
perturbation procedure to solve the master equation for the field mode density
operator.


title: f-Oscillators and Nonlinear Coherent States

abstract:
  The notion of f-oscillators generalizing q-oscillators is introduced. For
classical and quantum cases, an interpretation of the f-oscillator is provided
as corresponding to a special nonlinearity of vibration for which the frequency
of oscillation depends on the energy. The f-coherent states (nonlinear coherent
states) generalizing q-coherent states are constructed. Applied to quantum
optics, photon distribution function, photon number means, and dispersions are
calculated for the f-coherent states as well as the Wigner function and
Q-function. As an example, it is shown how this nonlinearity may affect the
Planck distribution formula.


title:
Wigner's Problem and Alternative Commutation Relations for Quantum
  Mechanics

abstract:
  It is shown, that for quantum systems the vectorfield associated with the
equations of motion may admit alternative Hamiltonian descriptions, both in the
Schr\"odinger and Heisenberg pictures. We illustrate these ambiguities in terms
of simple examples.


title: Properties of Squeezed-State Excitations

abstract:
  The photon distribution function of a discrete series of excitations of
squeezed coherent states is given explicitly in terms of Hermite polynomials of
two variables. The Wigner and the coherent-state quasiprobabilities are also
presented in closed form through the Hermite polynomials and their limiting
cases. Expectation values of photon numbers and their dispersion are
calculated. Some three-dimensional plots of photon distributions for different
squeezing parameters demonstrating oscillatory behaviour are given.


title:
Alternative approach to electromagnetic field quantization in nonlinear
  and inhomogeneous media

abstract:
  A simple approach is proposed for the quantization of the electromagnetic
field in nonlinear and inhomogeneous media. Given the dielectric function and
nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is
determined completely by this quantization method. From Heisenberg's equations
we derive Maxwell's equations for the field operators. When the nonlinearity
goes to zero, this quantization method returns to the generalized canonical
quantization procedure for linear inhomogeneous media [Phys. Rev. A, 43, 467,
1991]. The explicit Hamiltonians for the second-order and third-order nonlinear
quasi-steady-state processes are obtained based on this quantization procedure.


title: Experimental realization of any discrete operator

abstract:
  A straightforward argument shows that, by allowing counterfactual elements of
physical reality, any arbitrary discrete finite-dimensional operator
corresponds to an observable.


title:
Schroedinger cat-like states by conditional measurements on a
  beam-splitter

abstract:
  A scheme for generating Schr\"{o}dinger cat-like states of a single-mode
optical field by means of conditional measurement is proposed. Feeding into a
beam splitter a squeezed vacuum and counting the photons in one of the output
channels, the conditional states in the other output channel exhibit a number
of properties that are very similar to those of superpositions of two coherent
states with opposite phases. We present analytical and numerical results for
the photon-number and quadrature-component distributions of the conditional
states and their Wigner and Husimi functions. Further, we discuss the effect of
realistic photocounting on the states.


title:
Effect of Attenuation and Dispersion in the Communication Channel on the
  Secrecy of a Quantum Cryptosystem

abstract:
  The effects of dispersion in the communication channel on the secrecy of a
quantum cryptosystem based on single photon states with different frequencies
are studied. A maximum communication channel length which can still ensure the
secrecy of the key generation procedure is found.


title: Quantum Cryptography Based on the Time--Energy Uncertainty Relation

abstract:
  A new cryptosystem based on the fundamental time--energy uncertainty relation
is proposed. Such a cryptosystem can be implemented with both correlated photon
pairs and single photon states.


title: Quantum Physics and Computers

abstract:
  Recent theoretical results confirm that quantum theory provides the
possibility of new ways of performing efficient calculations. The most striking
example is the factoring problem. It has recently been shown that computers
that exploit quantum features could factor large composite integers. This task
is believed to be out of reach of classical computers as soon as the number of
digits in the number to factor exceeds a certain limit. The additional power of
quantum computers comes from the possibility of employing a superposition of
states, of following many distinct computation paths and of producing a final
output that depends on the interference of all of them. This ``quantum
parallelism'' outstrips by far any parallelism that can be thought of in
classical computation and is responsible for the ``exponential'' speed-up of
computation.
  This is a non-technical (or at least not too technical) introduction to the
field of quantum computation. It does not cover very recent topics, such as
error-correction.


title: Quantum Weight Enumerators

abstract:
  In a recent paper ([quant-ph/9610040]), Shor and Laflamme define two ``weight
enumerators'' for quantum error correcting codes, connected by a MacWilliams
transform, and use them to give a linear-programming bound for quantum codes.
We introduce two new enumerators which, while much less powerful at producing
bounds, are useful tools nonetheless. The new enumerators are connected by a
much simpler duality transform, clarifying the duality between Shor and
Laflamme's enumerators. We also use the new enumerators to give a simpler
condition for a quantum code to have specified minimum distance, and to extend
the enumerator theory to codes with block-size greater than 2.


title: Entropy and Uncertainty of Squeezed Quantum Open Systems

abstract:
  We define the entropy S and uncertainty function of a squeezed system
interacting with a thermal bath, and study how they change in time by following
the evolution of the reduced density matrix in the influence functional
formalism. As examples, we calculate the entropy of two exactly solvable
squeezed systems: an inverted harmonic oscillator and a scalar field mode
evolving in an inflationary universe. For the inverted oscillator with weak
coupling to the bath, at both high and low temperatures, $S\to r $, where r is
the squeeze parameter. In the de Sitter case, at high temperatures, $S\to
(1-c)r$ where $c = \gamma_0/H$, $\gamma_0$ being the coupling to the bath and H
the Hubble constant. These three cases confirm previous results based on more
ad hoc prescriptions for calculating entropy. But at low temperatures, the de
Sitter entropy $S\to (1/2-c)r$ is noticeably different. This result, obtained
from a more rigorous approach, shows that factors usually ignored by the
conventional approaches, i.e., the nature of the environment and the coupling
strength betwen the system and the environment, are important.


title: On The Power of Exact Quantum Polynomial Time

abstract:
  We investigate the power of quantum computers when they are required to
return an answer that is guaranteed correct after a time that is upper-bounded
by a polynomial in the worst case. In an oracle setting, it is shown that such
machines can solve problems that would take exponential time on any classical
bounded-error probabilistic computer.


title: Quantummechanical behaviour in a deterministic model

abstract:
  A deterministic model with a large number of continuous and discrete degrees
of freedom is described, and a statistical treatment is proposed. The model
exactly obeys a Schrodinger equation, which has to be interpreted exactly
according to the Copenhagen prescriptions. After applying a Hartree-Fock
approximation, the model appears to describe genuine quantum particles that
could be used as a starting point for field variables in a quantum field
theory. In the deterministic model it is essential that information loss
occurs, but the corresponding quantum system is unitary and exactly preserves
information. (To be published in Foundations of Physics Letters, Vol. 10, No
4.)


title: Direct particle interaction as the origin of the quantal behaviours

abstract:
  It is argued that the quantal behaviours may be understood in the framework
of direct particle interactions. A specific example is introduced. The assumed
potential predicts that at sufficiently large distances quantal behaviours
arise, while at very large distances gravitational-like forces are present. The
latter is true provided all particles have internal structures.


title: Some Observable Results of the Retarded Bohm's Theory

abstract:
  It is shown that the retarded Bohm's theory has at least four novel
properties. (1) The center of mass of an isolated two-body system is
accelerated. (2) Hydrogen-like atoms are unstable. (3) The distribution
function differs from the standard one. (4) The definition of energy needs some
care.


title: Is superluminal motion in relativistic Bohm's theory observable?

abstract:
  We show that the problem of superluminal motion in causal, particle
interpretation of bosonic fields is not observable at macroscopic distances.


title: On the position operator for massless particles

abstract:
  It is always stated that the position operator for massless particles has
non-comutting components. It is shown that the reason is that the commutation
relations between coordinates and momenta differs for massive and massless
particles. The correct one for massless particles and a position operator with
commuting components are derived.


title: On the Relativistic Quantum Force

abstract:
  In the extension of the de-Broglie-Bohm causal quantum theory of motion to
the relativistic particles, one faces with serious problems, like the problem
of superluminal motion. This forces many authors to believe that there is not
any satisfactory causal theory for particles of integer spin. In this paper, it
is shown that the quantal behaviour is the result of
direct-particle-interaction of the particle with all of its possibilities. The
formulation is, then, extended to the relativistic particles of arbitrary spin.
The presented theory has the following advantages. (1) It leads to a deeper
understanding of the quantal behaviour. (2) It has no superluminal motion. (3)
It is applicable to any spin. (4) It provides a framework for understanding the
problem of creation and annihilation of particles. (5) It provides a framework
for understanding the spin-statistics relationship. (6) It does not need the
two fundamental assumptions of the de-Broglie-Bohm quantum theory of motion,
i.e., the guiding-formula postulate and the statistical postulate.


title: Relativistic Operator Description of Photon Polarization

abstract:
  We present an operator approach to the description of photon polarization,
based on Wigner's concept of elementary relativistic systems. The theory of
unitary representations of the Poincare group, and of parity, are exploited to
construct spinlike operators acting on the polarization states of a photon at
each fixed energy momentum. The nontrivial topological features of these
representations relevant for massless particles, and the departures from the
treatment of massive finite spin representations, are highlighted and
addressed.


title: Quantization of Systems with Constraints

abstract:
  New measures for the quantization of systems with constraints are discussed
and applied to several examples, in particular, examples of alternative but
equivalent formulations of given first-class constraints, as well as a
comparison of regular and irregular constraints.


title: An Analog Analogue of a Digital Quantum Computation

abstract:
  We solve a problem, which while not fitting into the usual paradigm, can be
viewed as a quantum computation. Suppose we are given a quantum system
described by an N dimensional Hilbert space with a Hamiltonian of the form $E
|w >< w|$ where $| w>$ is an unknown (normalized) state. We show how to
discover $| w >$ by adding a Hamiltonian (independent of $| w >$) and evolving
for a time proportional to $N^{1/2}/E$. We show that this time is optimally
short. This process is an analog analogue to Grover's algorithm, a computation
on a conventional (!) quantum computer which locates a marked item from an
unsorted list of N items in a number of steps proportional to $N^{1/2}$.


title: Trapped Fermi gases

abstract:
  We study the properties of a spin-polarized Fermi gas in a harmonic trap,
using the semiclassical (Thomas-Fermi) approximation. Universal forms for the
spatial and momentum distributions are calculated, and the results compared
with the corresponding properties of a dilute Bose gas.


title: Threshold Estimate for Fault Tolerant Quantum Computation

abstract:
  I make a rough estimate of the accuracy threshold for fault tolerant quantum
computing with concatenated codes. First I consider only gate errors and use
the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011)
for fault tolerant error correction (FTEC) and the fault tolerant
implementation of elementary operations on states encoded by the 7-qubit code.
A simple computer simulation suggests a threshold for gate errors of the order
\epsilon \approx 10^{-3} or better. I also give a simple argument that the
threshold for memory errors is about 10 times smaller, thus \epsilon \approx
10^{-4}.


title:
Design of gates for quantum computation: the three-spin XOR gate in
  terms of two-spin interactions

abstract:
  We propose to design multispin quantum gates in which the input and output
two-state systems (spins) are not necessarily identical. We describe the
motivations for such studies and then derive an explicit general two-spin
interaction Hamiltonian which accomplishes the quantum XOR gate function for a
system of three spins: two input and one output.


title: Revisiting Bell's theorem for a class of down-conversion experiments

abstract:
  A certain class of parametric down-conversion Bell type experiments has the
following features. In the idealized perfect situation it is in only 50% of
cases that each observer receives a photon; in the other 50% of cases one
observer receives both photons of a pair while the other observer receives
none. The standard approach is to discard the events of the second type. Only
the remaining ones are used as the data input to some Bell inequalities. This
raises justified doubts whether such experiments could be ever genuine tests of
local realism. We propose to take into account these "unfavorable" cases and to
analyze the entire pattern of polarization and localization correlations. This
departure from the standard reasoning enables one to show that indeed the
experiments are true test of local realism.


title:
Off-shell indefinite-metric triple-bracket generalization of the Dirac
  equation

abstract:
  We present an off-shell indefinite-metric reformulation of the earlier
on-shell positive-metric triple bracket generalization of the Dirac equation.
The new version of the formalism solves the question of its manifest
covariance.


title: Interference in dielectrics and pseudo-measurements

abstract:
  Inserting a lossy dielectric into one arm of an interference experiment acts
in many ways like a measurement. If two entangled photons are passed through
the interferometer, a certain amount of information is gained about which path
they took, and the interference pattern in a coincidence count measurement is
suppressed. However, by inserting a second dielectric into the other arm of the
interferometer, one can restore the interference pattern. Two of these
pseudo-measurements can thus cancel each other out. This is somewhat analogous
to the proposed quantum eraser experiments.


title:
The structure of the quantum mechanical state space and induced
  superselection rules

abstract:
  The role of superselection rules for the derivation of classical probability
within quantum mechanics is investigated and examples of superselection rules
induced by the environment are discussed.


title: A quantum-mechanical Maxwell's demon

abstract:
  A Maxwell's demon is a device that gets information and trades it in for
thermodynamic advantage, in apparent (but not actual) contradiction to the
second law of thermodynamics. Quantum-mechanical versions of Maxwell's demon
exhibit features that classical versions do not: in particular, a device that
gets information about a quantum system disturbs it in the process. In
addition, the information produced by quantum measurement acts as an additional
source of thermodynamic inefficiency. This paper investigates the properties of
quantum-mechanical Maxwell's demons, and proposes experimentally realizable
models of such devices.


title:
Information-entropy and the space of decoherence functions in
  generalised quantum theory

abstract:
  In standard quantum theory, the ideas of information-entropy and of pure
states are closely linked. States are represented by density matrices $\rho$ on
a Hilbert space and the information-entropy $-tr(\rho\log\rho)$ is minimised on
pure states (pure states are the vertices of the boundary of the convex set of
states). The space of decoherence functions in the consistent histories
approach to generalised quantum theory is also a convex set. However, by
showing that every decoherence function can be written as a convex combination
of two other decoherence functions we demonstrate that there are no `pure'
decoherence functions.
  The main content of the paper is a new notion of information-entropy in
generalised quantum mechanics which is applicable in contexts in which there is
no a priori notion of time. Information-entropy is defined first on consistent
sets and then we show that it decreases upon refinement of the consistent set.
This information-entropy suggests an intrinsic way of giving a consistent set
selection criterion.


title: Decoherence and Initial Correlations in Quantum Brownian Motion

abstract:
  We analyze the evolution of a quantum Brownian particle starting from an
initial state that contains correlations between this system and its
environment. Using a path integral approach, we obtain a master equation for
the reduced density matrix of the system finding relatively simple expressions
for its time dependent coefficients. We examine the evolution of delocalized
initial states (Schr\"odinger's cats) investigating the effectiveness of the
decoherence process. Analytic results are obtained for an ohmic environment
(Drude's model) at zero temperature.


title:
Why We Don't Need Quantum Planetary Dynamics: Decoherence and the
  Correspondence Principle for Chaotic Systems

abstract:
  Violation of correspondence principle may occur for very macroscopic byt
isolated quantum systems on rather short timescales as illustrated by the case
of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and
classical predictions are expected to diverge on a timescale of approximately
20 years. Motivated by Hyperion, we review salient features of ``quantum
chaos'' and show that decoherence is the essential ingredient of the classical
limit, as it enables one to solve the apparent paradox caused by the breakdown
of the correspondence principle for classically chaotic systems.


title:
On a Class of Quantum Canonical Transformations and the Time-Dependent
  Harmonic Oscillator

abstract:
  Quantum canonical transformations corresponding to the action of the unitary
operator $e^{i\epsilon(t)\sqrt{f(x)}p\sqrt{f(x)}}$ is studied. It is shown that
for $f(x)=x$, the effect of this transformation is to rescale the position and
momentum operators by $e^{\epsilon(t)}$ and $e^{-\epsilon(t)}$, respectively.
This transformation is shown to lead to the identification of a previously
unknown class of exactly solvable time-dependent harmonic oscillators. It turns
out that the Caldirola-Kanai oscillator whose mass is given by $m=m_0 e^{\gamma
t}$, belongs to this class. It is also shown that for arbitrary $f(x)$, this
canonical transformations map the dynamics of a free particle with constant
mass to that of free particle with a position-dependent mass. In other words,
they lead to a change of the metric of the space.


title: Testing the equivalence principle through freely falling quantum objects

abstract:
  Free fall in a uniform gravitational field is revisited in the case of
quantum states with and without classical analogue. The interplay between
kinematics and dynamics in the evolution of a falling quantum test particle is
discussed allowing for a better understanding of the equivalence principle at
the operational level.


title: Quantum Equivalence Principle

abstract:
  A simple mapping procedure is presented by which classical orbits and path
integrals for the motion of a point particle in flat space can be transformed
directly into those in curved space with torsion. Our procedure evolved from
well-established methods in the theory of plastic deformations, where crystals
with defects are described mathematically as images of ideal crystals under
active nonholonomic coordinate transformations.
  Our mapping procedure may be viewed as a natural extension of Einstein's
famous equivalence principle. When applied to time-sliced path integrals, it
gives rise to a new "quantum equivalence principle" which determines short-time
action and measure of fluctuating orbits in spaces with curvature and torsion.
The nonholonomic transformations possesses a nontrivial Jacobian in the path
measure which produces in a curved space an additional term proportional to the
curvature scalar R, thus canceling a similar term found earlier by DeWitt. This
cancelation is important for correctly describing semiclassically and quantum
mechanically various systems such as the hydrogen atom, a particle on the
surface of a sphere, and a spinning top. It is also indispensable for the
process of bosonization, by which Fermi particles are redescribed by those
fields.


title: Minimal Irreversible Quantum Mechanics

abstract:
  It is demonstrated that, making minimal changes in ordinary quantum
mechanics, a reasonable irreversible quantum mechanics can be obtained. This
theory has a more general spectral decompositions, with eigenvectors
corresponding to unstable states that vanish when $t \to \infty .$ These
''Gamov vectors'' have zero norm, in such a way that the norm and the energy of
the physical states remain constant. The evolution operator has no inverse,
showing that we are really dealing with a time-asymmetric theory. Using
Friedrichs model reasonable physical results are obtained, e. g. : the
remaining of an unstable decaying state reappears, in the continuous spectrum
of the model, with its primitive energy.


title: Simplified quantum logic with trapped ions

abstract:
  We describe a simplified scheme for quantum logic with a collection of
laser-cooled trapped atomic ions. Building on the scheme of Cirac and Zoller,
we show how the fundamental controlled-NOT gate between a collective mode of
ion motion and the internal states of a single ion can be reduced to a single
laser pulse, and the need for a third auxiliary internal electronic state can
be eliminated.


title: Asymptotic Redundancies for Universal Quantum Coding

abstract:
  We investigate the question of whether or not there exists a noncommutative/
quantum extension of a recent (commutative probabilistic) result of Clarke and
Barron. They demonstrated that the Jeffreys' invariant prior of Bayesian theory
yields the common asymptotic (minimax and maximin) redundancy - the excess of
the encoding cost over the source entropy - of universal data compression in a
parametric setting. We study certain probability distributions for the
two-level quantum systems. We are able to compute exact formulas for the
corresponding redundancies, for which we find the asymptotic limits. These
results are very suggestive and do indeed point towards a possible quantum
extension of the result of Clarke and Barron.


title: Dynamical Localization in the Paul Trap

abstract:
  We show that quantum localization occurs in the center-of-mass motion of an
ion stored in a Paul trap and interacting with a standing laser field. The
present experimental state of the art makes the observation of this phenomenon
feasible.


title:
Comment on ``Protective measurements of the wave function of a single
  squeezed harmonic-oscillator state''

abstract:
  Alter and Yamamoto [Phys. Rev. A 53, R2911 (1996)] claimed to consider
``protective measurements'' [Phys. Lett. A 178, 38 (1993)] which we have
recently introduced. We show that the measurements discussed by Alter and
Yamamoto ``are not'' the protective measurements we proposed. Therefore, their
results are irrelevant to the nature of protective measurements.


title: HBT Interferometry for Sonoluminescence Bubble

abstract:
  The two-photon correlation of the light pulse emitted from a sonoluminescence
bubble is discussed. It is shown that several important information about the
mechanism of light emission, such as the time-scale and the shape of the
emission region could be obtained from the HBT interferometry. We also argue
that such a measurement may serve to reject one of the two currently suggested
emission mechanisms, i.e., thermal process versus dynamical Casimir effect.


title: Effects of noise on quantum error correction algorithms

abstract:
  It has recently been shown that there are efficient algorithms for quantum
computers to solve certain problems, such as prime factorization, which are
intractable to date on classical computers. The chances for practical
implementation, however, are limited by decoherence, in which the effect of an
external environment causes random errors in the quantum calculation. To combat
this problem, quantum error correction schemes have been proposed, in which a
single quantum bit (qubit) is ``encoded'' as a state of some larger number of
qubits, chosen to resist particular types of errors. Most such schemes are
vulnerable, however, to errors in the encoding and decoding itself. We examine
two such schemes, in which a single qubit is encoded in a state of $n$ qubits
while subject to dephasing or to arbitrary isotropic noise. Using both
analytical and numerical calculations, we argue that error correction remains
beneficial in the presence of weak noise, and that there is an optimal time
between error correction steps, determined by the strength of the interaction
with the environment and the parameters set by the encoding.


title: Quantum Stabilizer Codes and Classical Linear Codes

abstract:
  We show that within any quantum stabilizer code there lurks a classical
binary linear code with similar error-correcting capabilities, thereby
demonstrating new connections between quantum codes and classical codes. Using
this result -- which applies to degenerate as well as nondegenerate codes --
previously established necessary conditions for classical linear codes can be
easily translated into necessary conditions for quantum stabilizer codes.
Examples of specific consequences are: for a quantum channel subject to a
delta-fraction of errors, the best asymptotic capacity attainable by any
stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the
depolarizing channel with fidelity parameter delta, the best asymptotic
capacity attainable by any stabilizer code cannot exceed 1-H(delta).


title: Symmetries of the free Schrodinger Equation

abstract:
  An algorithm is proposed for research into the symmetrical properties of
theoretical and mathematical physics equations. The application of this
algorithm to the free Schrodinger equation permited us to establish that in
addition to the known Galilei symmetry, the free Schrodinger equation possesses
also the relativistic symmetry in some generalized sense. This property of the
free Schrodinger equation permits the equation to be extended into the
relativistic area of movements of a particle being studied.


title: Displaced and Squeezed Number States

abstract:
  After beginning with a short historical review of the concept of displaced
(coherent) and squeezed states, we discuss previous (often forgotten) work on
displaced and squeezed number states. Next, we obtain the most general
displaced and squeezed number states. We do this in both the functional and
operator (Fock) formalisms, thereby demonstrating the necessary equivalence. We
then obtain the time-dependent expectation values, uncertainties,
wave-functions, and probability densities. In conclusion, there is a discussion
on the possibility of experimentally observing these states.


title: Coherent and trajectory-coherent states of a damped harmonic oscillator

abstract:
  In this paper we construct the coherent and trajectory-coherent states of a
damped harmonic oscillator. We investigate the properties of this states.


title:
Extending the Lambda Calculus to Express Randomized and Quantumized
  Algorithms

abstract:
  This paper introduces a formal metalanguage called the lambda-q calculus for
the specification of quantum programming languages. This metalanguage is an
extension of the lambda calculus, which provides a formal setting for the
specification of classical programming languages. As an intermediary step, we
introduce a formal metalanguage called the lambda-p calculus for the
specification of programming languages that allow true random number
generation. We demonstrate how selected randomized algorithms can be programmed
directly in the lambda-p calculus. We also demonstrate how satisfiability can
be solved in the lambda-q calculus.


title: Strengths and Weaknesses of Quantum Computing

abstract:
  Recently a great deal of attention has focused on quantum computation
following a sequence of results suggesting that quantum computers are more
powerful than classical probabilistic computers. Following Shor's result that
factoring and the extraction of discrete logarithms are both solvable in
quantum polynomial time, it is natural to ask whether all of NP can be
efficiently solved in quantum polynomial time. In this paper, we address this
question by proving that relative to an oracle chosen uniformly at random, with
probability 1, the class NP cannot be solved on a quantum Turing machine in
time $o(2^{n/2})$. We also show that relative to a permutation oracle chosen
uniformly at random, with probability 1, the class $NP \cap coNP$ cannot be
solved on a quantum Turing machine in time $o(2^{n/3})$. The former bound is
tight since recent work of Grover shows how to accept the class NP relative to
any oracle on a quantum computer in time $O(2^{n/2})$.


title:
Quantum theory of motion of a time-dependent harmonic oscillator in the
  pilot-wave theory

abstract:
  The de Broglie-Bohm quantum trajectories are found in analytically closed
forms for the eigenstates and the coherent state of the Lewis-Riesenfeld (LR)
invariant of a time-dependent harmonic oscillator. It is also shown that an
eigenstate (a coherent state) of an invariant can be interpreted as squeezed
states obtained by squeezing an eigenstate (a coherent state) of another
invariant. This provides ways for a whole description of squeezed states.


title:
SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to
  coherent and intelligent states

abstract:
  We introduce the concept of algebra eigenstates which are defined for an
arbitrary Lie group as eigenstates of elements of the corresponding complex Lie
algebra. We show that this concept unifies different definitions of coherent
states associated with a dynamical symmetry group. On the one hand, algebra
eigenstates include different sets of Perelomov's generalized coherent states.
On the other hand, intelligent states (which are squeezed states for a system
of general symmetry) also form a subset of algebra eigenstates. We develop the
general formalism and apply it to the SU(2) and SU(1,1) simple Lie groups.
Complete solutions to the general eigenvalue problem are found in the both
cases, by a method that employs analytic representations of the algebra
eigenstates. This analytic method also enables us to obtain exact closed
expressions for quantum statistical properties of an arbitrary algebra
eigenstate. Important special cases such as standard coherent states and
intelligent states are examined and relations between them are studied by using
their analytic representations.


title:
Almost perfect squeezing at high intensities by stabilization from
  competing non-linearities

abstract:
  The squeezing properties of a cavity Second Harmonic Generation (SHG) system
with an added Kerr effect-like nonlinearity are studied as a function of the
intra-cavity photon number. The competition between the second and the third
order non-linearities shifts the Hopf bifurcation of the standard SHG towards
higher intra-cavity energies eventually completely stabilizing the system.
Remarkably, the noise suppression is at the same time strongly enhanced, so
that almost perfect squeezing is obtained for arbitrarily large intra-cavity
photon numbers. Possible experimental implementations are finally discussed.


title: The Mechanical Response of Vacuum

abstract:
  A path integral formulation is developed for the dynamic Casimir effect. It
allows us to study arbitrary deformations in space and time of the perfectly
reflecting (conducting) boundaries of a cavity. The mechanical response of the
intervening vacuum is calculated to linear order in the frequency-wavevector
plane. For a single corrugated plate we find a correction to mass at low
frequencies, and an effective shear viscosity at high frequencies; both
anisotropic. For two plates there is resonant dissipation for all frequencies
greater than the lowest optical mode of the cavity.


title: A Modification of Nambu's Mechanics

abstract:
  The Poisson, contact and Nambu brackets define algebraic structures on
$C^{\infty}(M)$ satisfying the Jacobi identity or its generalization. The
automorphism groups of these brackets are the symplectic, contact and volume
preserving diffeomorphism groups. We introduce a modification of the Nambu
bracket, which defines an evolution equation generating the whole
diffeomorphism group. The relation between the modified and usual Nambu
brackets is similar to the relation between the Poisson and contact structures.
We briefly discuss the problem of quantization of the modified bracket.


title: Magnetoresonances on a lasso graph

abstract:
  We consider a charged spinless quantum particle confined to a graph
consisting of a loop to which a halfline lead is attached; this system is
placed into a homogeneous magnetic field perpendicular to the loop plane. We
derive the reflection amplitude and show that there is an infinite ladder of
resonances; analyzing the resonance pole trajectories we show that half of them
turn into true embedded eigenvalues provided the flux through the loop is an
integer or halfinteger multiple of the flux unit $hc/e$. We also describe a
general method to solve the scattering problem on graphs of which the present
model is a simple particular case. Finally, we discuss ways in which a state
localized initially at the loop decays.


title:
Quantum Kinetic Theory III: Simulation of the Quantum Boltzmann Master
  Equation

abstract:
  We present results of simulations of a em quantum Boltzmann master equation
(QBME) describing the kinetics of a dilute Bose gas confined in a trapping
potential in the regime of Bose condensation. The QBME is the simplest version
of a quantum kinetic master equations derived in previous work. We consider two
cases of trapping potentials: a 3D square well potential with periodic boundary
conditions, and an isotropic harmonic oscillator. We discuss the stationary
solutions and relaxation to equilibrium. In particular, we calculate particle
distribution functions, fluctuations in the occupation numbers, the time
between collisions, and the mean occupation numbers of the one-particle states
in the regime of onset of Bose condensation.


title: Comment on "Loss-error compensation in quantum-state measurements"

abstract:
  In the two papers [T. Kiss, U. Herzog, and U. Leonhardt, Phys. Rev. A 52,
2433 (1995); U. Herzog, Phys. Rev. A 53, 1245 (1996)] with titles similar to
the one given above, the authors assert that in some cases it is possible to
compensate a quantum efficiency $\eta\leq 1/2$ in quantum-state measurements,
violating the lower bound 1/2 proved in a preceding paper [G. M. D'Ariano, U.
Leonhardt and H. Paul, Phys. Rev. A 52, R1801 (1995)]. Here we re-establish the
bound as unsurpassable for homodyning any quantum state, and show how the
proposed loss-compensation method would always fail in a real measurement
outside the allowed $\eta >1/2$ region.


title:
Systematic and statistical errors in homodyne measurements of the
  density matrix

abstract:
  We study both systematic and statistical errors in radiation density matrix
measurements. First we estimate the minimum number of scanning phases needed to
reduce systematic errors below a fixed threshold. Then, we calculate the
statistical errors, intrinsic in the procedure that gives the density matrix.
We present a detailed study of such errors versus the detectors quantum
efficiency $\eta$ and the matrix indexes in the number representation, for
different radiation states. For unit quantum efficiency, and for both coherent
and squeezed states, the statistical errors of the diagonal matrix elements
saturate for large n. On the contrary, off-diagonal errors increase with the
distance from the diagonal. For non unit quantum efficiency the statistical
errors along the diagonal do not saturate, and increase dramatically versus
both $1-\eta$ and the matrix indexes.


title: Homodyning as universal detection

abstract:
  Homodyne tomography - i. e. homodyning while scanning the local oscillator
phase - is now a well assessed method for ``measuring'' the quantum state. In
this paper I will show how it can be used as a kind of universal detection, for
measuring generic field operators, however at expense of some additional noise.
The general class of field operators that can be measured in this way is
presented, and includes also operators that are inaccessible to heterodyne
detection. The noise from tomographical homodyning is compared to that from
heterodyning, for those operators that can be measured in both ways. It turns
out that for some operators homodyning is better than heterodyning when the
mean photon number is sufficiently small. Finally, the robustness of the method
to additive phase-insensitive noise is analyzed. It is shown that just half
photon of thermal noise would spoil the measurement completely.


title: Proof of Kolmogorovian Censorship

abstract:
  Many argued (Accardi and Fedullo, Pitowsky) that Kolmogorov's axioms of
classical probability theory are incompatible with quantum probabilities, and
this is the reason for the violation of Bell's inequalities. Szab\'o showed
that, in fact, these inequalities are not violated by the experimentally
observed frequencies if we consider the real, ``effective'' frequencies. We
prove in this work a theorem which generalizes this result: ``effective''
frequencies associated to quantum events always admit a Kolmogorovian
representation, when these events are collected through different experimental
set ups, the choice of which obeys a classical distribution.


title: A Framework for Structured Quantum Search

abstract:
  A quantum algorithm for general combinatorial search that uses the underlying
structure of the search space to increase the probability of finding a solution
is presented. This algorithm shows how coherent quantum systems can be matched
to the underlying structure of abstract search spaces, and is analytically
simpler than previous structured search methods. The algorithm is evaluated
empirically with a variety of search problems, and shown to be particularly
effective for searches with many constraints. Furthermore, the algorithm
provides a simple framework for utilizing search heuristics. It also exhibits
the same phase transition in search difficulty as found for sophisticated
classical search methods, indicating it is effectively using the problem
structure.


title: Optimizing entropy relative to a channel or a subalgebra

abstract:
  After recalling definition, monotonicity, concavity, and continuity of a
channel's entropy with respect to a state (finite dimensional cases only), I
introduce the roof property, a convex analytic tool, and show its use in
treating an example. Full proofs and more examples will appear elsewhere. The
relation (a la Benatti) to accessible information is mentioned.


title: Capacities of Quantum Erasure Channels

abstract:
  The quantum analog of the classical erasure channel provides a simple example
of a channel whose asymptotic capacity for faithful transmission of intact
quantum states, with and without the assistance of a two-way classical side
channel, can be computed exactly. We derive the quantum and classical
capacities for the quantum erasure channel and related channels, and compare
them to the depolarizing channel, for which only upper and lower bounds on the
capacities are known.


title: Quantum lattice-gas models for the many-body Schrodinger equation

abstract:
  A general class of discrete unitary models are described whose behavior in
the continuum limit corresponds to a many-body Schrodinger equation. On a
quantum computer, these models could be used to simulate quantum many-body
systems with an exponential speedup over analogous simulations on classical
computers. On a classical computer, these models give an explicitly unitary and
local prescription for discretizing the Schrodinger equation. It is shown that
models of this type can be constructed for an arbitrary number of particles
moving in an arbitrary number of dimensions with an arbitrary interparticle
interaction.

categories: quant-ph comp-gas hep-lat hep-th nlin.CG


title: Born--Infeld gravitation: Spherically symmetric static solutions

abstract:
  In this paper attention is focused on gravitational sector of the
Born--Infeld theory, suggested in quant-ph/9608014. Vacuum equations for
gravitational field are derived. The asymptotic for modified Schwarzschild
solution is obtained, as a decomposition in parameter $L \approx 10^{-32}$ cm.
It is shown, that singularity at $r = 0$ is absent, being replaced by a `ball
of matter' with finite dimensions, such that density of matter is of order of
magnitude of the Planck's density. Another solution of the same symmetry is
obtained, corresponding to a closed space of finite volume of order $L^3$.


title: Robertson Intelligent States

abstract:
  Diagonalization of uncertainty matrix and minimization of Robertson
inequality for n observables are considered. It is proved that for even n this
relation is minimized in states which are eigenstates of n/2 independent
complex linear combinations of the observables. In case of canonical
observables this eigenvalue condition is also necessary. Such minimizing states
are called Robertson intelligent states (RIS).
  The group related coherent states (CS) with maximal symmetry (for semisimple
Lie groups) are particular case of RIS for the quadratures of Weyl generators.
Explicit constructions of RIS are considered for operators of su(1,1), su(2),
h_N and sp(N,R) algebras. Unlike the group related CS, RIS can exhibit strong
squeezing of group generators. Multimode squared amplitude squeezed states are
naturally introduced as sp(N,R) RIS. It is shown that the uncertainty matrices
for quadratures of q-deformed boson operators a_{q,j} (q > 0) and of any k
power of a_j = a_{1,j} are positive definite and can be diagonalized by
symplectic linear transformations. PACS numbers: 03.65.Fd, 42.50.Dv


title: Simulating quantum mechanics on a quantum computer

abstract:
  Algorithms are described for efficiently simulating quantum mechanical
systems on quantum computers. A class of algorithms for simulating the
Schrodinger equation for interacting many-body systems are presented in some
detail. These algorithms would make it possible to simulate nonrelativistic
quantum systems on a quantum computer with an exponential speedup compared to
simulations on classical computers. Issues involved in simulating relativistic
systems of Dirac and gauge particles are discussed.


title: Cooperative loss and decoherence in quantum computation and commuication

abstract:
  Cooperative effects in the loss (the amplitude damping) and decoherence (the
phase damping) of the qubits (two-state quantum systems) due to the inevitable
coupling to the same environment are investigated. It is found that the qubits
undergo the dissipation coherently in this case. In particular, for a special
kind of input states (called the coherence-preserving states), whose form
depends on the type of the coupling, loss and decoherence in quantum memory are
much reduced. Based on this phenomenon, a scheme by encoding the general input
states of the qubits into the corresponding coherence-preserving states is
proposed for reducing the cooperative loss and decoherence in quantum
computation or communication.


title:
Correlation between Quantum Mechanics and Classical Theory of Rotating
  Electron Models and Possible Experiment

abstract:
  It is shown that the point charge and magnetic moment of electron produce
together such a field that total electromagnetic momentum has a component
perpendicular to electron velocity. As a result classical electron models,
having magnetic moment, move not along a straight line, if there is no external
force, but along a spiral, the space period and radius of which are comparable
with de-Broglie wave length. Some other surprising coincidences with quantum
theory arise as a result of calculation. An experiment is proposed for direct
observation of quantum or of new type electron delocalization.


title: What is the Regularized Casimir Vacuum Energy Density?

abstract:
  The regularized total Casimir energy in spacetimes with boundaries is not in
general equal to the integral of the regularized energy density. This
paradoxical phenomenon is most transparently analyzed in the simple example of
a massless scalar field in 1+1 dimensions confined to a line element of length
$L$ and obeying Dirichlet boundary conditions.


title: The wave function in Quantum Mechanics

abstract:
  Through a new interpretation of Special Theory of Relativity and with a model
given for physical space, we can find a way to understand the basic principles
of Quantum Mechanics consistently from Classical Theory. It is supposed that
natural phenomena have a connection with intangible reality which cannot be
measured directly. Furthermore, the intangible reality is supposed as vacuum
particles -- stationary vacuum electrons as a model. In addition, 4-Dimensional
Complex Space is introduced, in which each dimension has an internal complex
space.


title: Quantum State Diffusion: from Foundations to Applications

abstract:
  Deeper insight leads to better practice. We show how the study of the
foundations of quantum mechanics has led to new pictures of open systems and to
a method of computation which is practical and can be used where others cannot.
We illustrate the power of the new method by a series of pictures that show the
emergence of classical features in a quantum world. We compare the development
of quantum mechanics and of the theory of (biological) evolution.


title: Coupled Q-oscillators as a model for vibrations of polyatomic molecules

abstract:
  The system of two $Q$-deformed oscillators coupled so that the total
Hamiltonian has the su$_Q$(2) symmetry is proved to be equivalent, to lowest
order approximation, to a system of two identical Morse oscillators coupled by
the cross-anharmonicity usually used empirically in describing vibrational
spectra of triatomic molecules. The symmetry also imposes a connection between
the self-anharmonicity of the Morse oscillators and the cross-anharmonicity
strength, which can be removed by replacing the $Q$-oscillators by deformed
anharmonic oscillators. The generalization to $n$ oscillators is
straightforward. The applicability of the formalism to highly symmetric
polyatomic molecules is discussed.


title: Quantum distribution functions for radial observables

abstract:
  For quantum systems with two dimensional configuration space we construct a
physical radial momentum observable. Rescaling the radius we find the dilatonic
degrees of freedom form a Weyl algebra. With this we construct the radial
Wigner quasi-probability distribution function.


title: Quantum Theory of Computation and Relativistic Physics

abstract:
  In the e-print is discussed a few steps to introducing of "vocabulary" of
relativistic physics in quantum theory of information and computation (QTI&C).
The behavior of a few simple quantum systems those are used as models in QTI&C
is tested by usual relativistic tools (transformation properties of wave
vectors, etc.). Massless and charged massive particles with spin 1/2 are
considered. Field theory is also discussed briefly.


title: Broadcasting of entanglement via local copying

abstract:
  We show that inseparability of quantum states can be partially broadcasted
(copied, cloned) with the help of local operations, i.e. distant parties
sharing an entangled pair of spin 1/2 states can generate two pairs of
partially nonlocally entangled states using only local operations. This
procedure can be viewed as an inversion of quantum purification procedures.


title: From quantum Bayesian inference to quantum tomography

abstract:
  We derive an expression for a density operator estimated via Bayesian quantum
inference in the limit of an infinite number of measurements.
  This expression is derived under the assumption that the reconstructed system
is in a pure state. In this case the estimation corresponds to an averaging
over a generalized microcanonical ensemble of pure states satisfying a set of
constraints imposed by the measured mean values of the observables under
consideration. We show that via the ``purification'' ansatz, statistical
mixtures can also be consistently reconstructed via the quantum Bayesian
inference scheme. In this case the estimation corresponds to averaging over the
generalized canonical ensemble of states satisfying the given constraints, and
the reconstructed density operator maximizes the von Neumann entropy (i.e.,
this density operator is equal to the generalized canonical density operator
which follows from the Jaynes principle of maximum entropy). We study in detail
the reconstruction of the spin-1/2 density operator and discuss the logical
connection between the three reconstruction schemes, i.e., (1) quantum Bayesian
inference, (2) reconstruction via the Jaynes principle of maximum entropy, and
(3) discrete quantum tomography.


title: Measure of Entaglement

abstract:
  The extent to which a given wave function, $\psi$, is entangled is measured
by minimizing the norm of $\psi$ minus all possible unentangled functions. This
measure is given by the largest eigenvalue of $\psi^\dagger \psi$, considered
as an operator. The definition is basis independent.


title: Bounds on Decoherence and Error

abstract:
  When a confined system interacts with its walls (treated quantum
mechanically), there is an intertwining of degrees of freedom. We show that
this need not lead to entanglement, hence decoherence. It will generally lead
to error. The wave function optimization required to avoid decoherence is also
examined.


title:
Does Clauser-Horne-Shimony-Holt Correlation or Freedman-Clauser
  Correlation lead to the largest violation of Bell's Inequality?

abstract:
  An inequality is deduced from Einstein's locality and a supplementary
assumption. This inequality defines an experiment which can actually be
performed with present technology to test local realism. Quantum mechanics
violate this inequality a factor of 1.5. In contrast, quantum mechanics
violates previous inequalities (for example, Clauser-Horne-Shimony-Holt
inequality of 1969, Freedman-Clauser inequality of 1972, Clauser-Horne
inequality of 1974) by a factor of $\sqrt 2$. Thus the magnitude of violation
of the inequality derived in this paper is approximately $20.7%$ larger than
the magnitude of violation of previous inequalities. This result can be
particularly important for the experimental test of locality.


title:
Exact wave functions and geometric phases of a generalized driven
  oscillator

abstract:
  The generalized invariant and its eigenstates of a general quadratic
oscillator are found. The Schr\"odinger wave functions for the eigenstates are
also found in analytically closed forms. The conditions for the existence of
the cyclic initial state (CIS) are studied and the corresponding nonadiabatic
Berry phase is calculated explicitly.


title: Quantum copying: Fundamental inequalities

abstract:
  How well one can copy an arbitrary qubit? To answer this question we consider
two arbitrary vectors in a two-dimensional state space and an abstract copying
transformation which will copy these two vectors. If the vectors are
orthogonal, then perfect copies can be made. If they are not, then errors will
be introduced. The size of the error depends on the inner product of the two
original vectors. We derive a lower bound for the amount of noise induced by
quantum copying. We examine both copying transformations which produce one copy
and transformations which produce many, and show that the quality of each copy
decreases as the number of copies increases.


title:
Comment on ``An Evolutionary Picture for Quantum Physics'' by Rudolf
  Haag

abstract:
  Widespread unjustified views on the role of the observer, the individuality
of quantum processes, the relation between decoherence and irreversibility,
Bell's quest for `beables', the direction of time, and the concept of
experience are revealed, whereby a better understanding is achieved of what the
evolutionary picture is all about and what is regarded as missing in already
existing realistic pictures.


title:
Quantum Interferometry, Measurement and Objectivity: Some Basic Features
  Revisited

abstract:
  The reduction paradigm of quantum interferometry and the objectivation
problem in quantum measurements are reanalyzed. Both are shown to be amenable
to straightforward mathematical treatment within "every-users" simple-minded
quantum mechanics without reduction postulate etc., using only its
probabilistic content.


title: Covariant Quantum Dynamical Semigroups: Unbounded generators

abstract:
  A survey of the probabilistic approaches to quantum dynamical semigroups with
unbounded generators is given. An emphasis is made upon recent advances in the
structural theory of covariant Markovian master equations. The relations with
the classical Levy-Khinchin formula are elucidated. As an example, a complete
characterizations of the Galilean covariant irreversible quantum Markovian
evolutions is given in terms of the corresponding quantum master and Langevin
equations. Important topics for future investigation are outlined.


title:
Reconstruction of quantum states of spin systems via the Jaynes
  principle of maximum entropy

abstract:
  We apply the Jaynes principle of maximum entropy for the partial
reconstruction of correlated spin states. We determine the minimum set of
observables which are necessary for the complete reconstruction of the most
correlated states of systems composed of spins-1/2 (e.g., the Bell and the
Greenberger-Horne-Zeilinger states). We investigate to what extent an
incomplete measurement can reveal nonclassical features of correlated spin
states.


title: Optimal Eavesdropping in Quantum Cryptography. I

abstract:
  We consider the Bennett-Brassard cryptographic scheme, which uses two
conjugate quantum bases. An eavesdropper who attempts to obtain information on
qubits sent in one of the bases causes a disturbance to qubits sent in the
other basis. We derive an upper bound to the accessible information in one
basis, for a given error rate in the conjugate basis. Independently fixing the
error rate in the conjugate bases, we show that both bounds can be attained
simultaneously by an optimal eavesdropping probe, consisting of two qubits. The
qubits' interaction and their subsequent measurement are described explicitly.
These results are combined to give an expression for the optimal information an
eavesdropper can obtain for a given average disturbance when her interaction
and measurements are performed signal by signal. Finally, the relation between
quantum cryptography and violations of Bell's inequalities is discussed.


title: Quantum Computers and Dissipation

abstract:
  We analyse dissipation in quantum computation and its destructive impact on
efficiency of quantum algorithms. Using a general model of decoherence, we
study the time evolution of a quantum register of arbitrary length coupled with
an environment of arbitrary coherence length. We discuss relations between
decoherence and computational complexity and show that the quantum
factorization algorithm must be modified in order to be regarded as efficient
and realistic.


title:
Coherent eavesdropping strategies for the 4-state quantum cryptography
  protocol

abstract:
  An elementary derivation of best eavesdropping strategies for the 4 state
BB84 quantum cryptography protocol is presented, for both incoherent and
two--qubit coherent attacks. While coherent attacks do not help Eve to obtain
more information, they are more powerful to reveal the whole message sent by
Alice. Our results are based on symmetric eavesdropping strategies, which we
show to be sufficient to analyze these kind of problems.


title: Microtubules: The neuronic system of the neurons?

abstract:
  In this talk we review recent work on integrable models for Microtubule (MT)
networks, subneural paracrystalline cytosceletal structures, which seem to play
a fundamental role in the neurons. We cast here the complicated MT dynamics in
the form of a 1+1-dimensional non-critical string theory, which can be
formulated in terms of (dual) Dirichlet branes, according to modern
perspectives. We suggest that the MTs are the microsites in the brain, for the
emergence of stable, macroscopic quantum coherent states, identifiable with the
``preconscious states''. Quantum space-time effects, as described by
non-critical string theory, trigger then an ``organized collapse'' of the
coherent states down to a specific or ``conscious state''. The whole process we
estimate to take O(1 sec), in excellent agreement with a plethora of
experimental/observational findings. The complete integrability of the stringy
model for MT proves sufficient in providing a satisfactory solution to memory
coding and capacity. Such features might turn out to be important for a model
of the brain as a quantum computer.


title:
Comment on ``A new efficient method for calculating perturbative
  energies using functions which are not square integrable'': regularization
  and justification

abstract:
  The method recently proposed by Skala and Cizek for calculating perturbation
energies in a strict sense is ambiguous because it is expressed as a ratio of
two quantities which are separately divergent. Even though this ratio comes out
finite and gives the correct perturbation energies, the calculational process
must be regularized to be justified. We examine one possible method of
regularization and show that the proposed method gives traditional quantum
mechanics results.


title:
Generalized Aharonov-Bohm effect, homotopy classes and Hausdorff
  dimension

abstract:
  We suggest as gedanken experiment a generalization of the Aharonov-Bohm
experiment, based on an array of solenoids. This experiment allows in principle
to measure the decomposition into homotopy classes of the quantum mechanical
propagator. This yields information on the geometry of the average path of
propagation and allows to determine its Hausdorff dimension.


title: Proper Dirac Quantization of Free Particle on D-Dimensional Sphere

abstract:
  We show that an unambiguous and correct quantization of the second-class
constrained system of a free particle on a sphere in $D$ dimensions is possible
only by converting the constraints to abelian gauge constraints, which are of
first class in Dirac's classification scheme. The energy spectrum is equal to
that of a pure Laplace-Beltrami operator with no additional constant arising
from the curvature of the sphere. A quantization of Dirac's modified Poisson
brackets for second-class constraints is also possible and unique, but must be
rejected since the resulting energy spectrum is physically incorrect.


title: The Quantum Jump Approach to Dissipative Dynamics in Quantum Optics

abstract:
  Dissipation, the irreversible loss of energy and coherence, from a
microsystem, is the result of coupling to a much larger macrosystem (or
reservoir) which is so large that one has no chance of keeping track of all of
its degrees of freedom. The microsystem evolution is then described by tracing
over the reservoir states, resulting in an irreversible decay as excitation
leaks out of the initially excited microsystems into the outer reservoir
environment. Earlier treatments of this dissipation described an ensemble of
microsystems using density matrices, either in Schroedinger picture with Master
equations, or in Heisenberg picture with Langevin equations. The development of
experimental techniques to study single quantum systems (for example single
trapped ions, or cavity radiation field modes) has stimulated the construction
of theoretical methods to describe individual realizations conditioned on a
particular observation record of the decay channel, in the environment. These
methods, variously described as Quantum Jump, Monte Carlo Wavefunction and
Quantum Trajectory methods are the subject of this review article. We discuss
their derivation, apply them to a number of current problems in quantum optics
and relate them to ensemble descriptions.


title: Quantised motion of an atom in a Gaussian-Laguerre beam

abstract:
  We quantise the centre of mass motion of a neutral Cs atom in the presence of
a classical Gaussian-Laguerre$_{10}$ light field in the large detuning limit.
This light field possesses orbital angular momentum which is transferred to the
atom via spontaneous emissions. We use quantum trajectory and analytic methods
to solve the master equation for the 2d centre of mass motion with recoil near
the centre of the beam. For appropriate parameters, we observe heating in both
the cartesian and polar observables within a few orbits of the atom in the
beam. The angular momentum, $\hat{L}$, shows a rapid diffusion which results in
$<\hat{L}>$ reaching a maximum and then decreasing to zero. We compare this
with analytic results obtained for an atom illuminated by a superposition of
Gaussian-Laguerre modes which possess no angular momentum, in the limit of no
recoil.


title: Quantum Cryptography without Public Announcement of Bases

abstract:
  This paper provides a simple variation of the basic ideas of the BB84 quantum
cryptographic scheme leading to a method of key expansion. A secure random
sequence (the bases sequence) determines the encoding bases in a proposed
scheme. Using the bases sequence repeatedly is proven to be safe by quantum
mechanical laws.


title: Trajectory-coherent states and the Heisenberg's uncertainty relation

abstract:
  In this paper we investigate the problem of minimization the Heisenberg's
uncertainty relation by the trajectory-coherent states. The conditions of
minimization for Hamiltonian and trajectory are obtained. We show that the
trajectory-coherent states minimize the Heisenberg's uncertainty relation for
special Cauchy problem for the Schr\"{o}dinger equation only.


title: Resource Letter GPP-1: Geometric Phases in Physics

abstract:
  This Resource Letter provides a guide to the literature on the geometric
angles and phases in classical and quantum physics. Journal articles and books
are cited for the following topics: anticipations of the geometric phase,
foundational derivations and formulations, books and review articles on the
subject, and theoretical and experimental elaborations and applications.


title: The Plight of `I Am'

abstract:
  This is a short metaphysical fable accentuating the conceptual difficulties
involved, and succinctly criticizing the approaches pursued since the inception
of quantum theory, in dealing with what is known collectively as `the
measurement problem.' It includes some landmark references, and has appeared in
the special issue of Metaphysical Review dedicated to Descartes on his 400th
birthday: Metaphysical Review, vol. 3, no. 1, July 1996.


title:
Proposal for an experiment to measure the Hausdorff dimension of quantum
  mechanical trajectories

abstract:
  We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm
effect, how to measure in principle the zig-zagness of the trajectory of
propagation (abberation from its classical trajectory) of a massive particle in
quantum mechanics. Experiment I is conceived to show that contributions from
quantum paths abberating from the classical trajectory are directly observable.
Experiment II is conceived to measure average length, scaling behavior and
critical exponent (Hausdorff dimension) of quantum mechanical paths.


title:
The Relevant Operators for the generalized time-dependent m-photon
  Jaynes-Cummings Hamiltonian

abstract:
  The m-photon Jaynes-Cummings Hamiltonian is a natural generalization of the
much studied Jaynes-Cummings Hamiltonian. In this short note we give the
relevant operators for the time-dependent generalized m-photon Jaynes-Cummings
Hamiltonian. The dynamical equations for these operators are also given. These
operators are needed and indeed are the basic building blocks for performing
calculations in the context of the Maximum Entropy Formalism.


title: Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit

abstract:
  It is shown that the optimum strategy of the eavesdropper, as described in
the preceding paper, can be expressed in terms of a quantum circuit in a way
which makes it obvious why certain parameters take on particular values, and
why obtaining information in one basis gives rise to noise in the conjugate
basis.


title:
Regular and Chaotic Coherent State Dynamics of Several Quantum Optical
  Models

abstract:
  The coherent state representations of the group $G = W_1 \otimes G_0$ (where
$G_0 = SU(2), SU(1,1)$) are used in computer simulation of the dynamics of
single two-level atom $(G_0 = SU(2))$ interacting with a quantized photon
cavity mode - the Jaynes - Cummings model (JCM) without the rotating wave
approximation and, in general, nonlinear in photon variables). The second case
(hyperbolic Jaynes - Cummings model (HJCM), $G_0 = SU(1,1))$ corresponds to the
quantum dynamics of quadratic nonlinear coupled oscillators (the parametric
resonance on double field frequency and a three - wave parametric processes of
nonlinear optics). Quasiclassical dynamical equations for parameters of
approximately factorizable coherent states for these models are derived and
regimes of motion for "atom" and field variables are analyzed.


title: Shape Invariance in the Calogero and Calogero-Sutherland Models

abstract:
  We show that the Calogero and Calogero-Sutherland models possess an N-body
generalization of shape invariance. We obtain the operator representation that
gives rise to this result, and discuss the implications of this result,
including the possibility of solving these models using algebraic methods based
on this shape invariance. Our representation gives us a natural way to
construct supersymmetric generalizations of these models, which are interesting
both in their own right and for the insights they offer in connection with the
exact solubility of these models.


title: Time and Events

abstract:
  Time plays a special role in Standard Quantum Theory. The concept of time
observable causes many controversies there. In Event Enhanced Quantum Theory
(in short: EEQT) Schroedinger's differential equation is replaced by a em
piecewise deterministic algorithm} that describes also the timing of events.
This allows us to revisit the problem of time of arrival in quantum theory.


title: Time of Arrival in Event Enhanced Quantum Theory

abstract:
  The new solution to the problem of time of arrival in quantum theory is
presented herein. It allows for computer simulation of particle counters and it
implies Born's interpretation. It also suggests new experiments that can answer
the question: can a quantum particle detect a detector without being detected?


title: A Generalization of Deutsch's Example

abstract:
  Quantum parallelism is the main feature of quantum computation. In 1985 D.
Deutsch showed that a single quantum computation may be sufficient to state
whether a two-valued function of a two-valued variable is constant or not.
Though the generalized problem with unconstrained domain and range size admits
no deterministic quantum solution, a fully probabilistic quantum algorithm is
presented in which quantum parallelism is harnessed to achieve a quicker
exploration of the domain with respect to the classical ``sampling'' strategy.


title:
The Landauer Resistance and Band Spectra for the Counting Quantum Turing
  Machine

abstract:
  The generalized counting quantum Turing machine (GCQTM) is a machine which,
for any N, enumerates the first $2^{N}$ integers in succession as binary
strings. The generalization consists of associating a potential with read-1
steps only. The Landauer Resistance (LR) and band spectra were determined for
the tight binding Hamiltonians associated with the GCQTM for energies both
above and below the potential height. For parameters and potentials in the
electron region, the LR fluctuates rapidly between very high and very low
values as a function of momentum. The rapidity and extent of the fluctuations
increases rapidly with increasing N. For N=18, the largest value considered,
the LR shows good transmission probability as a function of momentum with
numerous holes of very high LR values present. This is true for energies above
and below the potential height. It is suggested that the main features of the
LR can be explained by coherent superposition of the component waves reflected
from or transmitted through the $2^{N-1}$ potentials in the distribution. If
this explanation is correct, it provides a dramatic illustration of the effects
of quantum nonlocality.


title: Resonance statistics in a microwave cavity with a thin antenna

abstract:
  We propose a model for scattering in a flat resonator with a thin antenna.
The results are applied to rectangular microwave cavities. We compute the
resonance spacing distribution and show that it agrees well with experimental
data provided the antenna radius is much smaller than wavelengths of the
resonance wavefunctions.


title: Non--locality of particle spin: a consequence of interaction energy?

abstract:
  Neutron interference measurements with macroscopic beam separation allow to
study the influence of magnetic fields on spin properties. By calculating the
interaction energy with a dynamic and deterministic model, we are able to
establish that the phase shift on one component of the neutron beam is linear
with magnetic intensity, and equally, that interaction energy as well as phase
shifts do not depend on the orientation of the magnetic field. The theoretical
treatment allows the conclusion that the non-local properties of particle spin
derive from the classical equation for interaction energy and the fact, that
interaction energy does not depend on magnetic field orientation. Additionally,
it can be established that the 4 pi symmetry of spinors in this case depends on
the scaling of magnetic fields.


title:
Aharonov-Bohm interference in the presence of metallic mesoscopic
  cylinders

abstract:
  This work studies the interference of electrons in the presence of a line of
magnetic flux surrounded by a normal-conducting mesoscopic cylinder at low
temperature. It is found that, while there is a supplementary phase
contribution from each electron of the mesoscopic cylinder, the sum of these
individual supplementary phases is equal to zero, so that the presence of a
normal-conducting mesoscopic ring at low temperature does not change the
Aharonov-Bohm interference pattern of the incident electron. It is shown that
it is not possible to ascertain by experimental observation that the shielding
electrons have responded to the field of an incident electron, and at the same
time to preserve the interference pattern of the incident electron. It is also
shown that the measuring of the transient magnetic field in the region between
the two paths of an electron interference experiment with an accuracy at least
equal to the magnetic field of the incident electron generates a phase
uncertainty which destroys the interference pattern.


title:
Quantum Interference of Polarized Electrons in the Presence of Magnetic
  Strings

abstract:
  This work analyzes the effects of shielding on the Aharonov-Bohm scattering
of electrons endowed with spin. The interaction of polarized electrons with
bare and shielded magnetic strings is studied with the aid of the Dirac
equation. It is found that the difference between the amplitudes for the
scattering by bare and shielded strings of incident wave packets of width
$\delta$ and impact parameter $d$ is proportional to $\exp(-d^2/2\delta^2)$.


title:
Spontaneous Symmetry Breaking, Off-diagonal Long-range Order, and
  Nucleation of Quantum State

abstract:
  Spontaneous symmetry breaking originats in quantum mechanical measurement of
the relevant observable defining the physical situation, order parameter is the
average of this observable. A modification is made on the random-phase
postulate validating the ensemble description. Off-diagonal long-range order,
macroscopic wavefunction and interference effects in many-particle systems
present when there is a so-called nucleation of quantum state, which is
proposed to be the origin of spontaneous gauge symmetry breaking, for which
nonconservation of particle number N is not essential. The approach based on
nonvanishing expectation of the field operator, $<\hat{\psi}(\vec{r})>$, is
only a coherent-state approximation in thermodynamic limit. When $N \to
\infty$, this approach is equivalent, but $<\hat{\psi}(\vec{r})>$ is not the
macroscopic wavefunction.


title: Quantifying Entanglement

abstract:
  We present conditions every measure of entanglement has to satisfy and
construct a whole class of 'good' entanglement measures. The generalization of
our class of entanglement measures to more than two particles is
straightforward. We present a measure which has a statistical operational basis
that might enable experimental determination of the quantitative degree of
entanglement.


title: Efficient Quantum Transforms

abstract:
  Quantum mechanics requires the operation of quantum computers to be unitary,
and thus makes it important to have general techniques for developing fast
quantum algorithms for computing unitary transforms. A quantum routine for
computing a generalized Kronecker product is given. Applications include
re-development of the networks for computing the Walsh-Hadamard and the quantum
Fourier transform. New networks for two wavelet transforms are given. Quantum
computation of Fourier transforms for non-Abelian groups is defined. A slightly
relaxed definition is shown to simplify the analysis and the networks that
computes the transforms. Efficient networks for computing such transforms for a
class of metacyclic groups are introduced. A novel network for computing a
Fourier transform for a group used in quantum error-correction is also given.


title: A Theory of Fault-Tolerant Quantum Computation

abstract:
  In order to use quantum error-correcting codes to actually improve the
performance of a quantum computer, it is necessary to be able to perform
operations fault-tolerantly on encoded states. I present a general theory of
fault-tolerant operations based on symmetries of the code stabilizer. This
allows a straightforward determination of which operations can be performed
fault-tolerantly on a given code. I demonstrate that fault-tolerant universal
computation is possible for any stabilizer code. I discuss a number of examples
in more detail, including the five-qubit code.