title:
Time-Dependent Invariants and Green's Functions in the Probability
  Representation of Quantum Mechanics

abstract:
  In the probability representation of quantum mechanics, quantum states are
represented by a classical probability distribution, the marginal distribution
function (MDF), whose time dependence is governed by a classical evolution
equation. We find and explicitly solve, for a wide class of Hamiltonians, new
equations for the Green's function of such an equation, the so-called classical
propagator. We elucidate the connection of the classical propagator to the
quantum propagator for the density matrix and to the Green's function of the
Schr\"odinger equation. Within the new description of quantum mechanics we give
a definition of coherence solely in terms of properties of the MDF and we test
the new definition recovering well known results. As an application, the forced
parametric oscillator is considered . Its classical and quantum propagator are
found, together with the MDF for coherent and Fock states.


title: Zeta-Functions and Star-Products

abstract:
  We use the definition of a star (or Moyal or twisted) product to give a
phasespace definition of the $\zeta$-function. This allows us to derive new
closed expressions for the coefficients of the heat kernel in an asymptotic
expansion for operators of the form $\alpha p^2+v(q)$. For the particular case
of the harmonic oscillator we furthermore find a closed form for the Green's
function. We also find a relationship between star exponentials, path integrals
and Wigner functions, which in a simple example gives a relation between the
star exponential of the Chern-Simons action and knot invariants.


title: Quantum mechanical retrocausation? Call for nonlocal causal models!

abstract:
  A new possible version of multisimultaneous causality is proposed, and real
experiments allowing us to decide between this view and quantum mechanical
retrocausation are further discussed. The interest of testing quantum mechanics
against as many nonlocal causal models as possible is stressed.


title: Decoherence Control for Optical Qubits

abstract:
  Photons in cavities have been already used for the realization of simple
quantum gates [Q.A. Turchette, Phys. Rev. Lett. 75,4710 (1995)]. We present a
method for combatting decoherence in this case.


title: Optomechanical Cooling of a Macroscopic Oscillator by Homodyne Feedback

abstract:
  We propose a simple optomechanical model in which a mechanical oscillator
quadrature could be "cooled" well below its equilibrium temperature by applying
a suitable feedback to drive the orthogonal quadrature by means of the homodyne
current of the radiation field used to probe its position.


title: Quantum search on structured problems

abstract:
  This paper shows how a basic property of unitary transformations can be used
for meaningful computations. This approach immediately leads to search-type
applications, where it improves the number of steps by a square-root - a simple
minded search that takes N steps, can be improved to O(sqrt(N)) steps. The
quantum search algorithm is one of several immediate consequences of this
framework. Several novel search-related applications are presented.


title: No-cloning of Orthogonal States in Composite Systems

abstract:
  The no-cloning principle tells us that non-orthogonal quantum states cannot
be cloned, but it does not tell us that orthogonal states can always be cloned.
We suggest a situation where the cloning transformations are restricted,
leading to a novel type of no-cloning principle. In the case of a composite
system made of two subsystems: if the subsystems are only available one after
the other then there are various cases when orthogonal states cannot be cloned.
Surprising examples are given, which give a radically better insight regarding
the basic concepts of quantum cryptography.


title: On the Power of One Bit of Quantum Information

abstract:
  In standard quantum computation, the initial state is pure and the answer is
determined by making a measurement of some of the bits in the computational
basis. What can be accomplished if the initial state is a highly mixed state
and the answer is determined by measuring the expectation of $\sigma_z$ on the
first bit with bounded sensitivity? This is the situation in high temperature
ensemble quantum computation. We show that in this model it is possible to
perform interesting physics simulations which have no known efficient classical
algorithms, even though the model is less powerful then standard quantum
computing in the presence of oracles.


title:
Valuations on Functionally Closed Sets of Quantum Mechanical Observables
  and Von Neumann's 'No-Hidden-Variables' Theorem

abstract:
  We apply the machinery of projection lattices and von Neumann algebras to
analyze the question of how modal interpretations can (and do) circumvent von
Neumann's infamous 'no-hidden-variables' theorem.


title:
Operational Characterization of Simultaneous Measurements in Quantum
  Mechanics

abstract:
  Quantum mechanics predicts the joint probability distribution of the outcomes
of simultaneous measurements of commuting observables, but, in the state of the
art, has lacked the operational definition of simultaneous measurements. The
question is answered as to when the consecutive applications of measuring
apparatuses give a simultaneous measurement of their observables. For this
purpose, all the possible state reductions caused by measurements of an
observable is also characterized by their operations.


title: Quantum vs. Classical Communication and Computation

abstract:
  We present a simple and general simulation technique that transforms any
black-box quantum algorithm (a la Grover's database search algorithm) to a
quantum communication protocol for a related problem, in a way that fully
exploits the quantum parallelism. This allows us to obtain new positive and
negative results. The positive results are novel quantum communication
protocols that are built from nontrivial quantum algorithms via this
simulation. These protocols, combined with (old and new) classical lower
bounds, are shown to provide the first asymptotic separation results between
the quantum and classical (probabilistic) two-party communication complexity
models. In particular, we obtain a quadratic separation for the bounded-error
model, and an exponential separation for the zero-error model. The negative
results transform known quantum communication lower bounds to computational
lower bounds in the black-box model. In particular, we show that the quadratic
speed-up achieved by Grover for the OR function is impossible for the PARITY
function or the MAJORITY function in the bounded-error model, nor is it
possible for the OR function itself in the exact case. This dichotomy naturally
suggests a study of bounded-depth predicates (i.e. those in the polynomial
hierarchy) between OR and MAJORITY. We present black-box algorithms that
achieve near quadratic speed up for all such predicates.


title:
On the necessary conditions for the occurrence of the
  "environment-induced superselection rules"

abstract:
  We briefly summarize the main recently obtained results concerning existence
of the (effective) necessary conditions for the occurrence of the
"environment-induced superselection rules" (decoherence).


title: Time-Symmetrized Counterfactuals in Quantum Theory

abstract:
  Counterfactuals in quantum theory are briefly reviewed and it is argued that
they are very different from counterfactuals considered in the general
philosophical literature. The issue of time symmetry of quantum counterfactuals
is considered and a novel time-symmetric definition of quantum counterfactuals
is proposed. This definition is applied for analyzing several controversies
related to quantum counterfactuals.


title: Local Search Methods for Quantum Computers

abstract:
  Local search algorithms use the neighborhood relations among search states
and often perform well for a variety of NP-hard combinatorial search problems.
This paper shows how quantum computers can also use these neighborhood
relations. An example of such a local quantum search is evaluated empirically
for the satisfiability (SAT) problem and shown to be particularly effective for
highly constrained instances. For problems with an intermediate number of
constraints, it is somewhat less effective at exploiting problem structure than
incremental quantum methods, in spite of the much smaller search space used by
the local method.


title: Classical states via decoherence

abstract:
  The initial states which minimize the predictability loss for a damped
harmonic oscillator are identified as quasi-free states with a symmetry
dictated by the environment's diffusion coefficients. For an isotropic
diffusion in phase space, coherent states (or mixtures of coherent states) are
selected as the most stable ones.


title: A Limit on the Speed of Quantum Computation in Determining Parity

abstract:
  Consider a function f which is defined on the integers from 1 to N and takes
the values -1 and +1. The parity of f is the product over all x from 1 to N of
f(x). With no further information about f, to classically determine the parity
of f requires N calls of the function f. We show that any quantum algorithm
capable of determining the parity of f contains at least N/2 applications of
the unitary operator which evaluates f. Thus for this problem, quantum
computers cannot outperform classical computers.


title: Quantum Theory : A Pointer To An Independent Reality

abstract:
  While philosophy of science is the study of problems of knowledge concerning
science in general, there also exists - or should exist - a '' philosophy in
science'' directed at finding out in what ways our actual scientific knowledge
may validly contribute to the basic philosophical quest. Contrary to philosophy
of science, which is a subject for philosophers, philosophy in science calls on
the services of physicists. When, in its spirit, quantum theory and Bell's
theorem are used as touchstones, the two main traditional philosophical
approaches, realism and idealism, are found wanting. A more suitable conception
seems to be an intermediate one, in which the mere postulated existence of a
holistic and hardly knowable Mind-Independent Reality is found to have an
explaining power. Some corrections to comments by Schins of a previous work on
the same subject are incorporated.


title: Quantum state sensitivity to initial conditions

abstract:
  The different time-dependent distances of two arbitrarily close quantum or
classical-statistical states to a third fixed state are shown to imply an
experimentally relevant notion of state sensitivity to initial conditions. A
quantitative classification scheme of quantum states by their sensitivity and
instability in state space is given that reduces to the one performed by
classical-mechanical Lyapunov exponents in the classical limit


title:
General Approach to Functional Forms for the Exponential Quadratic
  Operators in Coordinate-Momentum Space

abstract:
  In a recent paper [Nieto M M 1996 Quantum and Semiclassical Optics, 8 1061;
quant-ph/9605032], the one dimensional squeezed and harmonic oscillator
time-displacement operators were reordered in coordinate-momentum space. In
this paper, we give a general approach for reordering multi-dimensional
exponential quadratic operator(EQO) in coordinate-momentum space. An explicit
computational formula is provided and applied to the single mode and
double-mode EQO through the squeezed operator and the time displacement
operator of the harmonic oscillator.


title: Quantum Lower Bounds by Polynomials

abstract:
  We examine the number T of queries that a quantum network requires to compute
several Boolean functions on {0,1}^N in the black-box model. We show that, in
the black-box model, the exponential quantum speed-up obtained for partial
functions (i.e. problems involving a promise on the input) by Deutsch and Jozsa
and by Simon cannot be obtained for any total function: if a quantum algorithm
computes some total Boolean function f with bounded-error using T black-box
queries then there is a classical deterministic algorithm that computes f
exactly with O(T^6) queries.
  We also give asymptotically tight characterizations of T for all symmetric f
in the exact, zero-error, and bounded-error settings. Finally, we give new
precise bounds for AND, OR, and PARITY. Our results are a quantum extension of
the so-called polynomial method, which has been successfully applied in
classical complexity theory, and also a quantum extension of results by Nisan
about a polynomial relationship between randomized and deterministic decision
tree complexity.


title:
Exact Solution of a Class of Three-Body Scattering Problems in One
  dimension

abstract:
  We present an exact solution of the three-body scattering problem for a one
parameter family of one dimensional potentials containing the Calogero and
Wolfes potentials as special limiting cases. The result is an interesting
nontrivial relationship between the final momenta $p'_i$ and the initial
momenta $p_i$ of the three particles. We also discuss another one parameter
family of potentials for all of which $p'_i=-p_i~(i=1,2,3)$.


title: Notes on nonlinear quantum algorithms

abstract:
  Recenty Abrams and Lloyd have proposed a fast algorithm that is based on a
nonlinear evolution of a state of a quantum computer. They have explicitly used
the fact that nonlinear evolutions in Hilbert spaces do not conserve scalar
products of states, and applied a description of separated systems taken from
Weinberg's nonlinear quantum mechanics. On the other hand it is known that
violation of orthogonality combined with the Weinberg-type description
generates unphysical, arbitrarily fast influences between noninteracting
systems. It was not therefore clear whether the algorithm is fast because
arbitrarily fast unphysical effects are involved. In these notes I show that
this is not the case. I analyze both algorithms proposed by Abrams and Lloyd on
concrete, simple models of nonlinear evolution. The description I choose is
known to be free of the unphysical influences (therefore it is not the Weinberg
one). I show, in particular, that the correct local formalism allows even to
simplify the algorithm.


title: Random quantum correlations and density operator distributions

abstract:
  Consider the question: what statistical ensemble corresponds to minimal prior
knowledge about a quantum system ? For the case where the system is in fact
known to be in a pure state there is an obvious answer, corresponding to the
unique unitarily-invariant measure on the Hilbert sphere. However, the problem
is open for the general case where states are described by density operators.
Here two approaches to the problem are investigated.
  The first approach assumes that the system is randomly correlated with a
second system, where the ensemble of composite systems is described by a random
pure state. Results for qubits randomly correlated with other systems are
presented, including average entanglement entropies. It is shown that maximum
correlation is guaranteed in the limit as one system becomes
infinite-dimensional.
  The second approach relies on choosing a metric on the space of density
operators, and generating a corresponding ensemble from the induced volume
element. Comparisons between the approaches are made for qubits, for which the
second approach (based on the Bures metric) yields the most symmetric, and
hence the least informative, ensemble of density operators.


title: Some remarks on the fragmentation of Bose condensates

abstract:
  We show how fragmentation of a Bose-Einstein condensate can occur given
repulsive inter-particle interactions and a non-uniform external potential.


title:
Decoherence, chaos, quantum-classical correspondence, and the
  algorithmic arrow of time

abstract:
  The environment -- external or internal degrees of freedom coupled to the
system -- can, in effect, monitor some of its observables. As a result, the
eigenstates of these observables decohere and behave like classical states:
Continuous destruction of superpositions leads to environment-induced
superselection (einselection). Here I investigate it in the context of quantum
chaos (i. e., quantum dynamics of systems which are classically chaotic).


title:
Threshold and non-linear behavior of lasers of $\Lambda$ and V -
  configurations

abstract:
  Dynamic properties of closed three level laser systems are investigated. Two
schemes of pumping - $\Lambda$ and V - are considered. It is shown that the
non-linear behavior of the photon number as a function of pump both near and
far above threshold is crucially different for these two configurations. In
particular, it is found that in the high pump regime laser can turn off in a
phase-transition-like manner in both $\Lambda$ and V schemes.


title: Acuasal Behavior in Quantum Electrodynamics

abstract:
  Acausal features of quantum electrodynamic processes are discussed. While
these processes are not present for the classical electrodynamic theory, in the
quantum electrodynamic theory, acausal processes are well known to exist. For
example, any Feynman diagram with a ``loop'' in space-time describes a
``particle'' which may move forward in time or backward in time or in
space-like directions. The engineering problems involved in experimentally
testing such causality violations on a macroscopic scale are explored.


title: Caldirola-Kanai Oscillator in Classical Formulation of Quantum Mechanics

abstract:
  The quadrature distribution for the quantum damped oscillator is introduced
in the framework of the formulation of quantum mechanics based on the
tomography scheme. The probability distribution for the coherent and Fock
states of the damped oscillator is expressed explicitly in terms of Gaussian
and Hermite polynomials, correspondingly.


title: Simple experimental methods for trapped ion quantum processors

abstract:
  Two techniques are described that simplify the experimental requirements for
measuring and manipulating quantum information stored in trapped ions. The
first is a new technique using electron shelving to measure the populations of
the Zeeman sublevels of the ground state, in an ion for which no cycling
transition exists from any of these sublevels. The second technique is laser
cooling to the vibrational ground state, without the need for a trap operating
in the Lamb-Dicke limit. This requires sideband cooling in a sub-recoil regime.
We present a thorough analysis of sideband cooling on one or a pair of
sidebands simultaneously.


title:
Spatially sequential turn-on of spontaneous emission from an atomic wave
  packet

abstract:
  We discuss a simple example demonstrating that spontaneous emission from
"space-time-superposed" atomic center-of-mass wave packets is nontrivially and
time-dependent modified with respect to the standard dipole-pattern typical of
"space-superposed" wave packets. Our approach provides an approximate
description of a nonsimultaneous interaction of electromagnetic field with
different parts of a wave packet.


title:
Entanglement engineering of one-photon wavepackets using a single-atom
  source

abstract:
  We propose a cavity-QED scheme for the controlled generation of sequences of
entangled single-photon wavepackets. A photon is created inside a cavity via an
active medium, such as an atom, and decays into the continuum of radiation
modes outside the cavity(coupled, for example to an optical fiber). Subsequent
wavepackets generated in this way behave as independent logical qubits. This
and the possibility of producing maximally entangled multi-qubit states suggest
many applications in quantum communication.


title: Enlargement of Calderbank Shor Steane quantum codes

abstract:
  It is shown that a classical error correcting code C = [n,k,d] which contains
its dual, C^{\perp} \subseteq C, and which can be enlarged to C' = [n,k' > k+1,
d'], can be converted into a quantum code of parameters [[ n, k+k' - n, min(d,
3d'/2) ]]. This is a generalisation of a previous construction, it enables many
new codes of good efficiency to be discovered. Examples based on classical Bose
Chaudhuri Hocquenghem (BCH) codes are discussed.


title: 1-way quantum finite automata: strengths, weaknesses and generalizations

abstract:
  We study 1-way quantum finite automata (QFAs). First, we compare them with
their classical counterparts. We show that, if an automaton is required to give
the correct answer with a large probability (over 0.98), then the power of
1-way QFAs is equal to the power of 1-way reversible automata. However, quantum
automata giving the correct answer with smaller probabilities are more powerful
than reversible automata.
  Second, we show that 1-way QFAs can be very space-efficient. Namely, we
construct a 1-way QFA which is exponentially smaller than any equivalent
classical (even randomized) finite automaton. This construction may be useful
for design of other space-efficient quantum algorithms.
  Third, we consider several generalizations of 1-way QFAs. Here, our goal is
to find a model which is more powerful than 1-way QFAs keeping the quantum part
as simple as possible.


title:
Quantum Mechanics in Cell Microtubules: Wild Imagination or Realistic
  Possibility?

abstract:
  We focus on potential mechanisms for `energy-loss-free' transport along the
cell microtubules, which could be considered as realizations of Fr\"ohlich's
ideas on the role of solitons for superconductivity and/or biological matter.
In particular, by representing the MT arrangements as `cavities',we present a
novel scenario on the formation of macroscopic (or mesoscopic) quantum-coherent
states, as a result of the (quantum-electromagnetic) interactions of the MT
dimers with the surrounding molecules of the ordered water in the interior of
the MT cylinders. We present some generic order of magnitude estimates of the
decoherence time in a typical model for MT dynamics. The role of (conjectured)
ferroelectric properties of MT arrangements on the above quantum phenomena is
emphasized. Based on these considerations, we also present a conjecture on the
role of the MT in `holographic' information processing, which resembles the
situation encountered in internal source X-ray holography in atomic physics.


title:
Aharonov-Bohm scattering of neutral atoms with induced electric dipole
  moments

abstract:
  We investigate the scattering of neutral polarizable atoms from an
electrically charged wire placed in a homogeneous magnetic field. The atoms
carry an induced electric dipole. The reflecting wire is discussed. We
calculate the scattering amplitude and cross section the practically more
important case that atoms are totally absorbed at the surface of the wire. If
the magnetic field is present, there is a dominating Aharonov-Bohm peak in the
forward direction followed by decreasing oscillations for larger angles. An
experimental realization of this modulated Aharonov-Bohm scattering should be
possible.


title: Basics of Quantum Computation

abstract:
  Quantum computers require quantum logic, something fundamentally different to
classical Boolean logic. This difference leads to a greater efficiency of
quantum computation over its classical counter-part. In this review we explain
the basic principles of quantum computation, including the construction of
basic gates, and networks. We illustrate the power of quantum algorithms using
the simple problem of Deutsch, and explain, again in very simple terms, the
well known algorithm of Shor for factorisation of large numbers into primes. We
then describe physical implementations of quantum computers, focusing on one in
particular, the linear ion-trap realization. We explain that the main obstacle
to building an actual quantum computer is the problem of decoherence, which we
show may be circumvented using the methods of quantum error correction.


title:
$C_{\lambda}$-extended harmonic oscillator and (para)supersymmetric
  quantum mechanics

abstract:
  $C_{\lambda}$-extended oscillator algebras are realized as generalized
deformed oscillator algebras. For $\lambda = 3$, the spectrum of the
corresponding bosonic oscillator Hamiltonian is shown to strongly depend on the
algebra parameters. A connection with cyclic shape invariant potentials is
noted. A bosonization of PSSQM of order two is obtained.


title: Quantum Robots and Environments

abstract:
  Quantum robots and their interactions with environments of quantum systems
are described and their study justified. A quantum robot is a mobile quantum
system that includes a quantum computer and needed ancillary systems on board.
Quantum robots carry out tasks whose goals include specified changes in the
state of the environment or carrying out measurements on the environment. Each
task is a sequence of alternating computation and action phases. Computation
phase activities include determination of the action to be carried out in the
next phase and possible recording of information on neighborhood environmental
system states. Action phase activities include motion of the quantum robot and
changes of neighborhood environment system states. Models of quantum robots and
their interactions with environments are described using discrete space and
time. To each task is associated a unitary step operator T that gives the
single time step dynamics. T = T_{a}+T_{c} is a sum of action phase and
computation phase step operators. Conditions that T_{a} and T_{c} should
satisfy are given along with a description of the evolution as a sum over paths
of completed phase input and output states. A simple example of a task carrying
out a measurement on a very simple environment is analyzed. A decision tree for
the task is presented and discussed in terms of sums over phase paths. One sees
that no definite times or durations are associated with the phase steps in the
tree and that the tree describes the successive phase steps in each path in the
sum.


title: Solvable three boson model with attractive delta function interactions

abstract:
  A one parameter solvable model for three bosons subject to delta function
interactions in one-dimension with periodic boundary conditions is studied. The
energy levels and wave functions are classified and given explicitly in terms
of three momenta. In particular, eigenstates and eigenvalues are described as
functions of the model parameter, c. Some of the states are given in terms of
complex momenta and represent dimer or trimer configurations for large negative
c. The asymptotic behaviour for small and large values of the parameter, and at
thresholds between real and complex momenta is provided. The properties of the
potential energy are also discussed.


title: Causality and Electromagnetic Transmissions Through Materials

abstract:
  There have been several experiments which hint at evidence for superluminal
transport of electromagnetic energy through a material slab. On the theoretical
side, it has appeared evident that acausal signals are indeed possible in
quantum electrodynamics. However, it is unlikely that superluminal signals can
be understood on the basis of a purely classical electrodynamic signals passing
through a material. The classical and quantum theories represent quite
different views, and it is the quantum view which may lead to violations of
Einstein causality.


title: Monotonicity of the quantum linear programming bound

abstract:
  The most powerful technique known at present for bounding the size of quantum
codes of prescribed minimum distance is the quantum linear programming bound.
Unlike the classical linear programming bound, it is not immediately obvious
that if the quantum linear programming constraints are satisfiable for
dimension K, that the constraints can be satisfied for all lower dimensions. We
show that the quantum linear programming bound is indeed monotonic in this
sense, and give an explicitly monotonic reformulation.


title:
On Quantum Nonlocality: Using Prediction of a Distant Measurement
  Outcome

abstract:
  We assume that an event caused by a correlation between outcomes of two
causally separated measurements is, by definition, a manifestation of quantum
nonlocality, or superluminal influence. An example of the Alice-Bob type is
given, with the characters replaced. The relationship between quantum
nonlocality and relativity theory is touched upon.


title: Einstein-Pauli-Yukawa Paradox --- What is the Physical Reality?

abstract:
  What is the momentum spectrum of a particle moving in an infinite deep square
well? Einstein, Pauli and Yukawa had adopted different point of view than that
in usual text books. The theoretical and experimental implication of this
problem is discussed.


title: On Quaternions and Monopoles

abstract:
  It is shown that the quaternionic Hilbert space formulation of quantum
mechanics allows a quantization, based on a generalized system of
imprimitivity, that leads to a description of the motion of a quantum particle
in the field of a magnetic monopole. The corresponding Hamilton operator is
linked to the theory of projective representations in the weakened form
proposed by Adler.


title: A Number of Quasi-Exactly Solvable N-body Problems

abstract:
  We present several examples of quasi-exactly solvable $N$-body problems in
one, two and higher dimensions. We study various aspects of these problems in
some detail. In particular, we show that in some of these examples the
corresponding polynomials form an orthogonal set and many of their properties
are similar to those of the Bender-Dunne polynomials. We also discuss QES
problems where the polynomials do not form an orthogonal set.

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


title:
Frequency Switching of Quantum Harmonic Oscillator with Time-Dependent
  Frequency

abstract:
  An explicit solution of the equation for the classical harmonic oscillator
with smooth switching of the frequency has been found . A detailed analysis of
a quantum harmonic oscillator with such frequency has been done on the base of
the method of linear invariants. It has been shown that such oscillator
possesses cofluctuant states, different from widely studied Glauber's coherent
and "ideal" squeezed states.


title: Ferroelectrics and their possible involvement in Biology

abstract:
  We present the main properties of ferroelectricity, with emphasis given to a
specific family of hydrated ferroelectric crystals, which can serve as model
systems for corresponding configurations in biology like the microtubules. An
experimental method is described, which allows to establish the ferroelectric
property of microtubules in suspension.


title:
Unconditional Security Of Quantum Key Distribution Over Arbitrarily Long
  Distances

abstract:
  Quantum key distribution is widely thought to offer unconditional security in
communication between two users. Unfortunately, a widely accepted proof of its
security in the presence of source, device and channel noises has been missing.
This long-standing problem is solved here by showing that, given fault-tolerant
quantum computers, quantum key distribution over an arbitrarily long distance
of a realistic noisy channel can be made unconditionally secure. The proof is
reduced from a noisy quantum scheme to a noiseless quantum scheme and then from
a noiseless quantum scheme to a noiseless classical scheme, which can then be
tackled by classical probability theory.


title: Efficient Quantum Key Distribution

abstract:
  We devise a simple modification that essentially doubles the efficiency of a
well-known quantum key distribution scheme proposed by Bennett and Brassard
(BB84). Our scheme assigns significantly different probabilities for the
different polarization bases during both transmission and reception to reduce
the fraction of discarded data. The actual probabilities used in the scheme are
announced in public. As the number of transmitted signals increases, the
efficiency of our scheme can be made to approach 100%. An eavesdropper may try
to break such a scheme by eavesdropping mainly along the predominant basis. To
defeat such an attack, we perform a refined analysis of accepted data: Instead
of lumping all the accepted data together to estimate a single error rate, we
separate the accepted data into various subsets according to the basis employed
and estimate an error rate for each subset {\it individually}.


title: Correlation between Correlations: Process and Time in Quantum Networks

abstract:
  We study a special inhomogeneous quantum network consisting of a ring of $M$
pseudo-spins (here $M = 4$) sequentially coupled to one and the same central
spin under the influence of given pulse sequences (quantum gate operations).
This architecture could be visualized as a quantum Turing machine with a cyclic
``tape''. Rather than input-output-relations we investigate the resulting
process, i.e. the correlation between one- and two-point expectation values
(``correlations'') over various time-steps. The resulting spatio-temporal
pattern exhibits many non-classical features including Zeno-effects, violation
of temporal Bell-inequalities, and quantum parallelism. Due to the strange web
of correlations being built-up, specific measurement outcomes for the tape may
refer to one or several preparation histories of the head. Specific families of
correlation functions are more stable with respect to dissipation than the
total wave-function.


title: Statistics and Quantum Chaos

abstract:
  We use multi-time correlation functions of quantum systems to construct
random variables with statistical properties that reflect the degree of
complexity of the underlying quantum dynamics.


title: Weakly bound states in 2+\epsilon dimensions

abstract:
  We study the critical behaviour near the threshold where a first bound state
appears at some value of coupling constant in an attractive short-range
potential in $2+\epsilon $ dimensions. We obtain general expression for the
binding energy near the threshold and also demonstrate that the critical region
is correctly described by an effective separable potential. The critical
exponent of the radius of weakly bound state is shown to coincide with the
correlation length exponent for the spin model in the large-N limit. In two
dimensions, where the binding energy is exponentially small in coupling
constant, we obtain a general analytic expression for the prefactor.


title: Remarks on a Nonlinear Quantum Theory

abstract:
  Motivated by recent proposals (Bialynicki-Birula, Mycielski; Haag, Bannier;
Weinberg; Doebner, Goldin) for nonlinear quantum mechanical evolution equations
for pure states some principal difficulties in the framework of usual quantum
theory, which is based on its inherent linear structure, are discussed. A
generic construction of nonlinear evolution equations through nonlinear gauge
transformations is indicated.


title: Quantum Coordinates of an Event in Local Quantum Physics

abstract:
  Recently it has been proposed, using the formalism of
positive-operator-valued measures, a possible definition of quantum coordinates
for events in the context of quantum mechanics. In this short note we analyze
this definition from the point of view of local algebras in the framework of
local quantum theories.


title: The Casimir Effect and Thermodynamic Instability

abstract:
  One loop field theory calculations of free energies quite often yield
violations of the stability conditions associated with the thermodynamic second
law. Perhaps the best known example involves the equation of state of black
holes. Here, it is pointed out that the Casimir force between two parallel
conducting plates also violates a thermodynamic stability condition normally
associated with the second law of thermodynamics.


title: Second-quantization of open systems using quasinormal modes

abstract:
  The second-quantization of a scalar field in an open cavity is formulated,
from first principles, in terms of the quasinormal modes (QNMs), which are the
eigensolutions of the evolution equation that decay exponentially in time as
energy leaks to the outside. This formulation provides a description involving
the cavity degrees of freedom only, with the outside acting as a (thermal or
driven) source. Thermal correlation functions and cavity Feynman propagators
are thus expressed in terms of the QNMs, labeled by a discrete index rather
than a continuous momentum. Single-resonance domination of the density of
states and the spontaneous decay rate is then given a proper foundation. This
is a first essential step towards the application of QNMs to cavity QED
phenomena, to be reported elsewhere.


title: Generation of phase-coherent states

abstract:
  An interaction scheme involving nonlinear $\chi^{(2)}$ media is suggested for
the generation of phase-coherent states (PCS). The setup is based on parametric
amplification of vacuum followed by up-conversion of the resulting twin-beam.
The involved nonlinear interactions are studied by the exact numerical
diagonalization. An experimentally achievable working regime to approximate PCS
with high conversion rate is given, and the validity of parametric
approximation is discussed.


title:
Simple Explicit Formulas for Gaussian Path Integrals with Time-Dependent
  Frequencies

abstract:
  Quadratic fluctuations require an evaluation of ratios of functional
determinants of second-order differential operators. We relate these ratios to
the Green functions of the operators for Dirichlet, periodic and antiperiodic
boundary conditions on a line segment. This permits us to take advantage of
Wronski's construction method for Green functions without knowledge of
eigenvalues. Our final formula expresses the ratios of functional determinants
in terms of an ordinary $2\times2$ -determinant of a constant matrix
constructed from two linearly independent solutions of a the homogeneous
differential equations associated with the second-order differential operators.
For ratios of determinants encountered in semiclassical fluctuations around a
classical solution, the result can further be expressed in terms of this
classical solution.
  In the presence of a zero mode, our method allows for a simple universal
regularization of the functional determinants. For Dirichlet's boundary
condition, our result is equivalent to Gelfand-Yaglom's.
  Explicit formulas are given for a harmonic oscillator with an arbitrary
time-dependent frequency.


title: Distributed Quantum Computation over Noisy Channels

abstract:
  We analyse the use of entangled states to perform quantum computations non
locally among distant nodes in a quantum network. The complexity associated
with the generation of multiparticle entangled states is quantified in terms of
the concept of global cost. This parameter allows us to compare the use of
physical resources in different schemes. We show that for ideal channels and
for a sufficiently large number of nodes, the use of maximally entangled states
is advantageous over uncorrelated ones. For noisy channels, one has to use
entanglement purification procedures in order to create entangled states of
high fidelity. We show that under certain circumstances a quantum network
supplied with a maximally entangled input still yields a smaller global cost,
provided that $n$ belongs to a given interval $n\in [n_{min},n_{max}]$. The
values of $n_{min}$ and $n_{max}$ crucially depend on the purification
protocols used to establish the $n$-- processor entangled states, as well as on
the presence of decoherence processes during the computation. The phase
estimation problem has been used to illustrate this fact.


title: Meaning of the Density Matrix

abstract:
  Protective measurement, which was proposed as a method of observing the
wavefunction of a single system, is extended to the observation of the density
matrix of a single system. d'Espagnat's definition of `proper mixture' is shown
to be improper because it does not allow for appropriate fluctuations. His
claim that there could be different mixtures corresponding to the same density
matrix is critically examined. These results provide a new meaning to the
density matrix, which gives it the same ontological status as the wavefunction
describing a pure state. This also enables quantum entropy to be associated
with a single system.


title: Local modification of the Abrams-Lloyd nonlinear algorithm

abstract:
  The nonlinear algorithms proposed recently by Abrams and Lloyd [Report No.
quant-ph/9801041] are fast but make an explicit use of an arbitrarily fast
unphysical transfer of information within a quantum computer. It is shown that
there exists a simplification of the second Abrams-Lloyd algorithm which
eliminates the unphysical effect but keeps the algorithm fast.


title:
Double Spiral Energy Surface in One-dimensional Quantum Mechanics of
  Generalized Pointlike Potentials

abstract:
  We analyze the eigenvalue problem of a quantum particle on the line with the
generalized pointlike potential of three parameter family. It is shown that the
energy surface in the parameter space has a set of singularities, around which
different eigenstates are connected in the form of paired spiral stairway. An
examplar wave-function aholonomy is displayed where the ground state is
adiabatically turned into the second excited state after cyclic rotation in the
parameter space.
  KEYWORDS: one-dimensional system, $\delta'$ potential, non-trivial topology
in quantum mechanics, exotic wave-function aholonomy

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


title: Quantization of the multidimensional rotor

abstract:
  We reconsider the problem of quantising a particle on the $D$-dimensional
sphere. Adopting a Lagrangian method of reducing the degrees of freedom, the
quantum Hamiltonian is found to be the usual Schr\"odinger operator without any
boundary term. The equivalence with the Dirac Hamiltonian approach is
demonstrated, either in the cartesian or in the curvilinear basis. We also
briefly comment on the path integral approach.


title: Effects of atomic diffraction on the Collective Atomic Recoil Laser

abstract:
  We formulate a wave atom optics theory of the Collective Atomic Recoil Laser,
where the atomic center-of-mass motion is treated quantum mechanically. By
comparing the predictions of this theory with those of the ray atom optics
theory, which treats the center-of-mass motion classically, we show that for
the case of a far off-resonant pump laser the ray optics model fails to predict
the linear response of the CARL when the temperature is of the order of the
recoil temperature or less. This is due to the fact that in theis temperature
regime one can no longer ignore the effects of matter-wave diffraction on the
atomic center-of-mass motion.


title:
Cooling the Collective Motion of Trapped Ions to Initialize a Quantum
  Register

abstract:
  We report preparation in the ground state of collective modes of motion of
two trapped 9Be+ ions. This is a crucial step towards realizing quantum logic
gates which can entangle the ions' internal electronic states. We find that
heating of the modes of relative ion motion is substantially suppressed
relative to that of the center-of-mass modes, suggesting the importance of
these modes in future experiments.


title:
Conditionally exactly solvable potentials: A supersymmetric construction
  method

abstract:
  We present in this paper a rather general method for the construction of
so-called conditionally exactly solvable potentials. This method is based on
algebraic tools known from supersymmetric quantum mechanics. Various families
of one-dimensional potentials are constructed whose corresponding Schr\"odinger
eigenvalue problem can be solved exactly under certain conditions of the
potential parameters. Examples of quantum systems on the real line, the half
line as well as on some finite interval are studied in detail.


title: The Measurement Problem and the Reduction Postulate of Quantum Mechanics

abstract:
  It is well known, that the causal Schr\"odinger evolution of a quantum state
is not compatible with the reduction postulate, even when decoherence is taken
into account. The violation of the causal evolution, introduced by the standard
reduction postulate distinguishes certain systems (as the measurement devices),
whose states are very close to statistical mixtures (as the ones resulting from
the process of decoherence). In these systems, this violation has not any
observable effect. In arbitrary quantum systems, the transition from the
initial density matrix to a diagonal matrix predicted by the standard reduction
postulate, would lead to a complete breakdown of the Schr\"odinger evolution,
and consequently would destroy all the predictive power of quantum mechanics.
What we show here, is that there is a modified version of the postulate that
allows to treat all the quantum mechanical systems on equal footing. The
standard reduction postulate may be considered as a good approximation, useful
for practical purposes, of this modified version which is consistent with the
Schr\"odinger evolution and via decoherence with the experimental results.
Within this approach, the physical role played by the reduction postulate is as
a tool for the computation of relative probabilities and consequently for the
determination of the probabilities of consistent histories.


title:
Berry's Phase in the Presence of a Stochastically Evolving Environment:
  A Geometric Mechanism for Energy-Level Broadening

abstract:
  The generic Berry phase scenario in which a two-level system is coupled to a
second system whose dynamical coordinate is slowly-varying is generalized to
allow for stochastic evolution of the slow system. The stochastic behavior is
produced by coupling the slow system to a heat resevoir which is modeled by a
bath of harmonic oscillators initially in equilibrium at temperature T, and
whose spectral density has a bandwidth which is small compared to the
energy-level spacing of the fast system. The well-known energy-level shifts
produced by Berry's phase in the fast system, in conjunction with the
stochastic motion of the slow system, leads to a broadening of the fast system
energy-levels. In the limit of strong damping and sufficiently low temperature,
we determine the degree of level-broadening analytically, and show that the
slow system dynamics satisfies a Langevin equation in which Lorentz-like and
electric-like forces appear as a consequence of geometrical effects. We also
determine the average energy-level shift produced in the fast system by this
mechanism.


title:
Another Comment on ``Quantum Entanglement and Nonexistence of
  Superluminal Signals''

abstract:
  We argue that the claim given in quant-ph/9801014 remains untenable in the
revised version. The fallacy in the proof is a misinterpretation of the
no-cloning and teleportation theorems, which do not involve time and reference
frames.


title:
Generalization of Dirac Non-Linear Electrodynamics, and Spinning Charged
  Particles

abstract:
  In this note we generalized the Dirac non-linear electrodynamics, by
introducing two potentials (namely, the vector potential A and the
pseudo-vector potential gamma^5 B of the electromagnetic theory with charges
and magnetic monopoles) and by imposing the pseudoscalar part of the product
omega.omega* to be zero, with omega = A + gamma^5 B. We show that the field
equations of such a theory possess a soliton-like solution which can represent
a priori a "charged particle", since it is endowed with a Coulomb field plus
the field of a magnetic dipole. The rest energy of the soliton is finite, and
the angular momentum stored in its electromagnetic field can be identified
--for suitable choices of the parameters-- with the spin of the charged
particle. Thus this approach seems to yield a classical model for the charged
(spinning) particle, which does not meet the problems met by earlier attempts
in the same direction.


title: New Families of Isospectral Hydrogen-like potentials

abstract:
  By applying algebraic techniques, we construct a two-parametric family of
strictly isospectral Hydrogen-like potentials as well as some of its
one-parametric limits. An additional one-parametric almost isospectral family
of Hydrogen-like potentials is also investigated. It is argued that the
construction of a SUSY partner Hamiltonian using a factorization energy
$\delta$ less than the ground state energy of the departure Hamiltonian is
unnecessarily restrictive.


title: No-cloning and superluminal signaling

abstract:
  The argument given by M.D. Westmoreland and B. Schumacher in quant-ph/9801014
leading to the purported conclusion that superluminal signaling violates the
no-cloning theorem is shown to be incorrect.


title: QED commutation relations for inhomogeneous Kramers-Kronig dielectrics

abstract:
  Recently a quantization scheme for the phenomenological Maxwell theory of the
full electromagnetic field in an inhomogeneous three-dimensional, dispersive,
and absorbing dielectric medium has been developed and applied to a system
consisting of two infinite half-spaces with a common planar interface (H.T.
Dung, L. Knoell, and D.-G. Welsch, Phys. Rev. A 57, in press). Here we show
that the scheme, which is based on the classical Green-tensor integral
representation of the electromagnetic field, applies to any inhomogeneous
medium. For this purpose we prove that the fundamental equal-time commutation
relations of QED are preserved for an arbitrarily space-dependent,
Kramers--Kronig consistent permittivity. Further, an extension of the
quantization scheme to linear media with bounded regions of amplification is
given, and the problem of anisotropic media is briefly addressed.


title:
Decoherence from internal degrees of freedom for cluster of
  mesoparticles : a hierarchy of master equations

abstract:
  A mesoscopic evolution equation for an ensemble of mesoparticles follows
after the elimination of internal degrees of freedom. If the system is composed
of a hierarchy of scales, the reduction procedure could be worked repeatedly
and the characterization of this iterating method is carried out. Namely, a
prescription describing a discrete hierarchy of master equations for the
density operator is obtained. Decoherence follows from the irreversible
coupling of the systems, defined by mesoscopic variables, to internal degrees
of freedom. We discuss briefly the existence of systems with the same dynamics
laws at different scales. We made an explicit calculation for an ensemble of
particles with internal harmonic interaction in an external anharmonic field.
New conditions related to the semiclassical limit for mesoscopic systems
(Wigner-function) are conjectured.


title: Entanglement of Assistance

abstract:
  The newfound importance of ``entanglement as a resource'' in quantum
computation and quantum communication compels us to quantify it in as many
distinct ways as possible. Here we explore a new measure of entanglement for
mixed quantum states of bipartite systems, which we name the Entanglement of
Assistance. We show it to be the maximum average entanglement of all pure-state
ensembles consistent with the given density matrix. In this sense, the
Entanglement of Assistance is a quantity directly dual to the more standard
Entanglement of Formation. With the help of lower and upper bounds, we
calculate the Entanglement of Assistance for a few cases and use these results
to show that it possesses the surprising property of superadditivity. We
believe that this may shed some light on the question of additivity for the
Entanglement of Formation.


title:
To Enjoy the Morning Flower in the Evening -- Is Special Relativity a
  Classical Theory?

abstract:
  The relation between the special relativity and quantum mechanics is
discussed. Based on the postulate that space-time inversion is equavalent to
particle-antiparticle transformation, the essence of special relativity is
explored and the relativistic modification on Stationary Schr\"{o}dinger
Equation is derived.


title: A short derivation of Feynman formula

abstract:
  The complex exponential weighting of Feynman formalism is seen to happen at
the classical level. (Finiteness of) Feynman path integral formula is suspected
then to appear as a consistency condition for the existence of certain Dirac
measures over functional spaces.


title:
Electron structure, Zitterbewegung, and the new non-linear Dirac-like
  equation

abstract:
  The recent literature shows a renewed interest, with various independent
approaches, in the classical theories for spin. Considering the possible
interest of those results, at least for the electron case, we purpose in this
paper to explore their physical and mathematical meaning, by the natural and
powerful language of Clifford algebras (which, incidentally, will allow us to
unify those different approaches). In such theories, the ordinary electron is
in general associated to the mean motion of a point-like "constituent" Q, whose
trajectory is a cylindrical helix. We find, in particular, that the object Q
obeys a new, non-linear Dirac-like equation, such that --when averaging over an
internal cycle (which corresponds to linearization)-- it transforms into the
ordinary Dirac equation (valid for the electron as a whole).


title: About Zitterbewegung and electron structure

abstract:
  We start from the spinning electron theory by Barut and Zanghi, which has
been recently translated into the Clifford algebra language. We "complete" such
a translation, first of all, by expressing in the Clifford formalism a
particular Barut-Zanghi (BZ) solution, which refers (at the classical limit) to
an internal helical motion with a time-like speed [and is here shown to
originate from the superposition of positive and negative frequency solutions
of the Dirac equation]. Then, we show how to construct solutions of the Dirac
equation describing helical motions with light-like speed, which meet very well
the standard interpretation of the velocity operator in the Dirac equation
theory (and agree with the solution proposed by Hestenes, on the basis
--however-- of ad-hoc assumptions that are unnecessary in the present
approach). The above results appear to support the conjecture that the
Zitterbewegung motion (a helical motion, at the classical limit) is responsible
for the electron spin.


title: Bose--Einstein solitons in highly asymmetric traps

abstract:
  We obtain analytic solutions to the Gross-Pitaevskii equation with negative
scattering length in highly asymmetric traps. We find that in these traps the
Bose--Einstein condensates behave like quasiparticles and do not expand when
the trapping in one direction is eliminated. The results can be applicable to
the control of the motion of Bose--Einstein condensates.


title: Relativistic formulation of quantum state diffusion?

abstract:
  The recently reported relativistic formulation of the well-known
non-relativistic quantum state diffusion is seriously mistaken. It predicts,
for instance, inconsistent measurement outcomes for the same system when seen
by two different inertial observers.


title: Flow equations for band--matrices

abstract:
  Continuous unitary transformations can be used to diagonalize or
approximately diagonalize a given Hamiltonian. In the last four years, this
method has been applied to a variety of models of condensed matter physics and
field theory. With a new generator for the continuous unitary transformation
proposed in this paper one can avoid some of the problems of former
applications. General properties of the new generator are derived. It turns out
that the new generator is especially useful for Hamiltonians with a banded
structure. Two examples, the Lipkin model, and the spin--boson model are
discussed in detail.

categories: quant-ph cond-mat.stat-mech math-ph math.MP nucl-th


title: Decoherence in nonclassical motional states of a trapped ion

abstract:
  The decoherence of nonclassical motional states of a trapped $^9 {\rm Be^+}$
ion in a recent experiment is investigated theoretically. Sources of
decoherence considered here destroy the characteristic coherent quantum
dynamics of the system but do not cause energy dissipation. Here they are first
introduced phenomenologically and then described using a microscopic
Hamiltonian formulation. Theoretical predictions are compared to experimental
results.


title: Decoherence, Chaos, and the Correspondence Principle

abstract:
  We present evidence that decoherence can produce a smooth
quantum-to-classical transition in nonlinear dynamical systems. High-resolution
tracking of quantum and classical evolutions reveals differences in expectation
values of corresponding observables. Solutions of master equations demonstrate
that decoherence destroys quantum interference in Wigner distributions and
washes out fine structure in classical distributions bringing the two closer
together. Correspondence between quantum and classical expectation values is
also re-established.


title: On multiphoton absorption by molecules

abstract:
  Rabi frequencies for multiphoton absorption by atoms or molecules that can be
characterized as two- or three-level systems are obtained in the cases of
single and double laser perturbations. If the ambiguity in the origin of
absolute energy is conveniently gauged off in the three-level model, there
appears an additional non linear frequency which is originated from the
separate evolution of a relative-frequency component induced in the whole
system by the simultaneous action of the two perturbations.


title: Quantum transfer functions, weak nonlocality and relativity

abstract:
  The method of transfer functions is developed as a tool for studying Bell
inequalities, alternative quantum theories and the associated physical
properties of quantum systems. Non-negative probabilities for transfer
functions result in Bell-type inequalities. The method is used to show that all
realistic Lorentz-invariant quantum theories, which give unique results and
have no preferred frame, can be ruled out on the grounds that they lead to weak
backward causality.


title: Quantum State Protection in Cavities

abstract:
  We show how an initially prepared quantum state of a radiation mode in a
cavity can be preserved for a long time using a feedback scheme based on the
injection of appropriately prepared atoms. We present a feedback scheme both
for optical cavities, which can be continuously monitored by a photodetector,
and for microwave cavities, which can be monitored only indirectly via the
detection of atoms that have interacted with the cavity field. We also discuss
the possibility of applying these methods for decoherence control in quantum
information processing.


title:
The Concept of Experimental Accuracy and Simultaneous Measurements of
  Position and Momentum

abstract:
  The concept of experimental accuracy is investigated in the context of the
unbiased joint measurement processes defined by Arthurs and Kelly. A
distinction is made between the errors of retrodiction and prediction. Four
error-disturbance relationships are derived, analogous to the single
error-disturbance relationship derived by Braginsky and Khalili in the context
of single measurements of position only. A retrodictive and a predictive
error-error relationship are also derived. The connection between these
relationships and the extended Uncertainty Principle of Arthurs and Kelly is
discussed. The similarities and differences between the quantum mechanical and
classical concepts of experimental accuracy are explored. It is argued that
these relationships provide grounds for questioning Uffink's conclusion, that
the concept of a simultaneous measurement of non-commuting observables is not
fruitful.


title:
Maximal Accuracy and Minimal Disturbance in the Arthurs-Kelly
  Simultaneous Measurement Process

abstract:
  The accuracy of the Arthurs-Kelly model of a simultaneous measurement of
position and momentum is analysed using concepts developed by Braginsky and
Khalili in the context of measurements of a single quantum observable. A
distinction is made between the errors of retrodiction and prediction. It is
shown that the distribution of measured values coincides with the initial state
Husimi function when the retrodictive accuracy is maximised, and that it is
related to the final state anti-Husimi function (the P representation of
quantum optics) when the predictive accuracy is maximised. The disturbance of
the system by the measurement is also discussed. A class of minimally
disturbing measurements is characterised. It is shown that the distribution of
measured values then coincides with one of the smoothed Wigner functions
described by Cartwright.


title: Quantum Mechanical Black Holes: Issues and Ramifications

abstract:
  The recent model of Quantum Mechanical Black Holes is discussed and its
implications for cosmology, particle structure, low dimensionality and other
issues are examined.


title: Tunneling catastrophes of the partition function

abstract:
  We use path-integrals to derive a general expression for the semiclassical
approximation to the partition function of a one-dimensional quantum-mechanical
system. Our expression depends solely on ordinary integrals which involve the
potential. For high temperatures, the semiclassical expression is dominated by
single closed paths. As we lower the temperature, new closed paths may appear,
including tunneling paths. The transition from single to multiple-path regime
corresponds to well-defined catastrophes. Tunneling sets in whenever they
occur. Our formula fully accounts for this feature.


title: Semiclassical Statistical Mechanics

abstract:
  We use a semiclassical approximation to derive the partition function for an
arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we
view as an example of finite temperature scalar Field Theory at a point. We
rely on Catastrophe Theory to analyze the pattern of extrema of the
corresponding path-integral. We exhibit the propagator in the background of the
different extrema and use it to compute the fluctuation determinant and to
develop a (nonperturbative) semiclassical expansion which allows for the
calculation of correlation functions. We discuss the examples of the single and
double-well quartic anharmonic oscillators, and the implications of our results
for higher dimensions.


title: The Error Principle

abstract:
  The problem of characterising the accuracy of, and disturbance caused by a
joint measurement of position and momentum is investigated. In a previous paper
the problem was discussed in the context of the unbiased measurements
considered by Arthurs and Kelly. It is now shown, that suitably modified
versions of these results hold for a much larger class of simultaneous
measurements. The approach is a development of that adopted by Braginsky and
Khalili in the case of a single measurement of position only. A distinction is
made between the errors of retrodiction and the errors of prediction. Two
error-error relationships and four error-disturbance relationships are derived,
supplementing the Uncertainty Principle usually so-called. In the general case
it is necessary to take into account the range of the measuring apparatus. Both
the ideal case, of an instrument having infinite range, and the case of a real
instrument, for which the range is finite, are discussed.


title: Decoherence: Concepts and Examples

abstract:
  We give a pedagogical introduction to the process of decoherence - the
irreversible emergence of classical properties through interaction with the
environment. After discussing the general concepts, we present the following
examples: Localisation of objects, quantum Zeno effect, classicality of fields
and charges in QED, and decoherence in gravity theory. We finally emphasise the
important interpretational features of decoherence.


title: Optimal Joint Measurements of Position and Momentum

abstract:
  The distribution of measured values for maximally accurate, unbiased
simultaneous measurements of position and momentum is investigated. It is
shown, that if the measurement is retrodictively optimal, then the distribution
of results is given by the initial state Husimi function (or Q-representation).
If the measurement is predictively optimal, then the distribution of results is
related to the final state anti-Husimi function (or P-representation). The
significance of this universal property for the interpretation of the Husimi
function is discussed.


title: Parametric up conversion of the vacuum

abstract:
  The theory of parametric down conversion of the vacuum, based on a real
zeropoint, or "vacuum" electromagnetic field, has been treated in earlier
articles. The same theory predicts a hitherto unsuspected phenomenon -
parametric up conversion of the vacuum. This article describes how the
phenomenon may be demonstrated experimentally.


title:
A topos perspective on the Kochen-Specker theorem: I. Quantum States as
  Generalized Valuations

abstract:
  The Kochen-Specker theorem asserts the impossibility of assigning values to
quantum quantities in a way that preserves functional relations between them.
We construct a new type of valuation which is defined on all operators, and
which respects an appropriate version of the functional composition principle.
The truth-values assigned to propositions are (i) contextual; and (ii)
multi-valued, where the space of contexts and the multi-valued logic for each
context come naturally from the topos theory of presheaves.
  The first step in our theory is to demonstrate that the Kochen-Specker
theorem is equivalent to the statement that a certain presheaf defined on the
category of self-adjoint operators has no global elements. We then show how the
use of ideas drawn from the theory of presheaves leads to the definition of a
generalized valuation in quantum theory whose values are sieves of operators.
In particular, we show how each quantum state leads to such a generalized
valuation.


title: Quantum repeaters for communication

abstract:
  In quantum communication via noisy channels, the error probability scales
exponentially with the length of the channel. We present a scheme of a quantum
repeater that overcomes this limitation. The central idea is to connect a
string of (imperfect) entangled pairs of particles by using a novel nested
purification protocol, thereby creating a single distant pair of high fidelity.
The scheme tolerates general errors on the percent level.


title: Dynamical suppression of decoherence in two-state quantum systems

abstract:
  The dynamics of a decohering two-level system driven by a suitable control
Hamiltonian is studied. The control procedure is implemented as a sequence of
radiofrequency pulses that repetitively flip the state of the system, a
technique that can be termed quantum "bang-bang" control after its classical
analog. Decoherence introduced by the system's interaction with a quantum
environment is shown to be washed out completely in the limit of continuous
flipping and greatly suppressed provided the interval between the pulses is
made comparable to the correlation time of the environment. The model suggests
a strategy to fight against decoherence that complements existing quantum
error-correction techniques.


title: Quantum cloning and the capacity of the Pauli channel

abstract:
  A family of quantum cloning machines is introduced that produce two
approximate copies from a single quantum bit, while the overall input-to-output
operation for each copy is a Pauli channel. A no-cloning inequality is derived,
describing the balance between the quality of the two copies. This also
provides an upper bound on the quantum capacity of the Pauli channel with
probabilities $p_x$, $p_y$ and $p_z$. The capacity is shown to be vanishing if
$(\sqrt{p_x},\sqrt{p_y},\sqrt{p_z})$ lies outside an ellipsoid whose pole
coincides with the depolarizing channel that underlies the universal cloning
machine.


title: Casimir Effect - The Classical Limit

abstract:
  The temperature dependence of the Casimir effect for the radiation field
confined between two conducting plates is analysed. The Casimir energy is shown
to decline exponentially with temperature while the Casimir entropy which is
defined in the text is shown to approach a limit which depends only on the
geometry of the constraining plates. The results are discussed in terms of the
relation between the Bose distribution function and the equipartition theorem -
a relation based on a study by Einstein and Stern circa 1913.


title: "Interaction-Free" Imaging

abstract:
  Using the complementary wave- and particle-like natures of photons, it is
possible to make ``interaction-free'' measurements where the presence of an
object can be determined with no photons being absorbed. We investigated
several ``interaction-free'' imaging systems, i.e. systems that allow optical
imaging of photosensitive objects with less than the classically expected
amount of light being absorbed or scattered by the object. With the most
promising system, we obtained high-resolution (10 \mu m), one-dimensional
profiles of a variety of objects (human hair, glass and metal wires, cloth
fibers), by raster scanning each object through the system. We discuss possible
applications and the present and future limits for interaction-free imaging.


title: Photon trains and lasing : The periodically pumped quantum dot

abstract:
  We propose to pump semiconductor quantum dots with surface acoustic waves
which deliver an alternating periodic sequence of electrons and holes. In
combination with a good optical cavity such regular pumping could entail
anti-bunching and sub-Poissonian photon statistics. In the bad-cavity limit a
train of equally spaced photons would arise.


title: Non-Markovian Quantum State Diffusion

abstract:
  We present a nonlinear stochastic Schroedinger equation for pure states
describing non-Markovian diffusion of quantum trajectories. It provides an
unravelling of the evolution of a quantum system coupled to a finite or
infinite number of harmonic oscillators, without any approximation. Its power
is illustrated by several examples, including measurement-like situations,
dissipation, and quantum Brownian motion. In some examples, we treat the
environment phenomenologically as an infinite reservoir with fluctuations of
arbitrary correlation. In other examples the environment consists of a finite
number of oscillators. In these quasi-periodic cases we see the reversible
decay of a `Schroedinger cat' state. Finally, our description of open systems
is compatible with different positions of the `Heisenberg cut' between system
and environment.


title:
A Dynamical Mechanism for the Selection of Physical States in `Geometric
  Quantization Schemes'

abstract:
  Geometric quantization procedures go usually through an extension of the
original theory (pre-quantization) and a subsequent reduction (selection of the
physical states). In this context we describe a full geometrical mechanism
which provides dynamically the desired reduction.


title: Quantum Computers Speed Up Classical with Probability Zero

abstract:
  Let $f$ denote length preserving function on words. A classical algorithm can
be considered as $T$ iterated applications of black box representing $f$,
beginning with input word $x$ of length $n$.
  It is proved that if $T=O(2^{n/(7+e)}), e >0$, and $f$ is chosen randomly
then with probability 1 every quantum computer requires not less than $T$
evaluations of $f$ to obtain the result of classical computation. It means that
the set of classical algorithms admitting quantum speeding up has probability
measure zero.
  The second result is that for arbitrary classical time complexity $T$ and $f$
chosen randomly with probability 1 every quantum simulation of classical
computation requires at least $\Omega (\sqrt {T})$ evaluations of $f$.


title: Self-homodyne tomography of a twin-beam state

abstract:
  A self-homodyne detection scheme is proposed to perform two-mode tomography
on a twin-beam state at the output of a nondegenerate optical parametric
amplifier. This scheme has been devised to improve the matching between the
local oscillator and the signal modes, which is the main limitation to the
overall quantum efficiency in conventional homodyning. The feasibility of the
measurement is analyzed on the basis of Monte-Carlo simulations, studying the
effect of non-unit quantum efficiency on detection of the correlation and the
total photon-number oscillations of the twin-beam state.


title: Minimal optimal generalized quantum measurements

abstract:
  Optimal and finite positive operator valued measurements on a finite number
$N$ of identically prepared systems have been presented recently. With physical
realization in mind we propose here optimal and minimal generalized quantum
measurements for two-level systems.
  We explicitly construct them up to N=7 and verify that they are minimal up to
N=5. We finally propose an expression which gives the size of the minimal
optimal measurements for arbitrary $N$.


title:
Metaplectic Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
  and Beyond

abstract:
  The metaplectic covariance for all forms of the Weyl-Wigner-Groenewold-Moyal
quantization is established with different realizations of the inhomogeneous
symplectic algebra. Beyond that, in its most general form $W_{\infty}$
-covariance of this quantization scheme is investigated, and explicit
expressions for the quantum-deformed Hamiltonian vector fields are presented.
In a general basis the structure constants of the $W_{\infty}$-algebra are
obtained and its subalgebras are analyzed.


title: Semiclassical Aspects of Quantum Mechanics by Classical Fluctuations

abstract:
  Building on a model recently proposed by F. Calogero, we postulate the
existence of a coherent, long--range universal tremor affecting any stable and
confined classical dynamical system. Deriving the characteristic fluctuative
unit of action for each classical interaction, we obtain in all cases its
numerical coincidence with the Planck action constant. We therefore suggest
that quantum corrections to classical dynamics can be simulated by suitable
classical stochastic fluctuations.


title:
Classical and Quantum Perturbation Theory for two Non--Resonant
  Oscillators with Quartic Interaction

abstract:
  We study the classical and quantum perturbation theory for two non--resonant
oscillators coupled by a nonlinear quartic interaction. In particular we
analyze the question of quantum corrections to the torus quantization of the
classical perturbation theory (semiclassical mechanics). We obtain up to the
second order of perturbation theory an explicit analytical formula for the
quantum energy levels, which is the semiclassical one plus quantum corrections.
We compare the "exact" quantum levels obtained numerically to the semiclassical
levels studying also the effects of quantum corrections.


title: Motion-Induced Radiation from a Dynamically Deforming Mirror

abstract:
  A path integral formulation is developed to study the spectrum of radiation
from a perfectly reflecting (conducting) surface. It allows us to study
arbitrary deformations in space and time. The spectrum is calculated to second
order in the height function. For a harmonic traveling wave on the surface, we
find many different regimes in which the radiation is restricted to certain
directions. It is shown that high frequency photons are emitted in a beam with
relatively low angular dispersion whose direction can be controlled by the
mechanical deformations of the plate.

categories: quant-ph cond-mat hep-th physics.atom-ph


title: Vibrational Decoherence in Ion-Trap Quantum Computers

abstract:
  Decoherence is studied in an attractive proposal for an actual implementation
of a quantum computer based on trapped ions. Emphasis is placed on the
decoherence arising from the vibrational motion of the ions, which is compared
with that due to spontaneous emission from excited states of the ions. The
calculation is made tractable by exploiting the vast difference in time scales
between the vibrational excitations and the intra-ionic electronic excitations.
Since the latter are several orders of magnitude faster, an adiabatic
approximation is used to integrate them out and find the inclusive probability
P(t) for the elec- tronic state of the ions to evolve as it would in the
absence of vibrational coupling, and the ions to evolve into any state
whatsoever. The decoherence time is found at zero temperature and for any
number of ions N in the computer. Comparison is made with the spontaneous
emission decoherence, and the implications for how trap voltages and other
parameters should be scaled with N are discussed.


title: Quantum Algorithms: Entanglement Enhanced Information Processing

abstract:
  We discuss the fundamental role of entanglement as the essential nonclassical
feature providing the computational speed-up in the known quantum algorithms.
We review the construction of the Fourier transform on an Abelian group and the
principles underlying the fast Fourier transform algorithm. We describe the
implementation of the FFT algorithm for the group of integers modulo 2^n in the
quantum context, showing how the group-theoretic formalism leads to the
standard quantum network and identifying the property of entanglement that
gives rise to the exponential speedup (compared to the classical FFT). Finally
we outline the use of the Fourier transform in extracting periodicities, which
underlies its utility in the known quantum algorithms.


title: A new orthogonalization procedure with an extremal property

abstract:
  Various methods of constructing an orthonomal set out of a given set of
linearly independent vectors are discussed. Particular attention is paid to the
Gram-Schmidt and the Schweinler-Wigner orthogonalization procedures. A new
orthogonalization procedure which, like the Schweinler- Wigner procedure, is
democratic and is endowed with an extremal property is suggested.


title: Statistical Mechanics of a Trapped Bose-Einstein Condensate

abstract:
  Bose-Einstein condensation (BEC) in a gas has now been achieved. Alkali atoms
($^{87}Rb$, $^{23}Na$ and $^{7}Li$) have been cooled to the point of
condensation (temperature of 100 nK) using laser cooling and trapping, followed
by magnetic trapping and evaporative cooling. This important experimental
result has also renewed the interest on theoretical studies of BEC. In this
contribution we discuss the statistical mechanics of the trapped BEC at zero
temperature. In particular, we study the stability of the condensate by using a
variational method with local and non-local interaction between the particles.


title: Hidden variables, quasi-sets, and elementary particles

abstract:
  We have recently showed that it is possible to deal with collections of
indistinguishable elementary particles (in the context of quantum mechanics) in
a set-theoretical framework by using hidden variables, in a sense. In the
present paper we use such a formalism as a model for quasi-set theory.
Quasi-set theory, based on Zermelo-Fraenkel set theory, was developed for
dealing with collections of indistinguishable but, in a sense, not identical
objects.


title: Quasi-set theory for bosons and fermions: quantum distributions

abstract:
  Quasi-set theory provides a mathematical background for dealing with
collections of indistinguishable elementary particles. In this paper, we show
how to obtain the quantum statistics into the scope of quasi-set theory and
discuss the Helium atom, which represents the simplest example where
indistinguishability plays an important role. A brief discussion about
indistinguishability and interference is also presented as well as other
related lines of work. One of the advantages of our approach is that one of the
most basic principles of quantum theory, namely, the Indistinguishability
Postulate, does not need to be assumed even implicetely in the axiomatic basis
of quantum mechanics.


title:
Quantum state engineering using conditional measurement on a beam
  splitter

abstract:
  State preparation via conditional output measurement on a beam splitter is
studied, assuming the signal mode is mixed with a mode prepared in a Fock state
and photon numbers are measured in one of the output channels. It is shown that
the mode in the other output channel is prepared in either a photon-subtracted
or a photon-added Jacobi polynomial state, depending upon the difference
between the number of photons in the input Fock state and the number of photons
in the output Fock state onto which it is projected. The properties of the
conditional output states are studied for coherent and squeezed input states,
and the probabilities of generating the states are calculated. Relations to
other states, such as near-photon-number states and squeezed-state-excitations,
are given and proposals are made for generating them by combining the scheme
with others. Finally, effects of realistic photocounting and Fock-state
preparation are discussed.


title: Pictures of quantum nuclear rotation beyond the correspondence principle

abstract:
  We analyze the time evolution of simple nuclear rotational wave packets (WP)
called circular, linear or elliptic, depending on squeezing parameter $\eta$,
assuming that $E=\hbar\omega_0 I(I+1)$. The scenario of fractional revivals
found by Averbukh and Perelman is adapted to symmetric WP and compared to that
which holds for asymmetric WP. In both cases various shapes are identified
under these lines in particular many cases of cloning. 'Mutants' WP are found
most often. Finally the time evolution of a WP formed by Coulomb excitation on
$^{238}$U and calculated by semiclassical theory is also presented.


title: Open system dynamics with non-Markovian quantum trajectories

abstract:
  A non-Markovian stochastic Schroedinger equation for a quantum system coupled
to an environment of harmonic oscillators is presented. Its solutions, when
averaged over the noise, reproduce the standard reduced density operator
without any approximation. We illustrate the power of this approach with
several examples, including exponentially decaying bath correlations and
extreme non-Markovian cases, where the `environment' consists of only a single
oscillator. The latter case shows the decay and revival of a `Schroedinger cat'
state. For strong coupling to a dissipative environment with memory, the
asymptotic state can be reached in a finite time. Our description of open
systems is compatible with different positions of the `Heisenberg cut' between
system and environment.


title:
Optimal compression of quantum information for one-qubit source at
  incomplete data: a new aspect of Jaynes principle

abstract:
  We consider the problem of optimal processing of quantum information at
incomplete experimental data characterizing the quantum source. In particular,
we then prove that for one-qubit quantum source the Jaynes principle offers a
simple scheme for optimal compression of quantum information. According to the
scheme one should process as if the density matrix of the source were actually
equal to the matrix of the Jaynes state.


title:
Coherent Dark States of Rubidium 87 in a Buffer Gas using Pulsed Laser
  Light

abstract:
  The coherent dark resonance between the hyperfine levels F=1, m=0 and F=2,
m=0 of the rubidium ground state has been observed experimentally with the
light of a pulsed mode-locked diode laser operating at the D1 transition
frequency. The resonance occurs whenever the pulse repetition frequency matches
an integer fraction of the rubidium 87 ground state hyperfine splitting of 6.8
GHz. Spectra have been taken by varying the pulse repetition frequency. Using
cells with argon as a buffer gas a linewidth as narrow as 149 Hz was obtained.
The rubidium ground state decoherence cross section 1.1*10^(-18) cm^2 for
collisions with xenon atoms has been measured for the first time with this
method using a pure isotope rubidium vapor cell and xenon as a buffer gas.


title: Geometry of the Hilbert space and the Quantum Zeno Effect

abstract:
  We show that the quadratic short time behaviour of transition probability is
a natural consequence of the inner product of the Hilbert space of the quantum
system. We prove that Schr\"odinger time evolution between two successive
measurements is not a necessary but only a sufficient condition for predicting
quantum Zeno effect. We provide a relation between the survival probability and
the underlying geometric structure such as the Fubini-Study metric defined on
the projective Hilbert space of the quantum system. This predicts the quantum
Zeno effect even for systems described by non-linear and non-unitary evolution
equations, within the collapse mechanism of the wavefunction during measurement
process. Two examples are studied, one is non-linear Schr\"odinger equation and
other is Gisin's equation and it is shown that one can observe quantum Zeno
effect for systems described by these equations.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics. 0.
  Preliminary considerations: Quantum mechanics from a geometric-observer's
  viewpoint

abstract:
  We propose a version of the non-relativistic quantum mechanics in which the
pure states of a quantum system are described as sections of a Hilbert
(generally infinitely-dimensional) fibre bundle over the space-time. There
evolution is governed via (a kind of) a parallel transport in this bundle. Some
problems concerning observables are considered. There are derived the equations
of motion for the state sections and observables. We show that up to a constant
the matrix of the coefficients of the evolution operator (transport) coincides
with the matrix of the Hamiltonian of the investigated quantum system.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics: I.
  Introduction. The evolution transport

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
but it is in harmony with the modern trends in theoretical physics and
potentially admits new generalizations in different directions. In it a pure
state of some quantum system is described by a state section (along paths) of a
(Hilbert) fibre bundle. Its evolution is determined through the bundle
(analogue of the) Schr\"odinger equation. Now the dynamical variables and the
density operator are described via bundle morphisms (along paths). The
mentioned quantities are connected by a number of relations derived in this
work.
  The present first part of this investigation is devoted to the introduction
of basic concepts on which the fibre bundle approach to quantum mechanics
rests. We show that the evolution of pure quantum-mechanical states can be
described as a suitable linear transport along paths, called evolution
transport, of the state sections in the Hilbert fibre bundle of states of a
considered quantum system.


title:
On Interbasis Expansion for Isotropic Oscillator on Two-Dimensional
  Sphere

abstract:
  In this article we analyze the isotropic oscillator system on the
two-dimensional sphere in the spherical systems of coordinates. The expansion
coefficients for transitions between three spherical bases of the oscillator
are calculated. It is shown that these coefficients are expressed through the
Clebsch-Gordan coefficients for SU(2) group analytically continued to real
values of their argument.


title: Consistency and Linearity in Quantum Theory

abstract:
  Quantum theory is formulated as the uniquely consistent way to manipulate
probability amplitudes. The crucial ingredient is a consistency constraint: if
the amplitude of a quantum process can be computed in two different ways, the
two answers must agree. The constraint is expressed in the form of functional
equations the solution of which leads to the usual sum and product rules for
amplitudes. An immediate consequence is that the Schrodinger equation must be
linear: non-linear variants of quantum mechanics violate the requirement of
consistency.
  PACS: 03.65.Bz, 03.65.Ca.

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


title: Quantum arrival time measurement and backflow effect

abstract:
  The current density for a freely evolving state without negative momentum
components can temporarily be negative. The operational arrival time
distribution, defined by the absorption rate of an ideal detector, is
calculated for a model detector and compared with recently proposed
distributions. Counterintuitive features of the backflow regime are discussed.


title: Optimal Cloning of Pure States

abstract:
  We construct the unique optimal quantum device for turning a finite number of
d-level quantum systems in the same unknown pure state \sigma into M systems of
the same kind, in an approximation of the M-fold tensor product of the state
\sigma.


title: Nonclassical evolution of a free particle

abstract:
  A conditional kinetic energy is defined in terms of the Wigner distribution.
It is shown that this kinetic energy may become negative for negative Wigner
distributions. A free particle wave packet with negative kinetic energy will
spread in a nonclassical manner.


title: Fluctuation, time-correlation function and geometric Phase

abstract:
  We establish a fluctuation-correlation theorem by relating the quantum
fluctuations in the generator of the parameter change to the time integral of
the quantum correlation function between the projection operator and force
operator of the ``fast'' system. By taking a cue from linear response theory we
relate the quantum fluctuation in the generator to the generalised
susceptibility. Relation between the open-path geometric phase, diagonal
elements of the quantum metric tensor and the force-force correlation function
is provided and the classical limit of the fluctuation-correlation theorem is
also discussed.


title:
Relationship between quantum decoherence times and solvation dynamics in
  condensed phase chemical systems

abstract:
  A relationship between the time scales of quantum coherence loss and
short-time solvent response for a solute/bath system is derived for a Gaussian
wave packet approximation for the bath. Decoherence and solvent response times
are shown to be directly proportional to each other, with the proportionality
coefficient given by the ratio of the thermal energy fluctuations to the
fluctuations in the system-bath coupling. The relationship allows the
prediction of decoherence times for condensed phase chemical systems from well
developed experimental methods.


title: Testing Bell's inequality using Aharonov-Casher effect

abstract:
  We propose the Aharonov-Casher (AC) effect for four entangled spin-half
particles carrying magnetic moments in the presence of impenetrable line
charge. The four particle state undergoes AC phase shift in two causually
disconnected region which can show up in the correlations between different
spin states of distant particles. This correlation can violate Bell's
inequality, thus displaying the non-locality for four particle entangled states
in an objective way. Also, we have suggested how to control the AC phase shift
locally at two distant locations to test Bell's inequality. We belive that
although the single particle AC effect may not be non-local but the entangled
state AC effect is a non-local one.


title: Sonoluminescence Unveiled ?

abstract:
  The widening phenomenology of Single Bubble Sonoluminescence (SBSL) is shown
to be in good agreement with a new approach to condensed matter, based on the
QED coherent interactions. Some remarkable properties of SBSL are shown to
emerge from the electromagnetic release of part of the latent heat of the
water's vapour-liquid phase transition occurring at the bubble surface after it
becomes supersonic.


title:
Quantum noise reduction in singly resonant sub/second harmonic
  generation

abstract:
  We study the quantum noise in the harmonic mode of a singly resonant
frequency doubler simultaneously driven in both modes. This simple extension of
the frequency doubler greatly improves its performance as a bright squeezed
light source. Specifically, for parameters corresponding to reported
experiments, 80 % of noise suppression is easily achieved, the phase of the
corresponding squeezed quadrature can be freely and easily chosen, and the
output power is nearly doubled.


title: A Design for a Quantum Time Machine

abstract: This paper has been retracted, for obvious reasons.


title: Metrical Quantization

abstract:
  Canonical quantization may be approached from several different starting
points. The usual approaches involve promotion of c-numbers to q-numbers, or
path integral constructs, each of which generally succeeds only in Cartesian
coordinates. All quantization schemes that lead to Hilbert space vectors and
Weyl operators---even those that eschew Cartesian coordinates---implicitly
contain a metric on a flat phase space. This feature is demonstrated by
studying the classical and quantum ``aggregations'', namely, the set of all
facts and properties resident in all classical and quantum theories,
respectively. Metrical quantization is an approach that elevates the flat phase
space metric inherent in any canonical quantization to the level of a
postulate. Far from being an unwanted structure, the flat phase space metric
carries essential physical information. It is shown how the metric, when
employed within a continuous-time regularization scheme, gives rise to an
unambiguous quantization procedure that automatically leads to a canonical
coherent state representation. Although attention in this paper is confined to
canonical quantization we note that alternative, nonflat metrics may also be
used, and they generally give rise to qualitatively different, noncanonical
quantization schemes.


title: Quantum strategies

abstract:
  We consider game theory from the perspective of quantum algorithms.
Strategies in classical game theory are either pure (deterministic) or mixed
(probabilistic). We introduce these basic ideas in the context of a simple
example, closely related to the traditional Matching Pennies game. While not
every two-person zero-sum finite game has an equilibrium in the set of pure
strategies, von Neumann showed that there is always an equilibrium at which
each player follows a mixed strategy. A mixed strategy deviating from the
equilibrium strategy cannot increase a player's expected payoff. We show,
however, that in our example a player who implements a quantum strategy can
increase his expected payoff, and explain the relation to efficient quantum
algorithms. We prove that in general a quantum strategy is always at least as
good as a classical one, and furthermore that when both players use quantum
strategies there need not be any equilibrium, but if both are allowed mixed
quantum strategies there must be.


title: Quantum Cloning in $d$ dimensions

abstract:
  The quantum state space $\cal S$ over a $d$-dimensional Hilbert space is
represented as a convex subset of a $D-1$-dimensional sphere $S_{D-1}\subset
{\bf{R}}^D$, where $D=d^2-1.$ Quantum tranformations (CP-maps) are then
associated with the affine transformations of ${\bf{R}}^D,$ and $N\mapsto M$
{\it cloners} induce polynomial mappings. In this geometrical setting it is
shown that an optimal cloner can be chosen covariant and induces a map between
reduced density matrices given by a simple contraction of the associated
$D$-dimensional Bloch vectors.


title: Consistency, Amplitudes and Probabilities in Quantum Theory

abstract:
  Quantum theory is formulated as the only consistent way to manipulate
probability amplitudes. The crucial ingredient is a consistency constraint: if
there are two different ways to compute an amplitude the two answers must
agree. This constraint is expressed in the form of functional equations the
solution of which leads to the usual sum and product rules for amplitudes. A
consequence is that the Schrodinger equation must be linear: non-linear
variants of quantum mechanics are inconsistent. The physical interpretation of
the theory is given in terms of a single natural rule. This rule, which does
not itself involve probabilities, is used to obtain a proof of Born's
statistical postulate. Thus, consistency leads to indeterminism.
  PACS: 03.65.Bz, 03.65.Ca.


title:
To Enjoy the Morning Flower in the Evening -- Where is the Subtlety of
  Quantum Mechanics?

abstract:
  Why does the $i=\sqrt{-1}$ appear essentially in the quantum mechanics? Why
are there operators and noncommutativity (the uncertainty relation) in the
quantum mechanics? Why are these two aspects closely related and indivisible?
In probing these problems, a new point of view is proposed tentatively.


title: Optimal quantum codes for preventing collective amplitude damping

abstract:
  Collective decoherence is possible if the departure between quantum bits is
smaller than the effective wave length of the noise field. Collectivity in the
decoherence helps us to devise more efficient quantum codes. We present a class
of optimal quantum codes for preventing collective amplitude damping to a
reservoir at zero temperature. It is shown that two qubits are enough to
protect one bit quantum information, and approximately $L+ 1/2 \log_2((\pi
L)/2)$ qubits are enough to protect $L$ qubit information when $L$ is large.
For preventing collective amplitude damping, these codes are much more
efficient than the previously-discovered quantum error correcting or avoiding
codes.


title: The Particle in the box: Intermode traces in the propagator

abstract:
  Characteristic structures such as canals and ridges --intermode traces--
emerge in the spacetime representation of the probability distribution of a
particle in a one-dimensional box. We show that the corresponding propagator
already contains these structures. We relate their visibility to the
factorization property of the initial wave packet.


title:
Quantum Information in Semiconductors: Noiseless Encoding in a
  Quantum-Dot Array

abstract:
  A potential implementation of quantum-computation schemes in
semiconductor-based structures is proposed. In particular, an array of quantum
dots is shown to be an ideal quantum register for a noiseless information
encoding. In addition to the suppression of phase-breaking processes in quantum
dots due to the well-known phonon bottleneck, we show that a proper quantum
encoding allows to realise a decoherence-free evolution on a time-scale long
compared to the femtosecond scale of modern ultrafast laser technology. This
result might open the way to the realization of semiconductor-based quantum
processors.


title: Field Oscillations in a Micromaser with Injected Atomic Coherence

abstract:
  The electric field in a lossless, regularly-pumped micromaser with injected
atomic coherence can undergo a period 2 oscillations in the steady state. The
field changes its value after a single atom passes through the micromaser
cavity, but returns to its original value after a second atom travels through.
We give a simple explanation for this phenomenon in terms of tangent and
cotangent states. We also examine the effect of cavity damping on this steady
state.