title:
Exactly solvable models of quantum mechanics including fluctuations in
  the framework of representation of the wave function by random process

abstract:
  The problem of quantum harmonic oscillator with "regular+random" square
frequency, subjected to "regular+random external force, is considered in
framework of representation of the wave function by complex-valued random
process. Average transition probabilities are calculated. Stochastic density
matrix method is developed, which is used for investigation of thermodinamical
characteristics of the system, such as entropy and average energy.


title: Photon localization and vacuum noise in optical measurements

abstract:
  Description of detection and emission in terms of the photon localization is
discussed. It is shown that the standard representation of plane waves of
photons should be revised to take into consideration the boundary conditions
caused by the presence of quantum emitters and detectors. In turn, the change
of the boundary conditions causes spatially inhomogeneous structure of the
electromagnetic vacuum which leads to the increase of the vacuum noise over the
level predicted in the frame of the model of plane photons.


title: Quantum Holonomies for Quantum Computing

abstract:
  Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum
information processing. In the HQC strategy information is encoded in
degenerate eigen-spaces of a parametric family of Hamiltonians. The
computational network of unitary quantum gates is realized by driving
adiabatically the Hamiltonian parameters along loops in a control manifold. By
properly designing such loops the non-trivial curvature of the underlying
bundle geometry gives rise to unitary transformations i.e., holonomies that
implement the desired unitary transformations. Conditions necessary for
universal QC are stated in terms of the curvature associated to the non-abelian
gauge potential (connection) over the control manifold. In view of their
geometrical nature the holonomic gates are robust against several kind of
perturbations and imperfections. This fact along with the adiabatic fashion in
which gates are performed makes in principle HQC an appealing way towards
universal fault-tolerant QC.


title: Nonlinear quantum evolution with maximal entropy production

abstract:
  We derive a well-behaved nonlinear extension of the non-relativistic
Liouville-von Neumann dynamics driven by maximal entropy production with
conservation of energy and probability. The pure state limit reduces to the
usual Schroedinger evolution, while mixtures evolve towards maximum entropy
equilibrium states with canonical-like probability distributions on energy
eigenstates. The linear, near-equilibrium limit is found to amount to an
essentially exponential relaxation to thermal equilibrium; a few elementary
examples are given. In addition, the modified dynamics is invariant under the
time-independent symmetry group of the hamiltonian, and also invariant under
the special Galilei group provided the conservation of total momentum is
accounted for as well. Similar extensions can be generated for, e.g.,
nonextensive systems better described by a Tsallis q-entropy.


title:
Generalization of the Peres criterion for local realism through
  nonextensive entropy

abstract:
  A bipartite spin-1/2 system having the probabilities $\frac{1+3x}{4}$ of
being in the Einstein-Podolsky-Rosen entangled state $|\Psi^-$$> \equiv
\frac{1}{\sqrt
2}(|$$\uparrow>_A|$$\downarrow>_B$$-|$$\downarrow>_A|$$\uparrow>_B)$ and
$\frac{3(1-x)}{4}$ of being orthogonal, is known to admit a local realistic
description if and only if $x<1/3$ (Peres criterion). We consider here a more
general case where the probabilities of being in the entangled states
$|\Phi^{\pm}$$> \equiv \frac{1}{\sqrt 2}(|$$\uparrow>_A|$$\uparrow>_B \pm
|$$\downarrow>_A|$$\downarrow>_B)$ and $|\Psi^{\pm}$$> \equiv \frac{1}{\sqrt
2}(|$$\uparrow>_A|$$\downarrow>_B \pm |$$\downarrow>_A|$$\uparrow>_B)$ (Bell
basis) are given respectively by $\frac{1-x}{4}$, $\frac{1-y}{4}$,
$\frac{1-z}{4}$ and $\frac{1+x+y+z}{4}$. Following Abe and Rajagopal, we use
the nonextensive entropic form $S_q \equiv \frac{1- Tr \rho^q}{q-1} (q \in
\cal{R}; $$S_1$$= -$ $Tr$ $ \rho \ln \rho)$ which has enabled a current
generalization of Boltzmann-Gibbs statistical mechanics, and determine the
entire region in the $(x,y,z)$ space where local realism is admissible. For
instance, in the vicinity of the EPR state, classical realism is possible if
and only if $x+y+z<1$, which recovers Peres' criterion when $x=y=z$. In the
vicinity of the other three states of the Bell basis, the situation is
identical. A critical-phenomenon-like scenario emerges. These results
illustrate the computational power of this new nonextensive-quantum-information
procedure.


title: Quantum Computing Using Electrons Floating on Liquid Helium

abstract:
  The system of electrons trapped in vacuum above the liquid helium surface
displays the highest mobilities known in condensed matter physics. We provide a
brief summary of the experimental and theoretical results obtained for this
system. We then show that a quasi-2D set of N > 10^8 electrons in vacuum
trapped in 1D hydrogenic levels above a micron-thick helium film can be used as
an easily manipulated strongly interacting set of quantum bits. Individual
electrons are laterally confined by micron sized metal pads below the helium.
Information is stored in the lowest hydrogenic levels. Using electric fields at
temperatures of 10 mK, changes in the wave function can be made in nanoseconds.
Wave function coherence times are .1 millisecond. The wave function is read out
using an inverted dc voltage which releases excited electrons from the surface,
or using SETs attached to the metal pads which control the electrons.


title: Raman Excited Spin Coherences in N-V Diamond

abstract:
  Raman excited spin coherences were experimentally observed in N-V diamond
color centers via nondegenerate four-wave mixing (NDFWM) and
electromagnetically induced transparency (EIT). The maximal absorption
suppression was found to be 17%, which corresponds to 70% of what is possible
given the random geometric orientation of the N-V center in diamond. In the
context of quantum computing in solids, this level of transparency represents
the efficient preparation of quantum bits (qubits), as well as ability to
perform arbitrary single qubit rotations.


title:
Numerical Experiments on The Capacity of Quantum Channel with Entangled
  Input States

abstract:
  The capacity of quantum channel with product input states was formulated by
the quantum coding theorem. However, whether entangled input states can enhance
the quantum channel is still open. It turns out that this problem is reduced to
aspecial case of the more general problem whether the capacity of product
quantum channel exhibits additivity. In the present study, we apply one of the
quantum Arimoto-Blahut type algorithms to the latter problem. The results
suggest that the additivity of product quantum channel capacity always holds
and that entangled input states cannot enhance the quantum channel capacity.


title:
Comment on "Conceptual Inadequacy of Shannon Information ..." by C.
  Brukner and A. Zeilinger

abstract:
  It is pointed out that the case for Shannon entropy and von Neumann entropy,
as measures of uncertainty in quantum mechanics, is not as bleak as suggested
in quant-ph/0006087. The main argument of the latter is based on one particular
interpretation of Shannon's H-function (related to consecutive measurements),
and is shown explicitly to fail for other physical interpretations. Further, it
is shown that Shannon and von Neumann entropies have in fact a common
fundamental significance, connected to the existence of a unique geometric
measure of uncertainty for classical and quantum ensembles. Some new properties
of the ``total information'' measure proposed in quant-ph/0006087 are also
given.


title: Interference of macroscopic superpositions

abstract:
  We propose a simple experimental procedure based on the Elitzur-Vaidman
scheme to test the persistence of macroscopic superpositions. We conjecture
that its implementation will reveal the persistence of superpositions of
macroscopic objects in the absence of a direct act of observation.


title: Relativistic Aharonov-Casher Phase in Spin One

abstract:
  The Aharonov-Casher (AC) phase is calculated in relativistic wave equations
of spin one. The AC phase has previously been calculated from the Dirac-Pauli
equation using a gauge-like technique \cite{MK1,MK2}. In the spin-one case, we
use Kemmer theory (a Dirac-like particle theory) to calculate the phase in a
similar manner. However the vector formalism, the Proca theory, is more widely
known and used. In the presence of an electromagnetic field, the two theories
are `equivalent' and may be transformed into one another. We adapt these
transformations to show that the Kemmer theory results apply to the Proca
theory. Then we calculate the Aharonov-Casher phase for spin-one particles
directly in the Proca formalism.


title:
A realistic interpretation of the density matrix II: The
  non-relativistic case

abstract:
  The interpretation proposed in quant-ph/9812011 is extended to the general
case of a non-relativistic particle moving in an arbitrary external potential.
It is shown that, even in this general case, "particle" solutions exist which
do not spread out with time, and remain well localized around their center of
mass; it is postulated that these are the only solutions which represent
individual physical particles. As a consequence two basic principles of
standard QM, namely the superposition principle and the wave-function collapse,
are shown to have no ontological meaning. Three simple applications of our
approach are then examined: the free particle, the linear harmonic oscillator
and the delta barrier potential; the corresponding "particle" solutions are
explicitly shown. Finally, it is argued that the persisting confusion about the
meaning of the wave-function (does it represent an individual particle or a
statistical ensemble?) calls for a non-linear extension of the Schroedinger
equation.


title: Quantum strategies of quantum measurement

abstract:
  In classical Monty Hall problem, one player can always win with probability
2/3. We generalize the problem to the quantum domain and show that a fair
two-party zero-sum game can be carried out if the other player is permitted to
adopt quantum measurement strategy.


title: Quantum no-deleting principle and some of its implications

abstract:
  Unmeasureability of a quantum state has important consequences in practical
implementation of quantum computers. Like copying, deleting of an unknown state
from among several copies is prohibited. This is called no-deletion prinicple.
Here, we present a no deleting principle for qudits. We obtain a bound on
$N$-to-$M$ deleting and show that the quality of deletion drops exponentially
with the number of copies to be deleted. In addition, we investigate
conditional, state-dependent and approximate quantum deleting of unknown
states. We prove that unitarity does not allow us to delete copies from an
alphabet of two non-orthogonal states exactly. Further, we show that
no-deleting principle is consistent with no-signalling.


title:
The Universality of the Quantum Fourier Transform in Forming the Basis
  of Quantum Computing Algorithms

abstract:
  The quantum Fourier transform (QFT) is a powerful tool in quantum computing.
The main ingredients of QFT are formed by the Walsh-Hadamard transform H and
phase shifts P(.), both of which are 2x2 unitary matrices as operators on the
two-dimensional 1-qubit space. In this paper, we show that H and P(.) suffice
to generate the unitary group U(2) and, consequently, through controlled-U
operations and their concatenations, the entire unitary group U(2^n) on
n-qubits can be generated. Since any quantum computing algorithm in an n-qubit
quantum computer is based on operations by matrices in U(2^n), in this sense we
have the universality of the QFT.


title:
Generalization of Grover's Algorithm to Multiobject Search in Quantum
  Computing, Part I: Continuous Time and Discrete Time

abstract:
  L. K. Grover's search algorithm in quantum computing gives an optimal,
quadratic speedup in the search for a single object in a large unsorted
database. In this paper, we generalize Grover's algorithm in a Hilbert-space
framework for both continuous and discrete time cases that isolates its
geometrical essence to the case where more than one object satisfies the search
criterion.


title:
Generalization of Grover's Algorithm to Multiobject Search in Quantum
  Computing, Part II: General Unitary Transformations

abstract:
  There are major advantages in a newer version of Grover's quantum algorithm
utilizing a general unitary transformation in the search of a single object in
a large unsorted database. In this paper, we generalize this algorithm to
multiobject search. We show the techniques to achieve the reduction of the
problem to one on an invariant subspace of dimension just equal to two.


title: Manipulation of Cold Atomic Collisions by Cavity QED Effects

abstract:
  We show how the dynamics of collisions between cold atoms can be manipulated
by a modification of spontaneous emission times. This is achieved by placing
the atomic sample in a resonant optical cavity. Spontaneous emission is
enhanced by a combination of multiparticle entanglement together with a higher
density of modes of the modified vacuum field, in a situation akin to
superradiance. A specific situation is considered and we show that this effect
can be experimentally observed as a large suppression in trap-loss rates.


title:
A unified approach for exactly solvable potentials in quantum mechanics
  using shift operators

abstract:
  We present a unified approach for solving and classifying exactly solvable
potentials. Our unified approach encompasses many well-known exactly solvable
potentials. Moreover, the new approach can be used to search systematically for
a new class of solvable potentials.


title: Feedback-stabilization of an arbitrary pure state of a two-level atom

abstract:
  Unit-efficiency homodyne detection of the resonance fluorescence of a
two-level atom collapses the quantum state of the atom to a stochastically
moving point on the Bloch sphere. Recently,Hofmann, Mahler, and Hess [Phys.
Rev. A {\bf 57}, 4877 (1998)] showed that by making part of the coherent
driving proportional to the homodyne photocurrent can stabilize the state to
any point on the bottom half of the sphere. Here we reanalyze their proposal
using the technique of stochastic master equations, allowing their results to
be generalized in two ways. First, we show that any point on the upper or lower
half, but not the equator, of the sphere may be stabilized. Second, we consider
non-unit-efficiency detection, and quantify the effectiveness of the feedback
by calculating the maximal purity obtainable in any particular direction in
Bloch space.


title: Full mechanical characterization of a cold damped mirror

abstract:
  We describe an experiment in which we have used a cold damping feedback
mechanism to reduce the thermal noise of a mirror around its mechanical
resonance frequency. The monitoring of the brownian motion of the mirror allows
to apply an additional viscous force without any thermal fluctuations
associated. This scheme has been experimentally implemented with the radiation
pressure of an intensity-modulated laser beam. Large noise reductions, up to 30
dB, have been obtained. We have also checked the mechanical response of the
cold damped mirror, and monitored its transient evolution between the cooled
regime and the room temperature equilibrium. A simple theoretical model allows
to fully explain the experimental results. A possible application to the active
cooling of the violin modes in a gravitational-wave interferometer is
discussed.


title:
The Classical Limit of Quantum Mechanics and the Fejer Sum of the
  Fourier Series Expansion of a Classical Quantity

abstract:
  In quantum mechanics, the expectation value of a quantity on a quantum state,
provided that the state itself gives in the classical limit a motion of a
particle in a definite path, in classical limit goes over to Fourier series
form of the classical quantity. In contrast to this widely accepted point of
view, a rigorous calculation shows that the expectation value on such a state
in classical limit exactly gives the Fej\'{e}r's arithmetic mean of the partial
sums of the Fourier series.


title: Distillation of vacuum entanglement to EPR pairs

abstract:
  It is shown that by means of local interactions between a quantized
relativistic field and a pair of non-entangled atoms, entanglement can be
extracted from the vacuum and delivered to the atoms. The resulting mixed state
of the atoms can be further distilled to EPR pairs. Therefore, in principle,
teleportation and other entanglement assisted quantum communication tasks can
rely on the vacuum alone as a resource for entanglement.


title: Reply to `No Contradictions between Bohmian and quantum mechanics'

abstract:
  Marchildon's claim (quant-ph/0007068) regarding Ghose's papers
(quant-ph/0001024 and 0003037) is shown to be erroneous.


title:
A simple proof of the unconditional security of relativistic quantum
  cryptography

abstract:
  A simple proof of the unconditional security of a relativistic quantum
cryptosystem based on orthogonal states is proposed. Restrictions imposed by
special relativity allow to substantially simplify the proof compared with the
non-relativistic cryptosystems involving non-orthogonal states. Important for
the proposed protocol is the spatio-temporal structure of the quantum states
which is actually ignored in the non-relativistic protocols employing only the
structure of the state space of the information carriers. As a consequence, the
simplification arises because of the inefficiency of collective measurements
which constitute the major problem in the non-relativistic case.


title:
Template-stripped gold surfaces with 0.4 nm rms roughness suitable for
  force measurements. Application to the Casimir force in the 20-100 nm range

abstract:
  Using a template-stripping method, macroscopic gold surfaces with
root-mean-square (rms) roughness less than 0.4 nm have been prepared, making
them useful for studies of surface interactions in the nanometer range. The
utility of such substrates is demonstrated by measurements of the Casimir force
at surface separations between 20 and 100 nm, resulting in good agreement with
theory. The significance and quantification of this agreement is addressed, as
well as some methodological aspects regarding the measurement of the Casimir
force with high accuracy.


title:
Frequency tuning of the whispering gallery modes of silica microspheres
  for CQED and spectroscopy

abstract:
  We have tuned the whispering gallery modes of a fused silica microresonator
over nearly 1 nm at 800 nm, i.e. over 0.5 FSR or 10^6 linewidths of the
resonator. This has been achieved by a new method based on the stretching of a
two-stem microsphere. The devices described below will permit new Cavity-QED
experiments with this high-Q optical resonator when it is desirable to optimize
its coupling to emitters with given transition frequencies. The tuning
capability demonstrated here is compatible with both UHV and low temperature
operation, which should be useful for future experiments with laser cooled
atoms or single quantum dots.


title: Universal Manipulation of a Single Qubit

abstract:
  We find the optimal universal way of manipulating a single qubit,
|psi(theta,phi)>, such that (theta,phi)->(theta-k,phi-l). Such optimal
transformations fall into two classes. For 0 =< k =< pi/2 the optimal map is
the identity and the fidelity varies monotonically from 1 (for k=0) to 1/2 (for
k=pi/2). For pi/2 =< k =< pi the optimal map is the universal-NOT gate and the
fidelity varies monotonically from 1/2 (for k=pi/2) to 2/3 (for k=pi). The
fidelity 2/3 is equal to the fidelity of measurement. It is therefore rather
surprising that for some values of k the fidelity is lower than 2/3.


title:
Quantum Interference Mechanism of Cooperative Optical Phenomena in
  Extended Media

abstract:
  In the quantum process of stimulated Raman scattering (SRS), a laser photon
propagating in a resonance medium undergoes multifold conversions into a Stokes
photon and back. The nontrivial ``cooperative'' behavior of the Stokes
component of light transmitted through the medium is proven to be completely
determined by the interference of scattering amplitudes in different
sub-channels of the Stokes channel, which obviously combines all the
sub-channels with an odd number of photon conversions. The theory of
superfluorescence is then derived as the limiting case of the SRS theory.


title:
A Note on Quantum Key Channel Efficiency and Security using Correlated
  Photon Beam Transmitters

abstract:
  Quantum-correlated photon sources provide a means of suppressing multiple
photon emission and thus improving the security and efficiency of quasi
single-photon quantum key distribution systems. We present illustrative
photon-counting statistics for a Poissonian source conditioned by photon number
measurements on a fully correlated twin beam with a non-ideal photon counter.
We show that high photon counting efficiency is needed to obtain significant
improvement in channel efficiency (bits per symbol) and/or security (in the
form of reduced Shannon entropy leakage) over a single beam source.


title: Early times in tunneling

abstract:
  Exact analytical solutions of the time-dependent Schr\"odinger equation with
the initial condition of an incident cutoff wave are used to investigate the
traversal time for tunneling. The probability density starts from a vanishing
value along the tunneling and transmitted regions of the potential. At the
barrier width it exhibits, at early times, a distribution of traversal times
that typically has a peak $\tau_p$ and a width $\Delta \tau$. Numerical results
for other tunneling times, as the phase-delay time, fall within $\Delta \tau$.
The B\"uttiker traversal time is the closest to $\tau_p$. Our results resemble
calculations based on Feynman paths if its noisy behaviour is ignored.


title: On the Problem of Programming Quantum Computers

abstract:
  We study effects of the physical realization of quantum computers on their
logical operation. Through simulation of physical models of quantum computer
hardware, we analyse the difficulties that are encountered in programming
physical implementations of quantum computers. We discuss the origin of the
instabilities of quantum algorithms and explore physical mechanisms to enlarge
the region(s) of stable operation.


title: Monge Metric on the Sphere and Geometry of Quantum States

abstract:
  Topological and geometrical properties of the set of mixed quantum states in
the N-dimensional Hilbert space are analysed. Assuming that the corresponding
classical dynamics takes place on the sphere we use the vector SU(2) coherent
states and the generalised Husimi distributions to define the Monge distance
between arbitrary two density matrices. The Monge metric has a simple
semiclassical interpretation and induces a non-trivial geometry. Among all pure
states the distance from the maximally mixed state \rho_*, proportional to the
identity matrix, admits the largest value for the coherent states, while the
delocalized 'chaotic' states are close to \rho_*. This contrasts the geometries
induced by the standard (trace, Hilbert-Schmidt or Bures) metrics, where the
distance from \rho_* is the same for all pure states. We discuss possible
physical consequences including unitary time evolution and the process of
decoherence. We introduce also a simplified Monge metric, defined in the space
of pure quantum states, and more suitable for numerical computation.


title: A logical description for perfect measurements

abstract:
  We reconsider the description for property transitions due to perfect
measurements, viewing them as a special case of general transitions that are
due to an externally imposed change. We propose a corresponding syntax
involving operational quantum logic and a fragment of non-commutative linear
logic.


title: Speed-up and entanglement in quantum searching

abstract:
  We investigate the issue of speed-up and the necessity of entanglement in
Grover's quantum search algorithm. We find that in a pure state implementation
of Grover's algorithm entanglement is present even though the initial and
target states are product states. In pseudo-pure state implementations, the
separability of the states involved defines an entanglement boundary in terms
of a bound on the purity parameter. Using this bound we investigate the
necessity of entanglement in quantum searching for these pseudo-pure state
implementations. If every active molecule involved in the ensemble is `charged
for' then in existing machines speed-up without entanglement is not possible.


title: Operational quantum logic: An overview

abstract:
  The term quantum logic has different connotations for different people,
having been considered as everything from a metaphysical attack on classical
reasoning to an exercise in abstract algebra. Our aim here is to give a uniform
presentation of what we call operational quantum logic, highlighting both its
concrete physical origins and its purely mathematical structure. To orient
readers new to this subject, we shall recount some of the historical
development of quantum logic, attempting to show how the physical and
mathematical sides of the subject have influenced and enriched one another.


title: Operational resolutions and state transitions in a categorical setting

abstract:
  We define a category with as objects operational resolutions and with as
morphisms - not necessarily deterministic - state transitions. We study
connections with closure spaces and join-complete lattices and sketch physical
applications related to evolution and compoundness. An appendix with
preliminaries on quantaloids is included.

categories: quant-ph math-ph math.CT math.DS math.MP


title: Operational Galois adjunctions

abstract:
  We present a detailed synthetic overview of the utilisation of categorical
techniques in the study of order structures together with their applications in
operational quantum theory. First, after reviewing the notion of residuation
and its implementation at the level of quantaloids we consider some standard
universal constructions and the extension of adjunctions to weak morphisms.
Second, we present the categorical formulation of closure operators and
introduce a hierarchy of contextual enrichments of the quantaloid of complete
join lattices. Third, we briefly survey physical state-property duality and the
categorical analysis of derived notions such as causal assignment and the
propagation of properties.


title:
Generalized quantum XOR-gate for quantum teleportation and state
  purification in arbitrary dimensional Hilbert spaces

abstract:
  A generalization of the quantum XOR-gate is presented which operates in
arbitrary dimensional Hilbert spaces. Together with one-particle Fourier
transforms this gate is capable of performing a variety of tasks which are
important for quantum information processing in arbitrary dimensional Hilbert
spaces. Among these tasks are the preparation of Bell states, quantum
teleportation and quantum state purification. A physical realization of this
generalized XOR-gate is proposed which is based on non-linear optical elements.


title:
Inversionless gain in a three-level system driven by a strong field and
  collisions

abstract:
  Inversionless gain in a three-level system driven by a strong external field
and by collisions with a buffer gas is investigated. The mechanism of
populating of the upper laser level contributed by the collision transfer as
well as by relaxation caused by a buffer gas is discussed in detail. Explicit
formulae for analysis of optimal conditions are derived. The mechanism
developed here for the incoherent pump could be generalized to other systems.


title: On quantum coding for ensembles of mixed states

abstract:
  We consider the problem of optimal asymptotically faithful compression for
ensembles of mixed quantum states. Although the optimal rate is unknown, we
prove upper and lower bounds and describe a series of illustrative examples of
compression of mixed states. We also discuss a classical analogue of the
problem.


title: Time of arrival in Classical and Quantum Mechanics

abstract:
  The time of arrival at an arbitrary position in configuration space can be
given as a function of the phase space variables for the Liouville integrable
systems of classical mechanics, but only for them. We review the Jacobi-Lie
transformation that explicitly implements this function of positions and
momenta. We then discuss the recently developed quantum formalism for the time
of arrival. We first analyze the case of free particles in one and three space
dimensions. Then, we apply the quantum version of the Jacobi-Lie transformation
to work out the time of arrival operator in the presence of interactions. We
discuss the formalism and its interpretation. We finish by disclosing the
presence (absence) of "instantaneous" tunneling for thin (thick) barriers.


title:
A sequence of unsharp measurements enabling a real time visualization of
  a quantum oscillation

abstract:
  The normalized state $\ket{\psi(t)}=c_1(t)\ket{1}+c_2(t)\ket{2}$ of a single
two-level system performs oscillations under the influence of a resonant
driving field. It is assumed that only one realization of this process is
available. We show that it is possible to approximately visualize in real time
the evolution of the system as far as it is given by $|c_2(t)|^2$. For this
purpose we use a sequence of particular unsharp measurements separated in time.
They are specified within the theory of generalized measurements in which
observables are represented by positive operator valued measures (POVM). A
realization of the unsharp measurements may be obtained by coupling the
two-level system to a meter and performing the usual projection measurements on
the meter only.


title: Error correction for mutually interacting qubits

abstract:
  For a simple model of mutually interacting qubits it is shown how the errors
induced by mutual interactions can be eliminated using concatenated coding. The
model is solved exactly for arbitrary interaction strength, for two well-known
codes, one and two levels deep: this allows one to see under which
circumstances error amplitudes add coherently or incoherently. For deeper
concatenation, approximate results are derived which make it possible to
calculate an approximate ``threshold'' value for the product of interaction
strength and free evolution time, below which the failure probability for an
encoded qubit decreases exponentially with the depth of the encoding. The
results suggest that concatenated coding could fully handle the errors arising
from mutual interactions, at no extra cost, in terms of resources needed, from
what would be required to deal with random environmental errors.


title:
Experimental realization of optimal detection strategies for
  overcomplete states

abstract:
  We present the results of generalized measurements of optical polarization
designed to provide one of three or four distinct outcomes. This has allowed us
to discriminate between nonorthogonal polarization states with an error
probability that is close to the minimum allowed by quantum theory. Employing
these optimal detection strategies on sets of three (trine) or four (tetrad)
equiprobable symmetric nonorthogonal polarization states, we obtain a mutual
information that exceeds the maximum value attainable using conventional (von
Neumann) polarization measurements.


title: Coherent control using adaptive learning algorithms

abstract:
  We have constructed an automated learning apparatus to control quantum
systems. By directing intense shaped ultrafast laser pulses into a variety of
samples and using a measurement of the system as a feedback signal, we are able
to reshape the laser pulses to direct the system into a desired state. The
feedback signal is the input to an adaptive learning algorithm. This algorithm
programs a computer-controlled, acousto-optic modulator pulse shaper. The
learning algorithm generates new shaped laser pulses based on the success of
previous pulses in achieving a predetermined goal.


title:
Are Rindler Quanta Real? Inequivalent particle concepts in quantum field
  theory

abstract:
  Philosophical reflection on quantum field theory has tended to focus on how
it revises our conception of what a particle is. However, there has been
relatively little discussion of the threat to the "reality" of particles posed
by the possibility of inequivalent quantizations of a classical field theory,
i.e., inequivalent representations of the algebra of observables of the field
in terms of operators on a Hilbert space. The threat is that each
representation embodies its own distinctive conception of what a particle is,
and how a "particle" will respond to a suitably operated detector. Our main
goal is to clarify the subtle relationship between inequivalent representations
of a field theory and their associated particle concepts. We also have a
particular interest in the Minkowski versus Rindler quantizations of a free
Boson field, because they respectively entail two radically different
descriptions of the particle content of the field in the very same region of
spacetime. We shall defend the idea that these representations provide
complementary descriptions of the same state of the field against the claim
that they embody completely incommensurable theories of the field.


title: Algebraic measures of entanglement

abstract:
  We study the rank of a general tensor $u$ in a tensor product $H_1\ot...\ot
H_k$. The rank of $u$ is the minimal number $p$ of pure states $v_1,...,v_p$
such that $u$ is a linear combination of the $v_j$'s. This rank is an algebraic
measure of the degree of entanglement of $u$. Motivated by quantum computation,
we completely describe the rank of an arbitrary tensor in $(\C^2)^{\ot 3}$ and
give normal forms for tensor states up to local unitary transformations. We
also obtain partial results for $(\C^2)^{\ot 4}$; in particular, we show that
the maximal rank of a tensor in $(\C^2)^{\ot 4}$ is equal to 4.


title: Quantum copying can increase the practically available information

abstract:
  While it is known that copying a quantum system does not increase the amount
of information obtainable about the originals, it may increase the amount
available in practice, when one is restricted to imperfect measurements. We
present a detection scheme which using imperfect detectors, and possibly noisy
quantum copying machines (that entangle the copies), allows one to extract more
information from an incoming signal, than with the imperfect detectors alone.
The case of single-photon detection with noisy, inefficient detectors and
copiers (single controlled-NOT gates in this case) is investigated in detail.
The improvement in distinguishability between a photon and vacuum is found to
occur for a wide range of parameters, and to be quite robust to random noise.
The properties that a quantum copying device must have to be useful in this
scheme are investigated.


title: Addition on a Quantum Computer

abstract:
  A new method for computing sums on a quantum computer is introduced. This
technique uses the quantum Fourier transform and reduces the number of qubits
necessary for addition by removing the need for temporary carry bits. This
approach also allows the addition of a classical number to a quantum
superposition without encoding the classical number in the quantum register.
This method also allows for massive parallelization in its execution.


title: Resonance Offset Tailored Pulses for NMR Quantum Computation

abstract:
  We describe novel composite pulse sequences which act as general rotors and
thus are suitable for nuclear magnetic resonance (NMR) quantum computation. The
Resonance Offset Tailoring To Enhance Nutations (ROTTEN) approach permits
perfect compensation of off-resonance errors at two selected frequencies placed
symmetrically around the frequency of the RF source.


title:
Coherence-controlled transparency and far-from-degenerate parametric
  gain in a strongly-absorbing Doppler-broadened medium

abstract:
  An inversionless gain of anti-Stokes radiation above the oscillation
threshold in an optically-dense far-from-degenerate double-Lambda
Doppler-broadened medium accompanied by Stokes gain is predicted. The outcomes
are illustrated with numerical simulations applied to sodium dimer vapor.
Optical switching from absorption to gain via transparency controlled by a
small variation of the medium and of the driving radiation parameters which are
at a level less than one photon per molecule is shown. Related video/audio
clips see in: A.K. Popov, S.A. Myslivets, and T.F. George, Optics Express Vol.
7, No 3, 148 (2000)(http://epubs.osa.org/oearchive/source/22947.htm) or
download: http://kirensky.krasn.ru/popov/opa/opa.htm


title:
The Backwards-Time Interpretation of Quantum Mechanics - Revisited With
  Experiment

abstract:
  The classic paper of Clauser et al proved that Bell's Theorem experiments
rule out all theories of physics which assume locality, time-forwards causality
and the existence of an objective real world. The Backwards-Time Interpretation
(BTI) tries to recover realism and locality by permitting backwards time
causality. BTI should permit dramatic simplification of the assumptions or
axioms of physics, but requires new work in fundamental mathematics, such as
new tools for the "closure of turbulence," the derivation of statistics
generated by ODE or PDE.
  Recent events like the Delayed Choice Quantum Eraser experiment of Kim, Shih
et al have increased mainstream interest in the possibility of backwards
causality. The Backwards Time Quantum Teleportation (BTQT) experiment will take
this further. True backwards time communication channels (BTCC) are absolutely
impossible in most formulations of quantum theory but only almost impossible in
the BTI formulation. This paper discusses BTQT, the issue of backwards
causality in different versions of quantum theory and new mathematical
developments. It defines a new object, the "entropy matrix," which leads to
closure of turbulence for PDE systems. Predictions of a common toy field theory
(real phi-3 QFT) are reproduced by the corresponding PDE model combined with a
new model of the micro/macro interface (2M/M).


title: Quantum cryptography using balanced homodyne detection

abstract:
  We report an experimental quantum key distribution that utilizes balanced
homodyne detection, instead of photon counting, to detect weak pulses of
coherent light. Although our scheme inherently has a finite error rate, it
allows high-efficiency detection and quantum state measurement of the
transmitted light using only conventional devices at room temperature. When the
average photon number was 0.1, an error rate of 0.08 and "effective" quantum
efficiency of 0.76 were obtained.


title: Transfer of quantum states using finite resources

abstract:
  We discuss the problem of transfering a qubit from Alice to Bob using a noisy
quantum channel and only finite resources. As the basic protocol for the
transfer we apply quantum teleportation. It turns out that for a certain
quality of the channel direct teleportation combined with qubit purification is
superior to entanglement purification of the channel. If, however, the quality
of the channel is rather low one should simply apply an estimation-preparation
scheme.


title: Long distance entanglement based quantum key distribution

abstract:
  A detailled analysis of quantum key distribution employing entangled states
is presented. We tested a system based on photon pairs entangled in energy-time
optimized for long distance transmission. It is based on a Franson type set-up
for monitoring quantum correlations, and uses a protocol analogous to BB84.
Passive state preparation is implemented by polarization multiplexing in the
interferometers. We distributed a sifted key of 0.4 Mbits at a raw rate of 134
Hz and with an error rate of 8.6% over a distance of 8.5 kilometers. We discuss
thoroughly the noise sources and practical difficulties associated with
entangled states systems. Finally the level of security offered by this system
is assessed and compared with that of faint laser pulses systems.


title: Encoding a qubit in an oscillator

abstract:
  Quantum error-correcting codes are constructed that embed a
finite-dimensional code space in the infinite-dimensional Hilbert space of a
system described by continuous quantum variables. These codes exploit the
noncommutative geometry of phase space to protect against errors that shift the
values of the canonical variables q and p. In the setting of quantum optics,
fault-tolerant universal quantum computation can be executed on the protected
code subspace using linear optical operations, squeezing, homodyne detection,
and photon counting; however, nonlinear mode coupling is required for the
preparation of the encoded states. Finite-dimensional versions of these codes
can be constructed that protect encoded quantum information against shifts in
the amplitude or phase of a d-state system. Continuous-variable codes can be
invoked to establish lower bounds on the quantum capacity of Gaussian quantum
channels.


title: Dynamics, Thermodynamics, and Time-Asymmetry

abstract:
064
There are two
schools, or lines of thought, that try to unify the apparently divergent laws
of dynamics and thermodynamics and to explain the observed time-asymmetry of
the universe, and most of its sub-systems, in spite of the fact that these
systems are driven by time-symmetric evolution equations. They will be called
the coarse-graining and the fine-graining schools (even if these names describe
only a part of their philosophy). Coarse-graining school obtains time-asymmetry
via a projection of the state space on a space of ''relevant'' states. The
corresponding projection of the primitive reversible evolution laws yields
effective irreversible evolution laws for the relevant states. Fine-graining
always use the same primitive reversible evolution laws. But these laws (in
adequate extensions of the usual spaces where these laws are formulated) have a
set of solutions $S$ that can be decompose in two subsets $S_{+\text{}}$ and
$S_{-}$ of time asymmetric solutions. Choosing one of these two sets, as the
arena to formulate the theory, time asymmetry is established. The aim of these
lectures is to explain, in the simplest- self-contained, unbiased, and, honest
way, the main characteristics of both schools and to point out the advantages
and disadvantages of both formalism, in such a way that, the polemic between
the schools, turns out to be explicit and organized in the mind of the reader
(who will be considered the supreme judge to give the final verdict).
  064
Some
cosmological features of the theory will be also considered, mainly the problem
of the low entropy initial state of the universe


title: The Time-Asymmetry and the Entropy Gap

abstract:
  The universe time-asymmetry is essentially produced by its low-entropy
unstable initial state. Using quanlitative arguments, Paul Davies has
demonstrated that the universe expansion may diminish the entropy gap,
therefore explaining its low-entropy state, with respect to the maximal
possible entropy at any time. This idea is implemented in a qualitative
way\thinspace in a simple homogeneous model. Some rough coincidence with
observational data are found


title: Renormalization and Short Distance Singular Structure

abstract:
  The relation between renormalization and short distance singular divergencies
in quantum field theory is studied. As a consequence a finite theory is
presented. It is shown that these divergencies are originated by the
multiplication of distributions (and worse defined mathematical objects). Some
of them are eliminated defining a multiplication based in dimensional
regularization while others disappear considering the states as functionals
over the observables space. Non renormalizable theories turn to be finite, but
anyhow they are endowed with infinite arbitrary constants.


title: Quantum authentication using entangled state

abstract:
  A scheme of quantum authentication is presented. Two parties share
Einstein-Podolsky-Rosen (EPR) pairs previously as the authentication key which
servers as encoder and decoder. The authentication is accomplished with local
controlled-NOT operations and unitary rotations. It is shown that our scheme is
secure even in the presence of an eavesdropper who has complete control over
both classical and quantum channels. Another character of this protocol is that
the EPR sources are reusable. The robustness of this protocol is also
discussed.


title:
Observation of power-law scaling for phase transitions in linear trapped
  ion crystals

abstract:
  We report an experimental confirmation of the power-law relationship between
the critical anisotropy parameter and ion number for the linear-to-zigzag phase
transition in an ionic crystal. Our experiment uses laser cooled calcium ions
confined in a linear radio-frequency trap. Measurements for up to 10 ions are
in good agreement with theoretical and numeric predictions. Implications on an
upper limit to the size of data registers in ion trap quantum computers are
discussed.


title: Secure quantum key distribution using squeezed states

abstract:
  We prove the security of a quantum key distribution scheme based on
transmission of squeezed quantum states of a harmonic oscillator. Our proof
employs quantum error-correcting codes that encode a finite-dimensional quantum
system in the infinite-dimensional Hilbert space of an oscillator, and protect
against errors that shift the canonical variables p and q. If the noise in the
quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor
e^r=1.34) is sufficient in principle to ensure the security of a protocol that
is suitably enhanced by classical error correction and privacy amplification.
Secure key distribution can be achieved over distances comparable to the
attenuation length of the quantum channel.


title: A semidefinite program for distillable entanglement

abstract:
  We show that the maximum fidelity obtained by a p.p.t. distillation protocol
is given by the solution to a certain semidefinite program. This gives a number
of new lower and upper bounds on p.p.t. distillable entanglement (and thus new
upper bounds on 2-locally distillable entanglement). In the presence of
symmetry, the semidefinite program simplifies considerably, becoming a linear
program in the case of isotropic and Werner states. Using these techniques, we
determine the p.p.t. distillable entanglement of asymmetric Werner states and
``maximally correlated'' states. We conclude with a discussion of possible
applications of semidefinite programming to quantum codes and 1-local
distillation.


title: New Lower Bound on Fermion Binding Energies

abstract:
  We derive a new lower bound for the ground state energy $E^{\rm F}(N,S)$ of N
fermions with total spin S in terms of binding energies $E^{\rm F}(N-1,S \pm
1/2)$ of (N-1) fermions. Numerical examples are provided for some simple
short-range or confining potentials.


title: Correlated Errors in Quantum Error Corrections

abstract:
  We show that errors are not generated correlatedly provided that quantum bits
do not directly interact with (or couple to) each other. Generally, this
no-qubits-interaction condition is assumed except for the case where two-qubit
gate operation is being performed. In particular, the no-qubits-interaction
condition is satisfied in the collective decoherence models. Thus, errors are
not correlated in the collective decoherence. Consequently, we can say that
current quantum error correcting codes which correct single-qubit-errors will
work in most cases including the collective decoherence.


title: Efficient Schemes for Reducing Imperfect Collective Decoherences

abstract:
  We propose schemes that are efficient when each pair of qubits undergoes some
imperfect collective decoherence with different baths. In the proposed scheme,
each pair of qubits is first encoded in a decoherence-free subspace composed of
two qubits. Leakage out of the encoding space generated by the imperfection is
reduced by the quantum Zeno effect. Phase errors in the encoded bits generated
by the imperfection are reduced by concatenation of the decoherence-free
subspace with either a three-qubit quantum error correcting code that corrects
only phase errors or a two-qubit quantum error detecting code that detects only
phase errors, connected with the quantum Zeno effect again.


title:
Private entanglement over arbitrary distances, even using noisy
  apparatus

abstract:
  We give a security proof of quantum cryptography based entirely on
entanglement purification. Our proof applies to all possible attacks
(individual and coherent). It implies the security of cryptographic keys
distributed with the help of entanglement-based quantum repeaters. We prove the
security of the obtained quantum channel which may not only be used for quantum
key distribution, but also for secure, albeit noisy, transmission of quantum
information.


title:
Continuous-time histories: observables, probabilities, phase space
  structure and the classical limit

abstract:
  In this paper we elaborate on the structure of the continuous-time histories
description of quantum theory, which stems from the consistent histories
scheme. In particular, we examine the construction of history Hilbert space,
the identification of history observables and the form of the decoherence
functional (the object that contains the probability information). It is shown
how the latter is equivalent to the closed-time-path (CTP) generating
functional. We also study the phase space structure of the theory first through
the construction of general representations of the history group (the analogue
of the Weyl group) and the implementation of a histories Wigner-Weyl transform.
The latter enables us to write quantum theory solely in terms of phase space
quantities. These results enable the implementation of an algorithm for
identifying the classical (stochastic) limit of a general quantum system.


title: Generation of eigenstates using the phase-estimation algorithm

abstract:
  The phase estimation algorithm is so named because it allows the estimation
of the eigenvalues associated with an operator. However it has been proposed
that the algorithm can also be used to generate eigenstates. Here we extend
this proposal for small quantum systems, identifying the conditions under which
the phase estimation algorithm can successfully generate eigenstates. We then
propose an implementation scheme based on an ion trap quantum computer. This
scheme allows us to illustrate two simple examples, one in which the algorithm
effectively generates eigenstates, and one in which it does not.


title: Structural Characterization of Compoundness

abstract:
  We recover the rays in the tensor product of Hilbert spaces within a larger
class of so called `states of compoundness', structured as a complete lattice
with the `state of separation' as its top element. At the base of the
construction lies the assumption that the cause of actuality of a property of
one of the (as individual considered) entities in the compound system can be
actuality of a property of the other one.


title: Product Bases in Quantum Information Theory

abstract:
  We review the role of product bases in quantum information theory. We prove
two conjectures which were made in DiVincenzo et al., quant-ph/9908070, namely
the existence of two sets of bipartite unextendible product bases, in arbitrary
dimensions, which are based on a tile construction. We pose some questions
related to complete product bases.


title: Approximation Errors

abstract:
  A bound on the error introduced by truncating a quantum addition is given.
This bound shows that only a few controlled rotation gates will be necessary to
get a reliable computation.


title: Hybrid quantum computing

abstract:
  Necessary and sufficient conditions are given for the construction of a
hybrid quantum computer that operates on both continuous and discrete quantum
variables. Such hybrid computers are shown to be more efficient than
conventional quantum computers for performing a variety of quantum algorithms,
such as computing eigenvectors and eigenvalues.


title: Quantum Distribution of Gaussian Keys with Squeezed States

abstract:
  A continuous key distribution scheme is proposed that relies on a pair of
canonically conjugate quantum variables. It allows two remote parties to share
a secret Gaussian key by encoding it into one of the two quadrature components
of a single-mode electromagnetic field. The resulting quantum cryptographic
information vs disturbance tradeoff is investigated for an individual attack
based on the optimal continuous cloning machine. It is shown that the
information gained by the eavesdropper then simply equals the information lost
by the receiver.


title: Quantum Algorithms for Weighing Matrices and Quadratic Residues

abstract:
  In this article we investigate how we can employ the structure of
combinatorial objects like Hadamard matrices and weighing matrices to device
new quantum algorithms. We show how the properties of a weighing matrix can be
used to construct a problem for which the quantum query complexity is
ignificantly lower than the classical one. It is pointed out that this scheme
captures both Bernstein & Vazirani's inner-product protocol, as well as
Grover's search algorithm.
  In the second part of the article we consider Paley's construction of
Hadamard matrices, which relies on the properties of quadratic characters over
finite fields. We design a query problem that uses the Legendre symbol chi
(which indicates if an element of a finite field F_q is a quadratic residue or
not). It is shown how for a shifted Legendre function f_s(i)=chi(i+s), the
unknown s in F_q can be obtained exactly with only two quantum calls to f_s.
This is in sharp contrast with the observation that any classical,
probabilistic procedure requires more than log(q) + log((1-e)/2) queries to
solve the same problem.


title: The histories interpretation: stability instead of consistency?

abstract:
  Using a reformulation of conventional results in decoherence theory, a
condition is proposed for singling out a distinguished class of histories which
includes those which use the ``pointer basis'' of Zurek.


title:
Classical representations for quantum-like systems through an axiomatics
  for context dependence

abstract:
  We introduce a definition for a 'hidden measurement system', i.e., a physical
entity for which there exist: (i) 'a set of non-contextual states of the entity
under study' and (ii) 'a set of states of the measurement context', and which
are such that all uncertainties are due to a lack of knowledge on the actual
state of the measurement context. First we identify an explicit criterion that
enables us to verify whether a given hidden measurement system is a
representation of a given couple $\Si,{\cal E}$ consisting of a set of states
$\Si$ and a set of measurements ${\cal E}$ ($=$ measurement system). Then we
prove for every measurement system that there exists at least one
representation as a hidden measurement system with $[0,1]$ as set of states of
the measurement context. Thus, we can apply this definition of a hidden
measurement system to impose an axiomatics for context dependence. We show that
in this way we always find classical representations (hidden measurement
representations) for general non-classical entities (e.g. quantum entities).


title: A classification of classical representations for quantum-like systems

abstract:
  For general non-classical systems, we study the different classical
representations that fulfill the specific context dependence imposed by the
hidden measurement system formalism introduced in quant-ph/0008061. We show
that the collection of non-equivalent representations has a poset structure. We
also show that in general, there exists no 'smallest' representation, since
this poset is not a semi-lattice. Then we study the possible representations of
quantum-like measurement systems. For example, we show that there exists a
classical representation of finite dimensional quantum mechanics with ${\Bbb
N}$ as a set of states for the measurement context, and we build an explicit
example of such a representation.


title: Interacting Stochastic Process and Renormalization Theory

abstract:
  A stochastic process with self-interaction as a model of quantum field theory
is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with
interaction of the form x^{(\alpha)}(t)^4, where $\alpha$ indicates the
fractional derivative. Using Bogoliubov's R-operation we investigate
ultraviolet divergencies for the various parameters $\alpha$. Ultraviolet
properties of this one-dimensional model in the case $\alpha=3/4$ are similar
to those in the $\phi^4_4$ theory but there are extra counterterms. It is shown
that the model is two-loops renormalizable. For $5/8\leq \alpha < 3/4$ the
model has a finite number of divergent Feynman diagrams. In the case
$\alpha=2/3$ the model is similar to the $\phi^4_3$ theory. If $0 \leq \alpha <
5/8$ then the model does not have ultraviolet divergencies at all. Finally if
$\alpha > 3/4$ then the model is nonrenormalizable. This model can be used for
a non-perturbative study of ultraviolet divergencies in quantum field theory
and also in theory of phase transitions.

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


title: Security of EPR-based Quantum Key Distribution

abstract:
  We propose a proof of the security of EPR-based quantum key distribution
against enemies with unlimited computational power. The proof holds for a
protocol using interactive error-reconciliation scheme. We assume in this paper
that the legitimate parties receive a given number of single photon signals and
that their measurement devices are perfect.


title: Universal quantum computation with two-level trapped ions

abstract:
  Although the initial proposal for ion trap quantum computation made use of an
auxiliary internal level to perform logic between ions, this resource is not
necessary in principle. Instead, one may perform such operations directly using
sideband laser pulses, operating with an arbitrary (sufficiently small)
Lamb-Dicke parameter. We explore the potential of this technique, showing how
to perform logical operations between the internal state of an ion and the
collective motional state and giving explicit constructions for a
controlled-not gate between ions.


title: "Shaking" of an atom in a non-stationary cavity

abstract:
  We consider an atom interacting with a quantized electromagnetic field inside
a cavity with variable parameters. The atom in the ground state located in the
initially empty cavity can be excited by variation of cavity parameters. We
have discovered two mechanisms of atomic excitation. The first arises due to
the interaction of the atom with the non-stationary electromagnetic field
created by modulation of cavity parameters. If the characteristic time of
variation of cavity parameters is of the order of the atomic transition time,
the processes of photon creation and atomic excitation are going on
simultaneously and hence excitation of the atom cannot be reduced to trivial
absorption of the photons produced by the dynamical Casimir effect. The second
mechanism is "shaking" of the atom due to fast modulation of its ground state
Lamb shift which takes place as a result of fast variation of cavity arameters.
The last mechanism has no connection with the vacuum dynamical Casimir effect.
Moreover, it opens a new channel of photon creation in the non-stationary
cavity. Nevertheless, the process of photon creation is altered by the presence
of the atom in the cavity, even if one disregards the existence of the new
channel. In particular, it removes the restriction for creation of only even
number of photons and also changes the expectation value for the number of
created photons. Our consideration is based on a simple model of a two-level
atom interacting with a single mode of the cavity field. Qualitatively our
results are valid for a real atom in a physical cavity.


title: Strictly isospectral potentials from excited quantum states

abstract:
  The strictly nonrelativistic isospectral scheme based on the general Riccati
solution and Darboux transformation function corresponding to excited states is
presented on the following examples: the harmonic oscillator, the square well,
and the hydrogen atom


title: Hybrid classical-quantum dynamics

abstract:
  A hybrid formalism is proposed for interacting classical and quantum sytems.
This formalism is mathematically consistent and reduces to standard classical
and quantum mechanics in the case of no interaction. However, in the presence
of interaction, the correspondence principle is violated.


title: Bures Geometry of the Three-Level Quantum Systems. I

abstract:
  We compute, using a formula of Dittmann, the Bures metric tensor (g) for the
eight-dimensional convex set of three-level quantum systems, employing a
newly-developed Euler angle-based parameterization of the 3 x 3 density
matrices. Most of the individual metric elements (g_{ij}) are found to be
expressible in relatively compact form, many of them in fact being exactly
zero.


title: Universal simulation of Markovian quantum dynamics

abstract:
  Although the conditions for performing arbitrary unitary operations to
simulate the dynamics of a closed quantum system are well understood, the same
is not true of the more general class of quantum operations (also known as
superoperators) corresponding to the dynamics of open quantum systems. We
propose a framework for the generation of Markovian quantum dynamics and study
the resources needed for universality. For the case of a single qubit, we show
that a single nonunitary process is necessary and sufficient to generate all
unital Markovian quantum dynamics, whereas a set of processes parametrized by
one continuous parameter is needed in general. We also obtain preliminary
results for the unital case in higher dimensions.


title: Toward the multiphoton parametric oscillators

abstract:
  We propose novel types of parametric oscillators generating both three-photon
and four-photon bright light which are accessible for an experiment. The
devices are based on the cascaded down-conversion processes and consist of
second-order media inserted in two-resonant mode cavity. Discussion of
dissipation and quantum features of the system are performed by the
quantum-jump simulation method and concerns to the Wigner functions. The
phase-space multistabilities and critical threshold behavior of three- and
four-photon subharmonics are obtained.


title:
Preparation and light-mediated distribution of motional state
  entanglement

abstract:
  We describe and analyse numerically schemes (i) for entangling orthogonal
motional modes of one or a few harmonically-trapped atoms or ions, and (ii) for
transferring the entanglement from one of these local modes to a distant
trapped atom (or atoms) via a light-mediated quantum state transfer procedure
proposed in previous work [A.S. Parkins and H.J. Kimble, J. Opt. B: Quantum
Semiclass. Opt. 1, 496 (1999)]. Possibilities arising from these schemes
include the generation of an Einstein-Podolsky-Rosen state in the positions and
momenta of distantly-separated trapped atoms and the preparation of delocalized
mesoscopic vibrational states.


title: Characterizing mixing and measurement in quantum mechanics

abstract:
  What fundamental constraints characterize the relationship between a mixture
$\rho = \sum_i p_i \rho_i$ of quantum states, the states $\rho_i$ being mixed,
and the probabilities $p_i$? What fundamental constraints characterize the
relationship between prior and posterior states in a quantum measurement? In
this paper we show that there are many surprisingly strong constraints on these
mixing and measurement processes that can be expressed simply in terms of the
eigenvalues of the quantum states involved. These constraints capture in a
succinct fashion what it means to say that a quantum measurement acquires
information about the system being measured, and considerably simplify the
proofs of many results about entanglement transformation.


title: Precise calculation of the Casimir force between gold surfaces

abstract:
  We analyse the result of precise measurement of the Casimir force between
bodies covered with gold. The values of the parameters used to extrapolate the
gold dielectric function to low frequencies are very important and discussed in
detail. The finite temperature effect is shown to exceed considerably the
experimental errors. The upper limit on the force is found which is smaller
than the measured force. Many experimental and theoretical uncertainties were
excluded with gold covering and we conclude that, possibly, a new force has
been detected at small separations between bodies.


title: Tuning the scattering length on the ground triplet state of Cs_2

abstract:
  We develop two schemes for tuning the scattering length on the ground triplet
state of Cs_2. First, an absolute value of the triplet scattering length of
^{133}Cs_2 is determined using the experimental data (Fioretti et al,
Eur.Phys.J. 5, 389 (1999)). We demonstrate that the large scattering length can
be made small and positive by coupling of the ^3\Sigma_u^+ (6S + 6S) potential
to the ^3\Pi_g state by strong off-resonant radiation. A weaker laser field
coupling the ^3\Sigma_u^+ (6S + 6S) continuum to the lowest bound level of the
excited ^3\Sigma_g^+ (6S + 6P) also leads to a small positive scattering
length. In addition, the scattering length of the ^{135}Cs isotope is found to
be positive. The method used solves the Schroedinger equation for two
electronic states coupled by an electromagnetic field with approximations
employed. The scattering length is determined from calculated continuum
wavefunctions of low energy.


title: Security of EPR-based Quantum Key Distribution using three bases

abstract:
  Modifications to a previous proof of the security of EPR-based quantum key
distribution are proposed. This modified version applies to a protocol using
three conjugate measurement bases rather than two. A higher tolerable error
rate is obtained for the three-basis protocol.


title: Diffraction of wave packets in space and time

abstract:
  The phenomenon of wave packet diffraction in space and time is described. It
consists in a diffraction pattern whose spatial location progresses with time.
The pattern is produced by wave packet quantum scattering off an attractive or
repulsive time independent potential. An analytical formula for the pattern at
$t\to\infty$ is derived both in one dimension and in three dimensions. The
condition for the pattern to exist is developed. The phenomenon is shown
numerically and analytically for the Dirac equation in one dimension also. An
experiment for the verification of the phenomenon is described and simulated
numerically.


title: Remote information concentration using a bound entangled state

abstract:
  Remote information concentration, the reverse process of quantum telecloning,
is presented. In this scheme, quantum information originally from a single
qubit, but now distributed into three spatially separated qubits, is remotely
concentrated back to a single qubit via an initially shared entangled state
without performing any global operations. This entangled state is an unlockable
bound entangled state and we analyze its properties.


title:
Phase diffusion as a model for coherent suppression of tunneling in the
  presence of noise

abstract:
  We study the stabilization of coherent suppression of tunneling in a driven
double-well system subject to random periodic $\delta-$function ``kicks''. We
model dissipation due to this stochastic process as a phase diffusion process
for an effective two-level system and derive a corresponding set of Bloch
equations with phase damping terms that agree with the periodically kicked
system at discrete times. We demonstrate that the ability of noise to localize
the system on either side of the double-well potenital arises from overdamping
of the phase of oscillation and not from any cooperative effect between the
noise and the driving field. The model is investigated with a square wave
drive, which has qualitatively similar features to the widely studied
cosinusoidal drive, but has the additional advantage of allowing one to derive
exact analytic expressions.


title:
Reply to Comment on "Counterfactual Entanglement and Nonlocal
  Correlations in Separable States"

abstract:
  Two objections have been raised to the arguments presented in O. Cohen, Phys.
Rev. A 60, 80 (1999). It is pointed out that neither objection has anything
whatsoever to do with the main subject matter of that paper, and shown that
both objections are based on misunderstandings of the examples to which they
relate.


title: A Feynman-Kac Formula for Anticommuting Brownian Motion

abstract:
  Motivated by application to quantum physics, anticommuting analogues of
Wiener measure and Brownian motion are constructed. The corresponding Ito
integrals are defined and the existence and uniqueness of solutions to a class
of stochastic differential equations is established. This machinery is used to
provide a Feynman-Kac formula for a class of Hamiltonians. Several specific
examples are considered.


title: Detection statistics in the micromaser

abstract:
  We present a general method for the derivation of various statistical
quantities describing the detection of a beam of atoms emerging from a
micromaser. The user of non-normalized conditioned density operators and a
linear master equation for the dynamics between detection events is discussed
as are the counting statistics, sequence statistics, and waiting time
statistics. In particular, we derive expressions for the mean number of
successive detections of atoms in one of any two orthogonal states of the
two-level atom. We also derive expressions for the mean waiting times between
detections. We show that the mean waiting times between de- tections of atoms
in like states are equivalent to the mean waiting times calculated from the
uncorrelated steady state detection rates, though like atoms are indeed
correlated. The mean waiting times between detections of atoms in unlike states
exhibit correlations. We evaluate the expressions for various detector
efficiencies using numerical integration, reporting re- sults for the standard
micromaser arrangement in which the cavity is pumped by excited atoms and the
excitation levels of the emerging atoms are measured. In addition, the atomic
inversion and the Fano-Mandel function for the detection of de-excited atoms is
calculated for compari- son to the recent experimental results of Weidinger et
al. [1], which reports the first observation of trapping states.


title: Wave Packet Echoes in the Motion of Trapped Atoms

abstract:
  We experimentally demonstrate and systematically study the stimulated revival
(echo) of motional wave packet oscillations. For this purpose, we prepare wave
packets in an optical lattice by non-adiabatically shifting the potential and
stimulate their reoccurence by a second shift after a variable time delay. This
technique, analogous to spin echoes, enables one even in the presence of strong
dephasing to determine the coherence time of the wave packets. We find that for
strongly bound atoms it is comparable to the cooling time and much longer than
the inverse of the photon scattering rate.


title: Exact relativistic time evolution for a step potential barrier

abstract:
  We derive an exact analytic solution to a Klein-Gordon equation for a step
potential barrier with cutoff plane wave initial conditions, in order to
explore wave evolution in a classical forbidden region. We find that the
relativistic solution rapidly evanesces within a depth $2x_p$ inside the
potential, where $x_p$ is the penetration length of the stationary solution.
Beyond the characteristic distance $2x_p$, a Sommerfeld-type precursor travels
along the potential at the speed of light, $c$. However, no spatial propagation
of a main wavefront along the structure is observed. We also find a non-causal
time evolution of the wavefront peak. The effect is only an apparent violation
of Einstein causality.


title:
Bell's theorem without inequalities and without probabilities for two
  observers

abstract:
  A proof of Bell's theorem using two maximally entangled states of two qubits
is presented. It exhibits a similar logical structure to Hardy's argument of
``nonlocality without inequalities''. However, it works for 100% of the runs of
a certain experiment. Therefore, it can also be viewed as a
Greenberger-Horne-Zeilinger-like proof involving only two spacelike separated
regions.


title:
Nonclassical Phenomena in Multiphoton Interferometry: More Stringent
  Tests Against Local Realism

abstract:
  The thesis is divided into three parts. In the first part a new theoretical
analysis of interferometric experiments by Alley-Shih, Ou-Mandel and the
entanglement swapping experiment is performed. It is shown that the double- and
single-photon distinguishability is not necessary for the experiments to be
genuine tests against local realism. In the second part, basing on simple
geometrical properties of Hilbert space, new, stronger Bell inequalities for M
qubits in a maximally entangled state are derived. Application of the same
method to two maximally entangled qubits yields an inequality for all possible
positions of the local measuring apparatus. Finally, the series of the
Greenberger-Horne- Zeilinger paradoxes for M maximally entangled quNits
observed via symmetric unbiased 2N ports is derived. The last part of the
thesis is devoted to the numerical approach to the Bell theorem. The necessary
and sufficient conditions for the violation of local realism in the case of two
and three maximally entangled qubits, on which each observer performs up to 10
(two qubits) and up to 5 (three qubits) local measurements, are shown. It is
also numerically shown that in the case of two maximally entangled quNits (3 <
N < 9) a properly defined magnitude of violation increases with N. In both
cases the approach neither involves any simplifications, or additional
assumptions, nor does it utilise any symmetries of the problem.


title:
Curve crossing in linear potential grids: the quasidegeneracy
  approximation

abstract:
  The quasidegeneracy approximation [V. A. Yurovsky, A. Ben-Reuven, P. S.
Julienne, and Y. B. Band, J. Phys. B {\bf 32}, 1845 (1999)] is used here to
evaluate transition amplitudes for the problem of curve crossing in linear
potential grids involving two sets of parallel potentials. The approximation
describes phenomena, such as counterintuitive transitions and saturation
(incomplete population transfer), not predictable by the assumption of
independent crossings. Also, a new kind of oscillations due to quantum
interference (different from the well-known St\"uckelberg oscillations) is
disclosed, and its nature discussed. The approximation can find applications in
many fields of physics, where multistate curve crossing problems occur.


title:
The Casimir Problem of Spherical Dielectrics: Quantum Statistical and
  Field Theoretical Approaches

abstract:
  The Casimir free energy for a system of two dielectric concentric nonmagnetic
spherical bodies is calculated with use of a quantum statistical mechanical
method, at arbitrary temperature. By means of this rather novel method, which
turns out to be quite powerful (we have shown this to be true in other
situations also), we consider first an explicit evaluation of the free energy
for the static case, corresponding to zero Matsubara frequency ($n=0$).
Thereafter, the time-dependent case is examined. For comparison we consider the
calculation of the free energy with use of the more commonly known field
theoretical method, assuming for simplicity metallic boundary surfaces.


title: Tripartite entanglement and quantum relative entropy

abstract:
  We establish relations between tripartite pure state entanglement and
additivity properties of the bipartite relative entropy of entanglement. Our
results pertain to the asymptotic limit of local manipulations on a large
number of copies of the state. We show that additivity of the relative entropy
would imply that there are at least two inequivalent types of asymptotic
tripartite entanglement. The methods used include the application of some
useful lemmas that enable us to analytically calculate the relative entropy for
some classes of bipartite states.


title: Effective Hamiltonian Approach to the Master Equation

abstract:
  A method of exactly solving the master equation is presented in this letter.
The explicit form of the solution is determined by the time evolution of a
composite system including an auxiliary system and the open system in question.
The effective Hamiltonian governing the time evolution of the composed system
are derived from the master equation. Two examples, the dissipative two-level
system and the damped harmonic oscillator, are presented to illustrate the
solving procedure.
  PACS number(s): 05.30.-d, 05.40.+j, 42.50.Ct


title: Quantum Measurement and Shannon Information, A Reply to M. J. W. Hall

abstract:
  Motivated by Hall's recent comment in quant-ph/0007116 we point out in some
detail the essence of our reasoning why we believe that Shannon's information
is not an adequate choice when defining the information gain in quantum
measurements as opposed to classical observations.


title: One Hundred Years of Quantum Physics

abstract:
  On the occasion of the 100th anniversary of the birth of the quantum idea,
the development, achievements, and promises of quantum mechanics are described.


title:
Resonance fluorescence in a band gap material: Direct numerical
  simulation of non-Markovian evolution

abstract:
  A numerical method of calculating the non-Markovian evolution of a driven
atom radiating into a structured continuum is developed. The formal solution
for the atomic reduced density matrix is written as a Markovian algorithm by
introducing a set of additional, virtual density matrices which follow, to the
level of approximation of the algorithm, all the possible trajectories of the
photons in the electromagnetic field. The technique is perturbative in the
sense that more virtual density matrices are required as the product of the
effective memory time and the effective coupling strength become larger. The
number of density matrices required is given by $3^{M}$ where $M$ is the number
of timesteps per memory time. The technique is applied to the problem of a
driven two-level atom radiating close to a photonic band gap and the
steady-state correlation function of the atom is calculated.


title:
A convenient method to prepare the effective pure state in a quantum
  ensemble

abstract:
  A simple method is proposed to prepare conveniently the effective pure state
|00...0><0...00| with any number of qubits in a quantum ensemble. The
preparation is based on the temporal averaging (Knill, Chuang, and Laflamme,
Phys.Rev.A 57, 3348(1998)). The quantum circuit to prepare the effective pure
state is designed in a unified and systematical form and is explicitly
decomposed completely into a product of a series of one-qubit quantum gates and
the two-qubit diagonal quantum gates. The preparation could be programmed and
implemented conveniently on an NMR quantum computer.


title: Entropy lower bounds of quantum decision tree complexity

abstract:
  We prove a general lower bound of quantum decision tree complexity in terms
of some entropy notion. We regard the computation as a communication process in
which the oracle and the computer exchange several rounds of messages, each
round consisting of O(log(n)) bits. Let E(f) be the Shannon entropy of the
random variable f(X), where X is uniformly random in f's domain. Our main
result is that it takes \Omega(E(f)) queries to compute any \emph{total}
function f. It is interesting to contrast this bound with the
\Omega(E(f)/log(n)) bound, which is tight for \emph{partial} functions. Our
approach is the polynomial method.


title:
Quantum Optical Discussion of Uncertainty and Complementarity in a
  Mach-Zehnder Interferometer

abstract:
  We discuss complementarity and uncertainty in a gedanken Which-Way
(Welcher-Weg) experiment in a Mach-Zehnder interferometer. Although a
Welcher-Weg measurement can be performed with only a negligible amount of
momentum change in the detector itself, the change in the interference pattern
must correspond to a change in the momentum distribution of the particle.
Entanglement between the Mach-Zehnder interferometer and the Welcher-Weg
measurement introduces orthogonality that disables the interference of the
particle, but simultaneously, it also generates a momentum transfer between the
particle and other parts of the whole entangled system (including macroscopic
parts). This analysis can be related to the Delayed Choice interpretation. We
show where the momentum change takes place and we conclude that entanglement is
the key to understand how complementarity (i.e. Which Way versus interference)
and the position-momentum uncertainty relation are interwoven.


title: Why do Bell experiments?

abstract:
  Experiments over three decades have been unable to demonstrate weak
nonlocality in the sense of Bell unambiguously, without loopholes. The last
important loophole remaining is the detection loophole, which is being tackled
by at least three experimental groups. This letter counters five common beliefs
about Bell experiments, and presents alternative scenarios for future
developments.


title: Invariants of Elementary Observations

abstract:
  As physics searches for invariants in observations, this paper looks for
invariants of probabilistic observation without assuming physical structure.
Structure emerges from the basic assumption of science that new information
shall lead to more accurate knowledge of the invariants. This leads to
statistically unique random variables for expressing observed information:
Complex probability amplitudes. Predictions are also just random variables
computed from observed data, and must become more accurate with more
observations as input. This singles out the quantum mechanical superposition
principle. The external conditions of a probabilistic experiment can themselves
be monitored at the most detailed level, resulting in observation of coicidence
probabilities. The invariants of any multi-coincidence experiment are the same
as those of a one-event experiment with the same number of possible outcomes.
An observable probability turns out to be controllable by two independent
experimental conditions, naturally parametrized as a direction in a
3-dimensional space. In summary, the probabilistic paradigm itself defines a
unique method of forming concepts and making predictions. The method appears
irrefutable within probability, because, whenever a prediction turns out wrong
the existence of an as yet unmonitored condition is postulated, and a formal
way to incoroporate it is shown. The Hilbert space formalism of quantum theory
seems to be isomorphic to this method.


title:
Control of Decoherence and Correlation in Single Quantum Dissipative
  Oscillator Systems

abstract:
  A single quantum dissipative oscillator described by the Lindblad equation
serves as a model for a nanosystem. This model is solved exactly by using the
ambiguity function. The solution shows the features of decoherence (spatial
extent of quantum behavior), correlation (spatial scale over which the system
localizes to its physical dimensions), and mixing (mixed- state spatial
correlation). A new relation between these length scales is obtained here. By
varying the parameters contained in the Lindblad equation, it is shown that
decoherence and correlation can be controlled. We indicate possible
interpretation of the Lindblad parameters in the context of experiments using
engineered reservoirs.


title: Uncertainty Relations for Entangled States

abstract:
  A generalized uncertainty relation for an entangled pair of particles is
obtained if we impose a symmetrization rule for all operators that we should
use when doing any calculation using the entangled wave function of the pair.
This new relation reduces to Heisenberg's uncertainty relation when the
particles have no correlation and suggests that we can have new lower bounds
for the product of position and momentum dispersions.


title: Control of open quantum systems dynamics

abstract:
  We investigate the control resources needed to effect arbitrary quantum
dynamics. We show that the ability to perform measurements on a quantum system,
combined with the ability to feed back the measurement results via coherent
control, allows one to control the system to follow any desired open-system
evolution. Such universal control can be achieved, in principle, through the
repeated application of only two coherent control operations and a simple
``Yes-No'' measurement.


title:
Lateral projection as a possible explanation of the nontrivial boundary
  dependence of the Casimir force

abstract:
  We find the lateral projection of the Casimir force for a configuration of a
sphere above a corrugated plate. This force tends to change the sphere position
in the direction of a nearest corrugation maximum. The probability distribution
describing different positions of a sphere above a corrugated plate is
suggested which is fitted well with experimental data demonstrating the
nontrivial boundary dependence of the Casimir force.


title: Dynamical localization and signatures of classical phase space

abstract:
  We study the dynamical localization of cold atoms in Fermi accelerator both
in position space and in momentum space. We report the role of classical phase
space in the development of dynamical localization phenomenon. We provide set
of experimentally assessable parameters to perform this work in laboratory.


title: Dynamical Revivals in Fermi Accelerator Model

abstract:
  We investigate quantum revivals in the dynamics of an atom in an atomic Fermi
accelerator. It is demonstrated that the external driving field influences the
revival time significantly. Analytical expressions are presented which are
based on semiclassical secular theory. These analytical results explain the
dependence of the revival time on the characteristic parameters of the problem
quantitatively in a simple way. They are in excellent agreement with numerical
results.


title:
Two-state system driven by imperfect pi pulses: an estimate of the error
  accumulation in bang-bang control methods

abstract:
  The evolution of a two-state system driven by a sequence of imperfect pi
pulses (with random phase or amplitude errors) is calculated. The resulting
decreased fidelity is used to derive a plausible limit on the performance of
"bang-bang" control methods for the suppression of decoherence.


title:
Off Resonant Pumping for Transition from Continuous to Discrete Spectrum
  and Quantum Revivals in Systems in Coherent States

abstract:
  We show that in parametrically driven systems and, more generally, in systems
in coherent states, off-resonant pumping can cause a transition from a
continuum energy spectrum of the system to a discrete one, and result in
quantum revivals of the initial state. The mechanism responsible for quantum
revivals in the present case is different from that in the non-linear
wavepacket dynamics of systems such as Rydberg atoms. We interpret the reported
phenomena as an optical analog of Bloch oscillations realized in Fock space and
propose a feasible scheme for inducing Bloch oscillations in trapped ions.


title: Diffraction of wave packets in space and time in three dimensions

abstract:
  A simple formula for the scattering of wave packets from a square well at
long times is derived. The expression shows that the phenomenon of wave packet
diffraction in space and time exists in three dimensions also. An experiment
for the verification of the phenomenon is described and simulated numerically.


title: Quantum nonlinear dynamics of continuously measured systems

abstract:
  Classical dynamics is formulated as a Hamiltonian flow on phase space, while
quantum mechanics is formulated as a unitary dynamics in Hilbert space. These
different formulations have made it difficult to directly compare quantum and
classical nonlinear dynamics. Previous solutions have focussed on computing
quantities associated with a statistical ensemble such as variance or entropy.
However a more direct comparison would compare classical predictions to the
quantum for continuous simultaneous measurement of position and momentum of a
single system. In this paper we give a theory of such measurement and show that
chaotic behaviour in classical systems can be reproduced by continuously
measured quantum systems.


title:
Fokker-Planck and Langevin Equations from Forward--Backward Path
  Integral

abstract:
  Starting from a forward--backward path integral of a point particle in a bath
of harmonic oscillators, we derive the Fokker-Planck and Langevin equations
with and without inertia. Special emphasis is placed upon the correct operator
order in the time evolution operator. The crucial step is the evaluation of a
Jacobian with a retarded time derivative by analytic regularization.


title:
Implementing universal multi-qubit quantum logic gates in three and
  four-spin systems at room temperature

abstract:
  In this paper, we present the experimental realization of multi-qubit gates
$% \Lambda_n(not) $ in macroscopic ensemble of three-qubit and four-qubit
molecules. Instead of depending heavily on the two-bit universal gate, which
served as the basic quantum operation in quantum computing, we use pulses of
well-defined frequency and length that simultaneously apply to all qubits in a
quantum register. It appears that this method is experimentally convenient when
this procedure is extended to more qubits on some quantum computation, and it
can also be used in other physical systems.


title: Atom Chip for Transporting and Merging Magnetically Trapped Atom Clouds

abstract:
  We demonstrate an integrated magnetic ``atom chip'' which transports cold
trapped atoms near a surface with very high positioning accuracy.
Time-dependent currents in a lithographic conductor pattern create a moving
chain of magnetic potential wells; atoms are transported in these wells while
remaining confined in all three dimensions. We achieve fluxes up to 10^6 /s
with a negligible heating rate. An extension of this ``atomic conveyor belt''
allows the merging of magnetically trapped atom clouds by unification of two
Ioffe-Pritchard potentials. Under suitable conditions, the clouds merge without
loss of phase space density. We demonstrate this unification process
experimentally.


title: Analogical Modeling and Quantum Computing

abstract:
  This paper serves as a bridge between quantum computing and analogical
modeling (a general theory for predicting categories of behavior in varying
contexts). Since its formulation in the early 1980s, analogical modeling has
been successfully applied to a variety of problems in language. Several
striking similarities between quantum mechanics and analogical modeling have
recently been noted: (1) traditional statistics can be derived from a
non-statistical basis by assuming data occurrences are accessed through a
spin-up state (given two equally probable quantum states, spin-up and
spin-down); (2) the probability of predicting a particular outcome is
determined by the squaring of an underlying linear measure and is the result of
decoherence (which occurs when a quantum system is observed); and (3) a natural
measure of certainty (called the agreement) is based on one chance of guessing
the right outcome and corresponds to the integrated squaring of Schroedinger's
wave equation.
  Analogical modeling considers all possible combiantions of a given context of
n variables, which is classical terms leads to an exponential explosion on the
order of 2**n. This paper proposes a quantum computational solution to this
exponentiality by applying a cycle of reversible quantum operators to all 2**n
possibilities, thus reducing the time and space of analogical modeling to a
polynomial order.


title: Quantum Bayes rule

abstract:
  We state a quantum version of Bayes's rule for statistical inference and give
a simple general derivation within the framework of generalized measurements.
The rule can be applied to measurements on N copies of a system if the initial
state of the N copies is exchangeable. As an illustration, we apply the rule to
N qubits. Finally, we show that quantum state estimates derived via the
principle of maximum entropy are fundamentally different from those obtained
via the quantum Bayes rule.


title:
Quantum computing and quantum measurement with mesoscopic Josephson
  junctions

abstract:
  Recent experimental demonstrations of quantum coherence of the charge and
flux states of Josephson junctions show that the quantum Josephson dynamics can
be used to develop scalable quantum logic circuits. In this work, I review the
basic concepts of Josephson tunneling and Josephson-junction qubits, and
discuss two problems of this tunneling motivated by quantum computing
applications. One is the theory of photon-assisted resonant flux tunneling in
SQUID systems used to demonstrate quantum coherence of flux. Another is the
problem of quantum measurement of charge with the SET electrometer. It is shown
that the SET electrometer at the Coulomb blockade threshold is the
quantum-limited detector with energy sensitivity reaching $\hbar/\sqrt{3}$ in
the resonant-tunneling regime.


title: Dynamics of quantum entanglement

abstract:
  A model of discrete dynamics of entanglement of bipartite quantum state is
considered. It involves a global unitary dynamics of the system and periodic
actions of local bistochastic or decaying channel. For initially pure states
the decay of entanglement is accompanied with an increase of von Neumann
entropy of the system. We observe and discuss revivals of entanglement due to
unitary interaction of both subsystems. For some mixed states having different
marginal entropies of both subsystems (one of them larger than the global
entropy and the other one one smaller) we find an asymmetry in speed of
entanglement decay. The entanglement of these states decreases faster, if the
depolarizing channel acts on the "classical" subsystem, characterized by
smaller marginal entropy.


title: Numerical Constructions of Perturbation Series in Quantum Mechanics

abstract:
  A few modified textbook Rayleigh-Schr\"{o}dinger perturbative representations
of bound states are reviewed. They were all inspired by an adaptive re-split of
the Hamiltonian, using nonstandard bases and the flexibility of normalization
of the wave functions.


title:
A unified (classical-quantum-statistical) formalism for continuous
  spectrum systems

abstract:
  A unified (classical-quantum-statistical) formalism for a system with
continuous spectrum is introduced. For this kind of systems ergodicity behavior
and the existence of microcanonical and canonical (KMS) equilibrium is proved.
It is argued that the continuous spectrum condition is essential for the
thermodynamical behavior


title: Applications of Integrated Magnetic Microtraps

abstract:
  Lithographically fabricated circuit patterns can provide magnetic guides and
microtraps for cold neutral atoms. By combining several such structures on the
same ceramic substrate, we have realized the first ``atom chips'' that permit
complex manipulations of ultracold trapped atoms or de Broglie wavepackets. We
show how to design magnetic potentials from simple conductor patterns and we
describe an efficient trap loading procedure in detail. Applying the design
guide, we describe some new microtrap potentials, including a trap which
reaches the Lamb-Dicke regime for rubidium atoms in all three dimensions, and a
rotatable Ioffe-Pritchard trap, which we also demonstrate experimentally.
Finally, we demonstrate a device allowing independent linear positioning of two
atomic clouds which are very tightly confined laterally. This device is well
suited for the study of one-dimensional collisions.


title: Self-Consistency of Thermal Jump Trajectories

abstract:
  It is problematic to interpret the quantum jumps of an atom interacting with
thermal light in terms of counts at detectors monitoring the atom's inputs and
outputs. As an alternative, we develop an interpretation based on a
self-consistency argument. We include one mode of the thermal field in the
system Hamiltonian and describe its interaction with the atom by an entangled
quantum state while assuming that the other modes induce quantum jumps in the
usual fashion. In the weak-coupling limit, the photon number expectation of the
selected mode is also seen to execute quantum jumps, although more generally,
for stronger coupling, Rabi oscillations are observed; the equilibrium photon
number distribution is a Bose-Einstein distribution. Each mode may be viewed in
isolation in a similar fashion, and summing over their weak-coupling jump rates
returns the net jump rates for the atom assumed at the outset.