title:
Nonlinear gauge interactions - A solution to the "measurement problem"
  in quantum mechanics?

abstract:
  We propose that the mechanism responsible for the ``collapse of the wave
function" (or "decoherence" in its broadest meaning) in quantum mechanics is
the nonlinearities already present in the theory via nonabelian gauge
interactions. Unlike all other models of spontaneous collapse, our proposal is,
to the best of our knowledge, the only one which does not introduce any new
elements into the theory. Indeed, unless the gauge interaction nonlinearities
are not used for exactly this purpose, one must then explain why the violation
of the superposition principle which they introduce does not destroy quantum
mechanics. A possible experimental test of the model would be to compare the
coherence lengths for, e.g., electrons and photons in a double-slit experiment.
The electrons should have a finite coherence length, while photons should have
a much longer (in principle infinite) coherence length.


title: A quantum computer only needs one universe

abstract:
  The nature of quantum computation is discussed. It is argued that, in terms
of the amount of information manipulated in a given time, quantum and classical
computation are equally efficient. Quantum superposition does not permit
quantum computers to ``perform many computations simultaneously'' except in a
highly qualified and to some extent misleading sense. Quantum computation is
therefore not well described by interpretations of quantum mechanics which
invoke the concept of vast numbers of parallel universes. Rather, entanglement
makes available types of computation process which, while not exponentially
larger than classical ones, are unavailable to classical systems. The essence
of quantum computation is that it uses entanglement to generate and manipulate
a physical representation of the correlations between logical entities, without
the need to completely represent the logical entities themselves.


title: PT-symmetric sextic potentials

abstract:
  The family of complex PT-symmetric sextic potentials is studied to show that
for various cases the system is essentially quasi-solvable and possesses real,
discrete energy eigenvalues. For a particular choice of parameters, we find
that under supersymmetric transformations the underlying potential picks up a
reflectionless part.


title: Planar Dirac Electron in Coulomb and Magnetic Fields

abstract:
  The Dirac equation for an electron in two spatial dimensions in the Coulomb
and homogeneous magnetic fields is discussed. For weak magnetic fields, the
approximate energy values are obtained by semiclassical method. In the case
with strong magnetic fields, we present the exact recursion relations that
determine the coefficients of the series expansion of wave functions, the
possible energies and the magnetic fields. It is found that analytic solutions
are possible for a denumerably infinite set of magnetic field strengths. This
system thus furnishes an example of the so-called quasi-exactly solvable
models. A distinctive feature in the Dirac case is that, depending on the
strength of the Coulomb field, not all total angular momentum quantum number
allow exact solutions with wavefunctions in reasonable polynomial forms.
Solutions in the nonrelativistic limit with both attractive and repulsive
Coulomb fields are briefly discussed by means of the method of factorization.


title: Speed of ion trap quantum information processors

abstract:
  We investigate theoretically the speed limit of quantum gate operations for
ion trap quantum information processors. The proposed methods use laser pulses
for quantum gates which entangle the electronic and vibrational degrees of
freedom of the trapped ions. Two of these methods are studied in detail and for
both of them the speed is limited by a combination of the recoil frequency of
the relevant electronic transition, and the vibrational frequency in the trap.
We have experimentally studied the gate operations below and above this speed
limit. In the latter case, the fidelity is reduced, in agreement with our
theoretical findings. //
  Changes: a) error in equ. 24 and table III repaired b) reference Jonathan et
al, quant-ph/ 0002092, added (proposes fast quantum gates using the AC-Stark
effect)


title:
Line narrowing via cavity-induced quantum interference in a $\Xi $-type
  atom

abstract:
  We show that cavity-induced interference may result in spectral line
narrowing in the absorption spectrum of a $\Xi$-type atom coupled to a
single-mode, frequency-tunable cavity field with a pre-selected polarization at
finite temperature.


title:
Cavity induced modifications to the resonance fluorescence and probe
  absorption of a laser-dressed V atom

abstract:
  A cavity-modified master equation is derived for a coherently driven, V-type
three-level atom coupled to a single-mode cavity in the bad cavity limit. We
show that population inversion in both the bare and dressed-state bases may be
achieved, originating from the enhancement of the atom-cavity interaction when
the cavity is resonant with an atomic dressed-state transition. The atomic
populations in the dressed state representation are analysed in terms of the
cavity-modified transition rates. The atomic fluorescence spectrum and probe
absorption spectrum also investigated, and it is found that the spectral
profiles may be controlled by adjusting the cavity frequency. Peak suppression
and line narrowing occur under appropriate conditions.


title: Cavity implementation of quantum interference in a $\Lambda$-type atom

abstract:
  A scheme for engineering quantum interference in a $\Lambda$-type atom
coupled to a frequency-tunable, single-mode cavity field with a pre-selected
polarization at finite temperature is proposed. Interference-assisted
population trapping, population inversions and probe gain at one sideband of
the Autler-Townes spectrum are predicted for certain cavity resonant
frequencies.


title: Noncanonical quantum optics

abstract:
  Modification of the right-hand-side of canonical commutation relations (CCR)
naturally occurs if one considers a harmonic oscillator with indefinite
frequency. Quantization of electromagnetic field by means of such a non-CCR
algebra naturally removes the infinite energy of vacuum but still results in a
theory which is very similar to quantum electrodynamics. An analysis of
perturbation theory shows that the non-canonical theory has an automatically
built-in cut-off but requires charge/mass renormalization already at the
nonrelativistic level. A simple rule allowing to compare perturbative
predictions of canonical and non-canonical theories is given. The notion of a
unique vacuum state is replaced by a set of different vacua. Multi-photon
states are defined in the standard way but depend on the choice of vacuum.
Making a simplified choice of the vacuum state we estimate corrections to
atomic lifetimes, probabilities of multiphoton spontaneous and stimulated
emission, and the Planck law. The results are practically identical to the
standard ones. Two different candidates for a free-field Hamiltonian are
compared.


title:
Non-orthogonal preferred projectors for modal interpretations of quantum
  mechanics

abstract:
  Modal interpretations constitute a particular approach to associating
dynamical variables with physical systems in quantum mechanics. Given the
`quantum logical' constraints that are typically adopted by such
interpretations, only certain sets of variables can be taken to be
simultaneously definite-valued, and only certain sets of values can be ascribed
to these variables at a given time. Moreover, each allowable set of variables
and values can be uniquely specified by a single `preferred' projector in the
Hilbert space associated with the system. In general, the preferred projector
can be one of several possibilities at a given time. In previous modal
interpretations, the different possible preferred projectors have formed an
orthogonal set. This paper investigates the consequences of adopting a
non-orthogonal set. We present three contributions on this issue: (1) we
provide an argument for such non-orthogonality, based on the assumption that
perfectly predictable measurements reveal pre-existing values of variables, an
assumption which has traditionally constituted a strong motivation for the
modal approach; (2) we generalize the existing framework for modal
interpretations to accommodate non-orthogonal preferred projectors; (3) we
present a novel type of modal interpretation wherein the set of preferred
projectors is fixed by a principle of entropy minimization, and we discuss some
of the successes and shortcomings of this proposal.


title:
Casimir and van der Waals force between two plates or a sphere (lens)
  above a plate made of real metals

abstract:
  The Casimir and van der Waals forces acting between two metallic plates or a
sphere (lens) above a plate are calculated accounting for the finite
conductivity of the metals. The simple formalism of surface modes is briefly
presented which allows the possibility to obtain the generalization of Lifshitz
results for the case of two semi-spaces covered by the thin layers. Additional
clarifications of the regularization procedure provides the means to obtain
reliable results not only for the force but also for the energy density. This,
in turn, leads to the value of the force for the configuration of a sphere
(lens) above a plate both of which are covered by additional layers. The
Casimir interaction between Al and Au test bodies is recalculated using the
optical tabulated data for the complex refractive index of these metals. The
computations turn out to be in agreement with the perturbation theory up to the
fourth order in relative penetration depth of electromagnetic zero point
oscillations into the metal. The disagreements between the results recently
presented in the literature are resolved. The Casimir force between Al bodies
covered by the thin Au layers is computed and the possibility to neglect
spatial dispersion effects is discussed as a function the layer thickness. The
van der Waals force is calculated including the transition region to the
Casimir force. The pure non-retarded van der Waals force law between Al and Au
bodies is shown to be restricted to a very narrow distance interval from 0.5 nm
to (2--4) nm. New, more exact, values of the Hamaker constant for Al and Au are
determined.


title: Quantum Communication with Correlated Nonclassical States

abstract:
  Nonclassical correlations between the quadrature-phase amplitudes of two
spatially separated optical beams are exploited to realize a two-channel
quantum communication experiment with a high degree of immunity to
interception. For this scheme, either channel alone can have an arbitrarily
small signal-to-noise ratio (SNR) for transmission of a coherent ``message''.
However, when the transmitted beams are combined properly upon authorized
detection, the encoded message can in principle be recovered with the original
SNR of the source. An experimental demonstration has achieved a 3.2 dB
improvement in SNR over that possible with correlated classical sources.
Extensions of the protocol to improve its security against eavesdropping are
discussed.


title: Coordinate Independence of of Quantum-Mechanical Path Integrals

abstract:
  We develop simple rules for performing integrals over products of
distributions in coordinate space. Such products occur in perturbation
expansions of path integrals in curvilinear coordinates, where the interactions
contain terms of the form dot q^2 q^n, which give rise to highly singular
Feynman integrals. The new rules ensure the invariance of perturbatively
defined path integrals under coordinate transformations.


title:
Ground state cooling, quantum state engineering and study of decoherence
  of ions in Paul traps

abstract:
  We investigate single ions of $^{40}Ca^+$ in Paul traps for quantum
information processing. Superpositions of the S$_{1/2}$ electronic ground state
and the metastable D$_{5/2}$ state are used to implement a qubit. Laser light
on the S$_{1/2} \leftrightarrow$ D$_{5/2}$ transition is used for the
manipulation of the ion's quantum state. We apply sideband cooling to the ion
and reach the ground state of vibration with up to 99.9% probability. Starting
from this Fock state $|n=0>$, we demonstrate coherent quantum state
manipulation. A large number of Rabi oscillations and a ms-coherence time is
observed. Motional heating is measured to be as low as one vibrational quantum
in 190 ms. We also report on ground state cooling of two ions.


title: Coherent Control of Magneto-optical Rotation

abstract: The paper has been withdrawn by authors.


title: Comment on Mohrhoff's "What quantum mechanics is trying to tell us"

abstract:
  Mohrhoff proposes using the Aharonov-Bergmann-Lebowitz (ABL) rule for
time-symmetric ``objective'' (meaning non-epistemic) probabilities
corresponding to the possible outcomes of not-actually-performed measurements
between specified pre- and post-selection measurement outcomes. It is
emphasized that the ABL rule was formulated on the assumption that such
intervening measurements are actually made and that it does not necessarily
apply to counterfactual situations. The exact nature of the application of the
ABL rule considered by Mohrhoff is made explicit and is shown to fall short of
his stated counterfactual claim.


title: Improved two-party and multi-party purification protocols

abstract:
  We present an improved protocol for entanglement purification of bipartite
mixed states using several states at a time rather than two at a time as in the
traditional recurrence method. We also present a generalization of the hashing
method to n-partite cat states, which achieves a finite yield of pure cat
states for any desired fidelity. Our results are compared to previous
protocols.


title:
Exact Solutions of the two-dimensional Schr\"{o}dinger equation with
  certain central potentials

abstract:
  By applying an ansatz to the eigenfunction, an exact closed form solution of
the Schr\"{o}dinger equation in 2D is obtained with the potentials,
$V(r)=ar^2+br^4+cr^6$, $V(r)=ar+br^2+cr^{-1}$ and
$V(r)=ar^2+br^{-2}+cr^{-4}+dr^{-6}$, respectively. The restrictions on the
parameters of the given potential and the angular momentum $m$ are obtained.


title: Private Quantum Channels and the Cost of Randomizing Quantum Information

abstract:
  We investigate how a classical private key can be used by two players,
connected by an insecure one-way quantum channel, to perform private
communication of quantum information. In particular we show that in order to
transmit n qubits privately, 2n bits of shared private key are necessary and
sufficient. This result may be viewed as the quantum analogue of the classical
one-time pad encryption scheme. From the point of view of the eavesdropper,
this encryption process can be seen as a randomization of the original state.
We thus also obtain strict bounds on the amount of entropy necessary for
randomizing n qubits.


title: Discussion: Are There Material Objects in Bohm's Theory

abstract:
  Bedard has argued that the 'minimalist' interpretation of Bohm's theory
"do[es] not make sense", essentially because one cannot account for bonding
properties in terms of particles cofigurations alone. I argue that while this
point is correct, the minimalist interpretation never sought to provide such an
explanation (nor is it incumbant upon this interpretation to do so).


title: Effectively classical quantum states for open systems

abstract:
  Notions of robust and "classical" states for an open quantum system are
introduced and discussed in the framework of the isometric-sweeping
decomposition of trace class operators. Using the predictability sieve proposed
by Zurek, ``quasi-classical'' states are defined. A number of examples
illustrating how the ``quasi-classical'' states correspond to classical points
in phase space connected with the measuring apparatus are presented.


title: Quantum authentication and key distribution using catalysis

abstract:
  Starting from Barnum's recent proposal to use entanglement and catalysis for
quantum secure identification [quant-ph/9910072], we describe a protocol for
quantum authentication and authenticated quantum key distribution. We argue
that our scheme is secure even in the presence of an eavesdropper who has
complete control over both classical and quantum channels.


title:
Quantum Fluctuations of a Single Trapped Atom: Transient Rabi
  Oscillations and Magnetic Bistability

abstract:
  Isolation of a single atomic particle and monitoring its resonance
fluorescence is a powerful tool for studies of quantum effects in
radiation-matter interaction. Here we present observations of quantum dynamics
of an isolated neutral atom stored in a magneto-optical trap. By means of
photon correlations in the atom's resonance fluorescence we demonstrate the
well-known phenomenon of photon antibunching which corresponds to transient
Rabi oscillations in the atom. Through polarization-sensitive photon
correlations we show a novel example of resolved quantum fluctuations:
spontaneous magnetic orientation of an atom. These effects can only be observed
with a single atom.


title: Dyon-Oscillator Duality

abstract:
  The dyon-oscillator duality presented in this lecture can be treated as a
prototype of the Seiberg-Witten duality in nonrelativistic quantum mechanics.
The key statement declares that in some spatial dimensions the oscillator-like
systems are dual to the atoms composed of the electrical charged particle and
dyon, i.e., monopoles provided by both magnetic and electric charge.

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


title: Gauss Sums and Quantum Mechanics

abstract:
  By adapting Feynman's sum over paths method to a quantum mechanical system
whose phase space is a torus, a new proof of the Landsberg-Schaar identity for
quadratic Gauss sums is given. In contrast to existing non-elementary proofs,
which use infinite sums and a limiting process or contour integration, only
finite sums are involved. The toroidal nature of the classical phase space
leads to discrete position and momentum, and hence discrete time. The
corresponding `path integrals' are finite sums whose normalisations are derived
and which are shown to intertwine cyclicity and discreteness to give a finite
version of Kelvin's method of images.


title: Cutoff dependence of the Casimir effect

abstract:
  The problem of calculating the Casimir force on two conducting planes by
means of the stress tensor is examined. The evaluation of this quantity is
carried out using an explicit regularization procedure which has its origin in
the underlying (2+1) dimensional Poincar\'{e} invariance of the system. The
force between the planes is found to depend on the ratio of two independent
cutoff parameters, thereby rendering any prediction for the Casimir effect an
explicit function of the particular calculational scheme employed. Similar
results are shown to obtain in the case of the conducting sphere.


title: Time discretization of functional integrals

abstract:
  Numerical evaluation of functional integrals usually involves a finite
(L-slice) discretization of the imaginary-time axis. In the auxiliary-field
method, the L-slice approximant to the density matrix can be evaluated as a
function of inverse temperature at any finite L as
$\rho_L(\beta)=[\rho_1(\beta/L)]^L$, if the density matrix $\rho_1(\beta)$ in
the static approximation is known. We investigate the convergence of the
partition function $Z_L(\beta)=Tr\rho_L(\beta)$, the internal energy and the
density of states $g_L(E)$ (the inverse Laplace transform of $Z_L$), as
$L\to\infty$. For the simple harmonic oscillator, $g_L(E)$ is a normalized
truncated Fourier series for the exact density of states. When the
auxiliary-field approach is applied to spin systems, approximants to the
density of states and heat capacity can be negative. Approximants to the
density matrix for a spin-1/2 dimer are found in closed form for all L by
appending a self-interaction to the divergent Gaussian integral and
analytically continuing to zero self-interaction. Because of this continuation,
the coefficient of the singlet projector in the approximate density matrix can
be negative. For a spin dimer, $Z_L$ is an even function of the coupling
constant for L<3: ferromagnetic and antiferromagnetic coupling can be
distinguished only for $L\ge 3$, where a Berry phase appears in the functional
integral. At any non-zero temperature, the exact partition function is
recovered as $L\to\infty$.


title: Stability properties of trapped Bose-Fermi gases mixture

abstract:
  The stability of Bose-Fermi gases trapped in an isotropic potentials at
ultracold temperature is strongly influenced by the interaction between the
fermions and the bosons. At zero temperature, the stability criterion is given
in this paper using variation method, the results show that whether a
fermion-boson mixture is stable depends mainly on the interaction between the
fermions and the bosons. For finite temperature, however, the stability is not
only related to the coupling constants, but also to the temperature. The
stability conditions for finite temperature are also derived and discuss in
details in this paper.


title: Quantum communication between atomic ensembles using coherent light

abstract:
  Protocols for quantum communication between massive particles, such as atoms,
are usually based on transmitting nonclassical light, and/or super-high finesse
optical cavities are normally needed to enhance interaction between atoms and
photons. We demonstrate a surprising result: an unknown quantum state can be
teleported from one free-space atomic ensemble to the other by transmitting
only coherent light. No non-classical light and no cavities are needed in the
scheme, which greatly simplifies its experimental implementation.


title: Transverse Isotropy in Identical Particle Scattering

abstract:
  It is pointed out that the cross section for the scattering of identical
charged bosons is isotropic over a broad angular range around 90 degrees when
the Sommerfeld parameter has a critical value, which depends exclusively on the
spin of the particle. A discussion of systems where this phenomenon can be
observed is presented.


title:
Universal construction of quantum computational networks in
  superconducting Josephson junctions

abstract:
  Any quantum computational network can be constructed with a sequence of the
two-qubit diagonal quantum gates and one-qubit gates in two-state quantum
systems. The universal construction of these quantum gates in the quantum
systems and of the quantum computational networks with these gates may be
achieved with the help of the operator algebra structure of Hamiltonians of the
systems and the properties of the multiple-quantum operator algebra subspaces
of the Liouville operator space and the specific properties of the quantum
algorithm corresponding to the quantum network. As an example, the two-qubit
diagonal gates are exactly prepared in detail in superconducting Josephson
junctions.


title:
Phase shift operator and cyclic evolution in finite dimensional Hilbert
  space

abstract:
  We address the problem of phase shift operator acting as time evolution
operator in Pegg-Barnett formalism. It is argued that standard shift operator
is inconsistent with the behaviour of the state vector under cyclic evolution.
We consider a generally deformed oscillator algebra at q-root of unity, as it
yields the same Pegg-Barnett operator and show that shift operator meets our
requirement.


title: Coherent States of Non-Linear Algebras:Application to Quantum Optics

abstract:
  We present a general unified approach for finding the coherent states of
polynomially deformed algebras such as the quadratic and Higgs algebras, which
are relevant for various multiphoton processes in quantum optics. We give a
general procedure to map these deformed algebras to appropriate Lie algebras.
This is used, for the non compact cases, to obtain the annihilation operator
coherent states, by finding the canonical conjugates of these operators.
  Generalized coherent states, in the Perelomov sense also follow from this
construction. This allows us to explicitly construct coherent states associated
with various quantum optical systems.


title:
Physical implementation for entanglement purification of Gaussian
  continuous variable quantum states

abstract:
  We give a detailed description of the entanglement purification protocol
which generates maximally entangled states with high efficiencies from
realistic Gaussian continuous variable entangled states. The physical
implementation of this protocol is extensively analyzed using high finesse
cavities and cavity enhanced cross Kerr nonlinearities. In particular, we take
into account many imperfections in the experimental scheme and calculate their
influences. Quantitative requirements are given for the relevant experimental
parameters.


title:
Remark on multi-particle observables and entangled states with constant
  complexity

abstract:
  We show that every density matrix of an n-particle system prepared by a
quantum network of constant depth is asymptotically commuting with the
mean-field observables. We introduce certain pairs of hypersurfaces in the
space of density matrices and give lower bounds for the depth of a network
which prepares states lying outside those pairs. The measurement of an
observable which is not asymptotically commuting with the mean-field
observables requires a network of depth in the order of log n, if one demands
the measurement to project the state into the eigenspace of the measured
observable.


title:
Testing the Symmetrization Postulate on Molecules with Three Identical
  Nuclei

abstract:
  We propose an experiment to look for possible small violations of the
symmetrization postulate of Quantum Mechanics, in systems composed by three
identical particles. Such violations could be detected by investigating the
population of particular roto-vibrational states of symmetrical molecules
containing three identical nuclei. We discuss the symmetry properties of such
states, and the implications of the symmetrization postulate and of the
spin-statistics. A high sensitivity spectroscopic investigation on simple
molecules such as SO3, BH3 and NH3 could lead to the first test of the
symmetrization postulate for spin-0 and spin-1/2 nuclei.


title: Recovering Coherence via Conditional Measurements

abstract:
  We show that conditional measurements on atoms following their interaction
with a resonant cavity field mode can be used to effectively counter the
decoherence of Fock-state superpositions due to cavity leakage.


title:
On the origin of noisy states whose teleportation fidelity can be
  enhanced through dissipation

abstract:
  Recently Badziag \emph{et al.} \cite{badziag} obtained a class of noisy
states whose teleportation fidelity can be enhanced by subjecting one of the
qubits to dissipative interaction with the environment via amplitude damping
channel (ADC). We show that such noisy states result while sharing the states
(| \Phi ^{\pm}> =\frac{1}{\sqrt{2}}(| 00> \pm | 11>)) across ADC. We also show
that under similar dissipative interactions different Bell states give rise to
noisy entangled states that are qualitatively very different from each other in
the sense, only the noisy entangled states constructed from the Bell states (|
\Phi ^{\pm}>) can \emph{}be made better sometimes by subjecting the unaffected
qubit to a dissipative interaction with the environment. Importantly if the
noisy state is non teleporting then it can always be made teleporting with this
prescription. We derive the most general restrictions on improvement of such
noisy states assuming that the damping parameters being different for both the
qubits. However this curious prescription does not work for the noisy entangled
states generated from (| \Psi ^{\pm}> =\frac{1}{\sqrt{2}}(| 01> \pm | 10>)).
This shows that an apriori knowledge of the noisy channel might be helpful to
decide which Bell state needs to be shared between Alice and Bob. \emph{}


title: Classical phase space and statistical mechanics of identical particles

abstract:
  Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.


title:
Quantum Computation with hot and cold ions:An assessment of proposed
  schemes

abstract:
  We present a brief critical review of the proposals for quantum computation
with trapped ions, with particular emphasis on the possibilities for quantum
computation without the need for cooling to the quantum ground state of the
ions' collective oscillatory modes.


title: Fidelity balance in quantum operations

abstract:
  I derive a tight bound between the quality of estimating the state of a
single copy of a $d$-level system, and the degree the initial state has to be
altered in course of this procedure. This result provides a complete analytical
description of the quantum mechanical trade-off between the information gain
and the quantum state disturbance expressed in terms of mean fidelities. I also
discuss consequences of this bound for quantum teleportation using nonmaximally
entangled states.


title: Nonlinear Decoherence in Quantum State Preparation of a Trapped Ion

abstract:
  We present a nonlinear decoherence model which models decoherence effect
caused by various decohereing sources in a quantum system through a nonlinear
coupling between the system and its environment, and apply it to investigating
decoherence in nonclassical motional states of a single trapped ion. We obtain
an exactly analytic solution of the model and find very good agreement with
experimental results for the population decay rate of a single trapped ion
observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it
et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).


title:
Trapped ions in laser fields: A benchmark for deformed quantum
  oscillators

abstract:
  Some properties of the non--linear coherent states (NCS), recognized by Vogel
and de Matos Filho as dark states of a trapped ion, are extended to NCS on a
circle, for which the Wigner functions are presented. These states are obtained
by applying a suitable displacement operator $D_{h}(\alpha) $ to the vacuum
state. The unity resolutions in terms of the projectors $| \alpha, h> < \alpha,
h^{-1}| ,| \alpha, h^{-1}> < \alpha, h| $ are presented together with a measure
allowing a resolution in terms of $| \alpha, h> < \alpha, h| $. $D_{h}(\alpha)
$ is also used for introducing the probability distribution funtion
$\rho_{A,h}(z) $ while the existence of a measure is exploited for extending
the P-representation to these states. The weight of the n-th Fock state of the
NCS relative to a trapped ion with Lamb-Dicke parameter $\eta ,$ oscillates so
wildly as $n$ grows up to infinity that the normalized NCS fill the open circle
$\eta ^{-1}$ in the complex $\alpha $-plane. In addition this prevents the
existence of a measure including normalizable states only. This difficulty is
overcome by introducing a family of deformations which are rational functions
of n, each of them admitting a measure. By increasing the degree of these
rational approximations the deformation of a trapped ion can be approximated
with any degree of accuracy and the formalism of the P-representation can be
applied.


title:
Incoherent scattering of light by a Bose--Einstein condensate of
  interacting atoms

abstract:
  We demonstrate that incoherent photon scattering by a Bose-Einstein
condensate of non-ideal atomic gas is enhanced due to bosonic stimulation of
spontaneous emission, similarly to coherent scattering in forward direction.
Necessary initial population of non-condensate states is provided by quantum
depletion of a condensate caused by interatomic repulsion.


title: Reply to Comment by A. Moroz

abstract:
  In (quant-ph/9911099 version 1) A. Moroz claims that the exponent $\eta$ from
the local photon density of states near a band gap edge $\rho(\omega) =
K(\vec{r}) |\omega_c - \omega|^\eta$ varies strongly with the position in the
crystal. We show that this is not the case and we demonstrate the error in his
analysis.


title: Quantum Computation and the localization of Modular Functors

abstract:
  The mathematical problem of localizing modular functors to neighborhoods of
points is shown to be closely related to the physical problem of engineering a
local Hamiltonian for a computationally universal quantum medium. For genus
$=0$ surfaces, such a local Hamiltonian is mathematically defined. Braiding
defects of this medium implements a representation associated to the Jones
polynomial and this representation is known to be universal for quantum
computation.


title: Focusing Vacuum Fluctuations

abstract:
  The focusing of the vacuum modes of a quantized field by a parabolic mirror
is investigated. We use a geometric optics approximation to calculate the
energy density and mean squared field averages for scalar and electromagnetic
fields near the focus. We find that these quantities grow as an inverse power
of the distance to the focus. There is an attractive Casimir-Polder force on an
atom which will draw it into the focus. Some estimates of the magnitude of the
effects of this focusing indicate that it may be observable.


title: Temporal Ordering in Quantum Mechanics

abstract:
  We examine the measurability of the temporal ordering of two events, as well
as event coincidences. In classical mechanics, a measurement of the
order-of-arrival of two particles is shown to be equivalent to a measurement
involving only one particle (in higher dimensions). In quantum mechanics, we
find that diffraction effects introduce a minimum inaccuracy to which the
temporal order-of-arrival can be determined unambiguously. The minimum
inaccuracy of the measurement is given by dt=1/E where E is the total kinetic
energy of the two particles. Similar restrictions apply to the case of
coincidence measurements. We show that these limitations are much weaker than
limitations on measuring the time-of-arrival of a particle to a fixed location.


title:
Disagreement between correlations of quantum mechanics and stochastic
  electrodynamics in the damped parametric oscillator

abstract:
  Intracavity and external third order correlations in the damped nondegenerate
parametric oscillator are calculated for quantum mechanics and stochastic
electrodynamics (SED), a semiclassical theory. The two theories yield greatly
different results, with the correlations of quantum mechanics being cubic in
the system's nonlinear coupling constant and those of SED being linear in the
same constant. In particular, differences between the two theories are present
in at least a mesoscopic regime. They also exist when realistic damping is
included. Such differences illustrate distinctions between quantum mechanics
and a hidden variable theory for continuous variables.


title: L'ordinateur quantique

abstract:
  Project of an undergraduate student in physics (4th year) about the concept
of quantum computers (QC) and its social impact. After a thourough theoretical
introduction (chap. 2), the recent debate about NMR-based QC is dealt with in
detail (chap. 3). Chapter 4 comments on the figure of the number of articles
published on the subject, showing the dramatic growth after the publication of
Shor's algorithm.


title: Theory of the Microscopic Maser Phase Transitions

abstract:
  Phase diagrams of the micromaser system are mapped out in terms of the
physical parameters at hand like the atom cavity transit time, the atom-photon
frequency detuning, the number of thermal photons and the probability for a
pump atom to be in its excited state. Critical fluctuations are studied in
terms of correlation measurements on atoms having passed through the micromaser
or on the microcavity photons themselves. At sufficiently large values of the
detuning we find a ``twinkling'' mode of the micromaser system. Detailed
properties of the trapping states are also presented.


title:
Generalized Noiseless Quantum Codes utilizing Quantum Enveloping
  Algebras

abstract:
  A generalization of the results of Rasetti and Zanardi concerning avoiding
errors in quantum computers by using states preserved by evolution is
presented. The concept of the dynamical symmetry is generalized from the level
of classical Lie algebras and groups, to the level of a dynamical symmetry
based on quantum Lie algebras and quantum groups (in the sense of Woronowicz).
An intrinsic dependence of the concept of dynamical symmetry on the
differential calculus (which holds also in the classical case) is stressed. A
natural connection between quantum states invariant under a quantum group
action, and quantum states preserved by the dynamical evolution is discussed.


title: A Beam Splitter for Guided Atoms on an Atom Chip

abstract:
  We have designed and experimentally studied a simple beam splitter for atoms
guided on an Atom Chip, using a current carrying Y-shaped wire and a bias
magnetic field. This beam splitter and other similar designs can be used to
build atom optical elements on the mesoscopic scale, and integrate them in
matterwave quantum circuits.


title: Computing with highly mixed states

abstract:
  We consider quantum computing in the k-qubit model where the starting state
of a quantum computer consists of k qubits in a pure state and n-k qubits in a
maximally mixed state. We ask the following question: is there a general method
for simulating an arbitrary m-qubit pure state quantum computation by a quantum
computation in the k-qubit model? We show that, under certain constraints, this
is impossible, unless m=O(k+ log n).


title: Fermionic quantum computation

abstract:
  We define a model of quantum computation with local fermionic modes (LFMs) --
sites which can be either empty or occupied by a fermion. With the standard
correspondence between the Foch space of $m$ LFMs and the Hilbert space of $m$
qubits, simulation of one fermionic gate takes $O(m)$ qubit gates and vice
versa. We show that using different encodings, the simulation cost can be
reduced to $O(\log m)$ and a constant, respectively. Nearest-neighbors
fermionic gates on a graph of bounded degree can be simulated at a constant
cost. A universal set of fermionic gates is found. We also study computation
with Majorana fermions which are basically halves of LFMs. Some connection to
qubit quantum codes is made.


title:
Spontaneous decay in the presence of dispersing and absorbing bodies:
  general theory and application to a spherical cavity

abstract:
  A formalism for studying spontaneous decay of an excited two-level atom in
the presence of dispersing and absorbing dielectric bodies is developed. An
integral equation, which is suitable for numerical solution, is derived for the
atomic upper-state-probability amplitude. The emission pattern and the power
spectrum of the emitted light are expressed in terms of the Green tensor of the
dielectric-matter formation including absorption and dispersion. The theory is
applied to the spontaneous decay of an excited atom at the center of a
three-layered spherical cavity, with the cavity wall being modeled by a
band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are
studied, the latter with special emphasis on the cases where the atomic
transition is (i) in the normal-dispersion zone near the medium resonance and
(ii) in the anomalous-dispersion zone associated with the band gap. In a
single-resonance approximation, conditions of the appearance of Rabi
oscillations and closed solutions to the evolution of the atomic state
population are derived, which are in good agreement with the exact numerical
results.


title:
Stochastic dynamics of electronic wave packets in fluctuating laser
  fields

abstract:
  The dynamics of a laser-excited Rydberg electron under the influence of a
fluctuating laser field are investigated. Rate equations are developed which
describe these dynamics in the limit of large laser bandwidths for arbitrary
types of laser fluctuations. These equations apply whenever all coherent
effects have already been damped out. The range of validity of these rate
equations is investigated in detail for the case of phase fluctuations. The
resulting asymptotic power laws are investigated which characterize the long
time dynamics of the laser-excited Rydberg electron and it is shown to which
extent these power laws depend on details of the laser spectrum.


title: "Interaction-free" discrimination between semi-transparent objects

abstract:
  Absorption-free (also known as ``interaction-free'') measurement aims to
detect the presence of an opaque object using a test particle without that
particle being absorbed by the object. Here we consider semi-transparent
objects which have an amplitude $\alpha$ of transmitting a particle while
leaving the state of the object unchanged and an amplitude $\beta$ of absorbing
the particle. The task is to devise a protocol that can decide which of two
known transmission amplitudes is present while ensuring that no particle
interacts with the object. We show that the probabilities of being able to
achieve this are limited by an inequality. This inequality implies that
absorption free distinction between complete transparency and any partial
transparency is always possible with probabilities approaching 1, but that two
partial transparencies can only be distinguished with probabilities less than
1.


title:
Error Avoiding Quantum Codes and Dynamical Stabilization of Grover's
  Algorithm

abstract:
  An error avoiding quantum code is presented which is capable of stabilizing
Grover's quantum search algorithm against a particular class of coherent
errors. This error avoiding code consists of states only which are factorizable
in the computational basis. Furthermore, its redundancy is smaller than the one
which is achievable with a general error correcting quantum code saturating the
quantum Hamming bound. The fact that this code consists of factorizable states
only may offer advantages for the implementation of quantum gates in the error
free subspace.


title: Conditional teleportation using optical squeezers and photon counting

abstract:
  We suggest a scheme of using two-mode squeezed vacuum for conditional
teleportation of quantum states of optical field. Alice mixes the input state
with one of the squeezed modes on another squeezing device and detects the
output photon numbers. The result is then communicated to Bob who shifts the
photon number of his part accordingly. This is a principally realizable
modification of the recent scheme [G.J. Milburn and S.L. Braunstein, Phys. Rev.
A 60, 937 (1999)] where measurements of photon number difference and phase sum
are considered. We show that for some classes of states this method can yield
very high fidelity of teleportation, nevertheless, the success probability may
be limited.


title:
Propagation of entangled light pulses through dispersive and absorbing
  channels

abstract:
  The modification of initially entangled light pulses passing through
dispersive and absorbing four-port devices is studied, using recently obtained
results on quantum state transformations [Phys. Rev. A 59, 4716 (1999)]. The
fidelity and indices of quantum correlations based on the von Neumann entropy
are calculated. Their dependence on both the pulse shape and the four-port
device parameters is studied. It is shown, that due to dispersion and
absorption the quantum correlations are reduced substantially for large initial
entanglement.


title:
A proof that measured data and equations of quantum mechanics can be
  linked only by guesswork

abstract:
  The design and operation of a quantum-mechanical device as a laboratory
instrument puts models written in equations of quantum mechanics in contact
with instruments. This contact is recordable in files of a Classical Digital
Process-control Computer (CPC) used both to calculate with the equations and to
manage the instruments. By noticing that equations and instruments make contact
in a CPC, we rewrite equations of quantum mechanics to explicitly include
functions of CPC-commands to the instruments. This sets up a proof that a
scientist's choice in linking mathematical models to instruments is
unresolvable without guesswork to narrow the set of models from which one is to
be chosen.
  As for implications of the proof, scientists inherit choices from the past
and frame choices for the future, choices open to guesswork and visible in CPC
files. To picture these choices, we adapt colored Petri nets, and the
availability of these net fragments makes choice and guesswork part and parcel
of physics.
  Net fragments as a means of expressing guess-demanding choices are applied to
portray guesswork needed in testing and calibrating a quantum computer. The
sample size required to test a quantum gate in a quantum computer is shown to
grow as the inverse square of the error allowed in implementing the gate.


title: Towards Nonadditive Quantum Information Theory

abstract:
  A definition of the nonadditive (nonextensive) conditional entropy indexed by
q is presented. Based on the composition law in terms of it, the
Shannon-Khinchin axioms are generalized and the uniqueness theorem is
established for the Tsallis entropy. The nonadditive conditional entropy, when
considered in the quantum context, is always positive for separable states but
takes negative values for entangled states, indicating its utility for
characterizing entanglement. A criterion deduced from it for separability of
the density matrix is examined in detail by using a bipartite spin-half system.
It is found that the strongest criterion for separability obtained by Peres
using an algebraic method is recovered in the present information-theoretic
approach.


title:
Does Quantum Nonlocality Exist? Bell's Theorem and the Many-Worlds
  Interpretation

abstract:
  Quantum nonlocality may be an artifact of the assumption that observers obey
the laws of classical mechanics, while observed systems obey quantum mechanics.
I show that, at least in the case of Bell's Theorem, locality is restored if
observed and observer are both assumed to obey quantum mechanics, as in the
Many-Worlds Interpretation. Using the MWI, I shall show that the apparently
"non-local" expectation value for the product of the spins of two widely
separated particles --- the "quantum" part of Bell's Theorem --- is really due
to a series of three purely local measurements. Thus, experiments confirming
"nonlocality" are actually confirming the MWI.


title:
Long Distance, Unconditional Teleportation of Atomic States Via Complete
  Bell State Measurements

abstract:
  This paper proposes a scheme for creating and storing quantum entanglement
over long distances. Optical cavities that store this long-distance
entanglement in atoms could then function as nodes of a quantum network, in
which quantum information is teleported from cavity to cavity. The
teleportation can be carried out unconditionally via measurements of all four
Bell states, using a method of sequential elimination.


title:
Comment on ``Quantum mechanics of an electron in a homogeneous magnetic
  field and a singular magnetic flux tube''

abstract:
  Recently Thienel [Ann. Phys. (N.Y.) 280 (2000), 140; quant-ph/9809047]
investigated the Pauli equation for an electron moving in a plane under the
influence of a perpendicular magnetic field which is the sum of a uniform field
and a singular flux tube. Here we criticise his claim that one cannot properly
solve this equation by treating the singular flux tube as the limiting case of
a flux tube of finite size.

categories: quant-ph cond-mat.mes-hall math-ph math.MP


title:
Local measurements of nonlocal observables and the relativistic
  reduction process

abstract:
  In this paper we reconsider the constraints which are imposed by relativistic
requirements to any model of dynamical reduction. We review the debate on the
subject and we call attention on the fundamental contributions by Aharonov and
Albert. Having done this we present a new formulation, which is much simpler
and more apt for our analysis, of the proposal put forward by these authors to
perform measurements of nonlocal observables by means of local interactions and
detections. We take into account recently proposed relativistic models of
dynamical reduction and we show that, in spite of some mathematical
difficulties related to the appearence of divergences, they represent a
perfectly appropriate conceptual framework which meets all necessary
requirements for a relativistic account of wave packet reduction. Subtle
questions like the appropriate way to deal with counterfactual reasoning in a
relativistic and nonlocal context are also analyzed in detail.


title: Quantum Computation by Geometrical Means

abstract:
  A geometrical approach to quantum computation is presented, where a
non-abelian connection is introduced in order to rewrite the evolution operator
of an energy degenerate system as a holonomic unitary. For a simple geometrical
model we present an explicit construction of a universal set of gates,
represented by holonomies acting on degenerate states.


title: Unconventional Quantum Computing Devices

abstract:
  This paper investigates a variety of unconventional quantum computation
devices, including fermionic quantum computers and computers that exploit
nonlinear quantum mechanics. It is shown that unconventional quantum computing
devices can in principle compute some quantities more rapidly than
`conventional' quantum computers.


title:
Interference-induced gain in Autler-Townes doublet of a V-type atom in a
  cavity

abstract:
  We study the Autler-Townes spectrum of a V-type atom coupled to a
single-mode, frequency-tunable cavity field at finite termperature, with a
pre-selected polarization in the bad cavity limit, and show that, when the mean
number of thermal photons $N\gg 1$ and the excited sublevel splitting is very
large (the same order as the cavity linewidth), the probe gain may occur at
either sideband of the doublet, depending on the cavity frequency, due to the
cavity-induced interference.


title:
Non-relativistic quantum electrodynamics for strong laser-atom
  interaction

abstract:
  A formulation of quantum electrodynamics is given that applies to atoms in a
strong laser field by perturbation theory in a non-relativistic regime. Dipole
approximation is assumed. The dual Dyson series, here discussed by referring it
to the Birkhoff theorem for singularly perturbed linear differential equations,
can be applied and a perturbation series obtained transforming the Hamiltonian
by a Pauli-Fierz transformation. But, if just few photons are present
high-order harmonics cannot be generated. So, it is proven that odd high-order
harmonics only appear when the laser field is intense and one can substitute
the creation and annihilation operators by the square root of the mean number
of photons taken to be huge, the field retaining its coherency property as
observed experimentally for harmonics. In this case, the Hamiltonian for
perturbation theory comes to the Kramers-Henneberger form. The theory has a
dipolar contribution when the free-electron quiver motion amplitude is larger
than the atomic radius. For a Coulomb potential one has that the outer electron
is periodically kicked, and so a prove is given that the same should happen to
Rydberg atoms in intense microwave fields. The distribution representing the
kicking has a Fourier series with just odd terms. Using a modified
Rayleigh-Schr\"odinger perturbation theory, it is shown that under the same
condition of validity of the quiver motion amplitude to atomic radius ratio,
the atomic wave function is only slightly modified by the laser field due to
the way the energy levels rearrange themselves. This gives a prove of
stabilization in the limit of laser frequency going to infinity. Then,
perturbation theory can be applied when the Keldysh parameter becomes smaller
with respect to the shifted distance between the energy levels of the atom.


title:
Entanglement transformation at absorbing and amplifying four-port
  devices

abstract:
  Dielectric four-port devices play an important role in optical quantum
information processing. Since for causality reasons the permittivity is a
complex function of frequency, dielectrics are typical examples of noisy
quantum channels, which cannot preserve quantum coherence. To study the effects
of quantum decoherence, we start from the quantized electromagnetic field in an
arbitrary Kramers--Kronig dielectric of given complex permittivity and
construct the transformation relating the output quantum state to the input
quantum state, without placing restrictions on the frequency. We apply the
formalism to some typical examples in quantum communication. In particular we
show that for entangled qubits the Bell-basis states $|\Psi^\pm>$ are more
robust against decoherence than the states $|\Phi^\pm>$.


title: Comment on the temperature dependence of the Casimir force

abstract:
  Linear in temperature correction to the Casimir force is discussed. The
correction is important for small separations between bodies tested in the
recent experiments and disappears in the case of perfect conductors.


title: Quantum mechanics with time-dependent parameters

abstract:
  Smooth composite bundles provide the adequate geometric description of
classical mechanics with time-dependent parameters. We show that the Berry's
phase phenomenon is described in terms of connections on composite Hilbert
space bundles.


title: Renormalization Group at finite temperature in Quantum Mechanics

abstract:
  We establish the exact renormalization group equation for the potential of a
one quantum particle system at finite and zero temperature. As an example we
use it to compute the ground state energy of the anharmonic oscillator. We
comment on an improvement of the Feynman Kleinert's variational method by the
renormalization group.


title: Many Body Problems with "Spin"-Related Contact Interactions

abstract:
  We study quantum mechanical systems with "spin"-related contact interactions
in one dimension. The boundary conditions describing the contact interactions
are dependent on the spin states of the particles. In particular we investigate
the integrability of $N$-body systems with $\delta$-interactions and point spin
couplings. Bethe ansatz solutions, bound states and scattering matrices are
explicitly given. The cases of generalized separated boundary condition and
some Hamiltonian operators corresponding to special spin related boundary
conditions are also discussed.


title: Renormalization Group in Quantum Mechanics

abstract:
  We establish the renormalization group equation for the running action in the
context of a one quantum particle system. This equation is deduced by
integrating each fourier mode after the other in the path integral formalism.
It is free of the well known pathologies which appear in quantum field theory
due to the sharp cutoff. We show that for an arbitrary background path the
usual local form of the action is not preserved by the flow. To cure this
problem we consider a more general action than usual which is stable by the
renormalization group flow. It allows us to obtain a new consistent
renormalization group equation for the action.


title:
Reversible combination of inequivalent kinds of multipartite
  entanglement

abstract:
  We present a family of tri-partite entangled states that, in an asymptotical
sense, can be reversibly converted into EPR states shared by only two of
parties (say B and C), and tripartite GHZ states. Thus we show that bipartite
and genuine tripartite entanglement can be reversibly combined in several
copies of a single tripartite state. For such states the corresponding
fractions of GHZ and of EPR states represent a complete quantification of their
(asymptotical) entanglement resources. More generally, we show that the three
different kinds of bipartite entanglement (AB, AC and BC EPR states) and
tripartite GHZ entanglement can be reversibly combined in a single state of
three parties. Finally, we generalize this result to any number of parties.


title: Quantum computation with abelian anyons

abstract:
  A universal quantum computer can be constructed using abelian anyons. Two
qubit quantum logic gates such as controlled-NOT operations are performed using
topological effects. Single-anyon operations such as hopping from site to site
on a lattice suffice to perform all quantum logic operations. Quantum
computation using abelian anyons shares some but not all of the robustness of
quantum computation using non-abelian anyons.


title: Simple computer model for the quantum Zeno effect

abstract:
  This paper presents a simple model for repeated measurement of a quantum
system: the evolution of a free particle, simulated by discretising the
particle's position. This model is easily simulated by computer and provides a
useful arena to investigate the effects of measurement upon dynamics, in
particular the slowing of evolution due to measurement (the `quantum Zeno
effect'). The results of this simulation are discussed for two rather different
sorts of measurement process, both of which are (simplified forms of)
measurements used in previous simulations of position measurement. A number of
interesting results due to measurement are found, and the investigation casts
some light on previous disagreements about the presence or absence of the Zeno
effect.


title: Elementary Excitations in Trapped BEC and Zero Mode Problem

abstract:
  We propose a natural expansion of the atomic field operator in studying
elementary excitations in trapped Bose-Einstein Condensation (BEC) system near
T=0K. Based on this expansion, a system of coupled equations for elementary
excitations, which is equivalent to the standard linearized GP equation, is
given to describe the collective excitation of BEC in a natual way.
Applications of the new formalism to the homogeneous case emphasize on the zero
mode and its relevant ground state of BEC.


title: A genuine reinterpretation of the Heisenberg's ("uncertainty") relations

abstract:
  In spite \smallskip of their popularity the \QTR{bf}{H}eisenberg's
(``uncertainty'') \QTR{bf}{R}elations (HR) still generate controversies. The
\QTR{bf}{T}raditional \QTR{bf}{I}nterpretation of HR (TIHR) dominate our days
science, although over the years a lot of its defects were signaled. These
facts justify a reinvestigation of the questions connected with the
interpretation / significance of HR. Here it is developped such a
reinvestigation starting with a revaluation of the main elements of TIHR. So
one finds that all the respective elements are troubled by insurmountable
defects. Then it results the indubitable failure of TIHR and the necessity of
its abandonment. Consequently the HR must be deprived of their quality of
crucial physical formulae. Moreover the HR are shown to be nothing but simple
fluctuations formulae with natural analogous in classical (non-quantum)
physics. The description of the maesuring uncertainties (traditionally
associated with HR) is approached from a new informational perspective. The
Planck's constant $\hbar $ (also associated with HR) is revealed to have a
significance of generic indicator for quantum stochasticity, similarly with the
role of Boltzmann's constant k in respect with the thermal stochasticity.


abstract:
  Candidates for quantum computing which offer only restricted control, e.g.,
due to lack of access to individual qubits, are not useful for general purpose
quantum computing. We present concrete proposals for the use of systems with
such limitations as RISQ - reduced instruction set quantum computers and
devices - for simulation of quantum dynamics, for multi-particle entanglement
and squeezing of collective spin variables. These tasks are useful in their own
right, and they also provide experimental probes for the functioning of quantum
gates in pre-mature proto-types of quantum computers.


title: Geometric Quantum Computation

abstract:
  We describe in detail a general strategy for implementing a conditional
geometric phase between two spins. Combined with single-spin operations, this
simple operation is a universal gate for quantum computation, in that any
unitary transformation can be implemented with arbitrary precision using only
single-spin operations and conditional phase shifts. Thus quantum geometrical
phases can form the basis of any quantum computation. Moreover, as the induced
conditional phase depends only on the geometry of the paths executed by the
spins it is resilient to certain types of errors and offers the potential of a
naturally fault-tolerant way of performing quantum computation.


title: Fundamental bounds on quantum measurements with a mixed apparatus

abstract:
  We consider the apparatus in a quantum measurement process to be in a mixed
state. We propose a simple upper bound on the probability of correctly
distinguishing any number of mixed states. We use this to derive fundamental
bounds on the efficiency of a measurement in terms of the temperature of the
apparatus.


title: Quantum Bit Escrow

abstract:
  Unconditionally secure bit commitment and coin flipping are known to be
impossible in the classical world. Bit commitment is known to be impossible
also in the quantum world. We introduce a related new primitive - {\em quantum
bit escrow}. In this primitive Alice commits to a bit $b$ to Bob. The
commitment is {\em binding} in the sense that if Alice is asked to reveal the
bit, Alice can not bias her commitment without having a good probability of
being detected cheating. The commitment is {\em sealing} in the sense that if
Bob learns information about the encoded bit, then if later on he is asked to
prove he was playing honestly, he is detected cheating with a good probability.
Rigorously proving the correctness of quantum cryptographic protocols has
proved to be a difficult task. We develop techniques to prove quantitative
statements about the binding and sealing properties of the quantum bit escrow
protocol.
  A related primitive we construct is a quantum biased coin flipping protocol
where no player can control the game, i.e., even an all-powerful cheating
player must lose with some constant probability, which stands in sharp contrast
to the classical world where such protocols are impossible.


title: Calculating the relative entropy of entanglement

abstract:
  We extend Vedral and Plenio's theorem (theorem 3 in Phys. Rev. A 57, 1619) to
a more general case, and obtain the relative entropy of entanglement for a
class of mixed states, this result can also follow from Rains' theorem 9 in
Phys. Rev. A 60, 179.


title: PT invariant Non-Hermitian Potentials with Real QES Eigenvalues

abstract:
  We show that at least the quasi-exactly solvable eigenvalues of the
Schr\"odinger equation with the potential $V(x) = -(\zeta \cosh 2x -iM)^2$ as
well as the periodic potential $V(x) = (\zeta \cos 2\theta -iM)^2$ are real for
the PT-invariant non-Hermitian potentials in case the parameter $M$ is any odd
integer. We further show that the norm as well as the weight functions for the
corresponding weak orthogonal polynomials are also real.


title: Multipartite pure-state entanglement and the generalized GHZ states

abstract:
  We show that not all 4-party pure states are GHZ reducible (i.e., can be
generated reversibly from a combination of 2-, 3- and 4-party maximally
entangled states by local quantum operations and classical communication
asymptotically) through an example, we also present some properties of the
relative entropy of entanglement for those 3-party pure states that are GHZ
reducible, and then we relate these properties to the additivity of the
relative entropy of entanglement.


title:
How behavior of systems with sparse spectrum can be predicted on a
  quantum computer

abstract:
  Call a spectrum of Hamiltonian sparse if each eigenvalue can be quickly
restored with accuracy $\epsilon$ from its rough approximation in within
$\epsilon_1$ by means of some classical algorithm. It is shown how a behavior
of system with sparse spectrum up to time $T=\frac{1-\rho}{14\epsilon}$ can be
predicted with fidelity $\rho$ on quantum computer in time
$t=\frac{4}{(1-\rho)\epsilon_1}$ plus the time of classical algorithm. The
quantum knowledge of Hamiltonian $H$ eigenvalues is considered as a wizard
Hamiltonian $W_H$ which action on any eigenvector of $H$ gives the
corresponding eigenvalue. Speedup of evolution for systems with sparse spectrum
is possible because for such systems wizard Hamiltonians can be quickly
simulated on a quantum computer. This simulation, generalizing Shor trick, is a
part of presented algorithm.
  In general case the action of wizard Hamiltonian cannot be simulated in time
smaller than the dimension of main space which is exponential of the size of
quantum system. For an arbitrary system (even for classical) its behavior
cannot be predicted on quantum computer even for one step ahead. This method
can be used also for restoration of a state of an arbitrary primary system in
time instant $-T$ in the past with the same fidelity which requires the same
time.


title: Discrete Moyal-type Representations for a Spin

abstract:
  In Moyal's formulation of quantum mechanics, a quantum spin s is described in
terms of continuous symbols, i.e. by smooth functions on a two-dimensional
sphere. Such prescriptions to associate operators with Wigner functions, P- or
Q-symbols, are conveniently expressed in terms of operator kernels satisfying
the Stratonovich-Weyl postulates. In analogy to this approach, a discrete Moyal
formalism is defined on the basis of a modified set of postulates. It is shown
that appropriately modified postulates single out a well-defined set of kernels
which give rise to discrete symbols. Now operators are represented by functions
taking values on (2s+1)(2s+1) points of the sphere. The discrete symbols
contain no redundant information, contrary to the continuous ones. The
properties of the resulting discrete Moyal formalism for a quantum spin are
worked out in detail and compared to the continuous formalism, and it is
illustrated by the example of a spin 1/2.


title: On the compatibility between the Markov property and the quantum jump

abstract:
  A brief analysis of the compatibility between the quantum jump and the Markov
property for quantum systems described by a stochastic evolution scheme is
presented.


title: The finite difference algorithm for higher order supersymmetry

abstract:
  The higher order supersymmetric partners of the Schroedinger's Hamiltonians
can be explicitly constructed by iterating a simple finite difference equation
corresponding to the Baecklund transformation. The method can completely
replace the Crum determinants. Its limiting, differential case offers some new
operational advantages.


title: Quantum Feedback for Protection of Schroedinger-cat states

abstract:
  We review the use of quantum feedback for combatting the decoherence of
Schroedinger-cat-like states in electromagnetic cavities, with special emphasys
on our recent proposal of an automatic mechanism based on the injection of
appropriately prepared ``probe'' and ``feedback'' Rydberg atoms. In the latter
scheme, the information transmission from the probe to the feedback atom is
directly mediated by a second auxiliary cavity. The detection efficiency for
the probe atom is no longer a critical parameter, and the decoherence time of
the linear superposition state can be significantly increased using presently
available technology.


title: Group Theoretical Quantum Tomography

abstract:
  The paper is devoted to the mathematical foundation of the quantum tomography
using the theory of square-integrable representations of unimodular Lie groups.


title: Quantum state protection using all-optical feedback

abstract:
  An all-optical feedback scheme in which the output of a cavity mode is used
to influence the dynamics of another cavity mode is considered. We show that
under ideal conditions, perfect preservation against decoherence of a generic
quantum state of the source mode can be achieved.


title: Quantum Computer as a Probabilistic Inference Engine

abstract:
  We propose a new class of quantum computing algorithms which generalize many
standard ones. The goal of our algorithms is to estimate probability
distributions. Such estimates are useful in, for example, applications of
Decision Theory and Artificial Intelligence, where inferences are made based on
uncertain knowledge. The class of algorithms that we propose is based on a
construction method that generalizes a Fredkin-Toffoli (F-T) construction
method used in the field of classical reversible computing. F-T showed how,
given any binary deterministic circuit, one can construct another binary
deterministic circuit which does the same calculations in a reversible manner.
We show how, given any classical stochastic network (classical Bayesian net),
one can construct a quantum network (quantum Bayesian net). By running this
quantum Bayesian net on a quantum computer, one can calculate any conditional
probability that one would be interested in calculating for the original
classical Bayesian net. Thus, we generalize the F-T construction method so that
it can be applied to any classical stochastic circuit, not just binary
deterministic ones. We also show that, in certain situations, our class of
algorithms can be combined with Grover's algorithm to great advantage.


title: Quantum Codes for Controlling Coherent Evolution

abstract:
  Control over spin dynamics has been obtained in NMR via coherent averaging,
which is implemented through a sequence of RF pulses, and via quantum codes
which can protect against incoherent evolution. Here, we discuss the design and
implementation of quantum codes to protect against coherent evolution. A
detailed example is given of a quantum code for protecting two data qubits from
evolution under a weak coupling (Ising) term in the Hamiltonian, using an
``isolated'' ancilla which does not evolve on the experimental time scale. The
code is realized in a three-spin system by liquid-state NMR spectroscopy on
13C-labelled alanine, and tested for two initial states. It is also shown that
for coherent evolution and isolated ancillae, codes exist that do not require
the ancillae to initially be in a (pseudo-)pure state. Finally, it is shown
that even with non-isolated ancillae quantum codes exist which can protect
against evolution under weak coupling. An example is presented for a six qubit
code that protects two data spins to first order.


title:
A Study of Quantum Error Correction by Geometric Algebra and
  Liquid-State NMR Spectroscopy

abstract:
  Quantum error correcting codes enable the information contained in a quantum
state to be protected from decoherence due to external perturbations. Applied
to NMR, quantum coding does not alter normal relaxation, but rather converts
the state of a ``data'' spin into multiple quantum coherences involving
additional ancilla spins. These multiple quantum coherences relax at differing
rates, thus permitting the original state of the data to be approximately
reconstructed by mixing them together in an appropriate fashion. This paper
describes the operation of a simple, three-bit quantum code in the product
operator formalism, and uses geometric algebra methods to obtain the
error-corrected decay curve in the presence of arbitrary correlations in the
external random fields. These predictions are confirmed in both the totally
correlated and uncorrelated cases by liquid-state NMR experiments on
13C-labeled alanine, using gradient-diffusion methods to implement these
idealized decoherence models. Quantum error correction in weakly polarized
systems requires that the ancilla spins be prepared in a pseudo-pure state
relative to the data spin, which entails a loss of signal that exceeds any
potential gain through error correction. Nevertheless, this study shows that
quantum coding can be used to validate theoretical decoherence mechanisms, and
to provide detailed information on correlations in the underlying NMR
relaxation dynamics.


title: Geometric Algebra in Quantum Information Processing

abstract:
  This paper develops a geometric model for coupled two-state quantum systems
(qubits), which is formulated using geometric (aka Clifford) algebra. It begins
by showing how Euclidean spinors can be interpreted as entities in the
geometric algebra of a Euclidean vector space. This algebra is then lifted to
Minkowski space-time and its associated geometric algebra, and the insights
this provides into how density operators and entanglement behave under Lorentz
transformations are discussed. The direct sum of multiple copies of space-time
induces a tensor product structure on the associated algebra, in which a
suitable quotient is isomorphic to the matrix algebra conventionally used in
multi-qubit quantum mechanics. Finally, the utility of geometric algebra in
understanding both unitary and nonunitary quantum operations is demonstrated on
several examples of interest in quantum information processing.


title: Phase space observables and isotypic spaces

abstract:
  We give necessary and sufficient conditions for the set of Neumark
projections of a countable set of phase space observable to constitute a
resolution of the identity, and we give a criteria for a phase space observable
to be informationally complete. The results will be applied to the phase space
observables arising from an irreducible representation of the Heisenberg group.


title:
A new conception experimental test of Bell inequalities using
  non-maximally entangled states

abstract:
  We report on a test of Bell inequalities using a non-maximally entangled
state, which represents an important step in the direction of eliminating the
detection loophole. The experiment is based on the creation of a polarisation
entangled state via the superposition, by use of an appropriate optics, of the
spontaneous fluorescence emitted by two non-linear crystals driven by the same
pumping laser. The alignment has profitably taken advantage from the use of an
optical amplifier scheme, where a solid state laser is injected into the
crystals together with the pumping laser. In principle a very high total
quantum efficiency can be reached using this configuration and thus the final
version of this experiment can lead to a resolution of the detection loophole,
we carefully discuss the conditions which must be satisfied for reaching this
result.


title:
A Lie algebraic approach to complex quasi exactly solvable potentials
  with real spectrum

abstract:
  We use a Lie algebraic technique to construct complex quasi exactly solvable
potentials with real spectrum. In particular we obtain exact solutions of a
complex sextic oscillator potential and also a complex potential belonging to
the Morse family.


title:
Collective versus local measurements on two parallel or antiparallel
  spins

abstract:
  We give a complete analysis of covariant measurements on two spins. We
consider the cases of two parallel and two antiparallel spins, and we consider
both collective measurements on the two spins, and measurements which require
only Local Quantum Operations and Classical Communication (LOCC). In all cases
we obtain the optimal measurements for arbitrary fidelities. In particular we
show that if the aim is determine as well as possible the direction in which
the spins are pointing, it is best to carry out measurements on antiparallel
spins (as already shown by Gisin and Popescu), second best to carry out
measurements on parallel spins and worst to be restricted to LOCC measurements.
If the the aim is to determine as well as possible a direction orthogonal to
that in which the spins are pointing, it is best to carry out measurements on
parallel spins, whereas measurements on antiparallel spins and LOCC
measurements are both less good but equivalent.


title: On unentangled Gleason theorems for quantum information theory

abstract:
  It is shown here that a strengthening of Wallach's Unentangled Gleason
Theorem can be obtained by applying results of the present authors on
generalised Gleason theorems for quantum multi-measures arising from
investigations of quantum decoherence functionals.


title: "Violating'' Clauser-Horne inequalities within classical mechanics

abstract:
  Some authors have raised the question whether the probabilities stemming from
a quantum mechanical computation are entitled to enter the Bell and the
Clauser-Horne inequalities. They have remarked that if the quantum
probabilities are given the status of conditional ones and the statistics for
the various settings of the detectors in a given experiment is properly kept
into account, the inequalities happen to be no longer violated. In the present
paper a classical simile modeled after the quantum mechanical instances is
closely scrutinised. It is shown that the neglect of the conditional character
of the probabilities in the classical model leads not only to ``violate'' the
Clauser-Horne inequalities, but also to contradict the very axioms of classical
probability theory.


title: Fast quantum gates for neutral atoms

abstract:
  We propose several schemes for implementing a fast two-qubit quantum gate for
neutral atoms with the gate operation time much faster than the time scales
associated with the external motion of the atoms in the trapping potential. In
our example, the large interaction energy required to perform fast gate
operations is provided by the dipole-dipole interaction of atoms excited to
low-lying Rydberg states in constant electric fields. A detailed analysis of
imperfections of the gate operation is given.


title:
Stability and instability in parametric resonance and quantum Zeno
  effect

abstract:
  A quantum mechanical version of a classical inverted pendulum is analyzed.
The stabilization of the classical motion is reflected in the bounded evolution
of the quantum mechanical operators in the Heisenberg picture. Interesting
links with the quantum Zeno effect are discussed.


title: Quantum Zeno Dynamics

abstract:
  The evolution of a quantum system undergoing very frequent measurements takes
place in a subspace of the total Hilbert space (quantum Zeno effect). The
dynamical properties of this evolution are investigated and several examples
are considered.


title:
Fibre bundle formulation of nonrelativistic quantum mechanics (full
  version)

abstract:
  We propose a new systematic fibre bundle formulation of nonrelativistic
quantum mechanics. The new form of the theory is equivalent to the usual one
and is in harmony with the modern trends in theoretical physics and potentially
admits new generalizations in different directions. In it the Hilbert space of
a quantum system (from conventional quantum mechanics) is replaced with an
appropriate Hilbert bundle of states and a pure state of the system is
described by a lifting of paths or section along paths in this bundle. The
evolution of a pure state is determined through the bundle (analogue of the)
Schr\"odinger equation. Now the dynamical variables and the density operator
are described via liftings of paths or morphisms along paths in suitable
bundles. The mentioned quantities are connected by a number of relations
derived in this work.


title: Two-mode Nonlinear Coherent States

abstract:
  Two-mode nonlinear coherent states are introduced in this paper. The pair
coherent states and the two-mode Perelomov coherent states are special cases of
the two-mode nonlinear coherent states. The exponential form of the two-mode
nonlinear coherent states is given. The photon-added or photon-subtracted
two-mode nonlinear coherent states are found to be two-mode nonlinear coherent
states with different nonlinear functions. The parity coherent states are
introduced as examples of two-mode nonlinear coherent states, and they are
superpositions of two corresponding coherent states. We also discuss how to
generate the parity coherent states in the Kerr medium.


title:
Quantum Computing Using Dissipation to Remain in a Decoherence-Free
  Subspace

abstract:
  We propose a new approach to the implementation of quantum gates in which
decoherence during the gate operations is strongly reduced. This is achieved by
making use of an environment induced quantum Zeno effect that confines the
dynamics effectively to a decoherence-free subspace.


title: Probability Current and Trajectory Representation

abstract:
  A unified form for real and complex wave functions is proposed for the
stationary case, and the quantum Hamilton-Jacobi equation is derived in the
three-dimensional space. The difficulties which appear in Bohm's theory like
the vanishing value of the conjugate momentum in the real wave function case
are surmounted. In one dimension, a new form of the general solution of the
quantum Hamilton-Jacobi equation leading straightforwardly to the general form
of the Schr\"odinger wave function is proposed. For unbound states, it is shown
that the invariance of the reduced action under a dilatation plus a rotation of
the wave function in the complex space implies that microstates do not appear.
For bound states, it is shown that some freedom subsists and gives rise to the
manifestation of microstates not detected by the Schr\"odinger wave function.


title: Relative entropy in quantum information theory

abstract:
  We review the properties of the quantum relative entropy function and discuss
its application to problems of classical and quantum information transfer and
to quantum data compression. We then outline further uses of relative entropy
to quantify quantum entanglement and analyze its manipulation.


title: Classical and quantum dynamics of a spin-1/2

abstract:
  We reply to a comment on `Semiclassical dynamics of a spin-1/2 in an
arbitrary magnetic field'.


title: Quantum Noise and Superluminal Propagation

abstract:
  Causal "superluminal" effects have recently been observed and discussed in
various contexts. The question arises whether such effects could be observed
with extremely weak pulses, and what would prevent the observation of an
"optical tachyon." Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett., vol.
81, 2190 (1998)] have argued that quantum noise will preclude the observation
of a superluminal group velocity when the pulse consists of one or a few
photons. In this paper we reconsider this question both in a general framework
and in the specific example, suggested by Chiao, Kozhekin, and Kurizki [Phys.
Rev. Lett., vol. 77, 1254 (1996)], of off-resonant, short-pulse propagation in
an optical amplifier. We derive in the case of the amplifier a signal-to-noise
ratio that is consistent with the general ARS conclusions when we impose their
criteria for distinguishing between superluminal propagation and propagation at
the speed c. However, results consistent with the semiclassical arguments of
CKK are obtained if weaker criteria are imposed, in which case the signal can
exceed the noise without being "exponentially large." We show that the quantum
fluctuations of the field considered by ARS are closely related to
superfluorescence noise. More generally we consider the implications of
unitarity for superluminal propagation and quantum noise and study, in addition
to the complete and truncated wavepackets considered by ARS, the residual
wavepacket formed by their difference. This leads to the conclusion that the
noise is mostly luminal and delayed with respect to the superluminal signal. In
the limit of a very weak incident signal pulse, the superluminal signal will be
dominated by the noise part, and the signal-to-noise ratio will therefore be
very small.


title: Teleportation using coupled oscillator states

abstract:
  We analyse the fidelity of teleportation protocols, as a function of resource
entanglement, for three kinds of two mode oscillator states: states with fixed
total photon number, number states entangled at a beam splitter, and the
two-mode squeezed vacuum state. We define corresponding teleportation protocols
for each case including phase noise to model degraded entanglement of each
resource.


title:
Self- and cross-phase modulation of ultrashort light pulses in an
  inertial Kerr medium: spectral control of squeezed light

abstract:
  Quantum theory of self-phase and cross-phase modulation of ultrashort light
pulses in the Kerr medium is developed with taking into account the response
time of an electronic nonlinearity. The correspondent algebra of time-dependent
Bose-operators is elaborated. It is established that the spectral region of the
pulse, where the quadrature fluctuations level is lower than the shot-noise
one, depends on the value of the nonlinear phase shift, the intensity of
another pulse, and the relaxation time of the nonlinearity. It is shown that
the frequency of the pulse spectrum at which the suppression of fluctuations is
maximum can be controlled by adjusting the other pulse intensity.


title: On quantum evolution as a parallel transport

abstract:
  Time-dependent quantum evolution is described by an algebraic connection on a
$C^\infty(R)$-module of sections of a $C^*$-algebra (or Hilbert) fibre bundle.


title: Persistent entanglement in arrays of interacting particles

abstract:
  We study the entanglement properties of a class of $N$ qubit quantum states
that are generated in arrays of qubits with an Ising-type interaction. These
states contain a large amount of entanglement as given by their Schmidt
measure. They have also a high {\em persistency of entanglement} which means
that $\sim N/2$ qubits have to be measured to disentangle the state. These
states can be regarded as an entanglement resource since one can generate a
family of other multi-particle entangled states such as the generalized GHZ
states of $<N/2$ qubits by simple measurements and classical communication
(LOCC).


title: Quantum to Classical Transition from the Cosmic Background Radiation

abstract:
  We have revisited the Ghirardi-Rimini-Weber-Pearle (GRWP) approach for
continuous dynamical evolution of the state vector for a macroscopic object.
Our main concern is to recover the decoupling of the state vector dynamics for
the center-of-mass (CM) and internal motion, as in the GRWP model, but within
the framework of the standard cosmology. In this connection we have taken the
opposite direction of the GRWP argument, that the cosmic background radiation
(CBR) has originated from a fundamental stochastic hitting process. We assume
the CBR as a clue of the Big Bang, playing a main role in the decoupling of the
state vector dynamics of the CM and internal motion. In our model, instead of
describing a continuous spontaneous localization (CSL) of a system of massive
particles as proposed by Ghirardi, Pearle and Rimini, the It\^{o} stochastic
equation accounts for the intervention of the CBR on the system of particles.
Essentially, this approach leads to a pre-master equation for both the CBR and
particles degrees of freedom. The violation of the principle of energy
conservation characteristic of the CSL model is avoided as well as the
additional assumption on the size of the GRWP's localization width necessary to
reach the decoupling between the collective and internal motions. Moreover,
realistic estimation for the decoherence time, exhibiting an interesting
dependence on the CBR temperature, is obtained. From the formula for the
decoherence time it is possible to analyze the transition from micro to macro
dynamics in both the early hot Universe and the nowadays cold one. The entropy
of the system under decoherence is analyzed and the emergent `pointer basis' is
discussed. In spite of not having imposed a privileged basis, in our model the
position still emerges as the preferred observable as in the CSL model.


title: Quantum computing with trapped ions, atoms and light

abstract:
  We first consider the basic requirements for a quantum computer, arguing for
the attractiveness of nuclear spins as information-bearing entities, and light
for the coupling which allows quantum gates. We then survey the strengths of
and immediate prospects for quantum information processing in ion traps. We
discuss decoherence and gate rates in ion traps, comparing methods based on the
vibrational motion with a method based on exchange of photons in cavity QED. We
then sketch the main features of a quantum computer designed to allow an
algorithm needing 10^6 Toffoli gates on 100 logical qubits. We find that around
200 ion traps linked by optical fibres and high-finesse cavities could perform
such an algorithm in a week to a month, using components at or near current
levels of technology.


title:
Which Kind of Two-Particle States Can Be Teleported through a
  Three-Particle Quantum Channel?

abstract:
  The use of a three-particle quantum channel to teleport entangled states
through a slight modification of the standard teleportation procedure is
studied. It is shown that it is not possible to perform successful
teleportation of an arbitrary and unknown two-particle entangled state,
following our version of the standard teleportation procedure. On the contrary,
it is shown which, and in how many different ways, particular classes of
two-particle states can be teleported.


title:
Bures Measures over the Spaces of Two and Three-Dimensional Density
  Matrices

abstract:
  Due to considerable recent interest in the use of density matrices for a wide
variety of purposes, including quantum computation, we present a general method
for their parameterizations in terms of Euler angles. We assert that this is of
more fundamental importance than (as several people have remarked to us) ``just
another parameterization of the density matrix.'' There are several uses to
which this methodology can be put. One that has received particular attention
is in the construction of certain distinguished (Bures) measures on the $(n^2
-1)$-dimensional convex sets of $n \times n$ density matrices.


title: Uncertainty rescued: Bohr's complementarity for composite systems

abstract:
  Generalized uncertainty relations may depend not only on the commutator
relation of two observables considered, but also on mutual correlations, in
particular, on entanglement. The equivalence between the uncertainty relation
and Bohr's complementarity thus holds in a much broader sense than anticipated.


title: Radiation Pressure as a Source of Decoherence

abstract:
  We consider the interaction of an harmonic oscillator with the quantum field
via radiation pressure. We show that a `Schrodinger cat' state decoheres in a
time scale that depends on the degree of `classicality' of the state
components, and which may be much shorter than the relaxation time scale
associated to the dynamical Casimir effect. We also show that decoherence is a
consequence of the entanglement between the quantum states of the oscillator
and field two-photon states. With the help of the fluctuation-dissipation
theorem, we derive a relation between decoherence and damping rates valid for
arbitrary values of the temperature of the field. Coherent states are selected
by the interaction as pointer states.


title: Wave Function Shredding by Sparse Quantum Barriers

abstract:
  We discuss a model in which a quantum particle passes through $\delta$
potentials arranged in an increasingly sparse way. For infinitely many barriers
we derive conditions, expressed in terms ergodic properties of wave function
phases, which ensure that the point and absolutely continuous parts are absent
leaving a purely singularly continuous spectrum. For a finite number of
barriers, the transmission coefficient shows extreme sensitivity to the
particle momentum with fluctuation in many different scales. We discuss a
potential application of this behavior for erasing the information carried by
the wave function.

categories: quant-ph cond-mat math-ph math.MP nlin.SI


title: Sampling the canonical phase from phase-space functions

abstract:
  We discuss the possibility of sampling exponential moments of the canonical
phase from the s-parametrized phase space functions. We show that the sampling
kernels exist and are well-behaved for any s>-1, whereas for s=-1 the kernels
diverge in the origin. In spite of that we show that the phase space moments
can be sampled with any predefined accuracy from the Q-function measured in the
double-homodyne scheme with perfect detectors. We discuss the effect of
imperfect detection and address sampling schemes using other measurable
phase-space functions. Finally, we discuss the problem of sampling the
canonical phase distribution itself.


title:
Contracting the Wigner-Kernel of a Spin to the Wigner-Kernel of a
  Particle

abstract:
  A general relation between the Moyal formalisms for a spin and a particle is
established. Once the formalism has been set up for a spin, the phase-space
description of a particle is obtained from the `contraction' of the group of
rotations to the group of translations. This is shown by explicitly contracting
a spin Wigner-kernel to the Wigner kernel of a particle. In fact, only one out
of 2^{2s} different possible kernels for a spin shows this behaviour.


title: Further Contents of Einstein's E = mc^{2}

abstract:
  The energy-mass content of Einstein's E = mc^{2} is well known. For a fixed
value of mass, E = mc^{2} is an energy-momentum relation which takes the form E
= \sqrt{m^{2} + p^{2}}. This relation was formulated in 1905 for point
particles. Since then, particles have become more complicated. They have
internal space-time structures. Massive particles carry the package of internal
variables including mass, spin and quarks, while massless particles have the
package containing helicity, gauge variables, and partons. The question then is
whether these two different packages of variables can be unified into one
single covariant package as E = mc^{2} does for the energy-momentum relations
for massive and massless particles. The answer to this question is YES.


title: Capacity of Quantum Channels Using Product Measurements

abstract:
  The capacity of a quantum channel for transmission of classical information
depends in principle on whether product states or entangled states are used at
the input, and whether product or entangled measurements are used at the
output. We show that when product measurements are used, the capacity of the
channel is achieved with product input states, so that entangled inputs do not
increase capacity. We show that this result continues to hold if sequential
measurements are allowed, whereby the choice of successive measurements may
depend on the results of previous measurements.
  We also present a new simplified expression which gives an upper bound for
the Shannon capacity of a channel, and which bears a striking resemblance to
the well-known Holevo bound.


title: EPR Test with Photons and Kaons: Analogies

abstract:
  We present a unified formalism describing EPR test using spin 1/2 particles,
photons and kaons. This facilitates the comparison between existing experiments
using photons and kaons. It underlines the similarities between birefringence
and polarization dependent losses that affects experiments using optical fibers
and mixing and decay that are intrinsic to the kaons. We also discuss the
limitation these two characteristics impose on the testing of Bell's
inequality.


title: Theory of Decoherence-Free Fault-Tolerant Universal Quantum Computation

abstract:
  Universal quantum computation on decoherence-free subspaces and subsystems
(DFSs) is examined with particular emphasis on using only physically relevant
interactions. A necessary and sufficient condition for the existence of
decoherence-free (noiseless) subsystems in the Markovian regime is derived here
for the first time. A stabilizer formalism for DFSs is then developed which
allows for the explicit understanding of these in their dual role as quantum
error correcting codes. Conditions for the existence of Hamiltonians whose
induced evolution always preserves a DFS are derived within this stabilizer
formalism. Two possible collective decoherence mechanisms arising from
permutation symmetries of the system-bath coupling are examined within this
framework. It is shown that in both cases universal quantum computation which
always preserves the DFS (*natural fault-tolerant computation*) can be
performed using only two-body interactions. This is in marked contrast to
standard error correcting codes, where all known constructions using one or
two-body interactions must leave the codespace during the on-time of the
fault-tolerant gates. A further consequence of our universality construction is
that a single exchange Hamiltonian can be used to perform universal quantum
computation on an encoded space whose asymptotic coding efficiency is unity.
The exchange Hamiltonian, which is naturally present in many quantum systems,
is thus *asymptotically universal*.


title:
Elastic scattering and bound states in the Aharonov-Bohm potential
  superimposed by an attractive $\rho^{-2}$ potential

abstract:
  We consider the elastic scattering and bound states of charged quantum
particles moving in the Aharonov-Bohm and an attractive $\rho^{-2}$ potential
in a partial wave approach. Radial solutions of the stationary Schr\"{o}dinger
equation are specified in such a way that the Hamiltonian of the problem is
self-adjoint. It is shown that they are not uniquely fixed but depend on open
parameters. The related physical consequences are discussed. The scattering
cross section is calculated and the energy spectrum of bound states is
obtained.


title: Parameters estimation in quantum optics

abstract:
  We address several estimation problems in quantum optics by means of the
maximum-likelihood principle. We consider Gaussian state estimation and the
determination of the coupling parameters of quadratic Hamiltonians. Moreover,
we analyze different schemes of phase-shift estimation. Finally, the absolute
estimation of the quantum efficiency of both linear and avalanche
photodetectors is studied. In all the considered applications, the Gaussian
bound on statistical errors is attained with a few thousand data.