title: Pseudo-reality and pseudo-adjointness of Hamiltonians

abstract:
  We define pseudo-reality and pseudo-adjointness of a Hamiltonian, $H$, as
$\rho H \rho^{-1}=H^\ast$ and $\mu H \mu^{-1}=H^\prime$, respectively. We prove
that the former yields the {\it necessary} condition for spectrum to be real
whereas the latter helps in fixing a definition for inner-product of the
eigenstates. Here we separate out adjointness of an operator from its
Hermitian-adjointness. It turns out that a Hamiltonian possessing real spectrum
is first pseudo-real, further it could be Hermitian, PT-symmetric or
pseudo-Hermitian.


title: An Ergodic Theorem for the Quantum Relative Entropy

abstract:
  We prove the ergodic version of the quantum Stein's lemma which was
conjectured by Hiai and Petz. The result provides an operational and
statistical interpretation of the quantum relative entropy as a statistical
measure of distinguishability, and contains as a special case the quantum
version of the Shannon-McMillan theorem for ergodic states. A version of the
quantum relative Asymptotic Equipartition Property (AEP) is given.


title:
Strong two-photon emission by a medium with periodically time-dependent
  refractive index

abstract:
  A two-photon emission of a medium with periodically time-dependent refractive
index is considered. The emission results from the zero-point fluctuations of
the medium. Usually this emission is very weak. However, it can be strongly
enhanced if the resonant condition $\omega_0$ = 2.94 $c/l_0$ is fulfilled (here
$\omega_0$ and $l_0 $ are the frequency and the amplitude of the oscillations
of the optical length of the medium, respectively). Besides, a medium with
resonant oscillations of the optical length performs the phase conjugated
reflection with high efficiency. A similar resonant enhancement of the
two-quantum emission of other bosons is also predicted.


title: Quantum mechanics emerging from "timeless" classical dynamics

abstract:
  We study classical Hamiltonian systems in which the intrinsic proper time
evolution parameter is related through a probability distribution to the
physical time, which is assumed to be discrete. In this way, a physical clock
with discrete states is introduced, which presently is still treated as
decoupled from the system. This is motivated by the recent discussion of
``timeless'' reparametrization invariant models, where discrete physical time
has been constructed based on quasi-local observables. Employing the
path-integral formulation of classical mechanics developed by Gozzi et al., we
show that these deterministic classical systems can be naturally described as
unitary quantum mechanical models. We derive the emergent quantum Hamiltonian
in terms of the underlying classical one. Such Hamiltonians typically need a
regularization - here performed by discretization - in order to arrive at
models with a stable groundstate in the continuum limit. This is demonstrated
in several examples, recovering and generalizing a model advanced by 't Hooft.


title: Quantum freeze of fidelity decay for a class of integrable dynamics

abstract:
  We discuss quantum fidelity decay of classically regular dynamics, in
particular for an important special case of a vanishing time averaged
perturbation operator, i.e. vanishing expectation values of the perturbation in
the eigenbasis of unperturbed dynamics. A complete semiclassical picture of
this situation is derived in which we show that the quantum fidelity of
individual coherent initial states exhibits three different regimes in time:
(i) first it follows the corresponding classical fidelity up to time
t1=hbar^(-1/2), (ii) then it freezes on a plateau of constant value, (iii) and
after a time scale t_2=min[hbar^(1/2) delta^(-2),hbar^(-1/2) delta^(-1)] it
exhibits fast ballistic decay as exp(-const. delta^4 t^2/hbar) where delta is a
strength of perturbation. All the constants are computed in terms of classical
dynamics for sufficiently small effective value hbar of the Planck constant. A
similar picture is worked out also for general initial states, and specifically
for random initial states, where t_1=1, and t_2=delta^(-1). This prolonged
stability of quantum dynamics in the case of a vanishing time averaged
perturbation could prove to be useful in designing quantum devices. Theoretical
results are verified by numerical experiments on the quantized integrable top.


title: An All Linear Optical Quantum Memory Based on Quantum Error Correction

abstract:
  When photons are sent through a fiber as part of a quantum communication
protocol, the error that is most difficult to correct is photon loss. Here, we
propose and analyze a two-to-four qubit encoding scheme, which can recover the
loss of one qubit in the transmission. This device acts as a repeater when it
is placed in series to cover a distance larger than the attenuation length of
the fiber, and it acts as an optical quantum memory when it is inserted in a
fiber loop. We call this dual-purpose device a ``quantum transponder.''


title: Laser cooling with ultrafast pulse trains

abstract:
  We propose a new laser cooling method for atomic species whose level
structure makes traditional laser cooling difficult. For instance, laser
cooling of hydrogen requires vacuum-ultraviolet laser light, while
multielectron atoms need laser light at many widely separated frequencies.
These restrictions can be eased by laser cooling on two-photon transitions with
ultrafast pulse trains. Laser cooling of hydrogen, antihydrogen, and carbon
appears feasible, and extension of the technique to molecules may be possible.


title:
Use of Quadrupolar Nuclei for Quantum Information processing by Nuclear
  Magnetic Resonance: Implementation of a Quantum Algorithm

abstract:
  Physical implementation of Quantum Information Processing (QIP) by
liquid-state Nuclear Magnetic Resonance (NMR), using weakly coupled spin-1/2
nuclei of a molecule, is well established. Nuclei with spin$>$1/2 oriented in
liquid crystalline matrices is another possibility. Such systems have multiple
qubits per nuclei and large quadrupolar couplings resulting in well separated
lines in the spectrum. So far, creation of pseudopure states and logic gates
have been demonstrated in such systems using transition selective
radio-frequency pulses. In this paper we report two novel developments. First,
we implement a quantum algorithm which needs coherent superposition of states.
Second, we use evolution under quadrupolar coupling to implement multi qubit
gates. We implement Deutsch-Jozsa algorithm on a spin-3/2 (2 qubit) system. The
controlled-not operation needed to implement this algorithm has been
implemented here by evolution under the quadrupolar Hamiltonian. This method
has been implemented for the first time in quadrupolar systems. Since the
quadrupolar coupling is several orders of magnitude greater than the coupling
in weakly coupled spin-1/2 nuclei, the gate time decreases, increasing the
clock speed of the quantum computer.


title: p-Mechanics and De Donder-Weyl Theory

abstract:
  The orbit method of Kirillov is used to derive the p-mechanical brackets
[quant-ph/0212101]. They generate the quantum (Moyal) and classic (Poisson)
brackets on respective orbits corresponding to representations of the
Heisenberg group. The extension of p-mechanics to field theory is made through
the De Donder-Weyl Hamiltonian formulation. The principal step is the
substitution of the Heisenberg group with Galilean. Keywords: Classic and
quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg
group, orbit method, deformation quantisation, representation theory, De
Donder-Weyl field theory, Galilean group, Clifford algebra, conformal M\"obius
transformation, Dirac operator


title:
General correlation functions of the Clauser-Horne-Shimony-Holt
  inequality for arbitrarily high-dimensional systems

abstract:
  We generalize the correlation functions of the Clauser-Horne-Shimony-Holt
(CHSH) inequality to arbitrarily high-dimensional systems. Based on this
generalization, we construct the general CHSH inequality for bipartite quantum
systems of arbitrarily high dimensionality, which takes the same simple form as
CHSH inequality for two-dimension. This inequality is optimal in the same sense
as the CHSH inequality for two dimensional systems, namely, the maximal amount
by which the inequality is violated consists with the maximal resistance to
noise. We also discuss the physical meaning and general definition of the
correlation functions. Furthermore, by giving another specific set of the
correlation functions with the same physical meaning, we realize the inequality
presented in [Phys. Rev. Lett. {\bf 88,}040404 (2002)].


title: Remarks on the nature of quantum computation

abstract:
  Two models of computer, a quantum and a classical "chemical machine" designed
to compute the relevant part of Shor's factoring algorithm are discussed. The
comparison shows that the basic quantum features believed to be responsible for
the exponential speed-up of quantum computations possess their classical
counterparts for the hybrid digital-analog computer. It is argued that the
measurement errors which cannot be fully corrected make the computation not
efficient for both models.


title: Loss induced collective subradiant Dicke behaviour in a multiatom sample

abstract:
  The exact dynamics of $N$ two-level atoms coupled to a common electromagnetic
bath and closely located inside a lossy cavity is reported. Stationary
radiation trapping effects are found and very transparently interpreted in the
context of our approach. We prove that initially injecting one excitation only
in the $N$ atoms-cavity system, loss mechanisms asymptotically drive the matter
sample toward a long-lived collective subradiant Dicke state. The role played
by the closeness of the $N$ atoms with respect to such a cooperative behavior
is brought to light and carefully discussed.


title: Quantum spiral bandwidth of entangled two-photon states

abstract:
  We put forward the concept of quantum spiral bandwidth of the spatial mode
function of the two-photon entangled state in spontaneous parametric
downconversion. We obtain the bandwidth using the eigenstates of the orbital
angular momentum of the biphoton states, and reveal its dependence with the
length of the down converting crystal and waist of the pump beam. The
connection between the quantum spiral bandwidth and the entropy of entanglement
of the quantum state is discussed.


title:
Spin dependent observable effect for free particles using the arrival
  time distribution

abstract:
  The mean arrival time of free particles is computed using the quantum
probability current. This is uniquely determined in the non-relativistic limit
of Dirac equation, although the Schroedinger probability current has an
inherent non-uniqueness. Since the Dirac probability current involves a
spin-dependent term, an arrival time distribution based on the probability
current shows an observable spin-dependent effect, even for free particles.
This arises essentially from relativistic quantum dynamics, but persists even
in the non-relativistic regime.


title:
Quantum Dynamics of the Oscillating Cantilever-Driven Adiabatic
  Reversals in Magnetic Resonance Force Microscopy

abstract:
  We simulated the quantum dynamics for magnetic resonance force microscopy
(MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR)
technique.
  We estimated the frequency shift of the cantilever vibrations and
demonstrated that this shift causes the formation of a Schrodinger cat state
which has some similarities and differences from the conventional MRFM
technique which uses cyclic adiabatic reversals of spins. The interaction of
the cantilever with the environment is shown to quickly destroy the coherence
between the two possible cantilever trajectories. We have shown that using
partial adiabatic reversals, one can produce a significant increase in the
OSCAR signal.


title:
Optical telecom networks as weak quantum measurements with post-
  selection

abstract:
  We show that weak measurements with post-selection, proposed in the context
of the quantum theory of measurement, naturally appear in the everyday physics
of fiber optics telecom networks through polarization-mode dispersion (PMD) and
polarization-dependent losses (PDL). Specifically, the PMD leads to a
time-resolved discrimination of polarization; the post-selection is done in the
most natural way: one post-selects those photons that have not been lost
because of the PDL. The quantum formalism is shown to simplify the calculation
of optical networks in the telecom limit of weak PMD.


title:
Three-mode entanglement by interlinked nonlinear interactions in optical
  $\chi^{(2)}$ media

abstract:
  We address the generation of fully inseparable three-mode entangled states of
radiation by interlinked nonlinear interactions in $\chi^{(2)}$ media. We show
how three-mode entanglement can be used to realize symmetric and asymmetric
telecloning machines, which achieve optimal fidelity for coherent states. An
experimental implementation involving a single nonlinear crystal where the two
interactions take place simultaneously is suggested. Preliminary experimental
results showing the feasibility and the effectiveness of the interaction scheme
with seeded crystal are also presented.


title:
Experimental demonstration of a high quality factor photonic crystal
  microcavity

abstract:
  Sub-threshold measurements of a photonic crystal (PC) microcavity laser
operating at 1.3 microns show a linewidth of 0.10 nm, corresponding to a
quality factor Q ~ 1.3x10^4. The PC microcavity mode is a donor-type mode in a
graded square lattice of air holes, with a theoretical Q ~ 10^5 and mode volume
Veff ~ 0.25 cubic half-wavelengths in air. Devices are fabricated in an
InAsP/InGaAsP multi-quantum well membrane and are optically pumped at 830 nm.
External peak pump power laser thresholds as low as 100 microWatts are also
observed.


title: Trapping and manipulating neutral atoms with electrostatic fields

abstract:
  We report on experiments with cold thermal $^7$Li atoms confined in combined
magnetic and electric potentials. A novel type of three-dimensional trap was
formed by modulating a magnetic guide using electrostatic fields. We observed
atoms trapped in a string of up to six individual such traps, a controlled
transport of an atomic cloud over a distance of 400$\mu$m, and a dynamic
splitting of a single trap into a double well potential. Applications for
quantum information processing are discussed.


title: Quantum Solution of Coordination Problems

abstract:
  We present a quantum solution to coordination problems that can be
implemented with present technologies. It provides an alternative to existing
approaches, which rely on explicit communication, prior commitment or trusted
third parties. This quantum mechanism applies to a variety of scenarios for
which existing approaches are not feasible.


title: Quantum Imaging and Metrology

abstract:
  The manipulation of quantum entanglement has found enormous potential for
improving performances of devices such as gyroscopes, clocks, and even
computers. Similar improvements have been demonstrated for lithography and
microscopy. We present an overview of some aspects of enhancement by quantum
entanglement in imaging and metrology.


title: Quantum marking and quantum erasure for neutral kaons

abstract:
  Entangled K0 anti-K0 pairs are shown to be suitable to discuss extensions and
tests of Bohr's complementarity principle through the quantum marking and
quantum erasure techniques suggested by M. O. Scully and K. Druehl [Phys. Rev.
A 25, 2208 (1982)]. Strangeness oscillations play the role of the traditional
interference pattern linked to wave-like behaviour, whereas the distinct
propagation in free space of the K_S and K_L components mimics the two possible
interferometric paths taken by particle-like objects.


title:
The geometry of entanglement: metrics, connections and the geometric
  phase

abstract:
  Using the natural connection equivalent to the SU(2) Yang-Mills instanton on
the quaternionic Hopf fibration of $S^7$ over the quaternionic projective space
${\bf HP}^1\simeq S^4$ with an $SU(2)\simeq S^3$ fiber the geometry of
entanglement for two qubits is investigated. The relationship between base and
fiber i.e. the twisting of the bundle corresponds to the entanglement of the
qubits. The measure of entanglement can be related to the length of the
shortest geodesic with respect to the Mannoury-Fubini-Study metric on ${\bf
HP}^1$ between an arbitrary entangled state, and the separable state nearest to
it. Using this result an interpretation of the standard Schmidt decomposition
in geometric terms is given. Schmidt states are the nearest and furthest
separable ones lying on, or the ones obtained by parallel transport along the
geodesic passing through the entangled state. Some examples showing the
correspondence between the anolonomy of the connection and entanglement via the
geometric phase is shown. Connections with important notions like the
Bures-metric, Uhlmann's connection, the hyperbolic structure for density
matrices and anholonomic quantum computation are also pointed out.


title:
Simultaneous near-field and far field spatial quantum correlations in
  spontaneous parametric down-conversion

abstract:
  We study the spatial correlations of quantum fluctuations that can be
observed in multi-mode spontaneous parametric down-conversion in the regime of
high gain. A stochastic model has been solved numerically to obtain
quantitative results beyond the stationary plane-wave pump approximation. The
pulsed shape of the pump beam and other features of the system, such as spatial
walk-off and diffraction are taken into account. Their effect on the spatial
quantum correlations predicted by the plane-wave pump theory is investigated,
both for near field and far field measurements, in a type I and in a type II
phase-matching configuration.


title: Numerical simulation of nonunitary gravity-induced localization

abstract:
  The localization of a quantum state is numerically exhibited in a nonunitary
Newtonian model for gravity. It is shown that an unlocalized state of a ball of
mass just above the expected threshold of 10^11 proton masses evolves into a
mixed state with vanishing coherences above some localization lengths.


title: Unconditionally Secure Multipartite Quantum Key Distribution

abstract:
  We consider the problem of secure key distribution among $n$ trustful agents:
the goal is to distribute an identical random bit-string among the $n$ agents
over a noisy channel such that eavesdroppers learn little about it. We study
the general situation where the only resources required are secure bipartite
key distribution and authenticated classical communication. Accordingly,
multipartite quantum key distribution can be proven unconditionally secure by
reducing the problem to the biparitite case and invoking the proof of security
of bipartite quantum key distribution.


title: Best conventional solutions to the King's Problem

abstract:
  In the King's Problem, a physicist is asked to prepare a d-state quantum
system in any state of her choosing and give it to a king who measures one of
(d+1) sets of mutually unbiased observables on it. The physicist is then
allowed to make a control measurement on the system, following which the king
reveals which set of observables he measured and challenges the physicist to
predict correctly all the eigenvalues he found. This paper obtains an upper
bound on the physicist's probability of success at this task if she is allowed
to make measurements only on the system itself (the "conventional" solution)
and not on the system as well as any ancillary systems it may have been coupled
to in the preparation phase, as in the perfect solutions proposed recently. An
optimal conventional solution, with a success probability of 0.7, is
constructed in d = 4; this is to be contrasted with the success probability of
0.902 for the optimal conventional solution in d = 2. The gap between the best
conventional solution and the perfect solution grows quite rapidly with
increasing d.


title: Entangling quantum measurement and its properties

abstract:
  We study the mathematical structure of superoperators describing quantum
measurements, including the \emph{entangling measurement}--the generalization
of the standard quantum measurement that results in entanglement between the
measurable system and apparatus. It is shown that the coherent information can
be effectively used for the analysis of such entangling measurements whose
possible applications are discussed as well.


title: Generation of Superposition Spin States in an Atomic Ensemble

abstract:
  A method for generating a mesoscopic superposition state of the collective
spin variable of a gas of atoms is proposed. The state consists of a
superposition of the atomic spins pointing in two slightly different
directions. It is obtained by using off resonant light to carry out Quantum Non
Demolition Measurements of the spins. The relevant experimental conditions,
which require very dense atomic samples, can be realized with presently
available techniques. Long-lived atomic superposition states may become useful
as an off-line resource for quantum computing with otherwise linear operations.


title: The moduli space of three qutrit states

abstract:
  We study the invariant theory of trilinear forms over a three-dimensional
complex vector space, and apply it to investigate the behaviour of pure
entangled three-partite qutrit states and their normal forms under local
filtering operations (SLOCC). We describe the orbit space of the SLOCC group
$SL(3,\C)^{\times 3}$ both in its affine and projective versions in terms of a
very symmetric normal form parameterized by three complex numbers. The
parameters of the possible normal forms of a given state are roots of an
algebraic equation, which is proved to be solvable by radicals. The structure
of the sets of equivalent normal forms is related to the geometry of certain
regular complex polytopes.


title:
Explicit effective Hamiltonians for general linear quantum-optical
  networks

abstract:
  Linear optical networks are devices that turn classical incident modes by a
linear transformation into outgoing ones. In general, the quantum version of
such transformations may mix annihilation and creation operators. We derive a
simple formula for the effective Hamiltonian of a general linear quantum
network, if such a Hamiltonian exists. Otherwise we show how the scattering
matrix of the network is decomposed into a product of three matrices that can
be generated by Hamiltonians.


title: Gaussian resolutions for equilibrium density matrices

abstract:
  A Gaussian resolution method for the computation of equilibrium density
matrices rho(T) for a general multidimensional quantum problem is presented.
The variational principle applied to the ``imaginary time'' Schroedinger
equation provides the equations of motion for Gaussians in a resolution of
rho(T) described by their width matrix, center and scale factor, all treated as
dynamical variables.
  The method is computationally very inexpensive, has favorable scaling with
the system size and is surprisingly accurate in a wide temperature range, even
for cases involving quantum tunneling. Incorporation of symmetry constraints,
such as reflection or particle statistics, is also discussed.


title: Quantum computing using dissipation (proceedings)

abstract:
  The principal obstacle to quantum information processing with many qubits is
decoherence. One source of decoherence is spontaneous emission which causes
loss of energy and information. Inability to control system parameters with
high precision is another possible source of error. As a solution we propose
quantum computing experiments using dissipation based on an environment-induced
quantum Zeno effect. As an example we present a simple scheme for quantum gate
implementations with cold trapped ions in the presence of cooling.


title:
Frequency up- and down-conversions in two-mode cavity quantum
  electrodynamics

abstract:
  In this letter we present a scheme for the implementation of frequency up-
and down-conversion operations in two-mode cavity quantum electrodynamics
(QED). This protocol for engineering bilinear two-mode interactions could
enlarge perspectives for quantum information manipulation and also be employed
for fundamental tests of quantum theory in cavity QED. As an application we
show how to generate a two-mode squeezed state in cavity QED (the original
entangled state of Einstein-Podolsky-Rosen).


title: Entanglement measure for any quantum states

abstract:
  The entanglement measure for multiqudits is proposed. This measure calculates
the partial entanglement distributed by subsystems and the complete
entanglement of the total system. This shows that we need to measure the
subsystem entanglements to explain the full description for multiqudit
entanglement. Furthermore, we extend the entanglement measure to mixed
multiqubits and the higher dimension Hilbert spaces.


title: Quantum Control of Expectation Values of Observables

abstract:
  We study the changes if any of the expectation value of a general observable
in a quantum system, the difficulties associated with the detection of these
changes, and the possible methods for correcting the system through unitary
control to maintain a constant average expectation value of the observable.


title: A Relevant Two Qubit Bell Inequality Inequivalent to the CHSH Inequality

abstract:
  We computationally investigate the complete polytope of Bell inequalities for
2 particles with small numbers of possible measurements and outcomes. Our
approach is limited by Pitowsky's connection of this problem to the
computationally hard NP problem. Despite this, we find that there are very few
relevant inequivalent inequalities for small numbers. For example, in the case
with 3 possible 2-outcome measurements on each particle, there is just one new
inequality. We describe mixed 2-qubit states which violate this inequality but
not the CHSH. The new inequality also illustrates a sharing of bi-partite
non-locality between three qubits: something not seen using the CHSH
inequality. It also inspires us to discover a class of Bell inequalities with m
possible n-outcome measurements on each particle.


title:
Even and odd q-deformed charge coherent states and their nonclassical
  properties

abstract:
  Even and odd q-deformed charge coherent states are constructed, their
(over)completeness proved and their generation explored. A $D$-algebra
realization of the SU$_q$(1,1) generators is given in terms of them. They are
shown to exhibit SU$_q$(1,1) squeezing and two-mode $q$-antibunching, but
neither one-mode, nor two-mode $q$-squeezing.

categories: quant-ph math-ph math.MP math.QA physics.optics


title: Observation of bosonic coalescence of photon pairs

abstract:
  Quantum theory predicts that two indistinguishable photons incident on a
beam-splitter interferometer stick together as they exit the device (the pair
emerges randomly from one port or the other). We use a special
photon-number-resolving energy detector for a direct loophole-free observation
of this quantum-interference phenomenon. Simultaneous measurements from two
such detectors, one at each beam-splitter output port, confirm the absence of
cross-coincidences.


title: Metric-dependent probabilities that two qubits are separable

abstract:
  In a previous study (quant-ph/0207181), we formulated a conjecture that
arbitrarily coupled qubits (describable by 4 x 4 density matrices) are
separable with an a priori probability of 8/(11 \pi^2) = 0.0736881. For this
purpose, we employed the normalized volume element of the Bures (minimal
monotone) metric as a probability distribution over the fifteen-dimensional
convex set of 4 x 4 density matrices. Here, we provide further/independent
(quasi-Monte Carlo numerical integration) evidence of a stronger nature (giving
an estimate of 0.0736858 vs. 0.0737012 previously) for this conjecture.
Additionally, employing a certain ansatz, we estimate the probabilities of
separability based on certain other monotone metrics of interest. However, we
find ourselves, at this point, unable to convincingly conjecture exact simple
formulas for these new (smaller) probabilities.


title:
Multi-photon, multi-mode polarization entanglement in parametric
  down-conversion

abstract:
  We study the quantum properties of the polarization of the light produced in
type II spontaneous parametric down-conversion in the framework of a multi-mode
model valid in any gain regime. We show that the the microscopic polarization
entanglement of photon pairs survives in the high gain regime (multi-photon
regime), in the form of nonclassical correlation of all the Stokes operators
describing polarization degrees of freedom.


title:
Polarization quantum properties in type-II Optical Parametric Oscillator
  below threshold

abstract:
  We study the far field spatial distribution of the quantum fluctuations in
the transverse profile of the output light beam generated by a type II Optical
Parametric Oscillator below threshold, including the effects of transverse
walk-off. We study how quadrature field correlations depend on the
polarization. We find spatial EPR entanglement in quadrature-polarization
components: For the far field points not affected by walk-off there is almost
complete noise suppression in the proper quadratures difference of any
orthogonal polarization components. We show the entanglement of the state of
symmetric intense, or macroscopic, spatial light modes. We also investigate
nonclassical polarization properties in terms of the Stokes operators. We find
perfect correlations in all Stokes parameters measured in opposite far field
points in the direction orthogonal to the walk-off, while locally the field is
unpolarized and we find no polarization squeezing.


title: Picturing Qubits in Phase Space

abstract:
  Focusing particularly on one-qubit and two-qubit systems, I explain how the
quantum state of a system of n qubits can be expressed as a real function--a
generalized Wigner function--on a discrete 2^n x 2^n phase space. The phase
space is based on the finite field having 2^n elements, and its geometric
structure leads naturally to the construction of a complete set of 2^n+1
mutually conjugate bases.


title: Measurement of the Casimir force between dissimilar metals

abstract:
  The first precise measurement of the Casimir force between dissimilar metals
is reported. The attractive force, between a Cu layer evaporated on a
microelectromechanical torsional oscillator, and an Au layer deposited on an
Al$_2$O$_3$ sphere, was measured dynamically with a noise level of 6
fN/$\sqrt{\rm{Hz}}$. Measurements were performed for separations in the 0.2-2
$\mu$m range. The results agree to better than 1% in the 0.2-0.5 $\mu$m range
with a theoretical model that takes into account the finite conductivity and
roughness of the two metals. The observed discrepancies, which are much larger
than the experimental precision, can be attributed to a lack of a complete
characterization of the optical properties of the specific samples used in the
experiment.


title: Detection of entanglement and Bell's inequality violation

abstract:
  We propose a new method for detecting entanglement of two qubits and discuss
its relation with the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality.
Without the need for full quantum tomography for the density matrix we can
experimentally detect the entanglement by measuring less than 9 local
observables for any given state. We show that this test is stronger than the
CHSH-Bell inequality and also gives an estimation for the degree of
entanglement. If prior knowledge is available we can further greatly reduce the
number of required local observables. The test is convenient and feasible with
present experimental technology.


title:
The role of squeezing in quantum key distribution based on homodyne
  detection and post-selection

abstract:
  The role of squeezing in quantum key distribution with continuous variables
based on homodyne detection and post-selection is investigated for several
specific eavesdropping strategies. It is shown that amplitude squeezing creates
strong correlations between the signals of the legitimate receiver and a
potential eavesdropper. Post-selection of the received pulses can therefore be
used to reduce the eavesdropper's knowledge of the raw key, which increases the
secret key rate by orders of magnitude over large distances even for modest
amounts of squeezing.


title: Exact results for Casimir forces using Surface Impedance: Nonlocal Media

abstract:
  We show that exact results are obtained for the calculation of Casimir forces
between arbitrary materials using the concept of surface impedances, obtaining
in a trivial way the force in the limit of perfect conductors and also Lifshitz
formula in the limit of semi-infinite media. As an example we present a full
and rigorous calculation of the Casimir force between two metallic half-spaces
described by a hydrodynamic nonlocal dielectric response.


title: Quantum walks on general graphs

abstract:
  Quantum walks, both discrete (coined) and continuous time, on a general graph
of N vertices with undirected edges are reviewed in some detail. The resource
requirements for implementing a quantum walk as a program on a quantum computer
are compared and found to be very similar for both discrete and continuous time
walks. The role of the oracle, and how it changes if more prior information
about the graph is available, is also discussed.


title:
Virtual Entanglement and Reconciliation Protocols for Quantum
  Cryptography with Continuous Variables

abstract:
  We discuss quantum key distribution protocols using quantum continuous
variables. We show that such protocols can be made secure against individual
gaussian attacks regardless the transmission of the optical line between Alice
and Bob. This is achieved by reversing the reconciliation procedure subsequent
to the quantum transmission, that is, using Bob's instead of Alice's data to
build the key. Although squeezing or entanglement may be helpful to improve the
resistance to noise, they are not required for the protocols to remain secure
with high losses. Therefore, these protocols can be implemented very simply by
transmitting coherent states and performing homodyne detection. Here, we show
that entanglement nevertheless plays a crucial role in the security analysis of
coherent state protocols. Every cryptographic protocol based on displaced
gaussian states turns out to be equivalent to an entanglement-based protocol,
even though no entanglement is actually present. This equivalence even holds in
the absence of squeezing, for coherent state protocols. This ``virtual''
entanglement is important to assess the security of these protocols as it
provides an upper bound on the mutual information between Alice and Bob if they
had used entanglement. The resulting security criteria are compared to the
separability criterion for bipartite gaussian variables. It appears that the
security thresholds are well within the entanglement region. This supports the
idea that coherent state quantum cryptography may be unconditionally secure.


title: Decoherence and the Loschmidt echo

abstract:
  Environment--induced decoherence causes entropy increase. It can be
quantified using, e.g., the purity $\varsigma={\rm Tr}\rho^2$. When the
Hamiltonian of a quantum system is perturbed, its sensitivity to such
perturbation can be measured by the Loschmidt echo $\bar M(t)$. It is given by
the average squared overlap between the perturbed and unperturbed state. We
describe the relation between the temporal behavior of $\varsigma(t)$ and $\bar
M(t)$. In this way we show that the decay of the Loschmidt echo can be analyzed
using tools developed in the study of decoherence. In particular, for systems
with a classically chaotic Hamiltonian the decay of $\varsigma$ and $\bar M$
has a regime where it is dominated by the classical Lyapunov exponents


title:
A quantum gate array can be programmed to evaluate the expectation value
  of any operator

abstract:
  A programmable gate array is a circuit whose action is controlled by input
data. In this letter we describe a special--purpose quantum circuit that can be
programmed to evaluate the expectation value of any operator $O$ acting on a
space of states of $N$ dimensions. The circuit has a program register whose
state $|\Psi(O)>_P$ encodes the operator $O$ whose expectation value is to be
evaluated. The method requires knowledge of the expansion of $O$ in a basis of
the space of operators. We discuss some applications of this circuit and its
relation to known instances of quantum state tomography.


title:
Operator-Schmidt decompositions and the Fourier transform, with
  applications to the operator-Schmidt numbers of unitaries

abstract:
  The operator-Schmidt decomposition is useful in quantum information theory
for quantifying the nonlocality of bipartite unitary operations. We construct a
family of unitary operators on C^n tensor C^n whose operator-Schmidt
decompositions are computed using the discrete Fourier transform. As a
corollary, we produce unitaries on C^3 tensor C^3 with operator-Schmidt number
S for every S in {1,...,9}. This corollary was unexpected, since it
contradicted reasonable conjectures of Nielsen et al [Phys. Rev. A 67 (2003)
052301] based on intuition from a striking result in the two-qubit case. By the
results of Dur, Vidal, and Cirac [Phys. Rev. Lett. 89 (2002) 057901
quant-ph/0112124], who also considered the two-qubit case, our result implies
that there are nine equivalence classes of unitaries on C^3 tensor C^3 which
are probabilistically interconvertible by (stochastic) local operations and
classical communication. As another corollary, a prescription is produced for
constructing maximally-entangled operators from biunimodular functions.
Reversing tact, we state a generalized operator-Schmidt decomposition of the
quantum Fourier transform considered as an operator C^M_1 tensor C^M_2 -->
C^N_1 tensor C^N_2, with M_1 x M_2 = N_1 x N_2. This decomposition shows (by
Nielsen's bound) that the communication cost of the QFT remains maximal when a
net transfer of qudits is permitted. In an appendix, a canonical procedure is
given for removing basis-dependence for results and proofs depending on the
"magic basis" introduced in [S. Hill and W. Wootters, "Entanglement of a pair
of quantum bits," Phys Rev. Lett 78 (1997) 5022-5025, quant-ph/9703041 (and
quant-ph/9709029)].


title: Modal dynamics for positive operator measures

abstract:
  The modal interpretation of quantum mechanics allows one to keep the standard
classical definition of realism intact. That is, variables have a definite
status for all time and a measurement only tells us which value it had.
However, at present modal dynamics are only applicable to situations that are
described in the orthodox theory by projective measures. In this paper we
extend modal dynamics to include positive operator measures (POMs). That is,
for example, rather than using a complete set of orthogonal projectors, we can
use an overcomplete set of nonorthogonal projectors. We derive the conditions
under which Bell's stochastic modal dynamics for projective measures reduce to
deterministic dynamics, showing (incidentally) that Brown and Hiley's
generalization of Bohmian mechanics [quant-ph/0005026, (2000)] cannot be thus
derived. We then show how {\em deterministic} dynamics for positive operators
can also be derived. As a simple case, we consider a Harmonic oscillator, and
the overcomplete set of coherent state projectors (i.e. the Husimi POM). We
show that the modal dynamics for this POM in the classical limit correspond to
the classical dynamics, even for the nonclassical number state $\ket{n}$. This
is in contrast to the Bohmian dynamics, which for energy eigenstates, the
dynamics are always non-classical.


title:
Semiclassical catastrophes and accumulative angular squeezing of a
  kicked quantum rotor

abstract:
  We present a detailed theory of spectacular semiclassical catastrophes
happening during the time evolution of a kicked quantum rotor (Phys.Rev. Lett.
{\bf 87}, 163601 (2001)). Both two- and three-dimensional rotational systems
are analyzed. It is shown that the wave function of the rotor develops a {\em
cusp} at a certain delay after a kick, which results in a sharply focused
rotational wave packet. The {\em cusp} is followed by a fold-type catastrophe
manifested in the {\em rainbow}-like moving angular singularities. In the
three-dimensional case, the rainbows are accompanied by additional singular
features similar to {\em glory} structures known in wave optics. These
catastrophes in the time-dependent angular wave function are well described by
the appropriate tools of the quasiclassical wave mechanics, i.e. by Airy and
Bessel approximations and Pearcey's functions. A scenario of "accumulative
squeezing" is also presented in which a specially designed train of short kicks
produces an unlimited narrowing of the rotor angular distribution. This
scenario is relevant for the molecular alignment by short laser pulses, and
also for atom lithography schemes in which cold atoms are focused by an optical
standing wave.


title: Nonlinear optics via double dark resonances

abstract:
  Double dark resonances originate from a coherent perturbation of a system
displaying electromagnetically induced transparency. We experimentally show and
theoretically confirm that this leads to the possibility of extremely sharp
resonances prevailing even in the presence of considerable Doppler broadening.
A gas of 87Rb atoms is subjected to a strong drive laser and a weak probe laser
and a radio frequency field, where the magnetic coupling between the Zeeman
levels leads to nonlinear generation of a comb of sidebands.


title: Comment on "Dense coding in entangled states"

abstract:
  In a recent Brief Report, Lee et al. [L. Lee, D. Ahn, and S.W. Hwang, Phys.
Rev. A 66, 024304 (2002)] have claimed that using pairwise entangled qubits
gives rise to an exponentially more efficient dense coding when two parties are
involved than using maximally entangled qubits shared among N parties. Here, we
show that their claim is not true.


title: Amplitude squeezed fiber Bragg grating solitons

abstract:
  Quantum fluctuations of optical fiber Bragg grating solitons are investigated
numerically by the back-propagation method. It is found for the first time that
the bandgap effects of the grating act as a nonlinear filter and cause the
soliton to be amplitude squeezed. The squeezing ratio saturates after a certain
grating length and the fundamental Bragg soliton produces the optimal squeezing
ratio.


title:
Zero-range potentials with Inner structure: fitting parameters for
  resonance scattering

abstract:
  The solution of the classical Fermi problem of low-energy neutron scattering
by nuclei, when the excitations of the nuclei in scattering processes are taken
into account, is found by the method of zero-range potentials with inner
structure. This model is a generalization of the Fermi zero-range potential
obtained by adding a non-trivial inner Hamiltonian and inner space with
indefinite metric. We propose a general principle of analyticity of the
Caley-transform of the S-scattering matrix, written as a function of wave
number. This permits us to evaluate all parameters of the model, including the
indefinite metric tensor of the inner space, once the spectrum of the inner
Hamiltonian, the scattering length and the effective radious are chosen.


title: Toward a Quantum Theory of Observation

abstract:
  The program of a physical concept of information is outlined in the framework
of quantum theory. A proposal is made for how to avoid the introduction of
axiomatic observables. The conventional (collapse) and the Everett
interpretations of quantum theory may in principle lead to different dynamical
consequences. Finally, a formal ensemble description not based on a concept of
lacking information is discussed.


title: Continuous variable entanglement using cold atoms

abstract:
  We present experimental demonstration of quadrature and polarization
entanglement generated via the interaction between a coherent linearly
polarized field and cold atoms in a high finesse optical cavity. The non linear
atom-field interaction produces two squeezed modes with orthogonal
polarizations which are used to generate a pair of non separable beams, the
entanglement of which is demonstrated by checking the inseparability criterion
for continuous variables recently derived by Duan et al. [Phys. Rev. Lett. 84,
2722 (2000)] and calculating the entanglement of formation [Giedke et al.,
Phys. Rev. Lett. 91, 107901 (2003)].


title: Why relativity allows quantum tunnelling to 'take no time'?

abstract:
  In quantum tunnelling, what appears an infinitely fast barrier traversal can
be explained in terms of an Aharonov-like weak measurement of the tunnelling
time, in which the role of the pointer is played by the particle's own
coordinate. A relativistic wavepacket is shown to be reshaped through a series
of subluminal shifts which together produce an anomalous 'superluminal' result.


title: Spectroscopy by frequency entangled photon pairs

abstract:
  Quantum spectroscopy was performed using the frequency-entangled broadband
photon pairs generated by spontaneous parametric down-conversion. An absorptive
sample was placed in front of the idler photon detector, and the frequency of
signal photons was resolved by a diffraction grating. The absorption spectrum
of the sample was measured by counting the coincidences, and the result is in
agreement with the one measured by a conventional spectrophotometer with a
classical light source.


title: Quantum Bit Commitment with a Composite Evidence

abstract:
  Entanglement-based attacks, which are subtle and powerful, are usually
believed to render quantum bit commitment insecure. We point out that the no-go
argument leading to this view implicitly assumes the evidence-of-commitment to
be a monolithic quantum system. We argue that more general evidence structures,
allowing for a composite, hybrid (classical-quantum) evidence, conduce to
improved security. In particular, we present and prove the security of the
following protocol: Bob sends Alice an anonymous state. She inscribes her
commitment $b$ by measuring part of it in the + (for $b = 0$) or $\times$ (for
$b=1$) basis. She then communicates to him the (classical) measurement outcome
$R_x$ and the part-measured anonymous state interpolated into other, randomly
prepared qubits as her evidence-of-commitment.


title:
A practically feasible entanglement assisted quantum key distribution
  protocol

abstract:
  We give an entanglement assisted scheme for quantum key distribution.
  The scheme requires the maximally entangled 2-qubit state but does not
require any quantum storage. The scheme is unconditionally secure under
whatever Eve's attack.
  Given the symmetric noisy channel with uncorrelated noise, our scheme can
tolerate the bit error rate up to
  26% in the 4-state case and 30% in the
  6-state respectively, respectively. These values are higher than those of all
currently known two-level-state schemes without using a quantum storage.


title: Complete population transfer in a degenerate 3-level atom

abstract:
  We find conditions required to achieve complete population transfer, via
coherent population trapping, from an initial state to a designated final state
at a designated time in a degenerate 3-level atom, where transitions are caused
by an external interaction. Complete population transfer from an initially
occupied state 1 to a designated state 2 occurs under two conditions. First,
there is a constraint on the ratios of the transition matrix elements of the
external interaction. Second, there is a constraint on the action integral over
the interaction, or "area", corresponding to the phase shift induced by the
external interaction. Both conditions may be expressed in terms of simple odd
integers.


title: Information Processing beyond Quantum Computation

abstract:
  Recent developments in quantum computation have made it clear that there is a
lot more to computation than the conventional Boolean algebra. Is quantum
computation the most general framework for processing information? Having
gathered the courage to go beyond the traditional definitions, we are now in a
position to answer: Certainly not. The meaning of a message being ``a
collection of building blocks'' can be explored in a variety of situations. A
generalised framework is proposed based on group theory, and it is illustrated
with well-known physical examples. A systematic information theoretical
approach is yet to be developed in many of these situations. Some directions
for future development are pointed out.


title:
Vacuum-field level shifts in a single trapped ion mediated by a single
  distant mirror

abstract:
  A distant mirror leads to a vacuum-induced level shift in a laser-excited
atom. This effect has been measured with a single mirror 25 cm away from a
single, trapped barium ion. This dispersive action is the counterpart to the
mirror's dissipative effect, which has been shown earlier to effect a change in
the ion's spontaneous decay [J. Eschner et al., Nature 413, 495-498 (2001)].
The experimental data are well described by 8-level optical Bloch equations
which are amended to take into account the presence of the mirror according to
the model in [U. Dorner and P. Zoller, Phys. Rev. A 66, 023816 (2002)].
Observed deviations from simple dispersive behavior are attributed to
multi-level effects.


title: Population control of 2s-2p transitions in hydrogen

abstract:
  We consider the time evolution of the occupation probabilities for the 2s-2p
transition in a hydrogen atom interacting with an external field, V(t). A
two-state model and a dipole approximation are used. In the case of degenerate
energy levels an analytical solution of the time-dependent Shroedinger equation
for the probability amplitudes exists. The form of the solution allows one to
choose the ratio of the field amplitude to its frequency that leads to temporal
trapping of electrons in specific states. The analytic solution is valid when
the separation of the energy levels is small compared to the energy of the
interacting radiation.


title:
How to reuse a one-time pad and other notes on authentication,
  encryption and protection of quantum information

abstract:
  Quantum information is a valuable resource which can be encrypted in order to
protect it. We consider the size of the one-time pad that is needed to protect
quantum information in a number of cases. The situation is dramatically
different from the classical case: we prove that one can recycle the one-time
pad without compromising security. The protocol for recycling relies on
detecting whether eavesdropping has occurred, and further relies on the fact
that information contained in the encrypted quantum state cannot be fully
accessed. We prove the security of recycling rates when authentication of
quantum states is accepted, and when it is rejected. We note that recycling
schemes respect a general law of cryptography which we prove relating the size
of private keys, sent qubits, and encrypted messages. We discuss applications
for encryption of quantum information in light of the resources needed for
teleportation. Potential uses include the protection of resources such as
entanglement and the memory of quantum computers. We also introduce another
application: encrypted secret sharing and find that one can even reuse the
private key that is used to encrypt a classical message. In a number of cases,
one finds that the amount of private key needed for authentication or
protection is smaller than in the general case.


title: Quasi exactly solvable (QES) equations with multiple algebraisations

abstract:
  We review three examples of quasi exactly solvable (QES) Hamitonians which
possess multiple algebraisations. This includes the most prominent example, the
Lame equation, as well as recently studied many-body Hamiltonians with
Weierstrass interaction potential and finally, a 2x2 coupled channel
Hamiltonian.


title:
Operator representations for a class of quantum entanglement measures
  and criterions

abstract:
  We find that a class of entanglement measures for bipartite pure state can be
expressed by the average values of quantum operators, which are related to any
complete basis of one partite operator space. Two specific examples are given
based on two different ways to generalize Pauli matrices to $d$ dimensional
Hilbert space and the case for identical particle system is also considered. In
addition, applying our measure to mixed state case will give a sufficient
condition for entanglement.


title: Nonperturbative Coherent Population Trapping: An Analytic Model

abstract:
  Coherent population trapping is shown to occur in a driven symmetric
double-well potential in the strong-field regime. The system parameters have
been chosen to reproduce the $0^{-}\leftrightarrow 3^{+}$ transition of the
inversion mode of the ammonia molecule. For a molecule initially prepared in
its lower doublet we find that, under certain circumstances, the $3^{+}$ level
remains unpopulated, and this occurs in spite of the fact that the laser field
is resonant with the $0^{-}\leftrightarrow 3^{+}$ transition and intense enough
so as to strongly mix the $0^{+}$ and $0^{-}$ ground states. This
counterintuitive result constitutes a coherent population trapping phenomenon
of nonperturbative origin which cannot be accounted for with the usual models.
We propose an analytic nonperturbative model which accounts correctly for the
observed phenomenon.


title:
Weak-Coupling-Like Time Evolution of Driven Four-Level Systems in the
  Strong-Coupling Regime

abstract:
  It is shown analytically that there exists a natural basis in terms of which
the nonperturbative time evolution of an important class of driven four-level
systems in the strong-coupling regime decouples and essentially reduces to the
corresponding time evolution in the weak-field regime, exhibiting simple Rabi
oscillations between the different relevant quantum states. The predictions of
the model are corroborated by an exact numerical calculation.


title: Unconventional geometric quantum computation

abstract:
  We propose a new class of unconventional geometric gates involving nonzero
dynamic phases, and elucidate that geometric quantum computation can be
implemented by using these gates. Comparing with the conventional geometric
gate operation, in which the dynamic phase shift must be removed or avoided,
the gates proposed here may be operated more simply. We illustrate in detail
that unconventional nontrivial two-qubit geometric gates with built-in fault
tolerant geometric features can be implemented in real physical systems.


title: Parametrization of Quantum States and Channels

abstract:
  In this manuscript, a parametrization of positive matrices together with some
of its many applications in quantum information theory is given.


title: The generalized MIC-Kepler system

abstract:
  This paper deals with dynamical system that generalizes the MIC-Kepler
system. It is shown that the Schr\"{o}dinger equation for this generalized
MIC-Kepler system can be separated in spherical and parabolic coordinates. The
spectral problem in spherical and parabolic coordinates is solved.


title: Method of extending hyperfine coherence times in Pr^3+:Y_2SiO_5

abstract:
  In this letter we present a method for increasing the coherence time of
praseodymium hyperfine ground state transitions in Pr^3+:Y_2SiO_5 by the
application of a specific external magnetic field. The magnitude and angle of
the external field is applied such that the Zeeman splitting of a hyperfine
transition is at a critical point in three dimensions, making the first order
Zeeman shift vanishingly small for the transition. This reduces the influence
of the magnetic interactions between the praseodymium ions and the spins in the
host lattice on the transition frequency. Using this method a phase memory time
of 82ms was observed, a value two orders of magnitude greater than previously
reported. It is shown that the residual dephasing is amenable quantum error
correction.


title:
Transient dynamics of light propagation in EIT medium and hidden
  symmetry of multi-bit quantum memory

abstract:
  We investigate the transient phenomenon or property of the propagation of an
optical probe field in a medium consisting of many $\Lambda$-type three-level
atoms coupled to this probe field and an classical driven field. We observe a
hidden symmetry and obtain an exact solution for this light propagation problem
by means of the spectral generating method. This solution enlightens us to
propose a practical protocol implementing the quantum memory robust for quantum
decoherence in a crystal. As an transient dynamic process this solution also
manifests an exotic result that a wave-packet of light will split into three
packets propagating at different group velocities. It is argued that
  "super-luminal group velocity" and "sub-luminal group velocity" can be
observed simultaneously in the same system. This interesting phenomenon is
expected to be demonstrated experimentally.


title:
Comment on "Bell's Theorem without Inequalities and without
  Probabilities for Two Observers"

abstract:
  In this Comment we show that Cabello's argument [Phys. Rev. Lett. 86, 1911
(2001)] which proves the nonlocal feature of any classical model of quantum
mechanics based on Einstein-Podolsky-Rosen (EPR) criterion of elements of
reality, must involve at least four distant observers rather than the two
employed by the author. Moreover we raise a remark on the necessity of
performing a real experiment confirming Cabello's argument.


title:
Classical chaos with Bose-Einstein condensates in tilted optical
  lattices

abstract:
  A widely accepted definition of ``quantum chaos'' is ``the behavior of a
quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics
of quantum-chaotic systems is nevertheless very different from that of their
classical counterparts. A fundamental reason for that is the linearity of
Schr{\"o}dinger equation. In this paper, we study the quantum dynamics of an
ultra-cold quantum degenerate gas in a tilted optical lattice and show that it
displays features very close to \emph{classical} chaos. We show that its phase
space is organized according to the Kolmogorov-Arnold-Moser theorem.


title: Uncertainty Principle: Classic and Quantum Aspects

abstract:
  Some aspects of application of the Uncertainty Principle in the range of
interaction radiation with matter surveyed. The procedure of adjustment is
proposed at calculation of values of an electromagnetic energy in a quantum
theory of a field.


title:
Comment on ''Surface-impedance approach solves problems with the thermal
  Casimir force between real metals''

abstract:
  In a recent paper, Geyer, Klimchitskaya, and Mostepanenko [Phys. Rev. A 67,
062102 (2003); quant-ph/0306038] proposed the final solution of the problem of
temperature correction to the Casimir force between real metals. The basic idea
was that one cannot use the dielectric permittivity in the frequency region
where a real current may arise leading to Joule heating of the metal. Instead,
the surface impedance approach is proposed as a solution of all contradictions.
The purpose of this comment is to show that (i) the main idea contradicts to
the fluctuation dissipation theorem, (ii) the proposed method to calculate the
force gives wrong value of the temperature correction since the contribution of
low frequency fluctuations is calculated with the impedance which is not
applicable at low frequencies. In the impedance approach the right result for
the reflection coefficients in the n=0 term of the Lifshitz formula is given.


title: Quantum teleportation via a W state

abstract:
  We investigate two schemes of the quantum teleportation with a $W$ state,
which belongs to a different class from a Greenberger-Horne-Zeilinger class. In
the first scheme, the $W$ state is shared by three parties one of whom, called
a sender, performs a Bell measurement. It is shown that quantum information of
an unknown state is split between two parties and recovered with a certain
probability. In the second scheme, a sender takes two particles of the $W$
state and performs positive operator valued measurements in two ways. For two
schemes, we calculate the success probability and the average fidelity. We show
that the average fidelity of the second scheme cannot exceed that of the first
one.


title: Quantum Correlation Games

abstract:
  A new approach to play games quantum mechanically is proposed. We consider
two players who perform measurements in an EPR-type setting. The payoff
relations are defined as functions of *correlations*, i.e. without reference to
classical or quantum mechanics. Classical bi-matrix games are reproduced if the
input states are classical and perfectly anti-correlated, that is, for a
classical correlation game. However, for a quantum correlation game, with an
entangled singlet state as input, qualitatively different solutions are
obtained. For example, the Prisoners' Dilemma acquires a Nash equilibrium if
the players both apply a mixed strategy. It appears to be conceptually
impossible to reproduce the properties of quantum correlation games within the
framework of classical games.


title: Gaussian Entanglement of Formation

abstract:
  We introduce a Gaussian version of the entanglement of formation adapted to
bipartite Gaussian states by considering decompositions into pure Gaussian
states only. We show that this quantity is an entanglement monotone under
Gaussian operations and provide a simplified computation for states of
arbitrary many modes. For the case of one mode per site the remaining
variational problem can be solved analytically. If the considered state is in
addition symmetric with respect to interchanging the two modes, we prove
additivity of the considered entanglement measure. Moreover, in this case and
considering only a single copy, our entanglement measure coincides with the
true entanglement of formation.


title: Spin-1/2 geometric phase driven by decohering quantum fields

abstract:
  We calculate the geometric phase of a spin-1/2 system driven by a one and two
mode quantum field subject to decoherence. Using the quantum jump approach, we
show that the corrections to the phase in the no-jump trajectory are different
when considering an adiabatic and non-adiabatic evolution. We discuss the
implications of our results from both the fundamental as well as quantum
computational perspective.


title:
Gleason-Type Derivations of the Quantum Probability Rule for Generalized
  Measurements

abstract:
  We prove a Gleason-type theorem for the quantum probability rule using frame
functions defined on positive-operator-valued measures (POVMs), as opposed to
the restricted class of orthogonal projection-valued measures used in the
original theorem. The advantage of this method is that it works for
two-dimensional quantum systems (qubits) and even for vector spaces over
rational fields--settings where the standard theorem fails. Furthermore, unlike
the method necessary for proving the original result, the present one is rather
elementary. In the case of a qubit, we investigate similar results for frame
functions defined upon various restricted classes of POVMs. For the so-called
trine measurements, the standard quantum probability rule is again recovered.


title:
Reply to Marinatto's comment on "Bell's theorem without inequalities and
  without probabilities for two observers"

abstract:
  It is shown that Marinatto's claim [Phys. Rev. Lett. 90, 258901 (2003)] that
the proof of "Bell's theorem without inequalities and without probabilities for
two observers" [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] requires four
spacelike separated observers rather than two is unjustified.


title: Sampling with quantum mechanics

abstract:
  A new algorithm for estimating the fraction of numbers that is present in a
superpositional state which satisfies a given condition,is introduced.This
algorithm is conceptually simple and does not require quantum Fourier
transform.Also the number of steps required does not depend on the size of the
data base to be searched.


title: Quantum Computing Without Entanglement

abstract:
  It is generally believed that entanglement is essential for quantum
computing. We present here a few simple examples in which quantum computing
without entanglement is better than anything classically achievable, in terms
of the reliability of the outcome after a xed number of oracle calls. Using a
separable (that is, unentangled) n-qubit state, we show that the Deutsch-Jozsa
problem and the Simon problem can be solved more reliably by a quantum computer
than by the best possible classical algorithm, even probabilistic. We conclude
that: (a) entanglement is not essential for quantum computing; and (b) some
advantage of quantum algorithms over classical algorithms persists even when
the quantum state contains an arbitrarily small amount of information|that is,
even when the state is arbitrarily close to being totally mixed.


title: Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State

abstract:
  The Grover quantum search algorithm is generalized to deal with an arbitrary
mixed initial state. The probability to measure a marked state as a function of
time is calculated, and found to depend strongly on the specific initial state.
The form of the function, though, remains as it is in the case of initial pure
state. We study the role of the von Neumann entropy of the initial state, and
show that the entropy cannot be a measure for the usefulness of the algorithm.
We give few examples and show that for some extremely mixed initial states
carrying high entropy, the generalized Grover algorithm is considerably faster
than any classical algorithm.


title: Ultra-fast propagation of Schr\"odinger waves in absorbing media

abstract:
  We identify the characteristic times of the evolution of a quantum wave
generated by a point source with a sharp onset in an absorbing medium. The
"traversal'' or "B\"uttiker-Landauer'' time (which grows linearly with the
distance to the source) for the Hermitian, non-absorbing case is substituted by
three different characteristic quantities. One of them describes the arrival of
a maximum of the density calculated with respect to position, but the maximum
with respect to time for a given position becomes independent of the distance
to the source and is given by the particle's ``survival time'' in the medium.
This later effect, unlike the Hartman effect, occurs for injection frequencies
under or above the cut-off, and for arbitrarily large distances. A possible
physical realization is proposed by illuminating a two-level atom with a
detuned laser.


title:
Radiating and Non-Radiating Current Distributions in Quantum
  Electrodynamics

abstract:
  The notion of ``radiating'' and ``non-radiating'' current sources in
classical electrodynamics plays an important role in calculations of direct and
inverse electromagnetic scattering problems. Such a decomposition of the
current is central for the notion of localized non-radiating electromagnetic
modes. A completely quantum electrodynamic view is explored in this work.
Photon emission and absorption current sources are classified as being either
radiating or non-radiating. This quantum classification corresponds,
respectively and exactly, to the notion of ``real'' and ``virtual'' photon
processes. Causal properties of both real and virtual electromagnetic fields
are discussed.


title:
Susceptibility and Group Velocity in a Fully Quantized Model For
  Electromagnetically Induced Transparency

abstract:
  We have developed a fully quantized model for EIT in which the decay rates
are taken into account. In this model, the general form of the susceptibility
and group velocity of the probe laser we obtained are operators. Their
expectation value and fluctuation can be obtained on the Fock space.
Furthermore the uncertainty of the group velocity under very weak intensity of
the controlling laser and the uncertainty relation between the phase operator
of coupling laser and the group velocity are approximately given. Considering
the decay rates of various levels, we may analyze the probe laser near
resonance in detail and calculate the fluctuation in both absorption and
dispersion. We also discuss how the fully quantized model reduces to a
semiclassical model when the mean photon numbers of the coupling laser is
getting large.


title: Adiabatic passage of collective excitations in atomic ensembles

abstract:
  We describe a theoretical scheme that allows for transfer of quantum states
of atomic collective excitation between two macroscopic atomic ensembles
localized in two spatially-separated domains. The conception is based on the
occurrence of double-exciton dark states due to the collective destructive
quantum interference of the emissions from the two atomic ensembles. With an
adiabatically coherence manipulation for the atom-field couplings by stimulated
Ramann scattering, the dark states will extrapolate from an exciton state of an
ensemble to that of another. This realizes the transport of quantum information
among atomic ensembles.


title:
Some Features of the Conditional $q$-Entropies of Composite Quantum
  Systems

abstract:
  The study of conditional $q$-entropies in composite quantum systems has
recently been the focus of considerable interest, particularly in connection
with the problem of separability. The $q$-entropies depend on the density
matrix $\rho$ through the quantity $\omega_q = Tr\rho^q$, and admit as a
particular instance the standard von Neumann entropy in the limit case $q\to
1$. A comprehensive numerical survey of the space of pure and mixed states of
bipartite systems is here performed, in order to determine the volumes in state
space occupied by those states exhibiting various special properties related to
the signs of their conditional $q$-entropies and to their connections with
other separability-related features, including the majorization condition.
Different values of the entropic parameter $q$ are considered, as well as
different values of the dimensions $N_1$ and $N_2$ of the Hilbert spaces
associated with the constituting subsystems. Special emphasis is paid to the
analysis of the monotonicity properties, both as a function of $q$ and as a
function of $N_1$ and $N_2$, of the various entropic functionals considered.


title:
Reply to "No spin-statistics connection in nonrelativistic quantum
  mechanics"

abstract:
  In a previous paper [quant-ph/0207017] I gave an elementary proof, starting
from stated assumptions of nonrelativistic quantum mechanics, that identical
spin-zero particles must be bosons. Since then it has been suggested that my
proof assumed its conclusion, and that it is based on a theory "quite different
from standard physics." [quant-ph/0304088] I show here that those two
statements are incorrect.


title:
Proposal for a simple quantum error correction test gate in linear
  optics

abstract:
  We describe a linear quantum optical circuit capable of demonstrating a
simple quantum error correction code in a four photon experiment.


title: Multielectronic Atom in Magnetic Field Revisited

abstract:
  The motion of a multi-electronic atom in an external electro-magnetic field
is reconsidered. We prove that according to classical mechanics and
electrodynamics, the assumption that the interaction with the magnetic field is
described by means of a potential energy is no valid, and the trajectory of the
center of mass can be deflected by a magnetic field, even if the internal
angular momentum is zero. The characteristic equation of the corresponding
hamiltonian is not separable in three degrees of freedom for the hydrogen atom.

categories: quant-ph hep-ph physics.atom-ph physics.class-ph


title: Quantum Kalman Filtering and the Heisenberg Limit in Atomic Magnetometry

abstract:
  The shot-noise detection limit in current high-precision atomic magnetometry
is a manifestation of quantum fluctuations that scale as the square root of N
in an ensemble of N particles. However, there is a general expectation that the
reduced projection noise provided by conditional spin-squeezing could be
exploited to surpass the conventional shot-noise limit. We show that continuous
measurement coupled with quantum Kalman filtering provides an optimal procedure
for magnetic detection limits that scale with 1/N, the Heisenberg squeezing
limit. Our analysis demonstrates the importance of optimal estimation
procedures for high bandwidth precision magnetometry.


title:
Misbelief and misunderstandings on the non--Markovian dynamics of a
  damped harmonic oscillator

abstract:
  We use the exact solution for the damped harmonic oscillator to discuss some
relevant aspects of its open dynamics often mislead or misunderstood. We
compare two different approximations both referred to as Rotating Wave
Approximation. Using a specific example, we clarify some issues related to
non--Markovian dynamics, non--Lindblad type dynamics, and positivity of the
density matrix.


title: Characterizing Entanglement via Uncertainty Relations

abstract:
  We derive a family of necessary separability criteria for finite-dimensional
systems based on inequalities for variances of observables. We show that every
pure bipartite entangled state violates some of these inequalities.
Furthermore, a family of bound entangled states and true multipartite entangled
states can be detected. The inequalities also allow to distinguish between
different classes of true tripartite entanglement for qubits. We formulate an
equivalent criterion in terms of covariance matrices. This allows us to apply
criteria known from the regime of continuous variables to finite-dimensional
systems.


title:
Multi-partite Quantum Entanglement versus Randomization: Fair and
  Unbiased Leader Election in Networks

abstract:
  In this paper we show that sufficient multi-partite quantum entanglement
helps in fair and unbiased election of a leader in a distributed network of
processors with only linear classical communication complexity. We show that a
total of $O(\log n)$ distinct multi-partite maximally entanglement sets (ebits)
are capable of supporting such a protocol in the presence of nodes that may lie
and thus be biased. Here, $n$ is the number of nodes in the network. We also
demonstrate the difficulty of performing unbiased and fair election of a leader
with linear classical communication complexity in the absence of quantum
entanglement even if all nodes have perfect random bit generators. We show that
the presence of a sufficient number $O(n/\log n)$ of biased agents leads to a
non-zero limiting probability of biased election of the leader, whereas, the
presence of a smaller number $O(\log n)$ of biased agents matters little. We
define two new related complexity classes motivated by the our leader election
problem and discuss a few open questions.


title: On Shor's channel extension and constrained channels

abstract:
  In this paper we give several equivalent formulations of the additivity
conjecture for constrained channels, which formally is substantially stronger
than the unconstrained additivity. To this end a characteristic property of the
optimal ensemble for such a channel is derived, generalizing the maximal
distance property. It is shown that the additivity conjecture for constrained
channels holds true for certain nontrivial classes of channels.
  Recently P. Shor showed that conjectured additivity properties for several
quantum information quantities are in fact equivalent. After giving an
algebraic formulation for the Shor's channel extension, its main asymptotic
property is proved. It is then used to show that additivity for two constrained
channels can be reduced to the same problem for unconstrained channels, and
hence, "global" additivity for channels with arbitrary constraints is
equivalent to additivity without constraints.


title: Pattern Formation in Wigner-like Equations via Multiresolution

abstract:
  We present the application of the variational-wavelet analysis to the
quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and
related equations corresponding to the nonlinear (polynomial) dynamical
problems. (Naive) deformation quantization, the multiresolution representations
and the variational approach are the key points. We construct the solutions via
the multiscale expansions in the generalized coherent states or high-localized
nonlinear eigenmodes in the base of the compactly supported wavelets and the
wavelet packets. We demonstrate the appearance of (stable) localized patterns
(waveletons) and consider entanglement and decoherence as possible
applications.


title: Photon-exchange effects on photon-pair transmission

abstract:
  It has been proposed that photon-exchange effects in atom-photon interactions
could lead to greatly enhanced optical nonlinearities. These might have
widespread application (e.g. quantum information). Here we demonstrate
experimentally that such exchange effects can indeed enhance the probability of
real absorption of photon pairs. Using nonclassical pairs of photons with
variable time separation, we observe a maximum suppression of pair transmission
by at least 5% with respect to the result for uncorrelated photons.


title:
Robust polarization-based quantum key distribution over collective-noise
  channel

abstract:
  We present two polarization-based protocols for quantum key distribution. The
protocols encode key bits in noiseless subspaces or subsystems, and so can
function over a quantum channel subjected to an arbitrary degree of collective
noise, as occurs, for instance, due to rotation of polarizations in an optical
fiber. These protocols can be implemented using only entangled photon-pair
sources, single-photon rotations, and single-photon detectors. Thus, our
proposals offer practical and realistic alternatives to existing schemes for
quantum key distribution over optical fibers without resorting to
interferometry or two-way quantum communication, thereby circumventing,
respectively, the need for high precision timing and the threat of Trojan horse
attacks.


title:
Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance
  in Quantum Mechanics

abstract:
  We investigate consequences of allowing the Hilbert space of a quantum system
to have a time-dependent metric. For a given possibly nonstationary quantum
system, we show that the requirement of having a unitary Schreodinger
time-evolution identifies the metric with a positive-definite (Ermakov-Lewis)
dynamical invariant of the system. Therefore the geometric phases are
determined by the metric. We construct a unitary map relating a given
time-independent Hilbert space to the time-dependent Hilbert space defined by a
positive-definite dynamical invariant. This map defines a transformation that
changes the metric of the Hilbert space but leaves the Hamiltonian of the
system invariant. We propose to identify this phenomenon with a quantum
mechanical analogue of the principle of general covariance of General
Relativity. We comment on the implications of this principle for geometrically
equivalent quantum systems and investigate the underlying symmetry group.


title:
Finitary and Infinitary Mathematics, the Possibility of Possibilities
  and the Definition of Probabilities

abstract:
  Some relations between physics and finitary and infinitary mathematics are
explored in the context of a many-minds interpretation of quantum theory. The
analogy between mathematical ``existence'' and physical ``existence'' is
considered from the point of view of philosophical idealism. Some of the ways
in which infinitary mathematics arises in modern mathematical physics are
discussed. Empirical science has led to the mathematics of quantum theory. This
in turn can be taken to suggest a picture of reality involving possible minds
and the physical laws which determine their probabilities. In this picture,
finitary and infinitary mathematics play separate roles. It is argued that
mind, language, and finitary mathematics have similar prerequisites, in that
each depends on the possibility of possibilities. The infinite, on the other
hand, can be described but never experienced, and yet it seems that sets of
possibilities and the physical laws which define their probabilities can be
described most simply in terms of infinitary mathematics.


title: Coherent State for a Relativistic Spinless Particle

abstract:
  The Klein-Gordon equation with scalar potential is considered. In the
Feshbach-Villars representation the annihilation operator for a linear
potential is defined and its eigenstates are obtained. Although the energy
levels in this case are not equally-spaced, depending on the eigenvalues of the
annihilation operator, the states are nearly coherent and squeezed. The
relativistic Poschl-Teller potential is introduced. It is shown that its energy
levels are equally-spaced. The coherence of time evolution of the eigenstates
of the annihilation operator for this potential is evaluated.


title:
Quantum computation of the Anderson transition in presence of
  imperfections

abstract:
  We propose a quantum algorithm for simulation of the Anderson transition in
disordered lattices and study numerically its sensitivity to static
imperfections in a quantum computer. In the vicinity of the critical point the
algorithm gives a quadratic speedup in computation of diffusion rate and
localization length, comparing to the known classical algorithms. We show that
the Anderson transition can be detected on quantum computers with $7 - 10$
qubits.


title: Multiple-Quantum Spin Dynamics of Entanglement

abstract:
  Dynamics of entanglement is investigated on the basis of exactly solvable
models of multiple-quantum (MQ) NMR spin dynamics. It is shown that the time
evolution of MQ coherences of systems of coupled nuclear spins in solids is
directly connected with dynamics of the quantum entanglement. We studied
analytically dynamics of entangled states for two- and three-spin systems
coupled by the dipole-dipole interaction. In this case dynamics of the quantum
entanglement is uniquely determined by the time evolution of MQ coherences of
the second order. The real part of the density matrix describing MQ dynamics in
solids is responsible for MQ coherences of the zeroth order while its imaginary
part is responsible for the second order. Thus, one can conclude that dynamics
of the entanglement is connected with transitions from the real part of the
density matrix to the imaginary one and vice versa. A pure state which
generalizes the GHZ and W states is found. Different measures of the
entanglement of this state are analyzed for three-partite systems.


title: Spin squeezing via atom - cavity field coupling

abstract:
  Spin squeezing via atom-field interactions is considered within the context
of the Tavis-Cummings model. An ensemble of N two-level atoms interacts with a
quantized cavity field. For all the atoms initially in their ground states, it
is shown that spin squeezing of both the atoms and the field can be achieved
provided the initial state of the cavity field has coherence between number
states differing by 2. Most of the discussion is restricted to the case of a
cavity field initially in a coherent state, but initial squeezed states for the
field are also discussed. Optimal conditions for obtaining squeezing are
obtained. An analytic solution is found that is valid in the limit that the
number of atoms is much greater than unity and is also much larger than the
average number of photons, inititally in the coherent state of the cavity
field. In this limit, the degree of spin squeezing increases with increasing a,
even though the field more closely resembles a classical field for which no
spin squeezing could be achieved.


title:
Spectral and thermodynamical properties of systems with noncanonical
  commutation rules: semiclassical approach

abstract:
  We study different quantum one dimensional systems with noncanonical
commutation rule $[x,p]=i\hbar (1+sH),$ where $H$ is the one particle
Hamiltonian and $s$ is a parameter. This is carried-out using semiclassical
arguments and the surmise $\hbar \to \hbar (1+sE),$ where $E$ is the energy. We
compute the spectrum of the potential box, the harmonic oscillator, and a more
general power-law potential $| x| ^{\nu}$% . With the above surmise, and
changing the size of the elementary cell in the phase space, we obtain an
expression for the partition function of these systems. We calculate the first
order correction in $s$ for the internal energy and heat capacity. We apply our
technique to the ideal gas, the phonon gas, and to $N$ non-interacting
particles with external potential like $| x| ^{\nu}$.


title: Spectral properties on a circle with a singularity

abstract:
  We investigate the spectral and symmetry properties of a quantum particle
moving on a circle with a pointlike singularity (or point interaction). We find
that, within the U(2) family of the quantum mechanically allowed distinct
singularities, a U(1) equivalence (of duality-type) exists, and accordingly the
space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus.
We explore the relationship of special subfamilies of the U(2) family to
corresponding symmetries, and identify the singularities that admit an N = 2
supersymmetry. Subfamilies that are distinguished in the spectral properties or
the WKB exactness are also pointed out. The spectral and symmetry properties
are also studied in the context of the circle with two singularities, which
provides a useful scheme to discuss the symmetry properties on a general basis.

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


title: Experimental Detection of Entanglement with Polarized Photons

abstract:
  We report on the first experimental realization of the entanglement witness
for polarization entangled photons. It represents a recently discovered
significant quantum information protocol which is based on few local
measurements. The present demonstration has been applied to the so-called
Werner states, a family of ''mixed'' quantum states that include both entangled
and non entangled states. These states have been generated by a novel high
brilliance source of entanglement which allows to continuously tune the degree
of mixedness.


title:
Decoherence and recoherence from vacuum fluctuations near a conducting
  plate

abstract:
  The interaction between particles and the electromagnetic field induces
decoherence generating a small suppression of fringes in an interference
experiment. We show that if a double slit--like experiment is performed in the
vicinity of a conducting plane, the fringe visibility depends on the position
(and orientation) of the experiment relative to the conductor's plane. This
phenomenon is due to the change in the structure of vacuum induced by the
conductor and is closely related to the Casimir effect. We estimate the fringe
visibility both for charged and for neutral particles with a permanent dipole
moment. The presence of the conductor may tend to increase decoherence in some
cases and to reduce it in others. A simple explanation for this peculiar
behavior is presented.


title: Influence of the detector's temperature on the quantum Zeno effect

abstract:
  In this paper we study the quantum Zeno effect using the irreversible model
of the measurement. The detector is modeled as a harmonic oscillator
interacting with the environment. The oscillator is subjected to the force,
proportional to the energy of the measured system. We use the Lindblad-type
master equation to model the interaction with the environment. The influence of
the detector's temperature on the quantum Zeno effect is obtained. It is shown
that the quantum Zeno effect becomes stronger (the jump probability decreases)
when the detector's temperature increases.


title: Weak measurement of arrival time

abstract:
  The arrival time probability distribution is defined by analogy with the
classical mechanics. The difficulty of requirement to have the values of
non-commuting operators is circumvented using the concept of weak measurements.
The proposed procedure is suitable to the free particles and to the particles
subjected to an external potential, as well. It is shown that such an approach
imposes an inherent limitation to the accuracy of the arrival time
determination.


title: On the uncertainty relations for angular observables and beyond them

abstract:
  For angular observables pairs (angular momentum-angle and number-phase) the
adequate reference element of normality is not the Robertson-Schr\"{o}dinger
uncertainty relation but a Schwarz formula regarding the quantum fluctuations.
Beyond such a fact the traditional interpretation of the uncertainty relations
appears as an unjustified doctrine.


title: On the quantum measurements from a reconsidered perspective

abstract:
  For theoretical approach of quantum measurements it is proposed a set of
reconsidered conjectures. The proposed approach implies linear functional
transformations for probability density and current but preserves the
expressions for operators of observables. The measuring uncertainties appear as
changes in the probabilistic estimators of observables.


title: Entanglement versus Correlations in Spin Systems

abstract:
  We consider pure quantum states of $N\gg 1$ spins or qubits and study the
average entanglement that can be \emph{localized} between two separated spins
by performing local measurements on the other individual spins. We show that
all classical correlation functions provide lower bounds to this
\emph{localizable entanglement}, which follows from the observation that
classical correlations can always be increased by doing appropriate local
measurements on the other qubits. We analyze the localizable entanglement in
familiar spin systems and illustrate the results on the hand of the Ising spin
model, in which we observe characteristic features for a quantum phase
transition such as a diverging entanglement length.


title: Anatomy of a quantum `bounce'

abstract:
  We discuss some of the properties of the `collision' of a quantum mechanical
wave packet with an infinitely high potential barrier, focusing on novel
aspects such as the detailed time-dependence of the momentum-space probability
density and the time variation of the uncertainty principle product $\Delta x_t
\cdot \Delta p_t$. We make explicit use of Gaussian-like wave packets in the
analysis, but also comment on other general forms.


title:
Maximal violation of Clauser-Horne-Shimony-Holt inequality for
  four-level systems

abstract:
  Clauser-Horne-Shimony-Holt inequality for bipartite systems of 4-dimension is
studied in detail by employing the unbiased eight-port beam splitters
measurements. The uniform formulae for the maximum and minimum values of this
inequality for such measurements are obtained. Based on these formulae, we show
that an optimal non-maximally entangled state is about 6% more resistant to
noise than the maximally entangled one. We also give the optimal state and the
optimal angles which are important for experimental realization.


title: Off-diagonal generalization of the mixed state geometric phase

abstract:
  The concept of off-diagonal geometric phases for mixed quantal states in
unitary evolution is developed. We show that these phases arise from three
basic ideas: (1) fulfillment of quantum parallel transport of a complete basis,
(2) a concept of mixed state orthogonality adapted to unitary evolution, and
(3) a normalization condition. We provide a method for computing the
off-diagonal mixed state phases to any order for unitarities that divide the
parallel transported basis of Hilbert space into two parts: one part where each
basis vector undergoes cyclic evolution and one part where all basis vectors
are permuted among each other. We also demonstrate a purification based
experimental procedure for the two lowest order mixed state phases and consider
a physical scenario for a full characterization of the qubit mixed state
geometric phases in terms of polarization-entangled photon pairs. An
alternative second order off-diagonal mixed state geometric phase, which can be
tested in single-particle experiments, is proposed.


title: Quantum Theory and Time Asymmetry

abstract:
  The relation between quantum measurement and thermodynamically irreversible
processes is investigated. The reduction of the state vector is fundamentally
asymmetric in time and shows an observer-relatedness which may explain the
double interpretation of the state vector as a representation of physical
states as well as of information about them. The concept of relevance being
used in all statistical theories of irreversible thermodynamics is shown to be
based on the same observer-relatedness. Quantum theories of irreversible
processes implicitly use an objectivized process of state vector reduction. The
conditions for the reduction are discussed, and I speculate that the final
(subjective) observer system might even be carried by a spacetime point.


title:
Comparing classical and quantum probability distributions for an
  asymmetric infinite well

abstract:
  We compare the classical and quantum mechanical position-space probability
densities for a particle in an asymmetric infinite well. In an idealized system
with a discontinuous step in the middle of the well, the classical and quantum
probability distributions agree fairly well, even for relatively small quantum
numbers, except for anomalous cases which are due to the unphysical nature of
the potential. We are able to derive upper and lower bounds on the differences
between the quantum and classical results. We also qualitatively discuss the
momentum-space probability densities for this system using intuitive ideas
about how much time a classical particle spends in various parts of the well.
This system provides an excellent example of a non-trivial, but tractable,
quantum mechanical bound state problem where the correlations between the
amplitude and curvature of quantum mechanical wavefunctions can be easily
compared to classical intuition about particle motion, with quantitative
success, but also warning of possible surprises in non-physical limiting cases.


title:
Bounds on the Probability of Success of Postselected Non-linear Sign
  Shifts Implemented with Linear Optics

abstract:
  The fundamental gates of linear optics quantum computation are realized by
using single photons sources, linear optics and photon counters. Success of
these gates is conditioned on the pattern of photons detected without using
feedback. Here it is shown that the maximum probability of success of these
gates is typically strictly less than 1. For the one-mode non-linear sign
shift, the probability of success is bounded by 1/2. For the conditional sign
shift of two modes, this probability is bounded by 3/4. These bounds are still
substantially larger than the highest probabilities shown to be achievable so
far, which are 1/4 and 2/27, respectively.


title:
Entangled states maximize the two qubit channel capacity for some Pauli
  channels with memory

abstract:
  We prove that a general upper bound on the maximal mutual information of
quantum channels is saturated in the case of Pauli channels with an arbitrary
degree of memory. For a subset of such channels we explicitly identify the
optimal signal states. We show analytically that for such a class of channels
entangled states are indeed optimal above a given memory threshold. It is
noteworthy that the resulting channel capacity is a non-differentiable function
of the memory parameter.


title: Quaternionic Computing

abstract:
  We introduce a model of computation based on quaternions, which is inspired
on the quantum computing model. Pure states are vectors of a suitable linear
space over the quaternions. Other aspects of the theory are the same as in
quantum computing: superposition and linearity of the state space, unitarity of
the transformations, and projective measurements. However, one notable
exception is the fact that quaternionic circuits do not have a uniquely defined
behaviour, unless a total ordering of evaluation of the gates is defined. Given
such an ordering a unique unitary operator can be associated with the
quaternionic circuit and a proper semantics of computation can be associated
with it.
  The main result of this paper consists in showing that this model is no more
powerful than quantum computing, as long as such an ordering of gates can be
defined. More concretely we show, that for all quaternionic computation using n
quaterbits, the behaviour of the circuit for each possible gate ordering can be
simulated with n+1 qubits, and this with little or no overhead in circuit size.
The proof of this result is inspired of a new simplified and improved proof of
the equivalence of a similar model based on real amplitudes to quantum
computing, which states that any quantum computation using n qubits can be
simulated with n+1 rebits, and in this with no circuit size overhead.
  Beyond this potential computational equivalence, however, we propose this
model as a simpler framework in which to discuss the possibility of a
quaternionic quantum mechanics or information theory. In particular, it already
allows us to illustrate that the introduction of quaternions might violate some
of the ``natural'' properties that we have come to expect from physical models.


title:
Ehrenfest theorem, Galilean invariance and nonlinear Schr\"odinger
  equations

abstract:
  Galilean invariant Schr\"odinger equations possessing nonlinear terms
coupling the amplitude and the phase of the wave function can violate the
Ehrenfest theorem. An example of this kind is provided. The example leads to
the proof of the theorem: A Galilean invariant Schr\"odinger equation derived
from a lagrangian density obeys the Ehrenfest theorem. The theorem holds for
any linear or nonlinear lagrangian.