title:
Comparison of Theory and Experiment for a One-Atom Laser in a Regime of
  Strong Coupling

abstract:
  Our recent paper reports the experimental realization of a one-atom laser in
a regime of strong coupling (Ref. [1]). Here we provide the supporting
theoretical analysis relevant to the operating regime of our experiment. By way
of a simplified four-state model, we investigate the passage from the domain of
conventional laser theory into the regime of strong coupling for a single
intracavity atom pumped by coherent external fields. The four-state model is
also employed to exhibit the vacuum-Rabi splitting and to calculate the optical
spectrum. We next extend this model to incorporate the relevant Zeeman
hyperfine states as well as a simple description of the pumping processes in
the presence of polarization gradients and atomic motion. This extended model
is employed to make quantitative comparisons with the measurements of Ref. [1]
for the intracavity photon number versus pump strength and for the photon
statistics as expressed by the intensity correlation function g2(tau).


title: Matter waves from localized quantum sources

abstract:
  Matter waves originating from a localized region in space appear commonly in
physics. Examples are photo-electrons, ballistic electrons in nanotechnology
devices (scanning-tunneling microscopy, quantum Hall effect), or atoms released
from a coherent source (atom laser). We introduce the energy-dependent Green
function as a suitable tool to calculate the arising currents. For some systems
experimental data is available and in excellent agreement with the presented
results.


title: Weak limits for quantum random walks

abstract:
  We formulate and prove a general weak limit theorem for quantum random walks
in one and more dimensions. With $X_n$ denoting position at time $n$, we show
that $X_n/n$ converges weakly as $n \to \infty$ to a certain distribution which
is absolutely continuous and of bounded support. The proof is rigorous and
makes use of Fourier transform methods. This approach simplifies and extends
certain preceding derivations valid in one dimension that make use of
combinatorial and path integral methods.


title:
Comment on "Critical assessment of the Schrodinger picture of quantum
  mechanics"

abstract:
  Recently, Faria et al [Phys. Lett. A 305 (2002) 322] discussed an example in
which the Heisenberg and the Schrodinger pictures of quantum mechanics gave
different results. We identify the mistake in their reasoning and conclude that
the example they discussed does not support the inequivalence of these two
pictures.


title: Necessary and sufficient condition for quantum-generated correlations

abstract:
  We present a non-linear inequality that completely characterizes the set of
correlation functions obtained from bipartite quantum systems, for the case in
which measurements on each subsystem can be chosen between two arbitrary
dichotomic observables. This necessary and sufficient condition is the maximal
strengthening of Cirel'son's bound.


title: Quantum key distribution based on time coding

abstract:
  A quantum key distribution protocol based on time coding uses delayed one
photon pulses with minimum time-frequency uncertainty product. Possible overlap
between the pulses induces an ambiguous delay measurement and ensures a secure
key exchange.


title: 4 states protocol for time coding quantum key distribution

abstract:
  Coherent one photon pulses are sent with four possible time delays with
respect to a reference. Ambiguity of the photon time detection resulting from
pulses overlap combined with interferometric measurement allows for secure key
exchange.


title: On improving single photon sources via linear optics and photodetection

abstract:
  In practice, single photons are generated as a mixture of vacuum with a
single photon with weights 1-p and p, respectively; here we are concerned with
increasing p by directing multiple copies of the single photon-vacuum mixture
into a linear optic device and applying photodetection on some outputs to
conditionally prepare single photon states with larger p. We prove that it is
impossible, under certain conditions, to increase p via linear optics and
conditional preparation based on photodetection, and we also establish a class
of photodetection events for which p can be improved. In addition we prove that
it is not possible to obtain perfect (p=1) single photon states via this method
from imperfect (p<1) inputs.


title:
Physical solution of 1D quantum N-boson system with zero-range pair
  interaction

abstract:
  The mathematically exact solution of a one-dimensional (1D) quantum
N-identical-boson system with zero-range pair interaction has been well known.
We find that this solution is non-physical, since there exists a paradox of its
energy expectation value, leading a basic contradiction to the mean-field
theory of the system. A new integral equation that is equivalent to the
corresponding Schrodinger one is established and its formally physical solution
is derived. Energy correction from the average potential and harmonic waves of
different momentums are demonstrated, and scattering amplitude of the physical
solution and mean-field theory of the system are discussed.


title: Z_N Gauge Theories on a Lattice and Quantum Memory

abstract:
  In the present paper we shall study (2+1) dimensional Z_N gauge theories on a
lattice. It is shown that the gauge theories have two phases, one is a Higgs
phase and the other is a confinement phase. We investigate low-energy
excitation modes in the Higgs phase and clarify relationship between the Z_N
gauge theories and Kitaev's model for quantum memory and quantum computations.
Then we study effects of random gauge couplings(RGC) which are identified with
noise and errors in quantum computations by Kitaev's model. By using a duality
transformation, it is shown that time-independent RGC give no significant
effects on the phase structure and the stability of quantum memory and
computations. Then by using the replica methods, we study Z_N gauge theories
with time-dependent RGC and show that nontrivial phase transitions occur by the
RGC.


title: Extension of the de Broglie-Bohm theory to the Ginzburg-Landau equation

abstract:
  The de Broglie-Bohm approach permits to assign well defined trajectories to
particles that obey the Schroedinger equation. We extend this approach to
electron pairs in a superconductor. In the stationary regime this extension is
completely natural; in the general case additional postulates are required.
This approach gives enlightening views for the absence of Hall effect in the
stationary regime and for the formation of permanent currents.


title: Spatial Localization and Relativistic Transformation of Quantum Spins

abstract:
  The purity of a reduced state for spins that is pure in the rest frame will
most likely appear to degrade because spin and momentum become mixed when
viewed by a moving observer. We show that such a boost-induced decrease in spin
purity observed in a moving reference frame is intrinsically related to the
spatial localization properties of the wave package observed in the rest frame.
Furthermore, we prove that, for any localized pure state with separable spin
and momentum in the rest frame, its reduced density matrix for spins inevitably
appears to be mixed whenever viewed from a moving reference frame.


title:
All information-theoretically secure key establishing protocols are
  quantum protocols

abstract:
  A theorem is proved which states that no classical key generating protocol
could ever be provably secure. Consequently, candidates for provably secure
protocols must rely on some quantum effect. Theorem relies on the fact that
BB84 Quantum key distribution protocol has been proven secure.


title: Entanglement Echoes in Quantum Computation

abstract:
  We study the stability of entanglement in a quantum computer implementing an
efficient quantum algorithm, which simulates a quantum chaotic dynamics. For
this purpose, we perform a forward-backward evolution of an initial state in
which two qubits are in a maximally entangled Bell state. If the dynamics is
reversed after an evolution time $t_r$, there is an echo of the entanglement
between these two qubits at time $t_e=2t_r$. Perturbations attenuate the
pairwise entanglement echo and generate entanglement between these two qubits
and the other qubits of the quantum computer.


title:
Continuously Guided Atomic Interferometry Using a Single-Zone Optical
  Excitation: Theoretical Analysis

abstract:
  In an atomic interferometer, the phase shift due to rotation is proportional
to the area enclosed by the split components of the atom. However, this model
is unclear for an atomic interferometer demonstrated recently by Shahriar et
al., for which the atom simply passes through a single-zone optical beam,
consisting of a pair of bichromatic counter-propagating beams. During the
passage, the atomic wave packets in two distinct internal states couple to each
other continuously. The two internal states trace out a complicated trajectory,
guided by the optical beams, with the amplitude and spread of each wavepacket
varying continuously. Yet, at the end of the single-zone excitation, there is
an interference with fringe amplitudes that can reach a visibility close to
unity. For such a situation, it is not clear how one would define the area of
the interferometer, and therefore, what the rotation sensitivity of such an
interferometer would be. In this paper we analyze this interferometer in order
to determine its rotation sensitivity, and thereby determine its effective
area. In many ways, the continuous interferometer (CI) can be thought of as a
limiting version of the Borde-Chu Interferometer (BCI). We identify a quality
factor that can be used to compare the performance of these interferometers.
Under conditions of practical interest, we show that the rotation sensitivity
of the CI can be comparable to that of the BCI. The relative simplicity of the
CI (e.g., elimination of the task of precise angular alignment of the three
zones) then makes it a potentially better candidate for practical atom
interferometry for rotation sensing.


title: Exploiting entanglement in communication channels with correlated noise

abstract:
  We develop a model for a noisy communication channel in which the noise
affecting consecutive transmissions is correlated. This model is motivated by
fluctuating birefringence of fiber optic links. We analyze the role of
entanglement of the input states in optimizing the classical capacity of such a
channel. Assuming a general form of an ensemble for two consecutive
transmissions, we derive tight bounds on the classical channel capacity
depending on whether the input states used for communication are separable or
entangled across different temporal slots. This result demonstrates that by an
appropriate choice, the channel capacity may be notably enhanced by exploiting
entanglement.


title:
Directed motion for delta-kicked atoms with broken symmetries:
  comparison between theory and experiment

abstract:
  We report an experimental investigation of momentum diffusion in the
delta-function kicked rotor where time symmetry is broken by a two-period
kicking cycle and spatial symmetry by an alternating linear potential. We
exploit this, and a technique involving a moving optical potential, to create
an asymmetry in the momentum diffusion that is due to the classical chaotic
diffusion. This represents a realization of a type of Hamiltonian quantum
ratchet.


title: Quantum Adiabatic Algorithm and Large Spin Tunnelling

abstract:
  We provide a theoretical study of the quantum adiabatic evolution algorithm
with different evolution paths proposed in [E. Farhi, et al.,
arXiv:quant-ph/0208135]. The algorithm is applied to a random binary
optimization problem (a version of the 3-Satisfiability problem) where the
n-bit cost function is symmetric with respect to the permutation of individual
bits. The evolution paths are produced, using the generic control Hamiltonians
H(\tau) that preserve the bit symmetry of the underlying optimization problem.
In the case where the ground state of H(0) coincides with the totally-symmetric
state of an n-qubit system the algorithm dynamics is completely described in
terms of the motion of a spin-n/2.
  We show that different control Hamiltonians can be parameterized by a set of
independent parameters that are expansion coefficients of H(\tau) in a certain
universal set of operators. Only one of these operators can be responsible for
avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic
algorithm. We show that it is possible to select a coefficient for this
operator that guarantees a polynomial complexity of the algorithm for all
problem instances. We show that a successful evolution path of the algorithm
always corresponds to the trajectory of a classical spin-n/2 and provide a
complete characterization of such paths.


title:
Absorption resonance and large negative delay in Rb vapor with buffer
  gas

abstract:
  We observe a narrow, isolated, two-photon absorption resonance in Rb for
large one-photon detuning in the presence of a buffer gas. In the absence of
buffer gas, a standard Lambda configuration of two laser frequencies gives rise
to electromagnetically induced transparency (EIT) for all values of one-photon
detuning throughout the inhomogeneously (Doppler) broadened line. However, when
a buffer gas is added and the one-photon detuning is comparable to or greater
than the Doppler width, an absorption resonance appears instead of the usual
EIT resonance. We also observe large negative group delay (~ -300 us for a
Gaussian pulse propagating through the media with respect to a reference pulse
not affected by the media), corresponding to a superluminal group velocity v_g=
-c/(3.6x10^6)=-84 m/s.


title: Blind Quantum Computation

abstract:
  We investigate the possibility of "having someone carry out the work of
executing a function for you, but without letting him learn anything about your
input". Say Alice wants Bob to compute some known function f upon her input x,
but wants to prevent Bob from learning anything about x. The situation arises
for instance if client Alice has limited computational resources in comparison
with mistrusted server Bob, or if x is an inherently mobile piece of data.
Could there be a protocol whereby Bob is forced to compute f(x) "blindly", i.e.
without observing x? We provide such a blind computation protocol for the class
of functions which admit an efficient procedure to generate random input-output
pairs, e.g. factorization. The cheat-sensitive security achieved relies only
upon quantum theory being true. The security analysis carried out assumes the
eavesdropper performs individual attacks.
  Keywords: Secure Circuit Evaluation, Secure Two-party Computation,
Information Hiding, Information gain vs disturbance.


title:
The Low-Frequency Character of the Thermal Correction to the Casimir
  Force between Metallic Films

abstract:
  The frequency spectrum of the finite temperature correction to the Casimir
force can be determined by use of the Lifshitz formalism for metallic plates of
finite conductivity. We show that the correction for the $TE$ electromagnetic
modes is dominated by frequencies so low that the plates cannot be modelled as
ideal dielectrics. We also address issues relating to the behavior of
electromagnetic fields at the surfaces and within metallic conductors, and
calculate the surface modes using appropriate low-frequency metallic boundary
conditions. Our result brings the thermal correction into agreement with
experimental results that were previously obtained. We suggest a series of
measurements that will test the veracity of our analysis.


title: Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay

abstract:
  We study, analytically and numerically, the stability of quantum motion for a
classically chaotic system. We show the existence of different regimes of
fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.


title:
Operator Method for Nonperturbative Calculation of the Thermodynamic
  Values in Quantum Statistics. Diatomic Molecular Gas

abstract:
  Operator method and cumulant expansion are used for nonperturbative
calculation of the partition function and the free energy in quantum
statistics. It is shown for Boltzmann diatomic molecular gas with some model
intermolecular potentials that the zeroth order approximation of the proposed
method interpolates the thermodynamic values with rather good accuracy in the
entire range of both the Hamiltonian parameters and temperature. The systematic
procedure for calculation of the corrections to the zeroth order approximation
is also considered.


title: Entanglement bounds for squeezed non-symmetric thermal state

abstract:
  I study the three parameters bipartite quantum Gaussian state called squeezed
asymmetric thermal state, calculate Gaussian entanglement of formation
analytically and the up bound of relative entropy of entanglement, compare them
with coherent information of the state.Based on the result obtained, one can
determine the relative entropy of entanglement of the state with infinitive
squeezing.


title: Wave equations with energy dependent potentials

abstract:
  We study wave equations with energy dependent potentials. Simple analytical
models are found useful to illustrate difficulties encountered with the
calculation and interpretation of observables. A formal analysis shows under
which conditions such equations can be handled as evolution equation of quantum
theory with an energy dependent potential. Once these conditions are met, such
theory can be transformed into ordinary quantum theory.


title: Can differently prepared mixed states be distinguished?

abstract:
  A measurement has been proposed by B. d'Espagnat that would distinguish from
one another some ensembles that are differently prepared but correspond to the
same density matrix. Here, the idea is modified so that it becomes applicable
to much more general situations. The method is illustrated in simple examples.
Some matter of concern might then be that information could be transmitted by
methods based on our idea in the EPR kind of experiments. A simple proof is
given that this is impossible.


title: Integrable systems as quantum mechanics

abstract:
  This is a mainly expository sketch showing how some integrable systems (e.g.
KP or KdV) can be viewed as quantum mechanical in nature.


title:
Review of studies about quantum communication and foundations of quantum
  mechanics at IENGF

abstract:
  In this proceeding I review the main experimental results obtained at IENGF
(Turin, Italy) by using a source of entangled photons realised superposing, by
means of an optical condenser, type I PDC produced in two crystals. More in
details, after having described how this source is built, I will report on a
Bell inequalities test obtained with it. Then I describe a recent innovative
double slit experiment realised with a similar scheme. Finally, I hint about
future developments of this activity at IENGF and in particular about a quantum
cryptographic scheme in d=4.


title: Optimization of quantum universal detectors

abstract:
  The expectation value <O> of an arbitrary operator O can be obtained via a
universal measuring apparatus that is independent of O, by changing only the
data-processing of the outcomes. Such a ``universal detector'' performs a joint
measurement on the system and on a suitable ancilla prepared in a fixed state,
and is equivalent to a positive operator valued measure (POVM) for the system
that is ``informationally complete''. The data processing functions generally
are not unique, and we pose the problem of their optimization, providing some
examples for covariant POVM's, in particular for SU(d) covariance group.


title: Quantum Error Correction in the Zeno Regime

abstract:
  In order to reduce errors, error correction codes (ECCs) need to be
implemented fast. They can correct the errors corresponding to the first few
orders in the Taylor expansion of the Hamiltonian of the interaction with the
environment. If implemented fast enough, the zeroth order error predominates
and the dominant effect is of error prevention by measurement (Zeno Effect)
rather than correction. In this ``Zeno Regime'', codes with less redundancy are
sufficient for protection. We describe such a simple scheme, which uses two
``noiseless'' qubits to protect a large number, $n$, of information qubits from
noise from the environment. The ``noisless qubits'' can be realized by treating
them as logical qubits to be encoded by one of the previously introduced
encoding schemes.


title: Implementing the fanout gate by a Hamiltonian

abstract:
  We show that, for even n, evolving n qubits according to a simple Hamiltonian
can be used to exactly implement an (n+1)-qubit parity gate, which is
equivalent in constant depth to an (n+1)-qubit fanout gate. We also observe
that evolving the Hamiltonian for three qubits results in an
inversion-on-three-way-equality gate, which together with single-qubit
operations is universal for quantum computation.


title: Coherence Time of a Solid-State Nuclear Qubit

abstract:
  We report NMR experiments using high-power, RF decoupling techniques to show
that a 29-Si nuclear spin qubit in a solid silicon crystal at room temperature
can preserve quantum phase for 10^9 precessional periods. The coherence times
we report are longer than for any other observed solid-state qubit by more than
four orders of magnitude. In high quality crystals, these times are limited by
residual dipolar couplings and can be further improved by isotopic depletion.
In defect-heavy samples, we provide evidence for decoherence limited by 1/f
noise. These results provide insight toward proposals for solid-state
nuclear-spin-based quantum memories and quantum computers based on silicon.


title: Number-phase Wigner function on extended Fock space

abstract:
  On the basis of the phase states, we present the correct integral expressions
of the two number-phase Wigner functions discovered so far. These correct forms
are derived from those defined in the extended Fock space with negative number
states. The analogous conditions to Wigner's original ones cannot lead to the
number-phase function uniquely. To show this fact explicitly, we propose
another function satisfying all these conditions. It is also shown that the
ununiqueness of the number-phase Wigner function result from the
phase-periodicity problem.


title:
"Measurement" as a neurophysical process: a hypothetical linear and
  deterministic scenario

abstract:
  Tunnel amplitudes of molecular configurations (like neuronal channel pores)
may be very sensitive to thermal vibrations of the barrier width
(vibration-assisted tunneling) resulting in pseudo-random spikes of widely
varying sizes. An observer who ``lives'' behind the barrier would experience as
an ``event'' an accidental minimum of the barrier width, the timing being
determined by the microstate of the neuron's heat bath. In two neurons, set to
detect a ``left'' or ``right'' state of an object, firing amplitudes typically
differ so much as to produce a quasi-selection of one option.


title: Quantum state restoration by quantum cloning and measurement

abstract:
  Copying information is an elementary operation in classical information
processing. However, copying seems rather different in the quantum regime.
Since the discovery of the universal quantum cloning machine, much has been
found from the fundamental point of view about quantum copying. But a basic
question as to the utility of universal quantum cloning remains. We have
considered its application in quantum state restoration by using cloning
circuit for state estimation. It might be expected that classical information
from the state estimation might help restore the quantum state that was
disturbed during transmission. We find that the fidelity of the final state is,
interestingly, independent of error probabilities inside the channel. However,
this also turns out to impose a severe constraint on our original aims.


title:
Optical Bistability and Collective Behavior of Atoms trapped in a High-Q
  Ring Cavity

abstract:
  We study the collective motion of atoms confined in an optical lattice
operating inside a high finesse ring cavity. A simplified theoretical model for
the dynamics of the system is developed upon the assumption of adiabaticity of
the atomic motion. We show that in a regime where the light shift per photon
times the number of atoms exceeds the line width of the cavity resonance, the
otherwise tiny retro-action of the atoms upon the light field becomes a
significant feature of the system, giving rise to dispersive optical
bistability of the intra-cavity field. A solution of the complete set of
classical equations of motion confirms these finding, however additional
non-adiabatic phenomena are predicted, as for example self-induced radial
breathing oscillations. We compare these results with experiments involving
laser-cooled 85Rb atoms trapped in an optical lattice inside a ring cavity with
a finesse of 180000. Temperature measurements conducted for moderate values of
the atom-cavity interaction demonstrate that intensity-noise induced heating is
kept at a very low level, a prerequisite for our further experiments. When we
operate at large values of the atom--cavity interaction we observe bistability
and breathing oscillations in excellent agreement with our theoretical
predictions.


title:
Quantum Logic Network for Probabilistic Teleportation of Two-Particle
  State of General Form

abstract:
  A simplification scheme of probabilistic teleportation of two-particle state
of general form is given. By means of the primitive operations consisting of
single-qubit gates, two-qubit controlled-not gates,
  Von Neumann measurement and classically controlled operations, we construct
an efficient quantum logical network for implementing the new scheme of
probabilistic teleportation of a two-particle state of general form.


title: Self Adjoint Extensions of Phase and Time Operators

abstract:
  It is shown that any real and even function of the phase (time) operator has
a self-adjoint extension and its relation to the general phase operator problem
is analyzed.


title: Buffer-gas induced absorption resonances in Rb vapor

abstract:
  We observe transformation of the electromagnetically induced transparency
(EIT) resonance into the absorption resonance in a $\Lambda$ interaction
configuration in a cell filled with $^{87}$Rb and a buffer gas. This
transformation occurs as a one-photon detuning of the coupling fields is varied
from the atomic transition. No such absorption resonance is found in the
absence of a buffer gas. The width of the absorption resonance is several times
smaller than the width of the EIT resonance, and the changes of absorption near
these resonances are about the same. Similar absorption resonances are detected
in the Hanle configuration in a buffered cell.


title: Proposed experiment to test the bounds of quantum correlations

abstract:
  Clauser-Horne-Shimony-Holt inequality can give values between the classical
bound, 2, and Tsirelson's bound, 2 \sqrt 2. However, for a given set of local
observables, there are values in this range which no quantum state can attain.
We provide the analytical expression for the corresponding bound for a
parametrization of the local observables introduced by Filipp and Svozil, and
describe how to experimentally trace it using a source of singlet states. Such
an experiment will be useful to identify the origin of the experimental errors
in Bell's inequality-type experiments and could be modified to detect
hypothetical correlations beyond those predicted by quantum mechanics.


title: Group velocity study in hot Rb vapor with buffer gas

abstract:
  We study the behavior of the group velocity of light under conditions of
electromagnetically induced transparency (EIT) in a Doppler broadened medium.
Specifically, we show how the group delay (or group velocity) of probe and
generated Stokes fields depends on the one-photon detuning of drive and probe
fields. We find that for atoms in a buffer gas the group velocity decreases
with positive one-photon detuning of the drive fields, and increases when the
fields are red detuned. This dependence is counter-intuitive to what would be
expected if the one-photon detuning resulted in an interaction of the light
with the resonant velocity subgroup.


title:
Lewis-Riesenfeld approach to the solutions of Schrodinger equation in
  the presence of the presence of a time-dependent linear potential

abstract:
  We reexamine the general solution of a Schr\"{o}dinger equation in the
presence of a time-dependent linear potential in configuration space based on
the Lewis-Riesenfeld framework. For comparison, we also solve the problem in
momentum space and then Fourier transform the solution to get the general wave
function. Appropriately choosing the weight function in the latter method, we
can obtain the same wave function as the former method. It is found that
non-Hermitian time-dependent linear invariant can be used to obtain
Gaussian-type wave-packet (GTWP) solutions of the time-dependent system. This
operator is a specific linear combination of the initial momentum and initial
position operators. This fact indicates that the constants of integration such
as the initial position and initial momentum that determine the classical
motion play important roles in the time-dependent quantum system. The
eigenfunction of the linear invariant is interpreted as a wave packet with a
"center of mass" moving along the classical trajectory, while the ratio between
the coefficients of the initial position and initial momentum determines the
width of the wave packet.


title:
Nonclassical photon pairs generated from a room-temperature atomic
  ensemble

abstract:
  We report experimental generation of non-classically correlated photon pairs
from collective emission in a room-temperature atomic vapor cell. The
nonclassical feature of the emission is demonstrated by observing a violation
of the Cauchy-Schwarz inequality. Each pair of correlated photons are separated
by a controllable time delay up to 2 microseconds. This experiment demonstrates
an important step towards the realization of the Duan-Lukin-Cirac-Zoller scheme
for scalable long-distance quantum communication.


title: A practice problem for Schr{\"o}dinger transmission

abstract:
  We present the case of quantal transmission through a smooth, single-piece
exponential potential, $V(x)=-V_0 e^{x/a}$, in contrast to the piece-wise
continuous potentials, as a pedagogic model to demonstrate the analytic
extraction of transmission (reflection) co-efficient.


title: Towards a geometrical interpretation of quantum information compression

abstract:
  Let S be the von Neumann entropy of a finite ensemble E of pure quantum
states. We show that S may be naturally viewed as a function of a set of
geometrical volumes in Hilbert space defined by the states and that S is
monotonically increasing in each of these variables. Since S is the Schumacher
compression limit of E, this monotonicity property suggests a geometrical
interpretation of the quantum redundancy involved in the compression process.
It provides clarification of previous work in which it was shown that S may be
increased while increasing the overlap of each pair of states in the ensemble.
As a byproduct, our mathematical techniques also provide a new interpretation
of the subentropy of E.


title:
Quantum theory as a statistical theory under symmetry and
  complementarity

abstract:
  The aim of the paper is to derive essential elements of quantum mechanics
from a parametric structure extending that of traditional mathematical
statistics. The main extensions, which also can be motivated from an applied
statistics point of view, relate to symmetry, the choice between complementary
experiments and hence complementary parametric models, and use of the fact that
there for simple systems always is a limited experimental basis that is common
to all potential experiments. Concepts related to transformation groups
together with the statistical concept of sufficiency are used in the
construction of the quantummechanical Hilbert space. The Born formula is
motivated through recent analysis by Deutsch and Gill, and is shown to imply
the formulae of elementary quantum probability/ quantum inference theory in the
simple case. Planck's constant, and the Schroedinger equation are also derived
from this conceptual framework. The theory is illustrated by one and by two
spin 1/2 particles; in particular, a statistical discussion of Bell's
inequality is given. Several paradoxes and related themes of conventional
quantum mechanics are briefly discussed in the setting introduced here.


title: Casimir stress on lossy magnetodielectric spheres

abstract:
  An expression for the Casimir stress on arbitrary dispersive and lossy linear
magnetodielectric matter at finite temperature, including left-handed material,
is derived and applied to spherical systems. To cast the relevant part of the
scattering Green tensor for a general magnetodielectric sphere in a convenient
form, classical Mie scattering is reformulated.


title: Decoherence-free dynamical and geometrical entangling phase gates

abstract:
  It is shown that entangling two-qubit phase gates for quantum computation
with atoms inside a resonant optical cavity can be generated via common laser
addressing, essentially, within one step. The obtained dynamical or geometrical
phases are produced by an evolution that is robust against dissipation in form
of spontaneous emission from the atoms and the cavity and demonstrates
resilience against fluctuations of control parameters. This is achieved by
using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903
(2002)] and employing entangling Raman- or STIRAP-like transitions that
restrict the time evolution of the system onto stable ground states.


title:
The role of coherence entropy of physical twin observables in
  entanglement

abstract:
  The concept of physical twin observables (PTO) for bipartite quantum
states,introduced and proved relevant for quantum information theory in recent
work, is substantially simplified. The relation of observable and state is
studied in detail from the point of view of coherence entropy. Properties of
this quantity are further explored. It is shown that, besides for pure states,
quantum discord (measure of entanglement) can be expressed through the
coherence entropy of a PTO complete in relation to the state.


title: Generation of entangled states of two atoms inside a leaky cavity

abstract:
  An in-depth theoretical study is carried out to examine the
quasi-deterministic entanglement of two atoms inside a leaky cavity. Two
$\Lambda$-type three-level atoms, initially in their ground states, may become
maximally entangled through the interaction with a single photon. By working
out an exact analytic solution, we show that the probability of success depends
crucially on the spectral function of the injected photon. With a cavity
photon, one can generate a maximally entangled state with a certain probability
that is always less than 50%. However, for an injected photon with a narrower
spectral width, this probability can be significantly increased. In particular,
we discover situations in which entanglement can be achieved in a single trial
with an almost unit probability.


title:
C. F. von Weizsaecker's Reconstruction of Physics: Yesterday, Today,
  Tomorrow

abstract:
  Carl Friedrich von Weizsaecker's thinking has always crossed the borders
between physics and philosophy. Being a physicist by training he still feels at
home in the physics community, as a philosopher by passion, however, his mind
cannot stop thinking at the limits of physics. His physical ideas are based on
the general conceptual and methodological preconditions of physical theories.
Such a line of reasoning about the foundations of physics has brought
Weizsaecker into an abstract program of a possible reconstruction of physics in
terms of yes-no-alternatives, which he called "ur-theory." I shall start this
paper with a review of the basic ideas of ur-theory: the definition of an ur
and the connection between ur-spinors and spacetime. I then go over to some of
ur-theory's present borders: the construction of quantized spacetime tetrads
and the difficulties to incorporate gravity and gauge theories. Finally, I
shall discuss the possible prospects of ur-theory -- partly with a view to
modern quantum gravity approaches, but mainly in connection with its
philosophical implications. Here, one of the crucial questions is, whether
form, or, modern, information is an entity per se and what particular
consequences this may have.


title: Uncertainty relations on the slit and Fisher information

abstract:
  Diffraction on the slit can be interpreted in accordance with the Heisenberg
uncertainty principle. This elementary example hints at the importance of the
information theory for the quantum physics. The role played by one particularly
interesting measure of information -- the Fisher information -- in quantum
measurements is further discussed in the context of quantum interferometry.


title: Entanglement swapping secures multiparty quantum communication

abstract:
  Extending the eavesdropping strategy devised by Zhang, Li and Guo [Phys. Rev.
A 63, 036301 (2001)], we show that the multiparty quantum communication
protocol based on entanglement swapping, which was proposed by Cabello
[quant-ph/0009025], is not secure. We modify the protocol so that entanglement
swapping can secure multiparty quantum communication, such as multiparty
quantum key distribution and quantum secret sharing of classical information,
and show that the modified protocol is secure against the Zhang-Li-Guo's
strategy for eavesdropping as well as the basic intercept-resend attack.


title:
On the one-particle reduced density matrices of a pure three-qutrit
  quantum state

abstract:
  We present a necessary and sufficient condition for three qutrit density
matrices to be the one-particle reduced density matrices of a pure three-qutrit
quantum state. The condition consists of seven classes of inequalities
satisfied by the eigenvalues of these matrices. One of them is a generalization
of a known inequality for the qubit case. Some of these inequalities are proved
algebraically whereas the proof of the others uses the fact that a continuous
function of the state must have a minimum. Construction of states satisfying
these inequalities relies on a representation of the convex set of the allowed
set of eigenvalues in terms of corner points. We also present a result for a
more general quantum system concerning the nature of the boundary surface of
the set of the allowed set of eigenvalues.


title:
Scalable photonic quantum computation through cavity-assisted
  interaction

abstract:
  We propose a scheme for scalable photonic quantum computation based on cavity
assisted interaction between single-photon pulses. The prototypical quantum
controlled phase-flip gate between the single-photon pulses is achieved by
successively reflecting them from an optical cavity with a single-trapped atom.
Our proposed protocol is shown to be robust to practical nose and experimental
imperfections in current cavity-QED setups.


title: Correlation Functions in Spin Chains and Information Theory

abstract:
  Antiferromagnetic spin chains play an important role in condensed matter
physics and statistical mechanics. Recently XXX spin chain was discussed in
relation to the information theory. We consider here localizable entanglement,
introduced recently by F.Verstraete, M.Popp and J.I.Cirac. That is how much
entanglement can be localized on two spins on average by performing local
measurements on the other individual spins in a system of many interacting
spins. We consider the ground state in antiferromagnetic spin chains and study
localizable entanglement between two spins as a function of the distance. We
start with isotropic spin chain.
  Then we study effect of anisotropy and magnetic field. We conclude that
anisotropy increases localizable entanglement. We found an explicit dependence
of critical exponents in XXZ spin chain on magnetic field. We discovered that
the cases of high symmetry corresponds to high sensitivity of magnetic field.
We also calculated the concurrence before the measurement to illustrate that
the measurment raises the concurrence.


title:
Quantum Computational Complexity in the Presence of Closed Timelike
  Curves

abstract:
  Quantum computation with quantum data that can traverse closed timelike
curves represents a new physical model of computation. We argue that a model of
quantum computation in the presence of closed timelike curves can be formulated
which represents a valid quantification of resources given the ability to
construct compact regions of closed timelike curves. The notion of
self-consistent evolution for quantum computers whose components follow closed
timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197
(1991)], implies that the evolution of the chronology respecting components
which interact with the closed timelike curve components is nonlinear. We
demonstrate that this nonlinearity can be used to efficiently solve
computational problems which are generally thought to be intractable. In
particular we demonstrate that a quantum computer which has access to closed
timelike curve qubits can solve NP-complete problems with only a polynomial
number of quantum gates.


title:
Optical-fiber based measurement of an ultra-small volume high-Q photonic
  crystal microcavity

abstract:
  A two-dimensional photonic crystal semiconductor microcavity with a quality
factor Q ~ 40,000 and a modal volume Veff ~ 0.9 cubic wavelengths is
demonstrated. A micron-scale optical fiber taper is used as a means to probe
both the spectral and spatial properties of the cavity modes, allowing not only
measurement of modal loss, but also the ability to ascertain the in-plane
localization of the cavity modes. This simultaneous demonstration of high-Q and
ultra-small Veff in an optical microcavity is of potential interest in quantum
optics, nonlinear optics, and optoelectronics. In particular, the measured Q
and Veff values could enable strong coupling to both atomic and quantum dot
systems in cavity quantum electrodynamics.


title: Atom Nanooptics Based on Photon Dots and Photon Holes

abstract:
  New types of light fields localized in nanometer-sized regions of space were
suggested and analyzed. The possibility of using these nanolocalized fields in
atom optics for atom focusing and localization is discussed.


title: Dynamical localization, measurements and quantum computing

abstract:
  We study numerically the effects of measurements on dynamical localization in
the kicked rotator model simulated on a quantum computer. Contrary to the
previous studies, which showed that measurements induce a diffusive probability
spreading, our results demonstrate that localization can be preserved for
repeated single-qubit measurements. We detect a transition from a localized to
a delocalized phase, depending on the system parameters and on the choice of
the measured qubit.


title: D-outcome measurement for a nonlocality test

abstract:
  For the purpose of the nonlocality test, we propose a general correlation
observable of two parties by utilizing local $d$-outcome measurements with
SU($d$) transformations and classical communications. Generic symmetries of the
SU($d$) transformations and correlation observables are found for the test of
nonlocality. It is shown that these symmetries dramatically reduce the number
of numerical variables, which is important for numerical analysis of
nonlocality. A linear combination of the correlation observables, which is
reduced to the Clauser-Horne-Shimony-Holt (CHSH) Bell's inequality for two
outcome measurements, is led to the Collins-Gisin-Linden-Massar-Popescu (CGLMP)
nonlocality test for $d$-outcome measurement. As a system to be tested for its
nonlocality, we investigate a continuous-variable (CV) entangled state with $d$
measurement outcomes. It allows the comparison of nonlocality based on
different numbers of measurement outcomes on one physical system. In our
example of the CV state, we find that a pure entangled state of any degree
violates Bell's inequality for $d(\ge 2)$ measurement outcomes when the
observables are of SU($d$) transformations.


title: Quantum dynamical entropy and decoherence rate

abstract:
  We investigate quantum dynamical systems defined on a finite dimensional
Hilbert space and subjected to an interaction with an environment. The rate of
decoherence of initially pure states, measured by the increase of their von
Neumann entropy, averaged over an ensemble of random pure states, is proved to
be bounded from above by the partial entropy used to define the ALF dynamical
entropy. The rate of decoherence induced by the sequence of the von Neumann
projectors measurements is shown to be maximal, if the measurements are
performed in a randomly chosen basis. The numerically observed linear increase
of entropies is attributed to free-independence of the measured observable and
the unitary dynamical map.


title:
Stationary two-atom entanglement induced by nonclassical two-photon
  correlations

abstract:
  A system of two two-level atoms interacting with a squeezed vacuum field can
exhibit stationary entanglement associated with nonclassical two-photon
correlations characteristic of the squeezed vacuum field. The amount of
entanglement present in the system is quantified by the well known measure of
entanglement called concurrence. We find analytical formulas describing the
concurrence for two identical and nonidentical atoms and show that it is
possible to obtain a large degree of steady-state entanglement in the system.
Necessary conditions for the entanglement are nonclassical two-photon
correlations and nonzero collective decay. It is shown that nonidentical atoms
are a better source of stationary entanglement than identical atoms. We discuss
the optimal physical conditions for creating entanglement in the system, in
particular, it is shown that there is an optimal and rather small value of the
mean photon number required for creating entanglement.


title:
Is negative refraction, perfect focusing compatible with quantum
  mechanics?

abstract:
  In light of experiments in atom optics, the compatibilty of negative
refraction, perfect focusing with quantum mechanics is brought into question.


title:
Analytical solution of the optimal laser control problem in two-level
  systems

abstract:
  The optimal control of two-level systems by time-dependent laser fields is
studied using a variational theory. We obtain, for the first time, general
analytical expressions for the optimal pulse shapes leading to global
maximization or minimization of different physical quantities. We present
solutions which reproduce and improve previous numerical results.


title: Computing a Turing-Incomputable Problem from Quantum Computing

abstract:
  A hypercomputation model named Infinite Square Well Hypercomputation Model
(ISWHM) is built from quantum computation. This model is inspired by the model
proposed by Tien D. Kieu quant-ph/0203034 and solves an Turing-incomputable
problem. For the proposed model and problem, a simulation of its behavior is
made. Furthermore, it is demonstrated that ISWHM is a universal quantum
computation model.


title: A One-Atom Laser in a Regime of Strong Coupling

abstract:
  Although conventional lasers operate with a large number of intracavity
atoms, the lasing properties of a single atom in a resonant cavity have been
theoretically investigated for more than a decade. Here we report the
experimental realization of such a one-atom laser operated in a regime of
strong coupling. Our experiment exploits recent advances in cavity quantum
electrodynamics that allow one atom to be isolated in an optical cavity in a
regime for which one photon is sufficient to saturate the atomic transition. In
this regime the observed characteristics of the atom-cavity system are
qualitatively different from those of the familiar many atom case.
Specifically, we present measurements of intracavity photon number versus pump
intensity that exhibit "thresholdless" behavior, and infer that the output flux
from the cavity mode exceeds that from atomic fluorescence by more than
tenfold. Observations of the second-order intensity correlation function
demonstrate that our one-atom laser generates manifestly nonclassical light
that exhibits both photon antibunching and sub-Poissonian photon statistics.


title:
Quantum no-key protocol for direct and secure transmission of quantum
  and classical messages

abstract:
  We present a quantum no-key protocol for direct and secure transmission of
quantum and classical messages based on simple Boolean function computation
with several quantum gates and Shamir's interactive idea of classical message
encryption. This protocol has inherent personal identification and message
authentication. It probably is the first quantum protocol that can resist the
man-in-the-middle attack by itself.


title: Local adiabatic quantum search with different paths

abstract:
  We report on a detailed analysis of generalization of the local adiabatic
search algorithm. Instead of evolving directly from an initial ground state
Hamiltonian to a solution Hamiltonian a different evolution path is introduced
and is shown that the time required to find an item in a database of size $N$
can be made to be independent of the size of the database by modifying the
Hamiltonian used to evolve the system.


title: Noise induced entanglement

abstract:
  We discuss the generation of entangled states of two two-level atoms coupled
simultaneously with a dissipated atom. The dissipation of the atom is supposed
to come from its coupling to a noise with adjustable intensity. We describe how
the entanglement between the atoms arise in such a situation, and wether a
noise except the white one could help preparation of entanglement. Besides, we
confirm that the entanglement is maximized for intermediate values of the noise
intensity, while it is a monotonic function of the spontaneous rates. This
resembles the phenomenon of stochastic resonance and sheds more light on the
idea to exploit noise in quantum information processing.


title: Entangled self-phase locked states of light

abstract:
  We explore in detail the possibility of generation of continuous-variable
(CV) entangled states of light fields with well-localized phases. We show that
such quantum states, called entangled self-phase locked states, can be
generated in nondegenerate optical parametric oscillator (NOPO) based on a
type-II phase-matched down-conversion combined with polarization mixer in a
cavity. A quantum theory of this device, recently realized in the experiment,
is developed for both sub-threshold and above-threshold operational regimes. We
show that the system providing relative phase coherence between two generated
modes also exhibits different types of quantum correlations between photon
numbers and phases of these modes. We quantify the entanglement as two-mode
squeezing and show that CV entanglement is realized for both unitary,
non-dissipative dynamics and for dissipative NOPO in the entire range of pump
field intensities.


title: Fluctuations of Quantum Random Walks on Circles

abstract:
  Temporal fluctuations in the Hadamard walk on circles are studied. A temporal
standard deviation of probability that a quantum random walker is positive at a
given site is introduced to manifest striking differences between quantum and
classical random walks. An analytical expression of the temporal standard
deviation on a circle with odd sites is shown and its asymptotic behavior is
considered for large system size. In contrast with classical random walks, the
temporal fluctuation of quantum random walks depends on the position and
initial conditions, since temporal standard deviation of the classical case is
zero for any site. It indicates that the temporal fluctuation of the Hadamard
walk can be controlled.


title: Stochastic Schrodinger equations

abstract:
  A derivation of stochastic Schrodinger equations is given using quantum
filtering theory. We study an open system in contact with its environment, the
electromagnetic field. Continuous observation of the field yields information
on the system: it is possible to keep track in real time of the best estimate
of the system's quantum state given the observations made. This estimate
satisfies a stochastic Schrodinger equation, which can be derived from the
quantum stochastic differential equation for the interaction picture evolution
of system and field together. Throughout the paper we focus on the basic
example of resonance fluorescence.


title: Number of quantal resonances

abstract:
  Employing the concept of time-delay, a relation is found which counts the
number of quantal resonances supported by a potential. Several simple and
advanced illustrations include a treatment of square-well, Dirac delta barrier,
an interesting physical situation from neutron reflectometry, and the Delta
resonance appearing in the scattering of \pi meson from proton.


title:
Continuous Multipartite Entangled State in Wigner Representation and the
  Violation of Zukowski-Brukner Inequality

abstract:
  We construct an explicit Wigner function for N-mode squeezed state. Based on
a previous observation that the Wigner function describes correlations in the
joint measurement of the phase-space displaced parity operator, we investigate
the non-locality of multipartite entangled state by the violation of
Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for
such squeezed state violate these inequalities by an amount that grows with the
number N.


title: Phase-control of directed diffusion in a symmetric optical lattice

abstract:
  We demonstrate the phenomenon of directed diffusion in a symmetric periodic
potential. This has been realized with cold atoms in a one-dimensional
dissipative optical lattice. The stochastic process of optical pumping leads to
a diffusive dynamics of the atoms through the periodic structure, while a
zero-mean force which breaks the temporal symmetry of the system is applied by
phase-modulating one of the lattice beams. The atoms are set into directed
motion as a result of the breaking of the temporal symmetry of the system.


title: Damping rates of the atomic velocity in Sisyphus cooling

abstract:
  We present a theoretical and experimental study of the damping process of the
atomic velocity in Sisyphus cooling. The relaxation rates of the atomic kinetic
temperature are determined for a 3D lin$\perp$lin optical lattice. We find that
the damping rates of the atomic temperature depend linearly on the optical
pumping rate, for a given depth of the potential wells. This is at variance
with the behavior of the friction coefficient as calculated from the spatial
diffusion coefficients within a model of Brownian motion. The origin of this
different behavior is identified by distinguishing the role of the trapped and
traveling atoms.


title:
Synchronization of Hamiltonian motion and dissipative effects in optical
  lattices: Evidence for a stochastic resonance

abstract:
  We theoretically study the influence of the noise strength on the excitation
of the Brillouin propagation modes in a dissipative optical lattice. We show
that the excitation has a resonant behavior for a specific amount of noise
corresponding to the precise synchronization of the Hamiltonian motion on the
optical potential surfaces and the dissipative effects associated with optical
pumping in the lattice. This corresponds to the phenomenon of stochastic
resonance. Our results are obtained by numerical simulations and correspond to
the analysis of microscopic quantities (atomic spatial distributions) as well
as macroscopic quantities (enhancement of spatial diffusion and pump-probe
spectra). We also present a simple analytical model in excellent agreement with
the simulations.


title: Mixing Property of Quantum Relative Entropy

abstract:
  An analogue of the mixing property of quantum entropy is derived for quantum
relative entropy.It is applied to the final state of ideal measurement and to
the spectral form of the second density operator. Three cases of states on a
directed straight line of relative entropy are discussed.


title: Exact interferometers for the concurrence and residual 3-tangle

abstract:
  In this paper we describe a set of circuits that can measure the concurrence
of a two qubit density matrix without requiring the deliberate addition of
noise. We then extend these methods to obtain a circuit to measure one type of
three qubit entanglement for pure states, namely the 3-tangle.


title: Symmetrized Schr\"{o}dinger Equation and General Complex Solution

abstract:
  We suggest the symmetrized Schr\"{o}dinger equation and propose a general
complex solution which is characterized by the imaginary units $i$ and
$\epsilon$. This symmetrized Schr\"{o}dinger equation appears some interesting
features.


title:
Chaos and Quantum-Classical Correspondence via Phase Space Distribution
  Functions

abstract:
  Quantum-classical correspondence in conservative chaotic Hamiltonian systems
is examined using a uniform structure measure for quantal and classical phase
space distribution functions. The similarities and differences between quantum
and classical time-evolving distribution functions are exposed by both
analytical and numerical means. The quantum-classical correspondence of
low-order statistical moments is also studied. The results shed considerable
light on quantum-classical correspondence.


title: Control of Dynamical Localization

abstract:
  Control over the quantum dynamics of chaotic kicked rotor systems is
demonstrated. Specifically, control over a number of quantum coherent phenomena
is achieved by a simple modification of the kicking field. These include the
enhancement of the dynamical localization length, the introduction of classical
anomalous diffusion assisted control for systems far from the semiclassical
regime, and the observation of a variety of strongly nonexponential lineshapes
for dynamical localization. The results provide excellent examples of
controlled quantum dynamics in a system that is classically chaotic and offer
new opportunities to explore quantum fluctuations and correlations in quantum
chaos.


title: Noiseless Quantum Circuits for the Peres Separability Criterion

abstract:
  In this Letter we give a method for constructing sets of simple circuits that
can determine the spectrum of a partially transposed density matrix, without
requiring either a tomographically complete POVM or the addition of noise to
make the spectrum non-negative. These circuits depend only on the dimension of
the Hilbert space and are otherwise independent of the state.


title:
Correlations of observables in chaotic states of macroscopic quantum
  systems

abstract:
  We study correlations of observables in energy eigenstates of chaotic systems
of a large size $N$. We show that the bipartite entanglement of two subsystems
is quite strong, whereas macroscopic entanglement of the total system is
absent. It is also found that correlations, either quantum or classical, among
less than $N/2$ points are quite small. These results imply that chaotic states
are stable. Invariance of these properties under local operations is also
shown.


title: Long distance quantum teleportation in a quantum relay configuration

abstract:
  A long distance quantum teleportation experiment with a fiber-delayed Bell
State Measurement (BSM) is reported. The source creating the qubits to be
teleported and the source creating the necessary entangled state are connected
to the beam splitter realizing the BSM by two 2 km long optical fibers. In
addition, the teleported qubits are analyzed after 2,2 km of optical fiber, in
another lab separated by 55 m. Time bin qubits carried by photons at 1310 nm
are teleported onto photons at 1550 nm. The fidelity is of 77%, above the
maximal value obtainable without entanglement. This is the first realization of
an elementary quantum relay over significant distances, which will allow an
increase in the range of quantum communication and quantum key distribution.


title:
Grandma's local realistic theory for the Einstein-Podolsky-Rosen-Bohm
  experiment

abstract:
  A local realistic theory is presented for Mermin's special case of the EPRB
experiment. The theory, which is readily extended to the general EPRB
experiment, reproduces all the predictions of quantum theory. It also reveals
that Bell, and also Hess and Philipp, had made an error in the mathematical
formulation of Einstein's locality or no action at a distance principle.


title: Robust Polynomials and Quantum Algorithms

abstract:
  We define and study the complexity of robust polynomials for Boolean
functions and the related fault-tolerant quantum decision trees, where input
bits are perturbed by noise. We compare several different possible definitions.
Our main results are
  * For every n-bit Boolean function f there is an n-variate polynomial p of
degree O(n) that robustly approximates it, in the sense that p(x) remains close
to f(x) if we slightly vary each of the n inputs of the polynomial.
  * There is an O(n)-query quantum algorithm that robustly recovers n noisy
input bits. Hence every n-bit function can be quantum computed with O(n)
queries in the presence of noise. This contrasts with the classical model of
Feige et al., where functions such as parity need Theta(n*log n) queries.
  We give several extensions and applications of these results.


title: A Semantic Approach to the Completeness Problem in Quantum Mechanics

abstract:
  The old Bohr-Einstein debate about the completeness of quantum mechanics (QM)
was held on an ontological ground. The completeness problem becomes more
tractable, however, if it is preliminarily discussed from a semantic viewpoint.
Indeed every physical theory adopts, explicitly or not, a truth theory for its
observative language, in terms of which the notions of semantic objectivity and
semantic completeness of the physical theory can be introduced and inquired. In
particular, standard QM adopts a verificationist theory of truth that implies
its semantic nonobjectivity; moreover, we show in this paper that standard QM
is semantically complete, which matches Bohr's thesis. On the other hand, one
of the authors has provided a Semantic Realism (or SR) interpretation of QM
that adopts a Tarskian theory of truth as correspondence for the observative
language of QM (which was previously mantained to be impossible); according to
this interpretation QM is semantically objective, yet incomplete, which matches
EPR's thesis. Thus, standard QM and the SR interpretation of QM come to
opposite conclusions. These can be reconciled within an integrationist
perspective that interpretes non-Tarskian theories of truth as theories of
metalinguistic concepts different from truth.


title: Spin transitions in time-dependent regular and random magnetic fields

abstract:
  We study the transition between Zeeman levels of an arbitrary spin placed
into a regular time-dependent field and a random field with the Gaussian
distribution. One component of the regular field changes its sign at some
moment of time, whereas another component does not change substantially. The
noise is assumed to be fast. In this assumption we find analytically the
ensemble average of the spin density matrix and its fluctuations.


title: Remote preparation of arbitrary ensembles and quantum bit commitment

abstract:
  The Hughston-Jozsa-Wootters theorem shows that any finite ensemble of quantum
states can be prepared "at a distance", and it has been used to demonstrate the
insecurity of all bit commitment protocols based on finite quantum systems
without superselection rules. In this paper, we prove a generalized HJW theorem
for arbitrary ensembles of states on a C*-algebra. We then use this result to
demonstrate the insecurity of bit commitment protocols based on infinite
quantum systems, and quantum systems with Abelian superselection rules.


title: Quantum interference of ultrastable twin optical beams

abstract:
  We report the first measurement of the quantum phase-difference noise of an
ultrastable nondegenerate optical parametric oscillator that emits twin beams
classically phase-locked at exact frequency degeneracy. The measurement
illustrates the property of a lossless balanced beam-splitter to convert
number-difference squeezing into phase-difference squeezing and, thus, provides
indirect evidence for Heisenberg-limited interferometry using twin beams. This
experiment is a generalization of the Hong-Ou-Mandel interference effect for
continuous variables and constitutes a milestone towards continuous-variable
entanglement of bright, ultrastable nondegenerate beams.


title: Quantum-state tomography for spin-l systems

abstract:
  We show that the density matrix of a spin-l system can be described entirely
in terms of the measurement statistics of projective spin measurements along a
minimum of 4l+1 different spin directions. It is thus possible to represent the
complete quantum statistics of any N-level system within the spherically
symmetric three dimensional space defined by the spin vector. An explicit
method for reconstructing the density matrix of a spin-1 system from the
measurement statistics of five non-orthogonal spin directions is presented and
the generalization to spin-l systems is discussed.


title:
Realistic interpretation of a superposition state does not imply a
  mixture

abstract:
  Contrary to previous claims, it is shown that, for an ensemble of either
single-particle systems or multi-particle systems, the realistic interpretation
of a superposition state that mathematically describes the ensemble does not
imply that the ensemble is a mixture. Therefore it cannot be argued that the
realistic interpretation is wrong on the basis that some predictions derived
from the mixture are different from the corresponding predictions derived from
the superposition state.


title: Minimum decoherence cat-like states in Gaussian noisy channels

abstract:
  We address the evolution of cat-like states in general Gaussian noisy
channels, by considering superpositions of coherent and squeezed-coherent
states coupled to an arbitrarily squeezed bath. The phase space dynamics is
solved and decoherence is studied keeping track of the purity of the evolving
state. The influence of the choice of the state and channel parameters on
purity is discussed and optimal working regimes that minimize the decoherence
rate are determined. In particular, we show that squeezing the bath to protect
a non squeezed cat state against decoherence is equivalent to orthogonally
squeezing the initial cat state while letting the bath be phase insensitive.


title: Analysis of Photoassociation Spectra for Giant Helium Dimers

abstract:
  We perform a theoretical analysis to interpret the spectra of purely
long-range helium dimers produced by photoassociation (PA) in an ultra-cold gas
of metastable helium atoms. The experimental spectrum obtained with the PA
laser tuned closed to the $2^3S_1\leftrightarrow 2^3P_0$ atomic line has been
reported in a previous Letter. Here, we first focus on the corrections to be
applied to the measured resonance frequencies in order to infer the molecular
binding energies. We then present a calculation of the vibrational spectra for
the purely long-range molecular states, using adiabatic potentials obtained
from perturbation theory. With retardation effects taken into account, the
agreement between experimental and theoretical determinations of the spectrum
for the $0_u^+$ purely long-range potential well is very good. The results
yield a determination of the lifetime of the $2^3P$ atomic state.


title:
Selective interactions in trapped ions: state reconstruction and quantum
  logic

abstract:
  We propose the implementation of selective interactions of atom-motion
subspaces in trapped ions. These interactions yield resonant exchange of
population inside a selected subspace, leaving the others in a highly
dispersive regime. Selectivity allows us to generate motional Fock (and other
nonclassical) states with high purity out of a wide class of initial states,
and becomes an unconventional cooling mechanism when the ground state is
chosen. Individual population of number states can be distinctively measured,
as well as the motional Wigner function. Furthermore, a protocol for
implementing quantum logic through a suitable control of selective subspaces is
presented.


title:
The wave function as a mathematical description of a free particle's
  possible motion: The 2-slit problem with attempted detection

abstract:
  Starting with a down to earth interpretation of quantum mechanics for a free
particle, the disappearance and reappearance of interference in the 2 slit
problem with a detector behind one are treated in detail. A partial
interpretation of quantum theory is employed which is simple, emphasizing
description, yet adequate for addressing the present problem.
  Given that the eigenvalue equation is essential to predict a free particle's
probability of collision, it is argued that there is equal need for a realistic
theory to describe its possible motion. Feynman's point-to-point space-time
wave packet is put forth and used as the appropriate description of the
field-free motion between collisions.
  For a particle in a conventional 2-slit experiment with attempted detection
behind one, the disappearance of interference is explained - both when the
detection succeeds and when it doesn't. Also a definite prediction is made,
when the inter-slit distance is reduced, of where the first signs of
interference should appear on the detection screen.


title: Optimal measurements for relative quantum information

abstract:
  We provide optimal measurement schemes for estimating relative parameters of
the quantum state of a pair of spin systems. We prove that the optimal
measurements are joint measurements on the pair of systems, meaning that they
cannot be achieved by local operations and classical communication. We also
demonstrate that in the limit where one of the spins becomes macroscopic, our
results reproduce those that are obtained by treating that spin as a classical
reference direction.


title: Einstein, Podolsky, Rosen, and Shannon

abstract:
  The EPR paradox (1935) is reexamined in the light of Shannon's information
theory (1948). The EPR argument did not take into account that the observers'
information was localized, like any other physical object.


title: Quantum States Estimation: Root Approach

abstract:
  Multiparametric statistical model providing stable reconstruction of
parameters by observations is considered. The only general method of this kind
is the root model based on the representation of the probability density as a
squared absolute value of a certain function, which is referred to as a
psi-function in analogy with quantum mechanics. The psi-function is represented
by an expansion in terms of an orthonormal set of functions. It is shown that
the introduction of the psi-function allows one to represent the Fisher
information matrix as well as statistical properties of the estimator of the
state vector (state estimator) in simple analytical forms. A new statistical
characteristic, a confidence cone, is introduced instead of a standard
confidence interval. The chi-square test is considered to test the hypotheses
that the estimated vector converges to the state vector of a general population
and that both samples are homogeneous. The expansion coefficients are estimated
by the maximum likelihood method. The method proposed may be applied to its
full extent to solve the statistical inverse problem of quantum mechanics (root
estimator of quantum states). In order to provide statistical completeness of
the analysis, it is necessary to perform measurements in mutually complementing
experiments (according to the Bohr terminology). The maximum likelihood
technique and likelihood equation are generalized in order to analyze quantum
mechanical experiments. It is shown that the requirement for the expansion to
be of a root kind can be considered as a quantization condition making it
possible to choose systems described by quantum mechanics from all statistical
models consistent, on average, with the laws of classical mechanics.


title: Slow Light in Doppler Broadened Two level Systems

abstract:
  We show that the propagation of light in a Doppler broadened medium can be
slowed down considerably eventhough such medium exhibits very flat dispersion.
The slowing down is achieved by the application of a saturating counter
propagating beam that produces a hole in the inhomogeneous line shape. In
atomic vapors, we calculate group indices of the order of 10^3. The
calculations include all coherence effects.


title: Informationally complete measurements and groups representation

abstract:
  Informationally complete measurements on a quantum system allow to estimate
the expectation value of any arbitrary operator by just averaging functions of
the experimental outcomes. We show that such kind of measurements can be
achieved through positive-operator valued measures (POVM's) related to unitary
irreducible representations of a group on the Hilbert space of the system. With
the help of frame theory we provide a constructive way to evaluate the
data-processing function for arbitrary operators.


title: The Many Worlds of Uncertainty

abstract:
  The status of the uncertainty relations varies between the different
interpretations of quantum mechanics. The aim of the current paper is to
explore their meanings within a certain neo-Everettian many worlds
interpretation. We will also look at questions that have been linked with the
uncertainty relations since Heisenberg's uncertainty principle: those of joint
and repeated measurement of non-commuting (or otherwise `incompatible')
observables. This will have implications beyond the uncertainty relations, as
we will see the fundamentally different way in which statistical statements are
interpreted in the neo-Everett theory that we use.


title:
A quantum computer using a trapped-ion spin molecule and microwave
  radiation

abstract:
  We propose a new design for a quantum information processor where qubits are
encoded into Hyperfine states of ions held in a linear array of individually
tailored microtraps and sitting in a spatially varying magnetic field. The
magnetic field gradient introduces spatially dependent qubit transition
frequencies and a type of spin-spin interaction between qubits. Single and
multi-qubit manipulation is achieved via resonant microwave pulses as in
liquid-NMR quantum computation while the qubit readout and reset is achieved
through trapped-ion fluorescence shelving techniques. By adjusting the
microtrap configurations we can tailor, in hardware, the qubit resonance
frequencies and coupling strengths. We show the system possesses a side-band
transition structure which does not scale with the size of the processor
allowing scalable frequency discrimination between qubits. By using large
magnetic field gradients, one can readout and reset the qubits in the ion chain
via frequency selective optical pulses avoiding the need for many tightly
focused laser beams for spatial qubit addressing.


title: Rotational invariance and the spin-statistics theorem

abstract:
  In this article the rotational invariance of entangled quantum states is
investigated as a possible cause of the Pauli exclusion principle. First, it is
shown that a certain class of rotationally invariant states can only occur in
pairs. This is referred to as the coupling principle. This in turn suggests a
natural classification of quantum systems into those containing coupled states
and those that do not. Surprisingly, it would seem that Fermi-Dirac statistics
follows as a consequence of this coupling while the Bose-Einstein follows by
breaking it. In section 5, the above approach is related to Pauli's original
spin-statistics theorem and finally in the last two sections, a theoretical
justification, based on Clebsch-Gordan coefficients and the experimental
evidence respectively, is presented.


title: Classical Teleportation of Classical States

abstract:
  The standard quantum teleportation scheme is deconstructed, and those aspects
of it that appear remarkable and "non-classical" are identified. An alternative
teleportation scheme, involving only classical states and classical
information, is then formulated, and it is shown that the classical scheme
reproduces all of these remarkable aspects, including those that had seemed
non-classical. This leads to a re-examination of quantum teleportation, which
suggests that its significance depends on the interpretation of quantum states.


title: Optimal Topological Test for Degeneracies of Real Hamiltonians

abstract:
  We consider adiabatic transport of eigenstates of real Hamiltonians around
loops in parameter space. It is demonstrated that loops that map to nontrivial
loops in the space of eigenbases must encircle degeneracies. Examples from
Jahn-Teller theory are presented to illustrate the test. We show furthermore
that the proposed test is optimal.


title: A note on Coulomb scattering amplitude

abstract:
  The summation of the partial wave series for Coulomb scattering amplitude,
$f^C(\theta)$ is avoided because the series is oscillatorily and divergent.
Instead, $f^C(\theta)$ is obtained by solving the Schr{\"o}dinger equation in
parabolic cylindrical co-ordinates which is not a general method. Here, we show
that a reconstructed series, $(1-\cos\theta) ^2f^C(\theta)$, is both convergent
and analytically summable.


title: A biphotons double slit experiment

abstract:
  In this paper we present a double slit experiment where two undistinguishable
photons produced by type I PDC are sent each to a well defined slit. Data about
the diffraction and interference patterns for coincidences are presented and
discussed. An analysis of these data allows a first test of standard quantum
mechanics against de Broglie-Bohm theory.


title:
Teleportation scheme implementing contextually the Universal Optimal
  Quantum Cloning Machine and the Universal Not Gate. Complete experimental
  realization

abstract:
  By a significant modification of the standard protocol of quantum state
Teleportation two processes ''forbidden'' by quantum mechanics in their exact
form, the Universal NOT gate and the Universal Optimal Quantum Cloning Machine,
have been implemented contextually and optimally by a fully linear method. In
particular, the first experimental demonstration of the Tele-UNOT Gate, a novel
quantum information protocol has been reported (cfr. quant-ph/0304070). A
complete experimental realization of the protocol is presented here.


title:
Entanglement structure of adjoint representation of unitary group and
  tomography of quantum states

abstract:
  The density matrix of composite spin system is discussed in relation to the
adjoint representation of unitary group U(n). The entanglement structure is
introduced as an additional ingredient to the description of the linear space
carrying the adjoint representation. Positive maps of density operator are
related to random matrices. The tomographic probability description of quantum
states is used to formulate the problem of separability and entanglement as the
condition for joint probability distribution of several random variables
represented as the convex sum of products of probabilities of random variables
describing the subsystems. The property is discussed as a possible criterion
for separability or entanglement. The convenient criterion of positivity of
finite and infinite matrix is obtained. The U(n)-tomogram of a multiparticle
spin state is introduced. The entanglement measure is considered in terms of
this tomogram.


title: Disentanglement as particles separate

abstract:
  Disentanglement refers to decoherence that destroys the quantum interference
terms between particles as they separate. This process reduces the pure
isotropic entangled EPR state to a mixed anisotropic state. Averaging over the
ensemble of states leads to correlations between separated particles that
satisfies Bell's inequalities. Applying disentanglement to EPR pairs of photons
shows that entanglement is characterized by various two-particle symmetry
properties. These symmetry properties are destroyed by disentanglement but
photon helicity is conserved. This is sufficient to account for the
correlations needed to resolve the EPR paradox. Apart from a numerical factor,
the functional form for the correlations due to entanglement and
disentanglement is identical, thereby making it difficult to distinguish
between the two in the current experiments.


title: Extremal covariant quantum operations and POVM's

abstract:
  We consider the convex sets of QO's (quantum operations) and POVM's (positive
operator valued measures) which are covariant under a general
finite-dimensional unitary representation of a group. We derive necessary and
sufficient conditions for extremality, and give general bounds for ranks of the
extremal POVM's and QO's. Results are illustrated on the basis of simple
examples.


title: Least paradoxical states of the Schr\"{o}dinger cat

abstract:
  Modeling the Schr\"{o}dinger cat by a two state system and assuming that the
cat is coupled to the environment we look for the least paradoxical states of
the Schr\"{o}dinger cat in the following way. We require the reduced density
matrix of the cat for one of the two states in the superposition to be the same
as the one for the total state while distinct from the reduced density matrix
of the cat for the other state in the superposition. We then look for the
reduced density matrices for which the cat is as alive as possible for the
first state (and as dead as possible for the second state). The resulting
states are those in which the probability for the cat to be alive (or dead) is
$1/2+\sqrt 2/4\approx 0.854$


title: Two examples of discrete-time quantum walks taking continuous steps

abstract:
  This note introduces some examples of quantum random walks in d-dimensional
Eucilidean space and proves the weak convergence of their rescaled n-step
densities. One of the examples is called the Plancherel quantum walk because
the "quantum coin flip" is the Fourier Integral (or Plancherel) Transform. The
other examples are the Birkhoff quantum walks, so named because the coin flips
are effected by means of measure preserving transformations to which the
Birkhoff's Ergodic Theorem is applied.


title:
Convex-roof extended negativity as an entanglement measure for bipartite
  quantum systems

abstract:
  We extend the concept of the negativity, a good measure of entanglement for
bipartite pure states, to mixed states by means of the convex-roof extension.
We show that the measure does not increase under local quantum operations and
classical communication, and derive explicit formulae for the entanglement
measure of isotropic states and Werner states, applying the formalism presented
by Vollbrecht and Werner [Phys. Rev. A {\bf 64}, 062307 (2001)].


title: Rotated and scaled center of mass tomography for several particles

abstract:
  The tomographic map of quantum state of a system with several degrees of
freedom which depends on one random variable, analogous to center of mass
considered in rotated and scaled reference frame in the phase space, is
constructed. Time evolution equation of the tomogram for this map is given in
explicit form. Properties of the map like the transition probabilities between
the different states and relation to the star product formalism are elucidated.
Example of multimode oscillator is considered in details. Symmetry properties
in respect to identical particles permutations are discussed in the framework
of proposed tomography scheme.


title: Quantum Modeling

abstract:
  We present a modification of Simon's algorithm that in some cases is able to
fit experimentally obtained data to appropriately chosen trial functions with
high probability. Modulo constants pertaining to the reliability and
probability of success of the algorithm, the algorithm runs using only
O(polylog(|Y|)) queries to the quantum database and O(polylog(|X|,|Y|))
elementary quantum gates where |X| is the size of the experimental data set and
|Y| is the size of the parameter space.We discuss heuristics for good
performance, analyze the performance of the algorithm in the case of linear
regression, both one-dimensional and multidimensional, and outline the
algorithm's limitations.


title: Local entanglement and quantum phase transition in the Hubbard model

abstract:
  The local entanglement $E_v$ of the one-dimensional Hubbard model is studied
on the basis of its Bethe-ansatz solution. The relationship between the local
entanglement and the on-site Coulomb interaction $U$ is obtained. Our results
show that $E_v$ is an even analytic function of $U$ at half-filling and it
reaches a maximum at the critical point U=0. The variation of the local
entanglement with the filling factor shows that the ground state with maximal
symmetry possesses maximal entanglement. The magnetic field makes the local
entanglement to decrease and approach to zero at saturated magnetization. The
on-site Coulomb interaction always suppresses the local entanglement.


title:
On the transfer of entanglement from a two-mode squeezed state to a pair
  of qubits

abstract:
  There have recently been interests in transferring entanglement between two
quantum systems in different Hilbert spaces. In particular, the study of
entanglement transfer from a continuous-variable to a qubit system has a
primary importance due to practical implications. A continuous-variable system
easily propagates entanglement while a qubit system is easy to manipulate. We
investigate conditions to entangle two two-level atoms for a broad-band
two-mode squeezed field driving the cavities where the atoms are.


title:
Correspondences and Quantum Description of Aharonov-Bohm and
  Aharonov-Casher Effects

abstract:
  We establish systematic consolidation of the Aharonov-Bohm and
Aharonov-Casher effects including their scalar counterparts. Their formal
correspondences in acquiring topological phases are revealed on the basis of
the gauge symmetry in non-simply connected spaces and the adiabatic condition
for the state of magnetic dipoles. In addition, investigation of basic two-body
interactions between an electric charge and a magnetic dipole clarifies their
appropriate relative motions and discloses physical interrelations between the
effects. Based on the two-body interaction, we also construct an exact
microscopic description of the Aharonov-Bohm effect, where all the elements are
treated on equal footing, i.e., magnetic dipoles are described
quantum-mechanically and electromagnetic fields are quantized. This microscopic
analysis not only confirms the conventional (semiclassical) results and the
topological nature but also allows one to explore the fluctuation effects due
to the precession of the magnetic dipoles with the adiabatic condition relaxed.


title: Quantum Measurement, Complexity and Discrete Physics

abstract:
  This paper presents a new modified quantum mechanics, Critical Complexity
Quantum Mechanics, which includes a new account of wavefunction collapse. This
modified quantum mechanics is shown to arise naturally from a fully discrete
physics, where all physical quantities are discrete rather than continuous. I
compare this theory with the spontaneous collapse theories of Ghirardi, Rimini,
Weber and Pearle and discuss some implications of the theory for a realist view
of the quantum realm.


title:
Analytic pulse design for selective population transfer in many-level
  quantum systems: maximizing amplitude of population oscillations

abstract:
  State selective preparation and manipulation of discrete-level quantum
systems such as atoms, molecules or quantum dots is a the ultimate tool for
many diverse fields such as laser control of chemical reactions, atom optics,
high-precision metrology and quantum computing. Rabi oscillations are one of
the simplest, yet potentially quite useful mechanisms for achieving such
manipulation. Rabi theory establishes that in the two-level systems resonant
drive leads to the periodic and complete population oscillations between the
two system levels. In this paper an analytic optimization algorithm for
producing Rabi-like oscillations in the general discrete many-level quantum
systems is presented.


title: Finite precision measurement nullifies Euclid's postulates

abstract:
  Following Meyer's argument (quant-ph/9905080) the set of all directions in
space is replaced by the dense subset of rational directions. The result
conflicts with Euclidean geometry.


title:
Non-linear and quantum optics of a type II OPO containing a birefringent
  element Part 1: Classical operation

abstract:
  We describe theoretically the main characteristics of the steady state regime
of a type II Optical Parametric Oscillator (OPO) containing a birefringent
plate. In such a device the signal and idler waves are at the same time
linearly coupled by the plate and nonlinearly coupled by the $\chi^{(2)}$
crystal. This mixed coupling allows, in some well-defined range of the control
parameters, a frequency degenerate operation as well as phase locking between
the signal and idler modes. We describe here a complete model taking into
account all possible effects in the system, \emph{i.e.} arbitrary rotation of
the waveplate, non perfect phase matching, ring and linear cavities. This model
is able to explain the detailed features of the experiments performed with this
system.


title: Monogamy of entanglement and other correlations

abstract:
  It has been observed by numerous authors that a quantum system being
entangled with another one limits its possible entanglement with a third
system: this has been dubbed the "monogamous nature of entanglement". In this
paper we present a simple identity which captures the trade-off between
entanglement and classical correlation, which can be used to derive rigorous
monogamy relations.
  We also prove various other trade-offs of a monogamy nature for other
entanglement measures and secret and total correlation measures.


title:
Exponential speed-up with a single bit of quantum information: Testing
  the quantum butterfly effect

abstract:
  We present an efficient quantum algorithm to measure the average fidelity
decay of a quantum map under perturbation using a single bit of quantum
information. Our algorithm scales only as the complexity of the map under
investigation, so for those maps admitting an efficient gate decomposition, it
provides an exponential speed up over known classical procedures. Fidelity
decay is important in the study of complex dynamical systems, where it is
conjectured to be a signature of quantum chaos. Our result also illustrates the
role of chaos in the process of decoherence.


title:
Entanglement Detection in Optical Lattices of Bosonic Atoms with
  Collective Measurements

abstract:
  The minimum requirements for entanglement detection are discussed for a spin
chain in which the spins cannot be individually accessed. The methods presented
detect entangled states close to a cluster state and a many-body singlet state,
and seem to be viable for experimental realization in optical lattices of
two-state bosonic atoms. The entanglement criteria are based on entanglement
witnesses and on the uncertainty of collective observables.


title: Long time Evolution of Quantum Averages Near Stationary Points

abstract:
  We construct explicit expressions for quantum averages in coherent states for
a Hamiltonian of degree 4 with a hyperbolic stagnation point. These expressions
are valid for all times and "collapse" (i.e., become infinite) along a discrete
sequence of times. We compute quantum corrections compared to classical
expressions. These corrections become significant over a time period of order C
log 1/\hbar.


title:
There exist non orthogonal quantum measurements that are perfectly
  repeatable

abstract:
  We show that, contrarily to the widespread belief, in quantum mechanics
repeatable measurements are not necessarily described by orthogonal
projectors--the customary paradigm of "observable". Nonorthogonal
repeatability, however, occurs only for infinite dimensions. We also show that
when a non orthogonal repeatable measurement is performed, the measured system
retains some "memory" of the number of times that the measurement has been
performed.


title: Experimental evidence for bounds on quantum correlations

abstract:
  We implemented the experiment proposed by Cabello [arXiv:quant-ph/0309172] to
test the bounds of quantum correlation. As expected from the theory we found
that, for certain choices of local observables, Cirel'son's bound of the
Clauser-Horne-Shimony-Holt inequality ($2\sqrt{2}$) is not reached by any
quantum states.


title: Addressing atoms in optical lattices with Bessel beams

abstract:
  A method of synthesizing localized optical fields with zeroes on a periodic
lattice is analyzed. The applicability to addressing atoms trapped in optical
lattices with low crosstalk is discussed.


title:
Inversionless light amplification and optical switching controlled by
  state-dependent alignment of molecules

abstract:
  We propose a method to achieve amplification without population inversion by
anisotropic molecules whose orientation by an external electric field is
state-dependent. It is based on decoupling of the lower-state molecules from
the resonant light while the excited ones remain emitting. The suitable class
of molecules is discussed, the equation for the gain factor is derived, and the
magnitude of the inversionless amplification is estimated for the typical
experimental conditions. Such switching of the sample from absorbing to
amplifying via transparent state is shown to be possible both with the aid of
dc and ac control electric fields.


title: Zeno dynamics and constraints

abstract:
  We investigate some examples of quantum Zeno dynamics, when a system
undergoes very frequent (projective) measurements that ascertain whether it is
within a given spatial region. In agreement with previously obtained results,
the evolution is found to be unitary and the generator of the Zeno dynamics is
the Hamiltonian with hard-wall (Dirichlet) boundary conditions. By using a new
approach to this problem, this result is found to be valid in an arbitrary
$N$-dimensional compact domain. We then propose some preliminary ideas
concerning the algebra of observables in the projected region and finally look
at the case of a projection onto a lower dimensional space: in such a situation
the Zeno ansatz turns out to be a procedure to impose constraints.


title: Quantum Lithography in Macroscopic Observations

abstract:
  We study the generalized Young's double-slit interference for the beam
produced in the spontaneously parametric down-conversion (SPDC). We find that
the sub-wavelength lithography can occur macroscopically in both the two-photon
intensity measurement and the single-photon spatial intensity correlation
measurement. We show the visibility and the strength of the interference fringe
related to the SPDC interaction. It may provide a strong quantum lithography
with a moderate visibility in practical application.


title: Single spin measurement using spin-orbital entanglement

abstract:
  Single spin measurement represents a major challenge for spin-based quantum
computation. In this article we propose a new method for measuring the spin of
a single electron confined in a quantum dot (QD). Our strategy is based on
entangling (using unitary gates) the spin and orbital degrees of freedom. An
{\em orbital qubit}, defined by a second, empty QD, is used as an ancilla and
is prepared in a known initial state. Measuring the orbital qubit will reveal
the state of the (unknown) initial spin qubit, hence reducing the problem to
the easier task of single charge measurement. Since spin-charge conversion is
done with unit probability, single-shot measurement of an electronic spin can
be, in principle, achieved. We evaluate the robustness of our method against
various sources of error and discuss briefly possible implementations.


title:
Fast light, slow light, and phase singularities: a connection to
  generalized weak values

abstract:
  We demonstrate that Aharonov-Albert-Vaidman (AAV) weak values have a direct
relationship with the response function of a system, and have a much wider
range of applicability in both the classical and quantum domains than
previously thought. Using this idea, we have built an optical system, based on
a birefringent photonic crystal, with an infinite number of weak values. In
this system, the propagation speed of a polarized light pulse displays both
superluminal and slow light behavior with a sharp transition between the two
regimes. We show that this system's response possesses two-dimensional,
vortex-antivortex phase singularities. Important consequences for optical
signal processing are discussed.


title:
Minimization of nonresonant effects in a scalable Ising spin quantum
  computer

abstract:
  The errors caused by the transitions with large frequency offsets
(nonresonant transitions) are calculated analytically for a scalable
solid-state quantum computer based on a one-dimensional spin chain with Ising
interactions between neighboring spins. Selective excitations of the spins are
enabled by a uniform gradient of the external magnetic field. We calculate the
probabilities of all unwanted nonresonant transitions associated with the flip
of each spin with nonresonant frequency and with flips of two spins: one with
resonant and one with nonresonant frequencies. It is shown that these errors
oscillate with changing the gradient of the external magnetic field. Choosing
the optimal values of this gradient allows us to decrease these errors by 50%.


title: The Gram Matrix of a PT-symmetric Quantum System

abstract:
  The eigenstates of a diagonalizable PT-symmetric Hamiltonian satisfy
unconventional completeness and orthonormality relations. These relations
reflect the properties of a pair of bi-orthonormal bases associated with
non-hermitean diagonalizable operators. In a similar vein, such a dual pair of
bases is shown to possess, in the presence of PT symmetry, a Gram matrix of a
particular structure: its inverse is obtained by simply swapping the signs of
some its matrix elements.