title: On Halting Process of Quantum Turing Machine

abstract:
  We prove that there is no algorithm to tell whether an arbitrarily
constructed Quantum Turing Machine has same time steps for different branches
of computation. We, hence, can not avoid the notion of halting to be
probabilistic in Quantum Turing Machine. Our result suggests that halting
scheme of Quantum Turing Machine and quantum complexity theory based upon the
existing halting scheme sholud be reexamined.


title: Optimal multiqubit operations for Josephson charge qubits

abstract:
  We introduce a method for finding the required control parameters for a
quantum computer that yields the desired quantum algorithm without invoking
elementary gates. We concentrate on the Josephson charge-qubit model, but the
scenario is readily extended to other physical realizations. Our strategy is to
numerically find any desired double- or triple-qubit gate. The motivation is
the need to significantly accelerate quantum algorithms in order to fight
decoherence.


title: Representation theorem for obsevables on a quantum logic

abstract:
  We study a conditional state on a quantum logic using Renyi's approach (or
Bayesian principle). This approach helps us to define independence of events
and differently from the situation in the classical theory of probability, if
an event $a$ is independent of an event $b$, then the event $b$ can be
dependent on the event $a$. We will show that we can define a $s$-map (function
for simultaneous measurements on a quantum logic). It can be shown that if we
have the conditional state we can define the $s$-map and conversely. By using
the $s$-map we can introduce joint distribution also for noncompatible
observables on a quantum logic.


title:
Teleportation and entanglement distillation in the presence of
  correlation among bipartite mixed states

abstract:
  The teleportation channel associated with an arbitrary bipartite state
denotes the map that represents the change suffered by a teleported state when
the bipartite state is used instead of the ideal maximally entangled state for
teleportation. This work presents and proves an explicit expression of the
teleportation channel for the teleportation using Weyl's projective unitary
representation of the space of 2n-tuples of numbers from Z/dZ for integers d>1,
n>0, which has been known for n=1. This formula allows any correlation among
the n bipartite mixed states, and an application shows the existence of
reliable schemes for distillation of entanglement from a sequence of mixed
states with correlation.


title: Entanglement between a qubit and the environment in the spin-boson model

abstract:
  The quantitative description of the quantum entanglement between a qubit and
its environment is considered. Specifically, for the ground state of the
spin-boson model, the entropy of entanglement of the spin is calculated as a
function of $\alpha$, the strength of the ohmic coupling to the environment,
and $\epsilon$, the level asymmetry. This is done by a numerical
renormalization group treatment of the related anisotropic Kondo model. For
$\epsilon=0$, the entanglement increases monotonically with $\alpha$, until it
becomes maximal for $\alpha \lim 1^-$. For fixed $\epsilon>0$, the entanglement
is a maximum as a function of $\alpha$ for a value, $\alpha = \alpha_M < 1$.


title: On Einstein Causality and Time Asymmetry in Quantum Physics

abstract:
  A theorem of Hegerfeldt shows that if the spectrum of the Hamiltonian is
bounded from below, then the propagation speed of certain probabilities does
not have an upper bound. We prove a theorem analogous to Hegerfeldt's that
appertains to asymmetric time evolutions given by a semigroup of operators. As
an application, we consider a characterization of relativistic quasistable
states by irreducible representations of the causal Poincare semigroup and
study the implications of the new theorem for this special case.


title:
Experimental implementation of an adiabatic quantum optimization
  algorithm

abstract:
  We report the realization of a nuclear magnetic resonance computer with three
quantum bits that simulates an adiabatic quantum optimization algorithm.
Adiabatic quantum algorithms offer new insight into how quantum resources can
be used to solve hard problems. This experiment uses a particularly well suited
three quantum bit molecule and was made possible by introducing a technique
that encodes general instances of the given optimization problem into an easily
applicable Hamiltonian. Our results indicate an optimal run time of the
adiabatic algorithm that agrees well with the prediction of a simple
decoherence model.


title:
Optimal strategy for a single-qubit gate and trade-off between opposite
  types of decoherence

abstract:
  We study reliable quantum information processing (QIP) under two different
types of environment. First type is Markovian exponential decay, and the
appropriate elementary strategy of protection of qubit is to apply fast gates.
The second one is strongly non-Markovian and occurs solely during operations on
the qubit. The best strategy is then to work with slow gates. If the two types
are both present, one has to optimize the speed of gate. We show that such a
trade-off is present for a single-qubit operation in a semiconductor quantum
dot implementation of QIP, where recombination of exciton (qubit) is Markovian,
while phonon dressing gives rise to the non-Markovian contribution.


title:
Perspectives for quantum state engineering via high non-linearity in a
  double-EIT regime

abstract:
  We analyse the possibilities for quantum state engineering offered by a model
for Kerr-type non-linearity enhanced by electromagnetically induced
transparency (EIT), which was recently proposed by Petrosyan and Kurizki [{\sl
Phys. Rev. A} {\bf 65}, 33833 (2002)]. We go beyond the semiclassical treatment
and derive a quantum version of the model with both a full Hamiltonian approach
and an analysis in terms of dressed states. The preparation of an entangled
coherent state via a cross-phase modulation effect is demonstrated. We briefly
show that the violation of locality for such an entangled coherent state is
robust against low detection efficiency. Finally, we investigate the
possibility of a bi-chromatic photon blockade realized via the interaction of a
low density beam of atoms with a bi-modal electromagnetic cavity which is
externally driven. We show the effectiveness of the blockade effect even when
more than a single atom is inside the cavity. The possibility to control two
different cavity modes allows some insights into the generation of an entangled
state of cavity modes.


title: Boundary of Quantum Evolution under Decoherence

abstract:
  Relaxation effects impose fundamental limitations on our ability to
coherently control quantum mechanical phenomena. In this letter, we establish
physical limits on how closely can a quantum mechanical system be steered to a
desired target state in the presence of relaxation. In particular, we
explicitly compute the maximum coherence or polarization that can be
transferred between coupled nuclear spins in the presence of very general
decoherence mechanisms that include cross-correlated relaxation. We give
analytical expressions for the control laws (pulse sequences) which achieve
these physical limits and provide supporting experimental evidence.
Exploitation of cross-correlation effects has recently led to the development
of powerful methods in NMR spectroscopy to study very large biomolecules in
solution. We demonstrate with experiments that the optimal pulse sequences
provide significant gains over these state of the art methods, opening new
avenues for spectroscopy of much larger proteins. Surprisingly, in spite of
very large relaxation rates, optimal control can transfer coherence without any
loss when cross-correlated relaxation rates are tuned to auto-correlated
relaxation rates.


title: Relativistic, Causal Description of Quantum Entanglement and Gravity

abstract:
  A possible solution to the problem of providing a spacetime description of
the transmission of signals for quantum entangled states is obtained by using a
bimetric spacetime structure, in which quantum entanglement measurements alter
the structure of the classical relativity spacetime. A bimetric gravity theory
locally has two lightcones, one which describes classical special relativity
and a larger lightcone which allows light signals to communicate quantum
information between entangled states, after a measurement device detects one of
the entangled states. The theory would remove the tension that exists between
macroscopic classical, local gravity and macroscopic nonlocal quantum
mechanics.


title:
Simple applications of Noether's first theorem in quantum mechanics and
  electromagnetism

abstract:
  Internal global symmetries exist for the free non-relativistic
Schr\"{o}dinger particle, whose associated Noether charges--the space integrals
of the wavefunction and the wavefunction multiplied by the spatial
coordinate--are exhibited. Analogous symmetries in classical electromagnetism
are also demonstrated.


title:
Semigroup techniques for the efficient classical simulation of optical
  quantum information

abstract:
  A framework to describe a broad class of physical operations (including
unitary transformations, dissipation, noise, and measurement) in a quantum
optics experiment is given. This framework provides a powerful tool for
assessing the capabilities and limitations of performing quantum information
processing tasks using current experimental techniques. The Gottesman-Knill
theorem is generalized to the infinite-dimensional representations of the group
stabilizer formalism and further generalized to include non-invertable
semigroup transformations, providing a theorem for the efficient classical
simulation of operations within this framework. As a result, we place powerful
constraints on obtaining computational speedups using current techniques in
quantum optics.


title: On Symmetric Sets of Projectors for Reconstruction of a Density Matrix

abstract:
  In this work are presented sets of projectors for reconstruction of a density
matrix for an arbitrary mixed state of a quantum system with the
finite-dimensional Hilbert space. It was discussed earlier [quant-ph/0104126] a
construction with (2n-1)n projectors for the dimension n. For n=2 it is a set
with six projectors associated with eigenvectors of three Pauli matrices, but
for n>2 the construction produces not such a `regular' set. In this paper are
revisited some results of previous work [quant-ph/0104126] and discussed
another, more symmetric construction with the Weyl matrix pair (as the
generalization of Pauli matrices). In the particular case of prime n it is the
mutually unbiased set with (n+1)n projectors. In appendix is shown an example
of application of complete sets for discussions about separability and random
robustness.


title: Quantum theory: Reconsideration of foundations

abstract:
  The purpose of the conference (the fourth in the series of Vaxjo conferences)
was to bring together scientists (physicists, mathematicians and philosophers)
who are interested in foundations of quantum physics. An emphasis was made on
both theory and experiment, the underlying objective being to offer to the
physical, mathematical and philosophic communities a truly interdisciplinary
conference as a privileged place for a scientific interaction. Due to the
actual increased role of foundations in the development of quantum information
theory as well as the necessity to reconsider foundations at the beginning of
the new millennium, the organizers of the conference decided that it was just
the right time for taking the scientific risk of trying this.


title:
Condition for unambiguous state discrimination with local operations and
  classical communication

abstract:
  We obtain a necessary and sufficient condition for a finite set of states of
a finite dimensional multiparticle quantum system to be amenable to unambiguous
discrimination using local operations and classical communication. This
condition is valid for states which may be be mixed, entangled or both. When
the support of the set of states is the entire multiparticle Hilbert space,
this condition is found to have an intriguing connection with the theory of
entanglement witnesses.


title: Elementary Derivation for Passage Times

abstract:
  When a quantum system undergoes unitary evolution in accordance with a
prescribed Hamiltonian, there is a class of states |psi> such that, after the
passage of a certain time, |psi> is transformed into a state orthogonal to
itself. The shortest time for which this can occur, for a given system, is
called the passage time. We provide an elementary derivation of the passage
time, and demonstrate that the known lower bound, due to Fleming, is typically
attained, except for special cases in which the energy spectra have
particularly simple structures. It is also shown, using a geodesic argument,
that the passage times for these exceptional cases are necessarily larger than
the Fleming bound. The analysis is extended to passage times for initially
mixed states.


title:
Experiment towards continuous-variable entanglement swapping: Highly
  correlated four-partite quantum state

abstract:
  We present a protocol for performing entanglement swapping with intense
pulsed beams. In a first step, the generation of amplitude correlations between
two systems that have never interacted directly is demonstrated. This is
verified in direct detection with electronic modulation of the detected
photocurrents. The measured correlations are better than expected from a
classical reconstruction scheme. In the entanglement swapping process, a
four--partite entangled state is generated. We prove experimentally that the
amplitudes of the four optical modes are quantum correlated 3 dB below shot
noise, which is due to the potential four--party entanglement.


title: Inequality for p-norms of positive matrices

abstract:
  This paper derives an inequality relating the p-norm of a positive 2 x 2
block matrix to the p-norm of the 2 x 2 matrix obtained by replacing each block
by its p-norm. The inequality had been known for integer values of p, so the
main contribution here is the extension to all values p >= 1. In a special case
the result reproduces Hanner's inequality. As an application in quantum
information theory, the inequality is used to obtain some results concerning
maximal p-norms of product channels.


title: Polarization qubit phase gate in driven atomic media

abstract:
  We present here an all--optical scheme for the experimental realization of a
quantum phase gate. It is based on the polarization degree of freedom of two
travelling single photon wave-packets and exploits giant Kerr nonlinearities
that can be attained in coherently driven ultracold atomic media.


title: The Casimir force between rough metallic plates

abstract:
  The Casimir force between two metallic plates is affected by their roughness
state. This effect is usually calculated through the so-called `proximity force
approximation' which is only valid for small enough wavevectors in the spectrum
of the roughness profile. We introduce here a more general description with a
wavevector-dependent roughness sensitivity of the Casimir effect. Since the
proximity force approximation underestimates the effect, a measurement of the
roughness spectrum is needed to achieve the desired level of accuracy in the
theory-experiment comparison.


title: Electromagnetic vacuum fluctuations, Casimir and Van der Waals forces

abstract:
  Electromagnetic vacuum fluctuations have observable consequences, like the
Casimir force between mirrors in vacuum. This force is now measured with good
accuracy and agreement with theory when the effect of imperfect reflection of
mirrors is properly taken into account. We discuss the simple case of bulk
metallic mirrors described by a plasma model and show that simple scaling laws
are obtained at the limits of long and short distances. The crossover between
the short and long-distance laws is quite similar to the crossover between Van
der Waals and Casimir-Polder forces for two atoms in vacuum. The result
obtained at short distances can be understood as the London interaction between
plasmon excitations at the surface of each bulk mirror.


title: Recent Experiments on the Casimir Effect: Description and Analysis

abstract: Contribution to the Seminaire Poincare, 2002


title: Effect of collision dephasing on atomic evolutions in a high-Q cavity

abstract:
  The decoherence mechanism of a single atom inside a high-Q cavity is studied,
and the results are compared with experimental observations performed by M.
Brune et al. [Phys. Rev. Lett. 76, 1800 (1996)]. Collision dephasing and cavity
leakage are considered as the major sources giving rise to decoherence effect.
In particular, we show that the experimental data can be fitted very well by
assuming suitable values of collision Stark shifts and dark count rate in the
detector.


title: Quantitative complementarity relations in bipartite systems

abstract:
  We introduce a complete set of complementary quantities in bipartite,
two-dimensional systems. Complementarity then relates the quantitative
entanglement measure concurrence which is a bipartite property to the
single-particle quantum properties predictability and visibility, for the most
general quantum state of two qubits. Consequently, from an interferometric
point of view, the usual wave-particle duality relation must be extended to a
``triality'' relation containing, in addition, the quantitative entanglement
measure concurrence, which has no classical counterpart and manifests a genuine
quantum aspect of bipartite systems. A generalized duality relation, that also
governs possible violations of the Bell's inequality, arises between single-
and bipartite properties.


title:
Implications of Lorentz covariance for the guidance equation in two-slit
  quantum interference

abstract:
  It is known that Lorentz covariance fixes uniquely the current and the
associated guidance law in the trajectory interpretation of quantum mechanics
for spin particles. In the non-relativistic domain this implies a guidance law
for the electron which differs by an additional spin-dependent term from that
originally proposed by de Broglie and Bohm. In this paper we explore some of
the implications of the modified guidance law. We bring out a property of
mutual dependence in the particle coordinates that arises in product states,
and show that the quantum potential has scalar and vector components which
implies the particle is subject to a Lorentz-like force. The conditions for the
classical limit and the limit of negligible spin are given, and the empirical
sufficiency of the model is demonstrated. We then present a series of
calculations of the trajectories based on two-dimensional Gaussian wave packets
which illustrate how the additional spin-dependent term plays a significant
role in structuring both the individual trajectories and the ensemble. The
single packet corresponds to quantum inertial motion. The distinct features
encountered when the wavefunction is a product or a superposition are explored,
and the trajectories that model the two-slit experiment are given. The latter
paths exhibit several new characteristics compared with the original de
Broglie-Bohm ones, such as crossing of the axis of symmetry.


title: Topological Quantum Gates with Quantum Dots

abstract:
  We present an idealized model involving interacting quantum dots that can
support both the dynamical and geometrical forms of quantum computation. We
show that by employing a structure similar to the one used in the Aharonov-Bohm
effect we can construct a topological two-qubit phase-gate that is to a large
degree independent of the exact values of the control parameters and therefore
resilient to control errors. The main components of the setup are realizable
with present technology.


title: Security of Quantum Key Distribution with entangled quNits

abstract:
  We consider a generalisation of Ekert's entanglement-based quantum
cryptographic protocol where qubits are replaced by qu$N$its (i.e.,
N-dimensional systems). In order to study its robustness against optimal
incoherent attacks, we derive the information gained by a potential
eavesdropper during a cloning-based individual attack. In doing so, we
generalize Cerf's formalism for cloning machines and establish the form of the
most general cloning machine that respects all the symmetries of the problem.
We obtain an upper bound on the error rate that guarantees the confidentiality
of quNit generalisations of the Ekert's protocol for qubits.


title: 3-Local Hamiltonian is QMA-complete

abstract:
  It has been shown by Kitaev that the 5-local Hamiltonian problem is
QMA-complete. Here we reduce the locality of the problem by showing that
3-local Hamiltonian is already QMA-complete.


title: Quantum Trajectories and Quantum Measurement Theory

abstract:
  Beyond their use as numerical tools, quantum trajectories can be ascribed a
degree of reality in terms of quantum measurement theory. In fact, they arise
naturally from considering continuous observation of a damped quantum system. A
particularly useful form of quantum trajectories is as linear (but non-unitary)
stochastic Schrodinger equations. In the limit where a strong local oscillator
is used in the detection, and where the system is not driven, these quantum
trajectories can be solved. This gives an alternate derivation of the
probability distributions for completed homodyne and heterodyne detection
schemes. It also allows the previously intractable problem of real-time
adaptive measurements to be treated. The results for an analytically soluble
example of adaptive phase measurements are presented, and future developments
discussed.


title: Geometry of the 3-Qubit State, Entanglement and Division Algebras

abstract:
  We present a generalization to 3-qubits of the standard Bloch sphere
representation for a single qubit and of the 7-dimensional sphere
representation for 2 qubits presented in Mosseri {\it et
al.}\cite{Mosseri2001}. The Hilbert space of the 3-qubit system is the
15-dimensional sphere $S^{15}$, which allows for a natural (last) Hopf
fibration with $S^8$ as base and $S^7$ as fiber. A striking feature is, as in
the case of 1 and 2 qubits, that the map is entanglement sensitive, and the two
distinct ways of un-entangling 3 qubits are naturally related to the Hopf map.
We define a quantity that measures the degree of entanglement of the 3-qubit
state. Conjectures on the possibility to generalize the construction for higher
qubit states are also discussed.


title: Entangled states and collective nonclassical effects in two-atom systems

abstract:
  We propose a review of recent developments on entanglement and non-classical
effects in collective two-atom systems and present a uniform physical picture
of the many predicted phenomena. The collective effects have brought into sharp
focus some of the most basic features of quantum theory, such as nonclassical
states of light and entangled states of multiatom systems. The entangled states
are linear superpositions of the internal states of the system which cannot be
separated into product states of the individual atoms. This property is
recognized as entirely quantum-mechanical effect and have played a crucial role
in many discussions of the nature of quantum measurements and, in particular,
in the developments of quantum communications. Much of the fundamental interest
in entangled states is connected with its practical application ranging from
quantum computation, information processing, cryptography, and interferometry
to atomic spectroscopy.


title: A pulsed source of continuous variable polarization entanglement

abstract:
  We have experimentally demonstrated polarization entanglement using
continuous variables in an ultra-short pulsed laser system at telecommunication
wavelengths. Exploiting the Kerr-nonlinearity of a glass fibre we generated a
polarization squeezed pulse with S2 the only non-zero Stokes parameter thus S1
and S3 being the conjugate pair. Polarization entanglement was generated by
interference of the polarization squeezed field with a vacuum on a 50:50 beam
splitter. The two resultant beams exhibit strong quantum noise correlations in
S1 and S3. The sum noise signal of S3 was at the respective shot noise level
and the difference noise signal of S1 fell 2.9dB below this value.


title: P,T,PT, and CPT invariance of Hermitian Hamiltonians

abstract:
  Currently, it has been claimed that certain Hermitian Hamiltonians have
parity (P) and they are PT-invariant. We propose generalized definitions of
time-reversal operator (T) and orthonormality such that all Hermitian
Hamiltonians are P, T, PT, and CPT invariant. The PT-norm and CPT-norm are
indefinite and definite respectively. The energy-eigenstates are either E-type
(e.g., even) or O-type (e.g., odd). C mimics the charge-conjugation symmetry
which is recently found to exist for a non-Hermitian Hamiltonian. For a
Hermitian Hamiltonian it coincides with P.


title: Two-particle interference in standard and Bohmian quantum mechanics

abstract:
  The compatibility of standard and Bohmian quantum mechanics has recently been
challenged in the context of two-particle interference, both from a theoretical
and an experimental point of view. We analyze different setups proposed and
derive corresponding exact forms for Bohmian equations of motion. The equations
are then solved numerically, and shown to reproduce standard quantum-mechanical
results.


title:
On entanglement capabilities in infinite dimensions or multi-dimensional
  entangled coherent states

abstract:
  An example is given of an interaction that produces an infinite amount of
entanglement in an infinitely short time, but only a finite amount in longer
times. The interaction arises from a standard Kerr nonlinearity and a 50/50
beamsplitter, and the initial state is a coherent state. For certain finite
interaction times multi-dimensional generalizations of entangled coherent
states are generated, for which we construct a teleportation protocol.
Similarities between probabilistic teleportation and unambiguous state
discrimination are pointed out.


title:
Contextual Realization of the Universal Quantum Cloning Machine and of
  the Universal-NOT gate by Quantum Injected Optical Parametric Amplification

abstract:
  A simultaneous, contextual experimental demonstration of the two processes of
cloning an input qubit and of flipping it into the orthogonal qubit is
reported. The adopted experimental apparatus, a Quantum-Injected Optical
Parametric Amplifier (QIOPA) is transformed simultaneously into a Universal
Optimal Quantum Cloning Machine (UOQCM) and into a Universal NOT
quantum-information gate. The two processes, indeed forbidden in their exact
form for fundamental quantum limitations, will be found to be universal and
optimal, i.e. the measured fidelity of both processes F<1 will be found close
to the limit values evaluated by quantum theory. A contextual theoretical and
experimental investigation of these processes, which may represent the basic
difference between the classical and the quantum worlds, can reveal in a
unifying manner the detailed structure of quantum information. It may also
enlighten the yet little explored interconnections of fundamental axiomatic
properties within the deep structure of quantum mechanics. PACS numbers:
03.67.-a, 03.65.Ta, 03.65.Ud


title:
Quantum Mechanics with Trajectories: Quantum Trajectories and Adaptive
  Grids

abstract:
  Although the foundations of the hydrodynamical formulation of quantum
mechanics were laid over 50 years ago, it has only been within the past few
years that viable computational implementations have been developed. One
approach to solving the hydrodynamic equations uses quantum trajectories as the
computational tool. The trajectory equations of motion are described and
methods for implementation are discussed, including fitting of the fields to
gaussian clusters.


title: A tomographic approach to quantum nonlocality

abstract:
  We propose a tomographic approach to study quantum nonlocality in continuous
variable quantum systems. On one hand we derive a Bell-like inequality for
measured tomograms. On the other hand, we introduce pseudospin operators whose
statistics can be inferred from the data characterizing the reconstructed
state, thus giving the possibility to use standard Bell's inequalities.
Illuminating examples are also discussed.


title: The Conflict between Bell-Zukowski Inequality and Bell-Mermin Inequality

abstract:
  We consider a two-particle/two-setting Bell experiment to visualize the
conflict between Bell-\.Zukowski inequality and Bell-Mermin inequality. The
experiment is reproducible by local realistic theories which are not
rotationally invariant. We found that the average value of the Bell-\.Zukowski
operator can be evaluated only by the two-particle/two-setting Bell experiment
in question. The Bell-\.Zukowski inequality reveals that the constructed local
realistic models for the experiment are not rotationally invariant. That is,
the two-particle Bell experiment in question reveals the conflict between
Bell-\.Zukowski inequality and Bell-Mermin inequality. Our analysis has found
the threshold visibility for the two-particle interference to reveal the
conflict noted above. It is found that the threshold visibility agrees with the
value to obtain a violation of the Bell-\.Zukowski inequality.


title: Quantum communication protocols using the vacuum

abstract:
  We speculate what quantum information protocols can be implemented between
two accelerating observers using the vacuum. Whether it is in principle
possible or not to implement a protocol depends on whether the aim is to end up
with classical information or quantum information. Thus, unconditionally secure
coin flipping seems possible but not teleportation.


title:
Squeezing Quantum Information through a Classical Channel: Measuring the
  "Quantumness" of a Set of Quantum States

abstract:
  In this paper we propose a general method to quantify how "quantum" a set of
quantum states is. The idea is to gauge the quantumness of the set by the
worst-case difficulty of transmitting the states through a purely classical
communication channel. Potential applications of this notion arise in quantum
cryptography, where one might like to use an alphabet of states that promises
to be the most sensitive to quantum eavesdropping, and in laboratory
demonstrations of quantum teleportation, where it is necessary to check that
quantum entanglement has actually been used in the protocol.


title:
New classes of n-copy undistillable quantum states with negative partial
  transposition

abstract:
  The discovery of entangled quantum states from which one cannot distill pure
entanglement constitutes a fundamental recent advance in the field of quantum
information. Such bipartite bound-entangled (BE) quantum states \emph{could}
fall into two distinct categories: (1) Inseparable states with positive partial
transposition (PPT), and (2) States with negative partial transposition (NPT).
While the existence of PPT BE states has been confirmed, \emph{only one} class
of \emph{conjectured} NPT BE states has been discovered so far. We provide
explicit constructions of a variety of multi-copy undistillable NPT states, and
conjecture that they constitute families of NPT BE states. For example, we show
that for every pure state of Schmidt rank greater than or equal to three, one
can construct n-copy undistillable NPT states, for any $n\geq1$. The abundance
of such conjectured NPT BE states, we believe, considerably strengthens the
notion that being NPT is only a necessary condition for a state to be
distillable.


title: Enhanced the thermal Entanglement in Anisotropy XYZ Heisenberg Chain

abstract:
  The thermal entanglement in Heisenberg $XYZ$ chain is investigated in the
presence of external magnetic field $B$. In the two-qubit system, the critical
magnetic field $B_c$ is increased because of introducing the interaction of the
z-component of two neighboring spins $J_z$. This interaction not only improves
the critical temperature $T_c,$ but also enhances the entanglement for
particular fixed $B$. We also analyze the pairwise entanglement between nearest
neighbors in three qubits. The pairwise entanglement, for a fixed $T$, can be
strong by controlling $B$ and $J_z$. PACS: 03.65. Ud, 03.67. -a, 75.10. Jm


title: Entangled Light in Moving Frames

abstract:
  We calculate the entanglement between a pair of polarization-entangled photon
beams as a function of the reference frame, in a fully relativistic framework.
We find the transformation law for helicity basis states and show that, while
it is frequency independent, a Lorentz transformation on a momentum-helicity
eigenstate produces a momentum-dependent phase. This phase leads to changes in
the reduced polarization density matrix, such that entanglement is either
decreased or increased, depending on the boost direction, the rapidity, and the
spread of the beam.


title:
Equivalence between the real time Feynman histories and the quantum
  shutter approaches for the "passage time" in tunneling

abstract:
  We show the equivalence of the functions $G_{\rm p}(t)$ and $|\Psi(d,t)|^2$
for the ``passage time'' in tunneling. The former, obtained within the
framework of the real time Feynman histories approach to the tunneling time
problem, using the Gell-Mann and Hartle's decoherence functional, and the
latter involving an exact analytical solution to the time-dependent
Schr\"{o}dinger equation for cutoff initial waves.


title: Quantised Three-Pillar Problem

abstract:
  This paper examines the quantum mechanical system that arises when one
quantises a classical mechanical configuration described by an underdetermined
system of equations. Specifically, we consider the well-known problem in
classical mechanics in which a beam is supported by three identical rigid
pillars. For this problem it is not possible to calculate uniquely the forces
supplied by each pillar. However, if the pillars are replaced by springs, then
the forces are uniquely determined. The three-pillar problem and its associated
indeterminacy is recovered in the limit as the spring constant tends to
infinity. In this paper the spring version of the problem is quantised as a
constrained dynamical system. It is then shown that as the spring constant
becomes large, the quantum analog of the ambiguity reemerges as a kind of
quantum anomaly.


title: Cold atoms in a high-Q ring-cavity

abstract:
  We report the confinement of large clouds of ultra-cold 85-Rb atoms in a
standing-wave dipole trap formed by the two counter-propagating modes of a
high-Q ring-cavity. Studying the properties of this trap we demonstrate loading
of higher-order transverse cavity modes and excite recoil-induced resonances.


title:
Derivation of the Symmetry Postulates for Identical Particles from
  Pilot-Wave Theories

abstract:
  The symmetries of the wavefunction for identical particles, including anyons,
are given a rigorous non-relativistic derivation within pilot-wave formulations
of quantum mechanics. In particular, parastatistics are excluded. The result
has a rigorous generalisation to n particles and to spinorial wavefunctions.
The relation to other non-relativistic approaches is briefly discussed.


title:
Polarization squeezing of intense pulses with a fiber Sagnac
  interferometer

abstract:
  We report on the generation of polarization squeezing of intense, short light
pulses using an asymmetric fiber Sagnac interferometer. The Kerr nonlinearity
of the fiber is exploited to produce independent amplitude squeezed pulses. The
polarization squeezing properties of spatially overlapped amplitude squeezed
and coherent states are discussed. The experimental results for a single
amplitude squeezed beam are compared to the case of two phase-matched,
spatially overlapped amplitude squeezed pulses. For the latter, noise variances
of -3.4dB below shot noise in the S0 and the S1 and of -2.8dB in the S2 Stokes
parameters were observed, which is comparable to the input squeezing magnitude.
Polarization squeezing, that is squeezing relative to a corresponding
polarization minimum uncertainty state, was generated in S1.


title:
Teleportation via thermally entangled state of a three-qubit Heisenberg
  XX ring

abstract:
  We consider quantum teleportation using the thermally entangled state of a
three-qubit Heisenberg XX ring as a resource. Our investigation reveals
interesting aspects of quantum entanglement not reflected by the pairwise
thermal concurrence of the state. In particular, two mixtures of different
pairs of W states, which result in the same concurrence, could yield very
differrent average teleportation fidelities.


title: Separable balls around the maximally mixed multipartite quantum states

abstract:
  We show that for an m-partite quantum system, there is a ball of radius
2^{-(m/2-1)} in Frobenius norm, centered at the identity matrix, of separable
(unentangled) positive semidefinite matrices. This can be used to derive an
epsilon below which mixtures of epsilon of any density matrix with 1 - epsilon
of the maximally mixed state will be separable. The epsilon thus obtained is
exponentially better (in the number of systems) than existing results. This
gives a number of qubits below which NMR with standard pseudopure-state
preparation techniques can access only unentangled states; with parameters
realistic for current experiments, this is 23 qubits (compared to 13 qubits via
earlier results). A ball of radius 1 is obtained for multipartite states
separable over the reals.


title: Entanglement purification of multi-mode quantum states

abstract:
  An iterative random procedure is considered allowing an entanglement
purification of a class of multi-mode quantum states. In certain cases, a
complete purification may be achieved using only a single signal state
preparation. A physical implementation based on beam splitter arrays and
non-linear elements is suggested. The influence of loss is analyzed in the
example of a purification of entangled N-mode coherent states.


title:
Adiabatic passage and dissociation controlled by interference of two
  laser-induced continuum structures

abstract:
  We have developed a theory of three-pulse coherent control of photochemical
processes. It is based on adiabatic passage and quantum coherence and
interference attributed to the lower-lying dissociation continuum and excited
upper discrete states, which are otherwise not connected to the ground state by
one-photon transitions. Novel opportunities offered by the proposed scheme are
demonstrated through extensive numerical simulations with the aid of a model
relevant to typical experiments. The opportunities for manipulating the
distribution of the population among discrete and continuous states with any
necessary ratio by the end of the pulses are demonstrated.


title:
Non-post-selection entanglement concentration by ordinary linear optical
  devices

abstract:
  Two remote parties, Alice and Bob initially share some non-maximally
entangled states. Through the entanglement concentration by local operation and
classical communication(LOCC), they may obtain an outcome of maximally
entangled states in the price of decreasing the number of pairs shared by them.
Recently, entanglement concentration have been experimently demonstrated by
post-selection (T. Yamamoto et al, Nature, 421, 343(2003) and Z. Zhao et al,
quant-ph/0301118). Here we give a modified scheme which can be used for the
entanglement concentration without any post selection by using only practically
existing linear optical devices. In particular, a sophisticated photon detector
to distinguish one photon or two photons is not required. Our scheme can be
used to really produce the event-ready maximally entangled pairs through LOCC
provided that the requested raw pairs are supplied deterministically. A
detailed experimental plan with spontaneous parametric down conversion(SPDC) is
shown.


title: Deformation Quantization of Nambu Mechanics

abstract:
  Phase Space is the framework best suited for quantizing superintegrable
systems--systems with more conserved quantities than degrees of freedom. In
this quantization method, the symmetry algebras of the hamiltonian invariants
are preserved most naturally, as illustrated on nonlinear $\sigma$-models,
specifically for Chiral Models and de Sitter $N$-spheres. Classically, the
dynamics of superintegrable models such as these is automatically also
described by Nambu Brackets involving the extra symmetry invariants of them.
The phase-space quantization worked out then leads to the quantization of the
corresponding Nambu Brackets, validating Nambu's original proposal, despite
excessive fears of inconsistency which have arisen over the years. This is a
pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points
of interpretation and care needed in appreciating the consistency of Quantum
Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see
T Curtright's contribution in these Proceedings [hep-th 0303088].


title: 1/N-expansions in non-relativistic quantum mechanics

abstract:
  An extensive number of numerical computations of energy 1/$N$ series using a
recursive Taylor series method are presented in this paper. The series are
computed to a high order of approximation and their behaviour on increasing the
order of approximation is examined.

categories: quant-ph hep-th math-ph math.MP physics.comp-ph


title: The Quantumness of a Set of Quantum States

abstract:
  This article is an introduction to quant-ph/0302092. We propose to quantify
how "quantum" a set of quantum states is. The quantumness of a set is the
worst-case difficulty of transmitting the states through a classical
communication channel. Potential applications of this measure arise in quantum
cryptography, where one might like to use an alphabet of states most sensitive
to quantum eavesdropping, and in lab demonstrations of quantum teleportation,
where it is necessary to check that entanglement has indeed been used.


title:
Applications of Coherent Population Transfer to Quantum Information
  Processing

abstract:
  We develop a theoretical framework for the exploration of quantum mechanical
coherent population transfer phenomena, with the ultimate goal of constructing
faithful models of devices for classical and quantum information processing
applications. We begin by outlining a general formalism for weak-field quantum
optics in the Schr\"{o}dinger picture, and we include a general
phenomenological representation of Lindblad decoherence mechanisms. We use this
formalism to describe the interaction of a single stationary multilevel atom
with one or more propagating classical or quantum laser fields, and we describe
in detail several manifestations and applications of electromagnetically
induced transparency. In addition to providing a clear description of the
nonlinear optical characteristics of electromagnetically transparent systems
that lead to ``ultraslow light,'' we verify that -- in principle -- a
multi-particle atomic or molecular system could be used as either a low power
optical switch or a quantum phase shifter. However, we demonstrate that the
presence of significant dephasing effects destroys the induced transparency,
and that increasing the number of particles weakly interacting with the probe
field only reduces the nonlinearity further. Finally, a detailed calculation of
the relative quantum phase induced by a system of atoms on a superposition of
spatially distinct Fock states predicts that a significant quasi-Kerr
nonlinearity and a low entropy cannot be simultaneously achieved in the
presence of arbitrary spontaneous emission rates. Within our model, we identify
the constraints that need to be met for this system to act as a one-qubit and a
two-qubit conditional phase gate.


title: Optical Detection of a Single Nuclear Spin

abstract:
  We propose a method to optically detect the spin state of a 31-P nucleus
embedded in a 28-Si matrix. The nuclear-electron hyperfine splitting of the
31-P neutral-donor ground state can be resolved via a direct frequency
discrimination measurement of the 31-P bound exciton photoluminescence using
single photon detectors. The measurement time is expected to be shorter than
the lifetime of the nuclear spin at 4 K and 10 T.


title: Classical and quantum communication without a shared reference frame

abstract:
  We show that communication without a shared reference frame is possible using
entangled states. Both classical and quantum information can be communicated
with perfect fidelity without a shared reference frame at a rate that
asymptotically approaches one classical bit or one encoded qubit per
transmitted qubit. We present an optical scheme to communicate classical bits
without a shared reference frame using entangled photon pairs and linear
optical Bell state measurements.


title:
A subexponential-time quantum algorithm for the dihedral hidden subgroup
  problem

abstract:
  We present a quantum algorithm for the dihedral hidden subgroup problem with
time and query complexity $O(\exp(C\sqrt{\log N}))$. In this problem an oracle
computes a function $f$ on the dihedral group $D_N$ which is invariant under a
hidden reflection in $D_N$. By contrast the classical query complexity of DHSP
is $O(\sqrt{N})$. The algorithm also applies to the hidden shift problem for an
arbitrary finitely generated abelian group.
  The algorithm begins with the quantum character transform on the group, just
as for other hidden subgroup problems. Then it tensors irreducible
representations of $D_N$ and extracts summands to obtain target
representations. Finally, state tomography on the target representations
reveals the hidden subgroup.


title: Non-locality:what are the odds?

abstract:
  As part of a challenge to critics of Bell's analysis of the EPR argument,
framed in the form of a bet, R. D. Gill formulated criteria to assure that all
non-locality is precluded from simulation-algorithms used to test Bell's
theorem. This is achieved in part by parceling out the subroutines for the
source and both detectors to three separate computers. He argues that, in light
of Bell's theorem, following these criteria absolutely precludes mimicking
EPR-B correlations as computed with Quantum Mechanics and observed in
experiments. Herein, nevertheless, we describe just such an local algorithm,
fully faithful to his criteria, that yields results mimicking exactly quantum
correlations. We observe that our simulation-algorithm succeeds by altering an
implicit assumption made by Bell to the equivalent effect that the source of
EPR pairs is a single Poisson process followed by deterministic detection.
Instead we assume the converse, namely that the source is deterministic but
detection involves multiple, independent Poisson processes, one at each
detector with an intensity given by Malus' Law. Finally, we speculate on some
consequences this might have for quantum computing algorithms.


title: An Introduction to Quantum Teleportation

abstract:
  Recent experiments confirm that quantum teleportation is possible at least
for states of photons and nuclear spins. The quantum teleportation is not only
a curious effect but a fundamental protocol of quantum communication and
quantum computing. The principles of the quantum teleportation and the
entanglement swapping are explained, and physical realizations of teleportation
of optical and atomic states are discussed.


title: Remarks on Causality in Relativistic Quantum Field Theory

abstract:
  It is shown that the correlations predicted by relativistic quantum field
theory in locally normal states between projections in local von Neumann
algebras $\cA(V_1),\cA(V_2)$ associated with spacelike separated spacetime
regions $V_1,V_2$ have a (Reichenbachian) common cause located in the union of
the backward light cones of $V_1$ and $V_2$. Further comments on causality and
independence in quantum field theory are made.


title:
Time operator for a quantum many-body system with SU(1,1) dynamical
  symmetry

abstract:
  The time operator canonically conjugated to the Hamiltonian of $N$
interacting particles on the line is constructed using SU(1,1) as a dynamical
symmetry. This hidden conformal symmetry enables us to make a group theoretic
analysis of the time operator in terms of SU(1,1) generators. At distances very
far from the interacting region the time operator is represented as a
generalization of the quantum "time-of-arrival" operator.


title:
Systematics of the Relationship between Vacuum Energy Calculations and
  Heat Kernel Coefficients

abstract:
  Casimir energy is a nonlocal effect; its magnitude cannot be deduced from
heat kernel expansions, even those including the integrated boundary terms. On
the other hand, it is known that the divergent terms in the regularized (but
not yet renormalized) total vacuum energy are associated with the heat kernel
coefficients. Here a recent study of the relations among the eigenvalue
density, the heat kernel, and the integral kernel of the operator
$e^{-t\sqrt{H}}$ is exploited to characterize this association completely.
Various previously isolated observations about the structure of the regularized
energy emerge naturally. For over 20 years controversies have persisted
stemming from the fact that certain (presumably physically meaningful) terms in
the renormalized vacuum energy density in the interior of a cavity become
singular at the boundary and correlate to certain divergent terms in the
regularized total energy. The point of view of the present paper promises to
help resolve these issues.


title: Representation of Entangled States

abstract:
  Associating a physical process with the pure entangled state 1/sqrt 2 (|00> +
|11>) is an idealization unless the pair is so prepared using an appropriate
quantum gate operating on a known state. Questions related to the reference
frame for measurement of the entangled state are considered. Some applications
are described.


title:
Exact time-dependent decoherence factor and its adiabatic classical
  limit

abstract:
  The present paper finds the complete set of exact solutions of the general
time-dependent dynamical models for quantum decoherence, by making use of the
Lewis-Riesenfeld invariant theory and the invariant-related unitary
transformation formulation. Based on this, the general explicit expression for
the decoherence factor is then obtained and the adiabatic classical limit of an
illustrative example is discussed. The result (i.e., the adiabatic classical
limit) obtained in this paper is consistent with what obtained by other
authors, and futhermore we obtain the more general results concerning the
time-dependent non-adiabatic quantum decoherence. It is shown that the
invariant theory is appropriate for treating both the time-dependent quantum
decoherence and the geometric phase factor.


title:
Geometric Phase and Helicity Inversion of Photons Propagating inside a
  Noncoplanarly Curved Optical Fiber

abstract:
  The Letter presents an exact expression for the non-adiabatic non-cyclic
geometric phase of photons propagating inside a noncoplanarly curved optical
fiber by using the Lewis-Riesenfeld invariant theory. It is shown that the
helicity inversion of photons arises in the curved fiber. Since we have exactly
solved the time-dependent Schr\"{o}dinger equation that governs the propagation
of photons in a curved fiber and, moreover, the chronological product is not
involved in this exact solution, our formulation therefore has several
advantages over other treatments based on the classical Maxwell's theory and
the Berry's adiabatic quantum theory. The potential application of helicity
inversion of photons to information science is briefly suggested.


title: Controllability of Quantum Systems

abstract:
  An overview and synthesis of results and criteria for open-loop
controllability of Hamiltonian quantum systems obtained using Lie group and Lie
algebra techniques is presented. Negative results for open-loop controllability
of dissipative systems are discussed, and the superiority of closed-loop
(feedback) control for quantum systems is established.


title:
Perturbation approach to the Casimir force between two bodies made of
  different real metals

abstract:
  The Casimir force acting between two test bodies made of different metals is
considered. The finiteness of the conductivity of the metals is taken into
account perturbatively up to the fourth order of the relative penetration
depths of electromagnetic zero-point oscillations into the metals. The
influence of nonzero temperature is computed explicitly for separate orders of
perturbation and found to be important in the zeroth and first orders only. The
configurations of two parallel plates and a sphere (spherical lens) above a
plate are considered made of $Au$ and $Cr$. The obtained results can be used to
take into account also the surface roughness. Thus, the total amount of the
Casimir force between different metals with all correction factors is
determined. This may be useful in various applications.


title: Noether conservation laws in quantum mechanics

abstract:
  Being quantized, conserved Noether symmetry functions are represented by
Hermitian operators in the space of solutions of the Schrodinger equation, and
their mean values are conserved.


title:
Entanglement induced by spontaneous emission in spatially extended
  two-atom systems

abstract:
  We investigate the role of the collective antisymmetric state in entanglement
creation by spontaneous emission in a system of two non-overlapping two-level
atoms. We calculate and illustrate graphically populations of the collective
atomic states and the Wootters entanglement measure (concurrence) for two sets
of initial atomic conditions. Our calculations include the dipole-dipole
interaction and a spatial separation between the atoms that the antisymmetric
state of the system is included throughout even for small interatomic
separations. It is shown that spontaneous emission can lead to a transient
entanglement between the atoms even if the atoms were prepared initially in an
unentangled state. We find that the ability of spontaneous emission to create
the transient entanglement relies on the absence of population in the
collective symmetric state of the system. For the initial state of only one
atom excited, the entanglement builds up rapidly in time and reaches a maximum
for the parameter values corresponding roughly to zero population in the
symmetric state. On the other hand, for the initial condition of both atoms
excited, the atoms remain unentangled until the symmetric state is depopulated.
A simple physical interpretation of these results is given in terms of the
diagonal states of the density matrix of the system. We also study entanglement
creation in a system of two non-identical atoms of different transition
frequencies. It is found that the entanglement between the atoms can be
enhanced compared to that for identical atoms, and can decay with two different
time scales resulting from the coherent transfer of the population from the
symmetric to the antisymmetric state. In addition, we find that a decaying
initial entanglement between the atoms can display a revival behaviour.


title: Requirement for quantum computation

abstract:
  We identify "proper quantum computation" with computational processes that
cannot be efficiently simulated on a classical computer. For optical quantum
computation, we establish "no-go" theorems for classes of quantum optical
experiments that cannot yield proper quantum computation, and we identify
requirements for optical proper quantum computation that correspond to
violations of assumptions underpinning the no-go theorems.


title:
Direct measurement of spatial Wigner function with area-integrated
  detection

abstract:
  We demonstrate experimentally a novel technique for characterizing transverse
spatial coherence using the Wigner distribution function. The presented method
is based on measuring interference between a pair of rotated and displaced
replicas of the input beam with an area-integrating detector, and it can be
superior in regimes when array detectors are not available. We analyze the
quantum optical picture of the presented measurement for single-photon signals
and discuss possible applications in quantum information processing.


title: Comment on "Quantum back-reaction through the Bohmian particle"

abstract:
  In this Comment I point out some limitations of the proposal of Prezhdo and
Brooksby for coupling quantum and classical degrees of freedom
(Phys.Rev.Lett.86(2001)3215) if it is pushed too far.


title:
The high energy limit of the trajectory representation of quantum
  mechanics

abstract:
  The trajectory representation in the high energy limit (Bohr correspondence
principle) manifests a residual indeterminacy. This indeterminacy is compared
to the indeterminacy found in the classical limit (Planck's constant to 0)
[Int. J. Mod. Phys. A 15, 1363 (2000)] for particles in the classically allowed
region, the classically forbiden region, and near the WKB turning point. The
differences between Bohr's and Planck's principles for the trajectory
representation are compared with the differences between these correspondence
principles for the wave representation. The trajectory representation in the
high energy limit is shown to go to neither classical nor statistical
mechanics. The residual indeterminacy is contrasted to Heisenberg uncertainty.
The relationship between indeterminacy and 't Hooft's information loss and
equivalence classes is investigated.


title:
Exact expression for decoherence factor in the time-dependent
  generalized Cini model

abstract:
  The present letter finds the complete set of exact solutions of the
time-dependent generalized Cini model by making use of the Lewis-Riesenfeld
invariant theory and the invariant-related unitary transformation formulation
and, based on this, the general explicit expression for the decoherence factor
is therefore obtained. This study provides us with a useful method to consider
the geometric phase and topological properties in the time-dependent quantum
decoherence process.


title: Algebraic treatment of super-integrable potentials

abstract:
  The so$(2,1)$ Lie algebra is applied to three classes of two- and
three-dimensional Smorodinsky-Winternitz super-integrable potentials for which
the path integral discussion has been recently presented in the literature. We
have constructed the Green's functions for two important super-integrable
potentials in $R^{2}.$ Among the super-integrable potentials in $R^{3}$, we
have considered two examples, one is maximally super-integrable and another one
minimally super-integrable. The discussion is made in various coordinate
systems. The energy spectrum and the suitably normalized wave functions of
bound and continuous states are then deduced.


title: Collective Sideband Cooling in an Optical Ring Cavity

abstract:
  We propose a cavity based laser cooling and trapping scheme, providing tight
confinement and cooling to very low temperatures, without degradation at high
particle densities. A bidirectionally pumped ring cavity builds up a resonantly
enhanced optical standing wave which acts to confine polarizable particles in
deep potential wells. The particle localization yields a coupling of the
degenerate travelling wave modes via coherent photon redistribution. This
induces a splitting of the cavity resonances with a high frequency component,
that is tuned to the anti-Stokes Raman sideband of the particles oscillating in
the potential wells, yielding cooling due to excess anti-Stokes scattering.
Tight confinement in the optical lattice together with the prediction, that
more than 50% of the trapped particles can be cooled into the motional ground
state, promise high phase space densities.


title: Controlled Quantum Open Systems

abstract:
  The theory of controlled quantum open systems describes quantum systems
interacting with quantum environments and influenced by external forces varying
according to given algorithms. It is aimed, for instance, to model quantum
devices which can find applications in the future technology based on quantum
information processing. One of the main problems making difficult the practical
implementations of quantum information theory is the fragility of quantum
states under external perturbations. The aim of this note is to present the
relevant results concerning ergodic properties of open quantum systems which
are useful for the optimization of quantum devices and noise (errors)
reduction. In particular we present mathematical characterization of the
so-called "decoherence-free subspaces" for discrete and continuous-time quantum
dynamical semigroups in terms of $C^*$-algebras and group representations. We
analyze the non-Markovian models also, presenting the formulas for errors in
the Born approximation. The obtained results are used to discuss the proposed
different strategies of error reduction.


title: Is Quantum Chaos Weaker Than Classical Chaos?

abstract:
  We investigate chaotic behavior in a 2-D Hamiltonian system - oscillators
with anharmonic coupling. We compare the classical system with quantum system.
Via the quantum action, we construct Poincar\'{e} sections and compute Lyapunov
exponents for the quantum system. We find that the quantum system is globally
less chaotic than the classical system. We also observe with increasing energy
the distribution of Lyapunov exponts approaching a Gaussian with a strong
correlation between its mean value and energy.


title:
Notes on Hallgren's efficient quantum algorithm for solving Pell's
  equation

abstract:
  Pell's equation is x^2-d*y^2=1 where d is a square-free integer and we seek
positive integer solutions x,y>0. Let (x',y') be the smallest solution (i.e.
having smallest A=x'+y'sqrt(d)). Lagrange showed that every solution can easily
be constructed from A so given d it suffices to compute A. It is known that A
can be exponentially large in d so just to write down A we need exponential
time in the input size log d. Hence we introduce the regulator R=ln A and ask
for the value of R to n decimal places. The best known classical algorithm has
sub-exponential running time O(exp(sqrt(log d)), poly(n)). Hallgren's quantum
algorithm gives the result in polynomial time O(poly(log d),poly(n)) with
probability 1/poly(log d). The idea of the algorithm falls into two parts:
using the formalism of algebraic number theory we convert the problem of
solving Pell's equation into the problem of determining R as the period of a
function on the real numbers. Then we generalise the quantum Fourier transform
period finding algorithm to work in this situation of an irrational period on
the (not finitely generated) abelian group of real numbers.
  These notes are intended to be accessible to a reader having no prior
acquaintance with algebraic number theory; we give a self contained account of
all the necessary concepts and we give elementary proofs of all the results
needed. Then we go on to describe Hallgren's generalisation of the quantum
period finding algorithm, which provides the efficient computational solution
of Pell's equation in the above sense.


title: Klein Paradox in Bosons

abstract:
  We show analytically that the {\it Zitterbewegung} and Klein Paradox, such
well known aspects of the Dirac Equation are not found in the case of Bosons.
We use the Kemmer-Duffin-Harish Chandra formalism with $\beta$ matrices to
arrive at our results


title: Risk-Sensitive Optimal Control of Quantum Systems

abstract:
  The importance of feedback control is being increasingly appreciated in
quantum physics and applications. This paper describes the use of optimal
control methods in the design of quantum feedback control systems, and in
particular the paper formulates and solves a risk-sensitive optimal control
problem. The resulting risk-sensitive optimal control is given in terms of a
new unnormalized conditional state, whose dynamics include the cost function
used to specify the performance objective. The risk-sensitive conditional
dynamic equation describes the evolution of our {\em knowledge} of the quantum
system tempered by our {\em purpose} for the controlled quantum system.
Robustness properties of risk-sensitive controllers are discussed, and an
example is provided.


title:
Experimental Test of Quantum Nonlocality in Four-photon
  Greenberger-Horne-Zeilinger Entanglement

abstract:
  We report the first experimental violation of local realism in four-photon
Greenberger-Horne-Zeilinger (GHZ) entanglement. In the experiment, the
non-statistical GHZ conflicts between quantum mechanics and local realism are
confirmed, within the experimental accuracy, by four specific measurements of
polarization correlations between four photons. In addition, our experimental
results not only demonstrate a violation of Mermin-Ardehali-Belinskii-Klyshko
inequality by 76 standard deviations, but also for the first time provide
sufficient evidence to confirm the existence of genuine four-particle
entanglement.


title:
Quantum circuit implementation of the Hamiltonian versions of Grover's
  algorithm

abstract:
  We analyze three different quantum search algorithms, the traditional
Grover's algorithm, its continuous-time analogue by Hamiltonian evolution, and
finally the quantum search by local adiabatic evolution. We show that they are
closely related algorithms in the sense that they all perform a rotation, at a
constant angular velocity, from a uniform superposition of all states to the
solution state. This make it possible to implement the last two algorithms by
Hamiltonian evolution on a conventional quantum circuit, while keeping the
quadratic speedup of Grover's original algorithm.


title: Compressing compound states

abstract:
  Quantum compression can be thought of not only as compression of a signal,
but also as a form of cooling. In this view, one is interested not in the
signal, but in obtaining purity. In compound systems, one may be interested to
cool the system to obtain {\it local purity} by use of local operations and
classical communication [Oppenheim et al. Phys. Rev. Lett. 89,180402 (2002)].
Here we compare it with usual compression and find that it can be represented
as compression with suitably restricted means.


title:
Information theoretic approach to single-particle and two-particle
  interference in multi-path interferometers

abstract:
  We propose entropic measures for the strength of single-particle and
two-particle interference in interferometric experiments where each particle of
a pair traverses a multi-path interferometer. Optimal single-particle
interference excludes any two-particle interference, and vice versa. We report
an inequality that states the compromises allowed by quantum mechanics in
intermediate situations, and identify a class of two-particle states for which
the upper bound is reached. Our approach is applicable to symmetric two-partite
systems of any finite dimension.


title: C, PT, and CPT invariance of pseudo-Hermitian Hamiltonians

abstract:
  We propose construction of a unique and definite metric ($\eta_+$),
time-reversal operator (T) and an inner product such that the pseudo-Hermitian
matrix Hamiltonians are C, PT, and CPT invariant and PT(CPT)-norm is indefinite
(definite). Here, P and C denote the generalized symmetries : parity and
charge-conjugation respectively. The limitations of the other current
approaches have been brought out.


title: Polarization squeezing in a four-level system

abstract:
  We present a theoretical study of an ensemble of X-like 4-level atoms placed
in an optical cavity driven by a linearly polarized field. We show that the
self-rotation (SR) process leads to polarization switching (PS). Below the PS
threshold, both the mean field mode and the orthogonal vacuum mode are
squeezed. We provide a simple analysis of the phenomena responsible for the
squeezing and trace the origin of vacuum squeezing not to SR, but to crossed
Kerr effect induced by the mean field. Last, we show that this vacuum squeezing
can be interpreted as polarization squeezing.


title:
On the Correlations Between Quantum Entanglement and q-Information
  Measures

abstract:
  In the present study we revisit the application of the $q$-information
measures $R_q$ of R\'enyi's and $S_q$ of Tsallis' to the discussion of special
features of two qubits systems. More specifically, we study the correlations
between the $q$-information measures and the entanglement of formation of a
general (pure or mixed) state $\rho$ describing a system of two qubits. The
analysis uses a Monte Carlo procedure involving the 15-dimensional 2-qubits
space of pure and mixed states, under the assumption that these states are
uniformly distributed according to the product measure recently introduced by
Zyczkowski {\it et al} [Phys. Rev. A {\bf 58} (1998) 883].


title: Entanglement of 2xK quantum systems

abstract:
  We derive an analytical expression for the lower bound of the concurrence of
mixed quantum states of composite 2xK systems. In contrast to other, implicitly
defined entanglement measures, the numerical evaluation of our bound is
straightforward. We explicitly evaluate its tightness for general mixed states
of 2x3 systems, and identify a large class of states where our expression gives
the exact value of the concurrence.


title: Population trapping in the one-photon mazer

abstract:
  We study the population trapping phenomenon for the one-photon mazer. With
this intent, the mazer theory is written using the dressed-state coordinate
formalism, simplifying the expressions for the atomic populations, the cavity
photon statistics, and the reflection and transmission probabilities. Under the
population trapping condition, evidence for new properties of the atomic
scattering is given. Experimental issues and possible applications are
discussed.


title: Can quantum imaging be classically simulated?

abstract:
  Quantum imaging has been demonstrated since 1995 by using entangled photon
pairs. The physics community named these experiments "ghost image", "quantum
crypto-FAX", "ghost interference", etc. Recently, Bennink et al. simulated the
"ghost" imaging experiment by two co-rotating k-vector correlated lasers. Did
the classical simulation simulate the quantum aspect of the "ghost" image? We
wish to provide an answer. In fact, the simulation is very similar to a
historical model of local realism. The goal of this article is to clarify the
different physics behind the two types of experiments and address the
fundamental issues of quantum theory that EPR was concerned with since 1935.


title: Nonlocality of Two-Mode Squeezing with Internal Noise

abstract:
  We examine the quantum states produced through parametric amplification with
internal quantum noise. The internal diffusion arises by coupling both modes of
light to a reservoir for the duration of the interaction time. The Wigner
function for the diffused two-mode squeezed state is calculated. The
nonlocality, separability, and purity of these quantum states of light are
discussed. In addition, we conclude by studying the nonlocality of two other
continuous variable states: the Werner state and the phase-diffused state for
two light modes.


title: Zero-Energy Flows and Vortex Patterns in Quantum Mechanics

abstract:
  We show that zero-energy flows appear in many particle systems as same as in
single particle cases in 2-dimensions. Vortex patterns constructed from the
zero-energy flows can be investigated in terms of the eigenstates in conjugate
spaces of Gel'fand triplets. Stable patterns are written by the superposition
of zero-energy eigenstates. On the other hand vortex creations and
annihilations are described by the insertions of unstable eigenstates with
complex-energy eigenvalues into the stable patterns. Some concrete examples are
presented in the 2-dimensional parabolic potential barrier case. %, i.e., $-m
\gamma^2 (x^2+y^2)/2$. We point out three interesting properties of the
zero-energy flows; (i) the absolute economy as for the energy consumption, (ii)
the infinite variety of the vortex patterns, and (iii) the absolute stability
of the vortex patterns .


title: New features of the thermal Casimir force at small separations

abstract:
  The difference of the thermal Casimir forces at different temperatures
between real metals is shown to increase with a decrease of the separation
distance. This opens new opportunities for the demonstration of the thermal
dependence of the Casimir force. Both configurations of two parallel plates and
a sphere above a plate are considered. Different approaches to the theoretical
description of the thermal Casimir force are shown to lead to different
measurable predictions.


title: Mutual first order coherence of phase-locked lasers

abstract:
  We argue that (first-order) coherence is a relative, and not an absolute,
property. It is shown how feedforward or feedback can be employed to make two
(or more) lasers relatively coherent. We also show that after the relative
coherence is established, the two lasers will stay relatively coherent for some
time even if the feedforward or feedback loop has been turned off, enabling,
e.g., demonstration of unconditional quantum teleportation using lasers.


title:
Competitive stochastic noises in coherently driven two-level atoms and
  quantum interference

abstract:
  A system of coherently-driven two-level atoms is analyzed in presence of two
independent stochastic perturbations: one due to collisions and a second one
due to phase fluctuations of the driving field. The behaviour of the quantum
interference induced by the collisional noise is considered in detail. The
quantum-trajectory method is utilized to reveal the phase correlations between
the dressed states involved in the interfering transition channels. It is shown
that the quantum interference induced by the collisional noise is remarkably
robust against phase noise. This effect is due to the fact that the phase
noise, similarly to collisions, stabilizes the phase-difference between the
dressed states.


title:
Bohmian particle trajectories in relativistic fermionic quantum field
  theory

abstract:
  The de Broglie-Bohm interpretation of quantum mechanics and quantum field
theory is generalized in such a way that it describes trajectories of
relativistic fermionic particles and antiparticles and provides a causal
description of the processes of their creation and destruction. A general
method of causal interpretation of quantum systems is developed and applied to
a causal interpretation of fermionic quantum field theory represented by
c-number valued wave functionals.


title: A prime factorization based on quantum dynamics on a spin ensemble (I)

abstract:
  In this paper it has been described how to use the unitary dynamics of
quantum mechanics to solve the prime factorization problem on a spin ensemble
without any quantum entanglement. The ensemble quantum computation for the
prime factorization is based on the basic principle that both a closed quantum
system and its ensemble obey the same unitary dynamics of quantum mechanics if
there is not any decoherence effect in both the quantum system and its
ensemble. It uses the NMR multiple-quantum measurement techniques to output the
quantum computational results that are the inphase multiple-quantum spectra of
the spin ensemble. It has been shown that the inphase NMR multiple-quantum
spectral intensities used to search for the period of the modular exponential
function may reduce merely in a polynomial form as the qubit number of the spin
ensemble. The time evolution process of the modular exponential operation on
the quantum computer obeys the unitary dynamics of quantum mechanics and hence
the computational output is governed by the quantum dynamics. This essential
difference between the quantum computer and the classical one could be the key
point for the quantum computation outperforming the classical one in the prime
factorization on a spin ensemble without any quantum entanglement. It has been
shown that the prime factorization based on the quantum dynamics on a spin
ensemble is locally efficient at least. This supports the conjecture that the
quantum dynamics could play an important role for the origin of power of
quantum computation and quantum entanglement could not be a unique resource to
achieve power of quantum computation in the prime factorization.


title:
Experimental multi-photon-resolving detector using a single avalanche
  photodiode

abstract:
  A multichannel detector has been constructed using a single avalanche
photodiode and a fiber-loop delay line. Detection probabilities of the channels
can be set using a variable-ratio coupler. The performance of the detector is
demonstrated on its capability to distinguish multi-photon states (containing
two or more photons) from the one-photon state and the vacuum state.


title:
Radiation to atom quantum mapping by collective recoil in Bose-Einstein
  condensate

abstract:
  We propose an experiment to realize radiation to atom continuous variable
quantum mapping, i.e. to teleport the quantum state of a single mode radiation
field onto the collective state of atoms with a given momentum out of a
Bose-Einstein condensate. The atoms-radiation entanglement needed for the
teleportation protocol is established through the interaction of a single mode
with the condensate in presence of a strong far off-resonant pump laser,
whereas the coherent atomic displacement is obtained by the same interaction
with the radiation in a classical coherent field. In principle, verification of
the protocol requires a joint measurement on the recoiling atoms and the
condensate, however, a partial verification involving populations, i.e.
diagonal matrix elements may be obtained through counting atoms experiments.


title:
Unified criterion for security of secret sharing in terms of violation
  of Bell inequality

abstract:
  In secret sharing protocols, a secret is to be distributed among several
partners so that leaving out any number of them, the rest do not have the
complete information. Strong multiqubit correlations in the state by which
secret sharing is carried out, had been proposed as a criterion for security of
such protocols against individual attacks by an eavesdropper. However we show
that states with weak multiqubit correlations can also be used for secure
secret sharing. That our state has weak multiqubit correlations, is shown from
the perspective of violation of local realism, and also by showing that its
higher order correlations are described by lower ones. We then present a
unified criterion for security of secret sharing in terms of violation of local
realism, which works when the secret sharing state is the
Greenberger-Horne-Zeilinger state (with strong multiqubit correlations), as
well as states of a different class (with weak multiqubit correlations).


title:
Development of an approximation scheme for quasi-exactly solvable
  double-well potentials

abstract:
  We make use of a recently developed method to, not only obtain the exactly
known eigenstates and eigenvalues of a number of quasi-exactly solvable
Hamiltonians, but also construct a convergent approximation scheme for locating
those levels, not amenable to analytical treatments. The fact that, the above
method yields an expansion of the wave functions in terms of corresponding
energies, enables one to treat energy as a variational parameter, which can be
effectively used for the identification of the eigenstates. It is particularly
useful for the quasi-exactly solvable systems, where the ground state is known
and a number of eigenstates are bounded, both below and above. The efficacy of
the procedure is illustrated by obtaining, the low-lying excited states of a
prototypical double-well potential, where the conventional techniques are not
very reliable. Our approach yields the approximate eigenfunctions and
eigenvalues, whose accuracy can be improved to any desired level, in a
controlled manner. Comparing the present results with those of an independent
numerical method, it was found that, the first few terms in our approximate
solutions are enough to yield the excited state eigenvalues, accurate upto the
third place of the decimal.


title: Hardy's Second Axiom is insufficiently general

abstract:
  Hardy (quant-ph/0101012) conjectures in his Axiom 2 that K=K(N), and that in
classical probability K=N, while in quantum mechanics K=N^2. We offer an
example in classical probability for which K=NV, V the number of independent
complete variables; with N=V this classical example satisfies the purported
quantal relation K=N^2.


title:
Surface plasmon resonance study of the actin-myosin sarcomeric complex
  and tubulin dimers

abstract:
  Biosensors based on the principle of surface plasmon resonance (SPR)
detection were used to measure biomolecular interactions in sarcomeres and
changes of the dielectric constant of tubulin samples with varying
concentration. At SPR, photons of laser light efficiently excite surface
plasmons propagating along a metal (gold) film. This resonance manifests itself
as a sharp minimum in the reflection of the incident laser light and occurs at
a characteristic angle. The dependence of the SPR angle on the dielectric
permittivity of the sample medium adjacent to the gold film allows the
monitoring of molecular interactions at the surface. We present results of
measurements of cross-bridge attachment/detachment within intact mouse heart
muscle sarcomeres and measurements on bovine tubulin molecules pertinent to
cytoskeletal signal transduction models.


title: A Computational Model for Quantum Measurement

abstract:
  Is the dynamical evolution of physical systems objectively a manifestation of
information processing by the universe? We find that an affirmative answer has
important consequences for the measurement problem. In particular, we calculate
the amount of quantum information processing involved in the evolution of
physical systems, assuming a finite degree of fine-graining of Hilbert space.
This assumption is shown to imply that there is a finite capacity to sustain
the immense entanglement that measurement entails. When this capacity is
overwhelmed, the system's unitary evolution becomes computationally unstable
and the system suffers an information transition (`collapse'). Classical
behaviour arises from the rapid cycles of unitary evolution and information
transitions.
  Thus, the fine-graining of Hilbert space determines the location of the
`Heisenberg cut', the mesoscopic threshold separating the microscopic, quantum
system from the macroscopic, classical environment. The model can be viewed as
a probablistic complement to decoherence, that completes the measurement
process by turning decohered improper mixtures of states into proper mixtures.
It is shown to provide a natural resolution to the measurement problem and the
basis problem.


title: Quantum walks based on an interferometric analogy

abstract:
  There are presently two models for quantum walks on graphs. The "coined" walk
uses discrete time steps, and contains, besides the particle making the walk, a
second quantum system, the coin, that determines the direction in which the
particle will move. The continuous walk operates with continuous time. Here a
third model for a quantum walk is proposed, which is based on an analogy to
optical interferometers. It is a discrete-time model, and the unitary operator
that advances the walk one step depends only on the local structure of the
graph on which the walk is taking place. No quantum coin is introduced. This
type of walk allows us to introduce elements, such as phase shifters, that have
no counterpart in classical random walks. Walks on the line and cycle are
discussed in some detail, and a probability current for these walks is
introduced. The relation to the coined quantum walk is also discussed. The
paper concludes by showing how to define these walks for a general graph.


title: Dyon-Oscillator Duality. Hidden Symmetry of the Yang-Coulomb Monopole

abstract:
  In this article, in the framework of an analytical approach and with help of
the generalized version of the Hurwitz transformation the five--dimensional
bound system composed of the Yang monople coupled to a particle of the isospin
by SU(2) and Coulomb interaction is constructed from the eight-dimensional
quantum oscillator. The generalized Runge-Lentz vector and the SO(6) group of
the hidden symmetry are established. It is also shown that group of hidden
symmetry makes it possible to calculate the spectrum of system by a pure
algebraic method.


title: Entanglement Cost of Three-Level Antisymmetric States

abstract:
  We show that the entanglement cost of the three-dimensional antisymmetric
states is one ebit.


title: Dynamical Reduction Models

abstract:
  The report presents an exhaustive review of the recent attempt to overcome
the difficulties that standard quantum mechanics meets in accounting for the
measurement (or macro-objectification) problem, an attempt based on the
consideration of nonlinear and stochastic modifications of the Schroedinger
equation. The proposed new dynamics is characterized by the feature of not
contradicting any known fact about microsystems and of accounting, on the basis
of a unique, universal dynamical principle, for wavepacket reduction and for
the classical behavior of macroscopic systems. We recall the motivations for
the new approach and we briefly review the other proposals to circumvent the
above mentioned difficulties which appeared in the literature. In this way we
make clear the conceptual and historical context characterizing the new
approach. After having reviewed the mathematical techniques (stochastic
differential calculus) which are essential for the rigorous and precise
formulation of the new dynamics, we discuss in great detail its implications
and we stress its relevant conceptual achievements. The new proposal requires
also to work out an appropriate interpretation; a procedure which leads us to a
reconsideration of many important issues about the conceptual status of
theories based on a genuinely Hilbert space description of natural processes.
We also discuss the possibility and the problems one meets in trying to develop
an analogous formalism for the relativistic case. Finally we discuss the
experimental implications of the new dynamics for various physical processes
which should allow, in principle, to test it against quantum mechanics.


title: Three qubit GHZ correlations and generalised Bell experiments

abstract:
  We present a brief historical introduction to the topic of Bell's theorem.
Next we present the surprising features of the three particle
Greenberger-Horne-Zeilinger (GHZ) states. Finally we shall present a method of
analysis of the GHZ correlations, which is based on a numerical approach, which
is effectively equivalent to the full set of Bell inequalities for correlation
functions for the given problem. The aim of our numerical approach is to answer
the following question. Do additional possible local settings lead for the GHZ
states to more pronounced violation of local realism (measured by the
resistance of the quantum nature of the correlations with respect ``white''
noise admixtures)?


title:
Negative Group Delay and Superluminal Propagation: An Electronic Circuit
  Approach

abstract:
  We present a simple electronic circuit which provides negative group delays
for band-limited, base-band pulses. It is shown that large time advancement
comparable to the pulse width can be achieved with appropriate cascading of
negative-delay circuits but eventually the out-of-band gain limits the number
of cascading. The relations to superluminality and causality are also
discussed.


title: On the Unnikrishnan approach to the notion of locality

abstract:
  Recent proposals by C.S. Unnikrishnan concerning locality and Bell's theorem
are critically analysed.


title: Separable states can be used to distribute entanglement

abstract:
  We show that no entanglement is necessary to distribute entanglement; that
is, two distant particles can be entangled by sending a third particle that is
never entangled with the other two. Similarly, two particles can become
entangled by continuous interaction with a highly mixed mediating particle that
never itself becomes entangled. We also consider analogous properties of
completely positive maps, in which the composition of two separable maps can
create entanglement.


title:
Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum
  Instantons

abstract:
  We discuss the recently proposed quantum action - its interpretation, its
motivation, its mathematical properties and its use in physics: quantum
mechanical tunneling, quantum instantons and quantum chaos.


title: Preparing remotely two instances of quantum state

abstract:
  In this short note, we propose a scheme, in which two instances of an
equatorial state (or a polar state) can be remotely prepared in one-shot
operation to different receivers with prior entanglement and 1 bit of
broadcasting. The trade-off curve between the amount of entanglement and the
achievable fidelity is derived.


title: Coherent States: A General Approach

abstract:
  A general procedure for constructing coherent states, which are eigenstates
of annihilation operators, related to quantum mechanical potential problems, is
presented. These coherent states, by construction are not potential specific
and rely on the properties of the orthogonal polynomials, for their derivation.
The information about a given quantum mechanical potential enters into these
states, through the orthogonal polynomials associated with it and also through
its ground state wave function. The time evolution of some of these states
exhibit fractional revivals, having relevance to the factorization problem.


title:
Cloning a real d-dimensional quantum state on the edge of the
  no-signaling condition

abstract:
  We investigate a new class of quantum cloning machines that equally duplicate
all real states in a Hilbert space of arbitrary dimension. By using the
no-signaling condition, namely that cloning cannot make superluminal
communication possible, we derive an upper bound on the fidelity of this class
of quantum cloning machines. Then, for each dimension d, we construct an
optimal symmetric cloner whose fidelity saturates this bound. Similar
calculations can also be performed in order to recover the fidelity of the
optimal universal cloner in d dimensions.


title: Cloning the entanglement of a pair of quantum bits

abstract:
  It is shown that any quantum operation that perfectly clones the entanglement
of all maximally-entangled qubit pairs cannot preserve separability. This
``entanglement no-cloning'' principle naturally suggests that some approximate
cloning of entanglement is nevertheless allowed by quantum mechanics. We
investigate a separability-preserving optimal cloning machine that duplicates
all maximally-entangled states of two qubits, resulting in 0.285 bits of
entanglement per clone, while a local cloning machine only yields 0.060 bits of
entanglement per clone.


title: Universal Compression of Ergodic Quantum Sources

abstract:
  For a real number $r>0$, let $F(r)$ be the family of all stationary ergodic
quantum sources with von Neumann entropy rates less than $r$. We prove that,
for any $r>0$, there exists a blind, source-independent block compression
scheme which compresses every source from $F(r)$ to $r n$ qubits per input
block length $n$ with arbitrarily high fidelity for all large $n$. As our
second result,we show that the stationarity and the ergodicity of a quantum
source $\{\rho_m \}_{m=1}^{\infty}$ are preserved by any trace-preserving
completely positive linear map of the tensor product form ${\cal E}^{\otimes
m}$, where a copy of ${\cal E}$ acts locally on each spin lattice site. We also
establish ergodicity criteria for so called classically-correlated quantum
sources.


title: A Magnetic Resonance Realization of Decoherence-Free Quantum Computation

abstract:
  We report the realization, using nuclear magnetic resonance techniques, of
the first quantum computer that reliably executes an algorithm in the presence
of strong decoherence. The computer is based on a quantum error avoidance code
that protects against a class of multiple-qubit errors. The code stores two
decoherence-free logical qubits in four noisy physical qubits. The computer
successfully executes Grover's search algorithm in the presence of arbitrarily
strong engineered decoherence. A control computer with no decoherence
protection consistently fails under the same conditions.


title: The Real Density Matrix

abstract:
  We introduce a nonsymmetric real matrix which contains all the information
that the usual Hermitian density matrix does, and which has exactly the same
tensor product structure. The properties of this matrix are analyzed in detail
in the case of multi-qubit (e.g. spin = 1/2) systems, where the transformation
between the real and Hermitian density matrices is given explicitly as an
operator sum, and used to convert the essential equations of the density matrix
formalism into the real domain.


title:
Superradiance from an ultrathin film of three-level V-type atoms:
  Interplay between splitting, quantum coherence and local-field effects

abstract:
  We carry out a theoretical study of the collective spontaneous emission
(superradiance) from an ultrathin film comprised of three-level atoms with
$V$-configuration of the operating transitions. As the thickness of the system
is small compared to the emission wavelength inside the film, the local-field
correction to the averaged Maxwell field is relevant. We show that the
interplay between the low-frequency quantum coherence within the subspace of
the upper doublet states and the local-field correction may drastically affect
the branching ratio of the operating transitions. This effect may be used for
controlling the emission process by varying the doublet splitting and the
amount of low-frequency coherence.


title:
Realistic simulations of single-spin nondemolition measurement by
  magnetic resonance force microscopy

abstract:
  A requirement for many quantum computation schemes is the ability to measure
single spins. This paper examines one proposed scheme: magnetic resonance force
microscopy, including the effects of thermal noise and back-action from
monitoring. We derive a simplified equation using the adiabatic approximation,
and produce a stochastic pure state unraveling which is useful for numerical
simulations.


title: Teleportation with a uniformly accelerated partner

abstract:
  In this work, we give a description of the process of teleportation between
Alice in an inertial frame, and Rob who is in uniform acceleration with respect
to Alice. The fidelity of the teleportation is reduced due to Unruh radiation
in Rob's frame. In so far as teleportation is a measure of entanglement, our
results suggest that quantum entanglement is degraded in non inertial frames.


title: Subspace preserving completely positive maps

abstract:
  A class of quantum channels and completely positive maps (CPMs) are
introduced and investigated. These, which we call subspace preserving (SP) CPMs
has, in the case of trace preserving CPMs, a simple interpretation as those
which preserve probability weights on a given orthogonal sum decomposition of
the Hilbert space of a quantum system. Several equivalent characterizations of
SP CPMs are proved and an explicit construction of all SP CPMs, is provided.
For a subclass of the SP channels a construction in terms of joint unitary
evolution with an ancilla system, is presented.


title: Subspace local quantum channels

abstract:
  A special class of quantum channels, named subspace local (SL), are defined
and investigated. The proposed definition of subspace locality of quantum
channels is an attempt to answer the question of what kind of restriction
should be put on a channel, if it is to act `locally' with respect to two
`locations', when these naturally correspond to a separation of the total
Hilbert space in an orthogonal sum of subspaces, rather than a tensor product
decomposition. It is shown that the set of SL channels decomposes into four
disjoint families of channels. Explicit expressions to generate all channels in
each family is presented. It is shown that one of these four families, the
local subspace preserving (LSP) channels, is precisely the intersection between
the set of subspace preserving channels and the SL channels. For a subclass of
the LSP channels, a special type of unitary representation using ancilla
systems is presented.


title: Gluing of completely positive maps

abstract:
  Gluings of completely positive maps (CPMs) are defined and investigated. As a
brief description of this concept consider a pair of `evolution machines', each
with the ability to evolve the internal state of a `particle' inserted into its
input. Each of these machines is characterized by a channel describing the
operation the internal state has experienced when the particle is returned at
the output. Suppose a particle is put in a superposition between the input of
the first and the second machine. Here it is shown that the total evolution
caused by a pair of such devices is not uniquely determined by the channels of
the two machines. Such `global' channels describing the machine pair are
examples of gluings of the two single machine channels. Under the limiting
assumption that all involved Hilbert spaces are finite-dimensional, an
expression which generates all subspace preserving gluings of a given pair of
CPMs, is derived. The nature of the non-uniqueness of gluings and its relation
to a proposed definition of subspace locality, is discussed.


title: Probability of intrinsic time-arrow from information loss

abstract:
  Time-arrow $s=+/-$, intrinsic to a concrete physical system, is associated
with the direction of information loss $\Delta I$ displayed by the random
evolution of the given system. When the information loss tends to zero the
intrinsic time-arrow becomes uncertain. We propose the heuristic relationship
$1/[1+exp(-s\Delta I)]$ for the probability of the intrinsic time-arrow. The
main parts of the present work are trying to confirm this heuristic equation.
The probability of intrinsic time arrow is defined by Bayesian inference from
the observed random process. From irreversible thermodynamic systems, the
proposed heuristic probabilities follow via the Gallavotti-Cohen relations
between time-reversed random processes. In order to explore the underlying
microscopic mechanism, a trivial microscopic process is analyzed and an obvious
discrepancy is identified. It can be resolved by quantum theory. The
corresponding trivial quantum process will exactly confirm the proposed
heuristic time-arrow probability.