title: Semiclassical Theory of Coherence and Decoherence

abstract:
  A general semiclassical approach to quantum systems with system-bath
interactions is developed. We study system decoherence in detail using a
coherent state semiclassical wavepacket method which avoids singularity issues
arising in the usual Green's function approach. We discuss the general
conditions under which it is approximately correct to discuss quantum
decoherence in terms of a ``dephasing'' picture and we derive semiclassical
expressions for the phase and phase distribution. Remarkably, an effective
system wavefunction emerges whose norm measures the decoherence and is
equivalent to a density matrix formulation.


title: Quantum gates on hybrid qudits

abstract:
  We introduce quantum hybrid gates that act on qudits of different dimensions.
In particular, we develop two representative two-qudit hybrid gates (SUM and
SWAP) and many-qudit hybrid Toffoli and Fredkin gates. We apply the hybrid SUM
gate to generating entanglement, and find that operator entanglement of the SUM
gate is equal to the entanglement generated by it for certain initial states.
We also show that the hybrid SUM gate acts as an automorphism on the Pauli
group for two qudits of different dimension under certain conditions. Finally,
we describe a physical realization of these hybrid gates for spin systems.


title: Perturbations can enhance qauntum search

abstract:
  In general, a quantum algorithm wants to avoid decoherence or perturbation,
since such factors may cause errors in the algorithm. In this letter, we will
supply the answer to the interesting question: can the factors seemingly
harmful to a quantum algorithm(for example, perturbations) enhance the
algorithm? We show that some perturbations to the generalized quantum search
Hamiltonian can reduce the running time and enhance the success probability. We
also provide the narrow bound to the perturbation which can be beneficial to
quantum search. In addition, we show that the error induced by a perturbation
on the Farhi and Gutmann Hamiltonian can be corrected by another perturbation.


title: Uhlmann's geometric phase in presence of isotropic decoherence

abstract:
  Uhlmann's mixed state geometric phase [Rep. Math. Phys. {\bf 24}, 229 (1986)]
is analyzed in the case of a qubit affected by isotropic decoherence treated in
the Markovian approximation. It is demonstrated that this phase decreases
rapidly with increasing decoherence rate and that it is most fragile to weak
decoherence for pure or nearly pure initial states. In the unitary case, we
compare Uhlmann's geometric phase for mixed states with that occurring in
standard Mach-Zehnder interferometry [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]
and show that the latter is more robust to reduction in the length of the Bloch
vector. We also describe how Uhlmann's geometric phase in the present case
could in principle be realized experimentally.


title: Proof of Bell's Inequalities for Generalized Hidden Variables Models

abstract:
  Several authors have recently claimed that Bell's inequalities (BI) do not
apply to certain types of generalized local hidden variables (HV) models. These
claims are rejected, by means of a proof of BI valid for a very broad class of
local HV models (deterministic or stochastic, with or without memory, time
dependent or time independent, setting dependent or setting independent, and
even allowing classical communication between the wings of the experiment). The
precise meaning of the locality requirement is clarified during the proof. The
exact roles of the two assumptions that amount to Bell's locality (parameter
independence and outcome independence) are explicitly shown, using each one of
them in a different step of the proof. using each one of them in a different
step of the proof.


title: Comment on "Bose-Einstein condensation in low-dimensional traps"

abstract:
  We show that the critical temperature of a one-dimensional gas confined by a
power-law potential should be lower than that in the paper of Vanderlei Bagnato
and Daniel Kleppner. Moreover, a sketch of the critical temperature is given in
some more details.


title: Qubit semantics and quantum trees

abstract:
  In the qubit semantics the \emph{meaning} of any sentence $\alpha$ is
represented by a \emph{quregister}: a unit vector of the $n$--fold tensor
product $\otimes^n \C^2$, where $n$ depends on the number of occurrences of
atomic sentences in $\alpha$. The logic characterized by this semantics, called
{\it quantum computational logic} (QCL), is {\it unsharp}, because the
non-contradiction principle is violated. We show that QCL does not admit any
logical truth. In this framework, any sentence $\alpha$ gives rise to a
\emph{quantum tree}, consisting of a sequence of unitary operators. The quantum
tree of $\alpha$ can be regarded as a quantum circuit that transforms the
quregister associated to the atomic subformulas of $\alpha$ into the quregster
associated to $\alpha$.


title: An invitation to Quantum Game Theory

abstract:
  Recent development in quantum computation and quantum information theory
allows to extend the scope of game theory for the quantum world. The paper
presents the history, basic ideas and recent development in quantum game
theory. In this context, a new application of the Ising chain model is
proposed.

categories: quant-ph cond-mat cs.GT hep-th math-ph math.MP


title: Diffraction phases in atom interferometers

abstract:
  Diffraction of atoms by laser is a very important tool for matter wave
optics. Although this process is well understood, the phase shifts induced by
this diffraction process are not well known. In this paper, we make analytic
calculations of these phase shifts in some simple cases and we use these
results to model the contrast interferometer recently built by the group of D.
Pritchard at MIT. We thus show that the values of the diffraction phases are
large and that they probably contribute to the phase noise observed in this
experiment.


title:
Green functions for generalized point interactions in 1D: A scattering
  approach

abstract:
  Recently, general point interactions in one dimension has been used to model
a large number of different phenomena in quantum mechanics. Such potentials,
however, requires some sort of regularization to lead to meaningful results.
The usual ways to do so rely on technicalities which may hide important
physical aspects of the problem. In this work we present a new method to
calculate the exact Green functions for general point interactions in 1D. Our
approach differs from previous ones because it is based only on physical
quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$.
Renormalization or particular mathematical prescriptions are not invoked. The
simple formulation of the method makes it easy to extend to more general
contexts, such as for lattices of $N$ general point interactions; on a line; on
a half-line; under periodic boundary conditions; and confined in a box.


title:
Controllability properties for finite dimensional quantum Markovian
  master equations

abstract:
  Various notions from geometric control theory are used to characterize the
behavior of the Markovian master equation for N-level quantum mechanical
systems driven by unitary control and to describe the structure of the sets of
reachable states. It is shown that the system can be accessible but neither
small-time controllable nor controllable in finite time. In particular, if the
generators of quantum dynamical semigroups are unital, then the reachable sets
admit easy characterizations as they monotonically grow in time. The two level
case is treated in detail.


title:
Classical limit for the scattering of Dirac particles in a magnetic
  field

abstract:
  We present a relativistic quantum calculation at first order in perturbation
theory of the differential cross section for a Dirac particle scattered by a
solenoidal magnetic field. The resulting cross section is symmetric in the
scattering angle as those obtained by Aharonov and Bohm (AB) in the string
limit and by Landau and Lifshitz (LL) for the non relativistic case. We show
that taking pr_0\|sin(\theta/2)|/\hbar<<1 in our expression of the differential
cross section it reduces to the one reported by AB, and if additionally we
assume \theta << 1 our result becomes the one obtained by LL. However, these
limits are explicitly singular in \hbar as opposed to our initial result. We
analyze the singular behavior in \hbar and show that the perturbative Planck's
limit (\hbar -> 0) is consistent, contrarily to those of the AB and LL
expressions. We also discuss the scattering in a uniform and constant magnetic
field, which resembles some features of QCD.


title:
Density matrix operatorial solution of the non--Markovian Master
  Equation for Quantum Brownian Motion

abstract:
  An original method to exactly solve the non-Markovian Master Equation
describing the interaction of a single harmonic oscillator with a quantum
environment in the weak coupling limit is reported. By using a superoperatorial
approach we succeed in deriving the operatorial solution for the density matrix
of the system. Our method is independent of the physical properties of the
environment. We show the usefulness of our solution deriving explicit
expressions for the dissipative time evolution of some observables of physical
interest for the system, such as, for example, its mean energy.


abstract:
  Exceptional points and double poles of the S matrix are both characterized by
the coalescence of a pair of eigenvalues. In the first case, the coalescence
causes a defect of the Hilbert space. In the second case, this is not so as
shown in prevoius papers. Mathematically, the reason for this difference is the
bi-orthogonality of the eigenfunctions of a non-Hermitian operator that is
ignored in the first case. The consequences for the topological structure of
the Hilbert space are studied and compared with existing experimental data.


title: Entanglement For Ideal Quantum Ensembles

abstract:
  This paper has been withdrawn by the authors, due to the discovery of paper
0201028 which predates it and contains most of it's results.


title: Eavesdropping on the "ping-pong" quantum communication protocol

abstract:
  The proposed eavesdropping scheme reveals that the quantum communication
protocol recently presented by Bostrom and Felbinger [Phys. Rev. Lett. 89,
187902 (2002)] is not secure as far as quantum channel losses are taken into
account.


title:
Lower limit on decoherence introduced by entangling two
  spatially-separated qubits

abstract:
  It is shown that a generalization of the fluctuation-dissipation theorem
places an upper bound on the figure of merit for any quantum gate designed to
entangle spatially-separated qubits. The bound depends solely on the spectral
properties of the environment. The bound applies even to systems performing a
quantum computation within a decoherence-free subspace, but might be optimized
by the use of non-equilibrium squeezed states of the environment, or by using
an environment system constructed to have response confined to certain
frequencies.


title:
Relation between the field quadratures and the characteristic function
  of a mirror

abstract:
  We analyze the possibility of measuring the state of a movable mirror by
using its interaction with a quantum field. We show that measuring the field
quadratures allows to reconstruct the characteristic function corresponding to
the mirror state.


title:
The Quantum Fourier Transform and Extensions of the Abelian Hidden
  Subgroup Problem

abstract:
  The quantum Fourier transform (QFT) has emerged as the primary tool in
quantum algorithms which achieve exponential advantage over classical
computation and lies at the heart of the solution to the abelian hidden
subgroup problem, of which Shor's celebrated factoring and discrete log
algorithms are a special case. We begin by addressing various computational
issues surrounding the QFT and give improved parallel circuits for both the QFT
over a power of 2 and the QFT over an arbitrary cyclic group. These circuits
are based on new insight into the relationship between the discrete Fourier
transform over different cyclic groups. We then exploit this insight to extend
the class of hidden subgroup problems with efficient quantum solutions. First
we relax the condition that the underlying hidden subgroup function be distinct
on distinct cosets of the subgroup in question and show that this relaxation
can be solved whenever G is a finitely-generated abelian group. We then extend
this reasoning to the hidden cyclic subgroup problem over the reals, showing
how to efficiently generate the bits of the period of any sufficiently
piecewise-continuous function on R. Finally, we show that this problem of
period-finding over R, viewed as an oracle promise problem, is strictly harder
than its integral counterpart. In particular, period-finding over R lies
outside the complexity class MA, a class which contains period-finding over the
integers.


title:
Modeling Decoherence and Decoherence-Free Subspaces in Complex
  Environments

abstract:
  A simplified Bogoliubov transform reduces a fully-interacting many-fermion
spin-1/2 system-plus-environment to a more tractable many-to-one variant. The
transform additionally yields exact solutions for bosonic multi-particle
interactions sans the approximation introduced by using discrete time steps to
deal with quantum parallelism. The decohering effect of relatively general
finite environments is therewith modeled and compared to the decohering effect
of an infinite environmental "bath." The anti-symmetric singlet state formed by
two maximally-entangled two-state particles is shown to be inherently
decoherence-free. As a quantum bit ("qubit") it is thus potentially superior to
any single-particle state.


title: Orthogonality relations for triple modes at dielectric boundary surfaces

abstract:
  We work out the orthogonality relations for the set of Carniglia-Mandel
triple modes which provide a set of normal modes for the source-free
electromagnetic field in a background consisting of a passive dielectric
half-space and the vacuum, respectively. Due to the inherent computational
complexity of the problem, an efficient strategy to accomplish this task is
desirable, which is presented in the paper. Furthermore, we provide all main
steps for the various proofs pertaining to different combinations of triple
modes in the orthogonality integral.


title: Realistic fast quantum gates with hot trapped ions

abstract:
  The "pushing gate" proposed by Cirac and Zoller in 2000 for quantum logic in
ion traps is discussed, in which a force is used to give a controlled push to a
pair of trapped ions and thus realize a phase gate. The original proposal had a
weakness in that it involved a hidden extreme sensitivity to the size of the
force. Also, the physical origin of this force was not fully addressed. Here,
we discuss the sensitivity and present a way to avoid it by choosing the
spatial form of the pushing force in an optimal way. We also analyse the effect
of imperfections in a pair of pi pulses which are used to implement a
"spin-echo" to cancel correlated errors. We present a physical model for the
force, namely the dipole force, and discuss the impact of unwanted photon
scattering, and of finite temperature of the ions. The main effect of the
temperature is to blur the phase of the gate owing to the ions exploring a
range of values of the force. When the distance scale of the force profile is
smaller than the ion separation, this effect is more important than the
high-order terms in the Coulomb repulsion which were originally discussed.
Overall, we find that whereas the "pushing gate" is not as resistant to
imperfections as was supposed, it remains a significant candidate for ion trap
quantum computing since it does not require ground state cooling, and in some
cases it does not require the Lamb-Dicke limit, while the gate rate is fast,
close to (rather than small compared to) the trap vibrational frequency.


title: Quantum control and the Strocchi map

abstract:
  Identifying the real and imaginary parts of wave functions with coordinates
and momenta, quantum evolution may be mapped onto a classical Hamiltonian
system. In addition to the symplectic form, quantum mechanics also has a
positive-definite real inner product which provides a geometrical
interpretation of the measurement process. Together they endow the quantum
Hilbert space with the structure of a K\"{a}ller manifold. Quantum control is
discussed in this setting. Quantum time-evolution corresponds to smooth
Hamiltonian dynamics and measurements to jumps in the phase space. This adds
additional power to quantum control, non unitarily controllable systems
becoming controllable by ``measurement plus evolution''. A picture of quantum
evolution as Hamiltonian dynamics in a classical-like phase-space is the
appropriate setting to carry over techniques from classical to quantum control.
This is illustrated by a discussion of optimal control and sliding mode
techniques.


title: Remarks on entanglement measures and non-local state distinguishability

abstract:
  We investigate the properties of three entanglement measures that quantify
the statistical distinguishability of a given state with the closest
disentangled state that has the same reductions as the primary state. In
particular, we concentrate on the relative entropy of entanglement with
reversed entries. We show that this quantity is an entanglement monotone which
is strongly additive, thereby demonstrating that monotonicity under local
quantum operations and strong additivity are compatible in principle. In
accordance with the presented statistical interpretation which is provided,
this entanglement monotone, however, has the property that it diverges on pure
states, with the consequence that it cannot distinguish the degree of
entanglement of different pure states. We also prove that the relative entropy
of entanglement with respect to the set of disentangled states that have
identical reductions to the primary state is an entanglement monotone. We
finally investigate the trace-norm measure and demonstrate that it is also a
proper entanglement monotone.


title: Quantum chaos and fractals with atoms in cavities

abstract:
  We study the coupled translational, electronic, and field dynamics of the
combined system "a two-level atom + a single-mode quantized field + a
standing-wave ideal cavity". We derive Hamilton -- Schr\"odinger equations for
probability amplitudes and averaged position and momentum of a point-like atom
interacting with the quantized field in a standing-wave cavity. They
constitute, in general, an infinite-dimensional set of equations with an
infinite number of integrals of motion which may be reduced to a dynamical
system with four degrees of freedom if the quantized field is supposed to be
initially prepared in a Fock state. This system is found to produce semiquantum
chaos with positive values of the maximal Lyapunov exponent. At large values of
detuning $|\delta|\gg 1$, the Rabi atomic oscillations are usually shallow, and
the dynamics is found to be almost regular. The Doppler -- Rabi resonance, deep
Rabi oscillations that may occur at any large value of $|\delta|$ to be equal
to $|\alpha p_0|$, is found numerically and described analytically (with
$\alpha$ to be the normalized recoil frequency and $p_0$ the initial atomic
momentum). Two gedanken experiments are proposed to detect manifestations of
semiquantum chaos in real experiments. In the chaotic regime values of the
population inversion $z_{out}$, measured with atoms after transversing a
cavity, are so sensitive to small changes in the initial inversion $z_{in}$
that the probability of detecting any value of $z_{out}$ in the admissible
interval becomes almost unity in a short time. Chaotic wandering of a two-level
atom in a quantized Fock field is shown to be fractal. Fractal-like structures,
typical for chaotic scattering, are numerically found in the dependence of the
time of exit of atoms from the cavity on their initial momenta.


title:
The rotating wave system-reservoir coupling: limitations and meaning in
  the non-Markovian regime

abstract:
  This paper deals with the dissipative dynamics of a quantum harmonic
oscillator interacting with a bosonic reservoir. The Master Equations based on
the Rotating Wave and on the Feynman-Vernon system--reservoir couplings are
compared highlighting differences and analogies. We discuss quantitatively and
qualitatively the conditions under which the counter rotating terms can be
neglected. By comparing the analytic solution of the heating function relative
to the two different coupling models we conclude that, even in the weak
coupling limit, the counter rotating terms give rise to a significant
contribution in the non--Markovian short time regime. The main result of this
paper is that such a contribution is actually experimentally measurable and
thus relevant for a correct description of the system dynamics.


title: The hydrogen atom in electric and magnetic fields : Pauli's 1926 article

abstract:
  The results obtained by Pauli, in his 1926 article on the hydrogen atom, made
essential use of the dynamical so(4) symmetry of the bound states. Pauli used
this symmetry to compute the perturbed energy levels of an hydrogen atom in a
uniform electric field (Stark effect) and in uniform electric and magnetic
fields. Although the experimental check of the single Stark effect on the
hydrogen atom has been studied experimentally, Pauli's results in mixed fields
have been studied only for Rydberg states of rubidium atoms in crossedfields
and lithium atoms in parallel fields.


title: Echo spectroscopy and Atom Optics Billiards

abstract:
  We discuss a recently demonstrated type of microwave spectroscopy of trapped
ultra-cold atoms known as "echo spectroscopy" [M.F. Andersen et. al., Phys.
Rev. Lett., in press (2002)]. Echo spectroscopy can serve as an extremely
sensitive experimental tool for investigating quantum dynamics of trapped atoms
even when a large number of states are thermally populated. We show numerical
results for the stability of eigenstates of an atom-optics billiard of the
Bunimovich type, and discuss its behavior under different types of
perturbations. Finally, we propose to use special geometrical constructions to
make a dephasing free dipole trap.


title: Phase states for a three-level atom interacting with quantum fields

abstract:
  We introduce phase operators associated with the algebra su(3), which is the
appropriate tool to describe three-level systems. The rather unusual properties
of this phase are caused by the small dimension of the system and are explored
in detail. When a three-level atom interacts with a quantum field in a cavity,
a polynomial deformation of this algebra emerges in a natural way. We also
introduce a polar decomposition of the atom-field relative amplitudes that
leads to a Hermitian relative-phase operator, whose eigenstates correctly
describe the corresponding phase properties. We claim that this is the natural
variable to deal with quantum interference effects in atom-field interactions.
We find the probability distribution for this variable and study its time
evolution in some special cases.


title: Application of information entropy to nuclei

abstract:
  Shannon's information entropies in position- and momentum- space and their
sum $S$ are calculated for various $s$-$p$ and $s$-$d$ shell nuclei using a
correlated one-body density matrix depending on the harmonic oscillator size
$b_0$ and the short range correlation parameter $y$ which originates from a
Jastrow correlation function. It is found that the information entropy sum for
a nucleus depends only on the correlation parameter $y$ through the simple
relation $S= s_{0A} + s_{1A} y^{-\lambda_{sA}}$, where $s_{0A}$, $s_{1A}$ and
$\lambda_{sA}$ depend on the mass number $A$. A similar approximate expression
is also valid for the root mean square radius of the nucleus as function of $y$
leading to an approximate expression which connects $S$ with the root mean
square radius. Finally, we propose a method to determine the correlation
parameter from the above property of $S$ as well as the linear dependence of
$S$ on the logarithm of the number of nucleons.


title: Infinitely entangled states

abstract:
  For states in infinite dimensional Hilbert spaces entanglement quantities
like the entanglement of distillation can become infinite. This leads naturally
to the question, whether one system in such an infinitely entangled state can
serve as a resource for tasks like the teleportation of arbitrarily many
qubits. We show that appropriate states cannot be obtained by density operators
in an infinite dimensional Hilbert space. However, using techniques for the
description of infinitely many degrees of freedom from field theory and
statistical mechanics, such states can nevertheless be constructed rigorously.
We explore two related possibilities, namely an extended notion of algebras of
observables, and the use of singular states on the algebra of bounded
operators. As applications we construct the essentially unique infinite
analogue of maximally entangled states, and the singular state used
heuristically in the fundamental paper of Einstein, Rosen and Podolsky.


title: Some remarks on Dirac's hole theory versus quantum field theory

abstract:
  Dirac's hole theory and quantum field theory are generally considered to be
equivalent to each other. However, it has recently been shown that this is not
necessarily the case. In this article we will discuss the reason for this lack
of equivalence and suggest a possible solution.


title:
Classical and Quantum Polynomial Reconstruction via Legendre Symbol
  Evaluation

abstract:
  We consider the problem of recovering a hidden monic polynomial f(X) of
degree d > 0 over the finite field F of p elements given a black box which, for
any x in F, evaluates the quadratic character of f(x). We design a classical
algorithm of complexity O(d^2 p^{d + c}), for any c > 0, and also show that the
quantum query complexity of this problem is O(d). Some of our results extend
those of Wim van Dam, Sean Hallgren and Lawrence Ip obtained in the case of a
linear polynomial f(X) = X + s (with unknown s); some are new even in this
case.


title: Multimode Hong-Ou-Mandel interference

abstract:
  We consider multimode two-photon interference at a beam splitter by photons
created by spontaneous parametric down-conversion. The resulting interference
pattern is shown to depend upon the transverse spatial symmetry of the pump
beam. In an experiment, we employ the first-order Hermite-Gaussian modes in
order to show that, by manipulating the pump beam, one can control the
resulting two-photon interference behavior. We expect these results to play an
important role in the engineering of quantum states of light for use in quantum
information processing and quantum imaging.


title: Secure communication using mesoscopic coherent states

abstract:
  We demonstrate theoretically and experimentally that secure communication
using intermediate-energy (mesoscopic) coherent states is possible. Our scheme
is different from previous quantum cryptographic schemes in that a short secret
key is explicitly used and in which quantum noise hides both the bit and the
key. This encryption scheme can be optically amplified. New avenues are open to
secure communications at high speeds in fiber-optic or free-space channels.


title:
Reversible transformations from pure to mixed states, and the unique
  measure of information

abstract:
  Transformations from pure to mixed states are usually associated with
information loss and irreversibility. Here, a protocol is demonstrated allowing
one to make these transformations reversible. The pure states are diluted with
a random noise source. Using this protocol one can study optimal
transformations between states, and from this derive the unique measure of
information. This is compared to irreversible transformations where one does
not have access to noise. The ideas presented here shed some light on attempts
to understand entanglement manipulations and the inevitable irreversibility
encountered there where one finds that mixed states can contain "bound
entanglement".


title:
Construction of extremal local positive operator-valued measures under
  symmetry

abstract:
  We study the local implementation of POVMs when we require only the faithful
reproduction of the statistics of the measurement outcomes for all initial
states. We first demonstrate that any POVM with separable elements can be
implemented by a separable super-operator, and develop techniques for
calculating the extreme points of POVMs under a certain class of constraint
that includes separability and PPT-ness. As examples we consider measurements
that are invariant under various symmetry groups (Werner, Isotropic,
Bell-diagonal, Local Orthogonal), and demonstrate that in these cases
separability of the POVM elements is equivalent to implementability via LOCC.
We also calculate the extrema of these classes of measurement under the groups
that we consider, and give explicit LOCC protocols for attaining them. These
protocols are hence optimal methods for locally discriminating between states
of these symmetries. One of many interesting consequences is that the best way
to locally discriminate Bell diagonal mixed states is to perform a 2-outcome
POVM using local von Neumann projections. This is true regardless of the cost
function, the number of states being discriminated, or the prior probabilities.
Our results give the first cases of local mixed state discrimination that can
be analysed quantitatively in full, and may have application to other problems
such as demonstrations of non-locality, experimental entanglement witnesses,
and perhaps even entanglement distillation.


title:
Remote information concentration by GHZ state and by bound entangled
  state

abstract:
  We compare remote information concentration by a maximally entangled GHZ
state with by an unlockable bound entangled state. We find that the bound
entangled state is as useful as the GHZ state, even do better than the GHZ
state in the context of communication security.


title: Coupling of effective one-dimensional two-level atoms to squeezed light

abstract:
  A cavity QED system is analyzed which duplicates the dynamics of a two-level
atom in free space interacting exclusively with broadband squeezed light. We
consider atoms in a three or four-level Lambda-configuration coupled to a
high-finesse optical cavity which is driven by a squeezed light field. Raman
transitions are induced between a pair of stable atomic ground states via the
squeezed cavity mode and coherent driving fields. An analysis of the reduced
master equation for the atomic ground states shows that a three-level atomic
system has insufficient parameter flexibility to act as an effective two-level
atom interacting exclusively with a squeezed reservoir. However, the inclusion
of a fourth atomic level, coupled dispersively to one of the two ground states
by an auxiliary laser field, introduces an extra degree of freedom and enables
the desired interaction to be realised. As a means of detecting the reduced
quadrature decay rate of the effective two-level system, we examine the
transmission spectrum of a weak coherent probe field incident upon the cavity.


title: Quantum Information and Relativity Theory

abstract:
  Quantum mechanics, information theory, and relativity theory are the basic
foundations of theoretical physics. The acquisition of information from a
quantum system is the interface of classical and quantum physics. Essential
tools for its description are Kraus matrices and positive operator valued
measures (POVMs). Special relativity imposes severe restrictions on the
transfer of information between distant systems. Quantum entropy is not a
Lorentz covariant concept. Lorentz transformations of reduced density matrices
for entangled systems may not be completely positive maps. Quantum field
theory, which is necessary for a consistent description of interactions,
implies a fundamental trade-off between detector reliability and
localizability. General relativity produces new, counterintuitive effects, in
particular when black holes (or more generally, event horizons) are involved.
Most of the current concepts in quantum information theory may then require a
reassessment.


title: Optical Lattice in a High Finesse Ring Resonator

abstract:
  An optical lattice with rubidium atoms ($^{85}Rb$) is formed inside a ring
resonator with a finesse of $1.8 \times 10^5$ and a large mode volume of 1.3
$mm^3$. We typically trap several times $10^6$ atoms at densities up to
$10^{12} cm^{-3}$ and temperatures between 25 and 125 $\mu K$. Despite of the
narrow bandwidth (17.3 kHz) of the cavity, heating due to intra--cavity
intensity fluctuations is kept at a low level, such that the time evolution of
the temperature is determined by evaporative cooling.


title: Remarks on the classical capacity of quantum channel

abstract:
  A direct proof of the relation between the one-shot classical capacity and
the minimal output entropy for covariant quantum channels is suggested. The
structure of covariant channels is described in some detail. A simple proof of
a general inequality for entanglement-assisted classical capacity is given.


title: Second order SUSY transformations with `complex energies'

abstract:
  Second order supersymmetry transformations which involve a pair of complex
conjugate factorization energies and lead to real non-singular potentials are
analyzed. The generation of complex potentials with real spectra is also
studied. The theory is applied to the free particle, one-soliton well and
one-dimensional harmonic oscillator.


title:
Reply to "Comment on "Some implications of the quantum nature of laser
  fields for quantum computations''''

abstract:
  In this revised reply to quant-ph/0211165, I address the question of the
validity of my results in greater detail, by comparing my predictions to those
of the Silberfarb-Deutsch model, and I deal at greater length with the beam
area paradox. As before, I conclude that my previous results are an
(order-of-magnitude) accurate estimate of the error probability introduced in
quantum logical operations by the quantum nature of the laser field. While this
error will typically (for a paraxial beam) be smaller than the total error due
to spontaneous emission, a unified treatment of both effects reveals that they
lead to formally similar constraints on the minimum number of photons per pulse
required to perform an operation with a given accuracy; these constraints agree
with those I have derived elsewhere.


title:
Reply to ``Comment on ``Some implications of the quantum nature of laser
  fields for quantum computations'' ''

abstract: We point out several superficialities in Itano's comment (quant-ph/0211165).


title: Cloning of Qubits of a Quantum Computer

abstract:
  A system of unitary transformations providing two optimal copies of an
arbitrary input cubit is obtained. An algorithm based on classical Boolean
algebra and allowing one to find any unitary transformation realized by the
quantum CNOT operators is proposed.


title: Geometric measure of entanglement for multipartite quantum states

abstract:
  The degree to which a pure quantum state is entangled can be characterized by
the distance or angle to the nearest unentangled state. This geometric measure
of entanglement, already present in a number of settings [A. Shimony, Ann. NY.
Acad. Sci. 755, p.675 (1995) and H. Barnum and N. Linden, J. Phys. A: Math.
Gen. 34, p.6787 (2001)], is explored for bipartite and multipartite pure and
mixed states. It is determined for arbitrary two-qubit mixed states and for
generalized Werner and isotropic states, and is also applied to certain
multipartite mixed states.


title: Quantum correlations in classical statistics

abstract:
  Quantum correlations can be naturally formulated in a classical statistical
system of infinitely many degrees of freedom. This realizes the underlying
non-commutative structure in a classical statistical setting. We argue that the
quantum correlations offer a more robust description with respect to the
precise definition of observables.


title: Time correlated quantum amplitude damping channel

abstract:
  We analyze the problem of sending classical information through qubit
channels where successive uses of the channel are correlated. This work extends
the analysis of C. Macchiavello and G. M. Palma to the case of a non-Pauli
channel - the amplitude damping channel. Using the channel description outlined
in S. Daffer, et al, we derive the correlated amplitude damping channel. We
obtain a similar result to C. Macchiavello and G. M. Palma, that is, that under
certain conditions on the degree of channel memory, the use of entangled input
signals may enhance the information transmission compared to the use of product
input signals.


title:
Fast and secure key distribution using mesoscopic coherent states of
  light

abstract:
  This work shows how two parties A and B can securely share sequences of
random bits at optical speeds. A and B possess true-random physical sources and
exchange random bits by using a random sequence received to cipher the
following one to be sent. A starting shared secret key is used and the method
can be described as an unlimited one-time-pad extender. It is demonstrated that
the minimum probability of error in signal determination by the eavesdropper
can be set arbitrarily close to the pure guessing level. Being based on the
$M$-ry encryption protocol this method also allows for optical amplification
without security degradation, offering practical advantages over the BB84
protocol for key distribution.


title: Multipartite entangled states in coupled quantum dots and cavity-QED

abstract:
  We investigate the generation of multipartite entangled state in a system of
N quantum dots embedded in a microcavity and examine the emergence of genuine
multipartite entanglement by three different characterizations of entanglement.
At certain times of dynamical evolution one can generate multipartite entangled
coherent exciton states or multiqubit $W$ states by initially preparing the
cavity field in a superposition of coherent states or the Fock state with one
photon, respectively. Finally we study environmental effects on multipartite
entanglement generation and find that the decay rate for the entanglement is
proportional to the number of excitons.


title: Entanglement capability of self-inverse Hamiltonian evolution

abstract:
  We determine the entanglement capability of self-inverse Hamiltonian
evolution, which reduces to the known result for Ising Hamiltonian, and
identify optimal input states for yielding the maximal entanglement rate. We
introduce the concept of the operator entanglement rate, and find that the
maximal operator entanglement rate gives a lower bound on the entanglement
capability of a general Hamiltonian.


title: New results on the parametrisation of complex Hadamard matrices

abstract:
  In this paper we provide an analytical procedure which leads to a system of
  $(n-2)^2$ polynomial equations whose solutions give the parameterisation of
the complex $n\times n$ Hadamard matrices. It is shown that in general the
Hadamard matrices depend on a number of arbitrary phases and a lower bound for
this number is given. The moduli equations define interesting geometrical
objects whose study will shed light on the parameterisation of Hadamard
matrices, as well as on some interesting geometrical varieties defined by them.


title:
Practical scheme for the optimal measuremnet in quantum interferometric
  devices

abstract:
  We apply a Kennedy-type detection scheme, which was originally proposed for a
binary communications system, to interferometric sensing devices. We show that
the minimum detectable perturbation of the proposed system reaches the ultimate
precision bound which is predicted by Neyman-Pearson hypothesis testing. To
provide concrete examples, we apply our interferometric scheme to phase shift
detection by using coherent and squeezed probe fields.


title: Anisotropic harmonic oscillator in a static electromagnetic field

abstract:
  A nonrelativistic charged particle moving in an anisotropic harmonic
oscillator potential plus a homogeneous static electromagnetic field is
studied. Several configurations of the electromagnetic field are considered.
The Schr\"odinger equation is solved analytically in most of the cases. The
energy levels and wave functions are obtained explicitly. In some of the cases,
the ground state obtained is not a minimum wave packet, though it is of the
Gaussian type. Coherent and squeezed states and their time evolution are
discussed in detail.


title: Entangling strings of neutral atoms in 1D atomic pipeline structures

abstract:
  We study a string of neutral atoms with nearest neighbor interaction in a 1D
beam splitter configuration, where the longitudinal motion is controlled by a
moving optical lattice potential. The dynamics of the atoms crossing the beam
splitter maps to a 1D spin model with controllable time dependent parameters,
which allows the creation of maximally entangled states of atoms by crossing a
quantum phase transition. Furthermore, we show that this system realizes
protected quantum memory, and we discuss the implementation of one- and
two-qubit gates in this setup.


title:
Thermal emissivity for finite three-dimensional photonic band gap
  crystals

abstract:
  We discuss the results of computer model for the thermal emissivity of a
three-dimensional photonic band gap (PBG) crystal, specifically an inverted
opal structure. The thermal emittance for a range of frequencies and angles is
calculated.


title: Quantum Communication Through an Unmodulated Spin Chain

abstract:
  We propose a scheme for using an unmodulated and unmeasured spin-chain as a
channel for short distance quantum communications. The state to be transmitted
is placed on one spin of the chain and received later on a distant spin with
some fidelity. We first obtain simple expressions for the fidelity of quantum
state transfer and the amount of entanglement sharable between any two sites of
an arbitrary Heisenberg ferromagnet using our scheme. We then apply this to the
realizable case of an open ended chain with nearest neighbor interactions. The
fidelity of quantum state transfer is obtained as an inverse discrete cosine
transform and as a Bessel function series. We find that in a reasonable time, a
qubit can be directly transmitted with better than classical fidelity across
the full length of chains of up to 80 spins. Moreover, the spin-chain channel
allows distillable entanglement to be shared over arbitrarily large distances.


title: Expressing Decoherence with Spectral and Stochastic Methods

abstract:
  We suggest a novel proposal to express decoherence in open quantum systems by
jointly employing spectral and stochastic methods. This proposal, which
basically perturbs the unitary evolution operator in a random fashion, allows
us to embrace both markovian and nonmarkovian situations with little extra
effort. We argue that it can be very suitable to deal with models where an
approximation neglecting some degrees of freedom is undertaken. Mathematical
simplicity is also obtained both to solve some master equations and to arrive
at experimentally measured decoherence functions.


title: Large N Quantum Cryptography

abstract:
  In quantum cryptography, the level of security attainable by a protocol which
implements a particular task $N$ times bears no simple relation to the level of
security attainable by a protocol implementing the task once. Useful partial
security, and even near-perfect security in an appropriate sense, can be
obtained for $N$ copies of a task which itself cannot be securely implemented.
We illustrate this with protocols for quantum bit string commitment and quantum
random number generation between mistrustful parties.


title: Entanglement from the vacuum

abstract:
  We explore the entanglement of the vacuum of a relativistic field by letting
a pair of causally disconnected probes interact with the field. We find that,
even when the probes are initially non-entangled, they can wind up to a final
entangled state. This shows that entanglement persists between disconnected
regions in the vacuum. However the probe entanglement, unlike correlations,
vanishes once the regions become sufficiently separated. The relation between
entropy, correlations and entanglement is discussed.


title: Generalized Quantum Games with Nash Equilibrium

abstract:
  We define generalized quantum games by introducing the coherent payoff
operators and propose a simple scheme to illustrate it. The scheme is
implemented with a single spin qubit system and two entangled qubit system. The
Nash Equilibrium Theorem is proved for the models.


title:
On Solvable Potentials for One Dimensional Schroedinger and
  Fokker-Planck Equations

abstract:
  One construction of exactly-solvable potentials for Fokker-Planck equation is
considered based on supersymmetric quantum mechanics approach.


title: Some Properties of the Computable Cross Norm Criterion for Separability

abstract:
  The computable cross norm (CCN) criterion is a new powerful analytical and
computable separability criterion for bipartite quantum states, that is also
known to systematically detect bound entanglement. In certain aspects this
criterion complements the well-known Peres positive partial transpose (PPT)
criterion. In the present paper we study important analytical properties of the
CCN criterion. We show that in contrast to the PPT criterion it is not
sufficient in dimension 2 x 2. In higher dimensions we prove theorems
connecting the fidelity of a quantum state with the CCN criterion. We also
analyze the behaviour of the CCN criterion under local operations and identify
the operations that leave it invariant. It turns out that the CCN criterion is
in general not invariant under local operations.


title:
The Quantum Query Complexity of 0-1 Knapsack and Associated Claw
  Problems

abstract:
  We first give an $\O(2^{n/3})$ quantum algorithm for the 0-1 Knapsack problem
with $n$ variables. More generally, for 0-1 Integer Linear Programs with $n$
variables and $d$ inequalities we give an $\O(2^{n/3}n^d)$ quantum algorithm.
For $d =o(n/\log n)$ this running time is bounded by $\O(2^{n(1/3+\epsilon)})$
for every $\epsilon>0$ and in particular it is better than the $\O(2^{n/2})$
upper bound for general quantum search. To investigate whether better
algorithms for these NP-hard problems are possible, we formulate a
\emph{symmetric} claw problem corresponding to 0-1 Knapsack and study its
quantum query complexity. For the symmetric claw problem we establish a lower
bound of $\O(2^{n/4})$ for its quantum query complexity. We have an
$\O(2^{n/3})$ upper bound given by essentially the same quantum algorithm that
works for Knapsack. Additionally, we consider CNF satisfiability of CNF
formulas $F$ with no restrictions on clause size, but with the number of
clauses in $F$ bounded by $cn$ for a constant $c$, where $n$ is the number of
variables. We give a $2^{(1-\alpha)n/2}$ quantum algorithm for satisfiability
in this case, where $\alpha$ is a constant depending on $c$.


title: Entanglement sharing in one-particle states

abstract:
  Entanglement sharing among sites of one-particle states is considered using
the measure of concurrence. These are the simplest in an hierarchy of
number-specific states of many qubits and corresponds to ``one-magnon'' states
of spins. We study the effects of onsite potentials that are both integrable
and nonintegrable. In the integrable case we point to a metal-insulator
transition that reflects on the way entanglement is shared. In the
nonintegrable case the average entanglement content increases and saturates
along with a transition to classical chaos. Such quantum chaotic states are
shown to have universal concurrence distributions that are modified Bessel
functions derivable within random matrix theory. Time-reversal breaking and
time evolving states are shown to possess significantly higher entanglement
sharing capacity that eigenstates of time-reversal symmetric systems. We use
the ordinary Harper and kicked Harper Hamiltonians as model systems.


title:
Experimental study for Yuen-Kim protocol of quantum key distribution
  with unconditional secure

abstract:
  In this report, we simulate practical feature of Yuen-Kim protocol for
quantum key distribution with unconditional secure. In order to demonstrate
them experimentally by intensity modulation/direct detection(IMDD) optical
fiber communication system, we use simplified encoding scheme to guarantee
security for key information(1 or 0). That is, pairwise M-ary intensity
modulation scheme is employed. Furthermore, we give an experimental
implementation of YK protocol based on IMDD.


title: Detecting genuine multipartite continuous-variable entanglement

abstract:
  We derive necessary conditions in terms of the variances of position and
momentum linear combinations for all kinds of separability of a multi-party
multi-mode continuous-variable state. Their violations can be sufficient for
genuine multipartite entanglement, provided the combinations contain both
conjugate variables of all modes. Hence a complete state determination, for
example by detecting the entire correlation matrix of a Gaussian state, is not
needed.


title:
Quantum Mechanical Motion of Relativistic Particle in Non-Continuous
  Spacetime

abstract:
  The quantum mechanical motion of a relativistic particle in a non-continuous
spacetime is investigated. The spacetime model is a dense, rationale subset of
two-dimensional Minkowski spacetime. Solutions of the Dirac equation are
calculated using a generalized version of Feynman's checkerboard model. They
turn out to be closely related to the continuum propagator.


title: Spin 1/2 Particle on a Cylinder with Radial Magnetic Field

abstract:
  We study the motion of a charged quantum particle, constrained on the surface
of a cylinder, in the presence of a radial magnetic field. When the spin of the
particle is neglected, the system essentially reduces to an infinite family of
simple harmonic oscillators, equally spaced along the axis of the cylinder.
Interestingly enough, it can be used as a quantum Fourier transformer, with
convenient visual output. When the spin 1/2 of the particle is taken into
account, a non-conventional perturbative analysis results in a recursive closed
form for the corrections to the energy and the wavefunction, for all
eigenstates, to all orders in the magnetic moment of the particle. A simple
two-state system is also presented, the time evolution of which involves an
approximate precession of the spin perpendicularly to the magnetic field. A
number of plots highlight the findings while several three-dimensional
animations have been made available on the web.


title: Unconditionally Secure Quantum Key Distribution In Higher Dimensions

abstract:
  In search of a quantum key distribution scheme that could stand up for more
drastic eavesdropping attack, I discover a prepare-and-measure scheme using
$N$-dimensional quantum particles as information carriers where $N$ is a prime
power. Using the Shor-Preskill-type argument, I prove that this scheme is
unconditional secure against all attacks allowed by the laws of quantum
physics. Incidentally, for $N = 2^n > 2$, each information carrier can be
replaced by $n$ entangled qubits. And in this case, I discover an eavesdropping
attack on which no unentangled-qubit-based prepare-and-measure quantum key
distribution scheme known to date can generate a provably secure key. In
contrast, this entangled-qubit-based scheme produces a provably secure key
under the same eavesdropping attack whenever $N \geq 16$. This demonstrates the
advantage of using entangled particles as information carriers to combat
certain eavesdropping strategies.


title: Quantum secret sharing without entanglement

abstract:
  After analysing the main quantum secret sharing protocol based on the
entanglement states, we propose an idea to directly encode the qubit of quantum
key distributions, and then present a quantum secret sharing scheme where only
product states are employed. As entanglement, especially the inaccessable
multi-entangled state, is not necessary in the present quantum secret sharing
protocol, it may be more applicable when the number of the parties of secret
sharing is large. Its theoretic efficiency is also doubled to approach 100%.


title: Maximal p-norms of entanglement breaking channels

abstract:
  It shown that when one of the components of a product channel is entanglement
breaking, the output state with maximal p-norm is always a product state. This
result complements Shor's theorem that both minimal entropy and Holevo capacity
are additive for entanglement breaking channels. It is also shown how Shor's
results can be recovered from the p-norm results by considering their behavior
for p close to one.


title: Optical Bell-state analysis in the coincidence basis

abstract:
  Many quantum information protocols require a Bell-state measurement of
entangled systems. Most optical Bell-state measurements utilize two-photon
interference at a beam splitter. By creating polarization-entangled photons
with spontaneous parametric down-conversion using a first-order
Hermite-Gaussian pump beam, we invert the usual interference behavior and
perform an incomplete Bell-state measurement in the coincidence basis. We
discuss the possibility of a complete Bell-state measurement in the coincidence
basis using hyperentangled states [Phys. Rev. A, \textbf{58}, R2623 (1998)].


title: On the entanglement structure in quantum cloning

abstract:
  We study the entanglement properties of the output state of a universal
cloning machine. We analyse in particular bipartite and tripartite entanglement
of the clones, and discuss the ``classical limit'' of infinitely many output
copies.


title: Some remarks on Bell's Inequality tests

abstract:
  We emphasize the difficulties of an experiment that can definitely
discriminate between local realistic hidden variables theories and quantum
mechanics using the Bell CHSH inequalities and a real measurement apparatus. In
particular we analyze some examples in which the noise in real instruments can
alter the experimental results, and the nontrivial problem to find a real "fair
sample" of particles to test the inequalities.


title: Reducible field quantization (II): Electrons

abstract:
  Quantization of free Dirac fields is formulated in terms of a reducible
representation of CAR. Similarly to the bosonic case we arrive at field
operators which are indeed operators and not operator valued distributions.
Observables such as four-momentum and charge can be defined without any need of
normal ordering.


title:
The Conal representation of Quantum States and Non Trace-Preserving
  Quantum Operations

abstract:
  We represent generalized density matrices of a $d$-complex dimensional
quantum system as a subcone of a real pointed cone of revolution in
$\mathbb{R}^{d^2}$, or indeed a Minkowskian cone in $\mathbb{E}^{1,d^2-1}$.
Generalized pure states correspond to certain future-directed light-like
vectors of $\mathbb{E}^{1,d^2-1}$. This extension of the Generalized Bloch
Sphere enables us to cater for non-trace-preserving quantum operations, and in
particluar to view the per-outcome effects of generalized measurements. We show
that these consist of the product of an orthogonal transform about the axis of
the cone of revolution and a positive real linear transform. We give detailed
formulae for the one qubit case and express the post-measurement states in
terms of the initial state vectors and measurement vectors. We apply these
results in order to find the information gain versus disturbance tradeoff in
the case of two equiprobable pure states. Thus we recover Fuchs and Peres'
formula in an elegant manner.


title:
Aspects of the competition between atom-field and field-environment
  couplings under the influence of an external source in dispersive
  Jaynes-Cummings model

abstract:
  We give a fully description of the dynamics of an atom dispersively coupled
to a field mode in a dissipative environment fed by an external source. The
competition between the unitary atom-field (which leads to entanglement) and
the dissipative field-environment couplings are investigated in detail. We find
the time evolution of the global atom-field system for any initial state and we
show that atom-field steady state is at most classically correlated. For an
initial state chosen, we evaluate the purity loss of the global system and of
atomic and field subsystems as a function of time. We find that the source will
tend to compensate for the dissipation of the field intensity and to accelerate
decoherence of the global and atomic states. Moreover, we show that the degree
of entanglement of the atom-field state, for the particular initial state
chosen, can be completely quantified by concurrence. Analytical expression for
time evolution of the concurrence is given.


title: General Theorems on Decoherence in the Thermodynamic Limit

abstract:
  We extend the results on decoherence in the thermodynamic limit [M. Frasca,
Phys. Lett. A {\bf 283}, 271 (2001)] to general Hamiltonians. It is shown that
N independent particles, initially properly prepared, have a set of observables
behaving classically in the thermodynamic limit. This particular set of
observables is then coupled to a quantum system that in this way decoheres so
to have the density matrix in a mixed form. This gives a proof of the
generality of this effect.


title: Entropic Geometry from Logic

abstract:
  We produce a probabilistic space from logic, both classical and quantum,
which is in addition partially ordered in such a way that entropy is monotone.
In particular do we establish the following equation:
  Quantitative Probability = Logic + Partiality of Knowledge + Entropy.
  That is: 1. A finitary probability space \Delta^n (=all probability measures
on {1,...,n}) can be fully and faithfully represented by the pair consisting of
the abstraction D^n (=the object up to isomorphism) of a partially ordered set
(\Delta^n,\sqsubseteq), and, Shannon entropy; 2. D^n itself can be obtained via
a systematic purely order-theoretic procedure (which embodies introduction of
partiality of knowledge) on an (algebraic) logic. This procedure applies to any
poset A; D_A\cong(\Delta^n,\sqsubseteq) when A is the n-element powerset and
D_A\cong(\Omega^n,\sqsubseteq), the domain of mixed quantum states, when A is
the lattice of subspaces of a Hilbert space.
  (We refer to http://web.comlab.ox.ac.uk/oucl/publications/tr/rr-02-07.html
for a domain-theoretic context providing the notions of approximation and
content.)

categories: quant-ph gr-qc math-ph math.LO math.MP math.PR


title: Security of quantum key distribution with imperfect devices

abstract:
  We prove the security of the Bennett-Brassard (BB84) quantum key distribution
protocol in the case where the source and detector are under the limited
control of an adversary. Our proof applies when both the source and the
detector have small basis-dependent flaws, as is typical in practical
implementations of the protocol. We derive a general lower bound on the
asymptotic key generation rate for weakly basis-dependent eavesdropping
attacks, and also estimate the rate in some special cases: sources that emit
weak coherent states with random phases, detectors with basis-dependent
efficiency, and misaligned sources and detectors.


title: Bargmann potentials and Marchenko transformations

abstract:
  The Marchenko phase-equivalent transformation of the Schr\"{o}dinger equation
for two coupled channels is discussed. The combination of the Marchenko
transformations valid in the Bargmann potential case is suggested.


title: Trapping atoms in the vacuum field of a cavity

abstract:
  The aim of this work is to find ways to trap an atom in a cavity. In contrast
to other approaches we propose a method where the cavity is basically in the
vacuum state and the atom in the ground state. The idea is to induce a spatial
dependent AC Stark shift by irradiating the atom with a weak laser field, so
that the atom experiences a trapping force. The main feature of our setup is
that dissipation can be strongly suppressed. We estimate the lifetime of the
atom as well as the trapping potential parameters and compare our estimations
with numerical simulations.


title: The polynomial invariants of four qubits

abstract:
  We describe explicitly the algebra of polynomial functions on the Hilbert
space of four qubit states which are invariant under the SLOCC group
$SL(2,{\mathbb C})^{4}$. From this description, we obtain a closed formula for
the hyperdeterminant in terms of low degree invariants.


title:
Method for implementation of universal quantum logic gates in a scalable
  Ising spin quantum computer

abstract:
  We present protocols for implementation of universal quantum gates on an
arbitrary superposition of quantum states in a scalable solid-state Ising spin
quantum computer. The spin chain is composed of identical spins 1/2 with the
Ising interaction between the neighboring spins. The selective excitations of
the spins are provided by the gradient of the external magnetic field. The
protocols are built of rectangular radio-frequency pulses. The phase and
probability errors caused by unwanted transitions are minimized and computed
numerically.


title:
Upper bound by Kolmogorov complexity for the probability in computable
  POVM measurement

abstract:
  We apply algorithmic information theory to quantum mechanics in order to shed
light on an algorithmic structure which inheres in quantum mechanics.
  There are two equivalent ways to define the (classical) Kolmogorov complexity
K(s) of a given classical finite binary string s. In the standard way, K(s) is
defined as the length of the shortest input string for the universal
self-delimiting Turing machine to output s. In the other way, we first
introduce the so-called universal probability m, and then define K(s) as -log_2
m(s) without using the concept of program-size. We generalize the universal
probability to a matrix-valued function, and identify this function with a POVM
(positive operator-valued measure). On the basis of this identification, we
study a computable POVM measurement with countable measurement outcomes
performed upon a finite dimensional quantum system. We show that, up to a
multiplicative constant, 2^{-K(s)} is the upper bound for the probability of
each measurement outcome s in such a POVM measurement. In what follows, the
upper bound 2^{-K(s)} is shown to be optimal in a certain sense.


title: The Boson Normal Ordering Problem and Generalized Bell Numbers

abstract:
  For any function F(x) having a Taylor expansion we solve the boson normal
ordering problem for F[(a*)^r a^s], with r,s positive integers,[a,a*]=1, i.e.
we provide exact and explicit expressions for its normal form which has all a's
to the right. The solution involves integer sequences of numbers which, for r,s
>=1, are generalizations of the conventional Bell and Stirling numbers whose
values they assume for r=s=1. A complete theory of such generalized
combinatorial numbers is given including closed-form expressions (extended
Dobinski - type formulas), recursion relations and generating functions. These
last are special expectation values in boson coherent states.


title:
Amplitude and phase representation of quantum invariants for the time
  dependent harmonic oscillator

abstract:
  The correspondence between classical and quantum invariants is established.
The Ermakov Lewis quantum invariant of the time dependent harmonic oscillator
is translated from the coordinate and momentum operators into amplitude and
phase operators. In doing so, Turski's phase operator as well as
Susskind-Glogower operators are generalized to the time dependent harmonic
oscillator case. A quantum derivation of the Manley-Rowe relations is shown as
an example.


title:
Evolution of quantum systems with a scaling type of time-dependent
  Hamiltonians

abstract:
  We introduce a new class of quantum models with time-dependent Hamiltonians
of a special scaling form. By using a couple of time-dependent unitary
transformations, the time evolution of these models is expressed in terms of
related systems with time-independent Hamiltonians. The mapping of dynamics can
be performed in any dimension, for an arbitrary number of interacting particles
and for any type of the scaling interaction potential. The exact solvability of
a "dual" time-independent Hamiltonian automatically means the exact solvability
of the original problem with model time-dependence.


title: Some Applications for an Euler Angle Parameterization of SU(N) and U(N)

abstract:
  Here we apply our SU(N) and U(N) parameterizations to the question of
entanglement in the two qubit and qubit/qutrit system. In particular, the group
operations which entangle a two qubit pure state will be given, as well as the
corresponding manifold that the operations parameterize. We also give the
volume of this manifold, as well as the hypothesized volume for the set of all
entangled two qubit pure and mixed states. Extension of this work to the
qubit/qutrit system will also be given.


title: Experimental Observation of Quantum Reflection in the High Energy Limit

abstract:
  We present first experimental data on the high energy behavior of helium
atoms quantum reflecting from the nanoscopically disordered surface of a quartz
crystal. The use of the light, stable and inert He atom not only opens the
unique possibility of measuring quantum reflectivity in the thusfar
inaccessible limit of high energies, but also allows the determination of the
gas-solid interaction potential. The specularly reflected intensity from the
rough surface shows a change of 5 orders of magnitude within an incident
angular range of less than 6 degrees. By separating out the influence of
surface disorder the quantum reflection coefficient for the smooth surface is
deduced. Firstly, the data confirm the high energy asymptotic behavior of the
reflection, defined by the non-retarded attractive van der Waals potential. The
experiment shows very good agreement with our calculations covering the entire
energy region, in which also Casimir forces play a role. Parameters for the
gas-solid interaction perfectly match those reported in literature in the
vicinity of the potential minimum.


title: The Instantonic Approach with Non-Equivalent Vacua

abstract:
  We study the quantum-mechanical tunneling phenomenon in models which include
the existence of non-equivalent vacua. For such a purpose we evaluate the
euclidean propagator between two minima of the potential at issue in terms of
the quadratic fluctuations over the corresponding instantons. The effect of the
multi-instanton configurations are included by means of the alternate
dilute-gas approximation.


title: What is the speed of quantum information?

abstract:
  We study the apparent nonlocality of quantum mechanics as a transport
problem. If space is a physical entity through which quantum information (QI)
must be transported, then one can define its speed. If not, QI exists apart
from space, making space in some sense `nonphysical'. But we can still assign a
`speed' of QI to such models based on their properties. In both cases,
classical information must still travel at $c$, though in the latter case the
origin of local spacetime itself is a puzzle. We consider the properties of
different regimes for this speed of QI, and relevant quantum interpretations.
For example, we show that the Many Worlds Interpretation (MWI) is nonlocal
because it is what we call `spatially complete'.


title: Quantum information processing with trapped ions

abstract:
  Experiments directed towards the development of a quantum computer based on
trapped atomic ions are described briefly. We discuss the implementation of
single qubit operations and gates between qubits. A geometric phase gate
between two ion qubits is described. Limitations of the trapped-ion method such
as those caused by Stark shifts and spontaneous emission are addressed.
Finally, we describe a strategy to realize a large-scale device.


title:
Describing the Patterns of Nature: Information and the Structure of
  Physical Theories

abstract: This paper has been withdrawn by the author


title: Optimizing the fast Rydberg quantum gate

abstract:
  The fast phase gate scheme, in which the qubits are atoms confined in sites
of an optical lattice, and gate operations are mediated by excitation of
Rydberg states, was proposed by Jaksch et al. Phys. Rev. Lett. 85, 2208 (2000).
A potential source of decoherence in this system derives from motional heating,
which occurs if the ground and Rydberg states of the atom move in different
optical lattice potentials. We propose to minimize this effect by choosing the
lattice photon frequency \omega so that the ground and Rydberg states have the
same frequency-dependent polarizability \alpha(omega). The results are
presented for the case of Rb.


title: Semiclassical quantisation rules for the Dirac and Pauli equations

abstract:
  We derive explicit semiclassical quantisation conditions for the Dirac and
Pauli equations. We show that the spin degree of freedom yields a contribution
which is of the same order of magnitude as the Maslov correction in
Einstein-Brillouin-Keller quantisation. In order to obtain this result a
generalisation of the notion of integrability for a certain skew product flow
of classical translational dynamics and classical spin precession has to be
derived. Among the examples discussed is the relativistic Kepler problem with
Thomas precession, whose treatment sheds some light on the amazing success of
Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1--91].


title:
Entanglement generation and multiparticle interferometry with neutral
  atoms

abstract:
  We study the preparation and manipulation of states involving a small number
of interacting particles. By controlling the splitting and fusing of potential
wells, we show how to interconvert Mott-insulator-like and trapped BEC-like
states. We also discuss the generation of "Schr\"odinger cat" states by
splitting a microtrap and taking into practical consideration the asymmetry
between the resulting wells. These schemes can be used to perform multiparticle
interferometry with neutral atoms, where interference effects can be observed
only when all the participating particles are measured.


title: Information and fundamental elements of the structure of quantum theory

abstract:
  Niels Bohr wrote: "There is no quantum world. There is only an abstract
quantum physical description. It is wrong to think that the task of physics is
to find out how Nature is. Physics concerns what we can say about Nature." In
an analogous way, von Weizsaecker suggested that the notion of the elementary
alternative, the "Ur", should play a pivotal role when constructing physics.
Both approaches suggest that the concept of information should play an
essential role in the foundations of any scientific description of Nature. We
show that if, in our description of Nature, we use one definite proposition per
elementary constituent of Nature, some of the essential characteristics of
quantum physics, such as the irreducible randomness of individual events,
quantum complementary and quantum entanglement, arise in a natural way. Then
quantum physics is an elementary theory of information.


title: A Local Mathematical Model for EPR-Experiments

abstract:
  In this paper we give a detailed and simplified version of our original
mathematical model published first in the Proceedings of the National Academy
of Science. We hope that this will clarify some misinterpretations of our
original paper.


title:
Photodetachment in superintense fields: the problem of stabilization and
  a role of rescattering wavepacket's fragments

abstract:
  Photodetachment in ultrastrong laser field in two spatial dimensions is
investigated numerically. The problem of an adiabatic stabilization is
discussed, in particular it is shown that a quick drift in the direction of the
electric field and a magnetic drift cannot be avoided simultaneously. A
qualitative behavior of the packet for a short-range binding potential is
contrasted with that for a soft-core potential, in particular dynamical effects
due to a rescattering of the fragments separated from the main packet are
demonstrated.


title:
Logarithmic perturbation theory for radial Klein-Gordon equation with
  screened Coulomb potentials via $\hbar$ expansions

abstract:
  The explicit semiclassical treatment of logarithmic perturbation theory for
the bound-state problem within the framework of the radial Klein-Gordon
equation with attractive real-analytic screened Coulomb potentials, contained
time-component of a Lorentz four-vector and a Lorentz-scalar term, is
developed. Based upon $\hbar$-expansions and suitable quantization conditions a
new procedure for deriving perturbation expansions is offered. Avoiding
disadvantages of the standard approach, new handy recursion formulae with the
same simple form both for ground and excited states have been obtained. As an
example, the perturbation expansions for the energy eigenvalues for the
Hulth\'en potential containing the vector part as well as the scalar component
are considered.


title: Engineering Progressive Decoherence with Quantum Jumps in Charge Qubit

abstract:
  For the Josephson junction charge qubits with macroscopically quantum
natures, we propose a theoretical scheme to observe the loss of quantum
coherence through coupling such qubit system to an engineered reservoir, the
harmonic oscillator mode in the LC circuit formed by the inductor and the
separated capacitors. Similar to the usual cavity QED system in form, this
charge qubit system with engineered couplings shows the quantum jumps (C.P.Sun
et al Fortschr. Phys. \textbf{43}, 585 (1995))in a progressive decoherence
process. Corresponding to two components of superposition of two charge states,
the inductor evolves simultaneously towards two distinct quasi-classical states
entangling with two states of the charge qubit. Then it induces the quantum
decoherence for the induced squeezing macroscopically in the LC mode.


title:
Influence of damping on the vanishing of the electro-optic effect in
  chiral isotropic media

abstract:
  Using first principles, it is demonstrated that radiative damping alone
cannot lead to a nonvanishing electro-optic effect in a chiral isotropic
medium. This conclusion is in contrast with that obtained by a calculation in
which damping effects are included using the standard phenomenological model.
We show that these predictions differ because the phenomenological damping
equations are valid only in regions where the frequencies of the applied
electromagnetic fields are nearly resonant with the atomic transitions. We also
show that collisional damping can lead to a nonvanishing electrooptic effect,
but with a strength sufficiently weak that it is unlikely to be observable
under realistic laboratory conditions.


title: Violation of local uncertainty relations as a signature of entanglement

abstract:
  Entangled states represent correlations between two separate systems that are
too precise to be represented by products of local quantum states. We show that
this limit of precision for the local quantum states of a pair of N-level
systems can be defined by an appropriate class of uncertainty relations. The
violation of such local uncertainty relations may be used as an experimental
test of entanglement generation.


title: The norm-1-property of a quantum observable

abstract:
  A normalized positive operator measure $X\mapsto E(X)$ has the
norm-1-property if $\no{E(X)}=1$ whenever $E(X)\ne O$. This property reflects
the fact that the measurement outcome probabilities for the values of such
observables can be made arbitrary close to one with suitable state
preparations. Some general implications of the norm-1-property are
investigated. As case studies, localization observables, phase observables, and
phase space observables are considered.


title: A Foray into Quantum Dynamics

abstract:
  The dynamics of a quantum mechanical particle in a time-independent potential
are found to contain many interesting phenomena. These are direct consequences
of the (typical) existence of more than one time scale governing the problem.
This gives rise to full revivals of initial wavepackets, fractional revivals
(multiple wavepackets appearing at fractions of the revival time) and the
striking quantum carpets. A variety of analytic techniques are used to consider
the interference that gives rise to these phenomena while skirting calculations
involving cross-terms. Novel results include a new theorem on the weighting
coefficients $a_m$ that govern fractional revivals, a demonstration that
$\Psi_{cl}$, the function that governs the distribution and features of these
fractional revivals, really does behave classically, a treatment of the
wavepacket dephasing in the infinite square well by means of the Poisson
summation formula, and a correct analysis of the spatial distribution of
intermode traces. Also, this work presents a coherent treatment of these
phenomena, which before now did not exist.


title: Quantum Chaos via the Quantum Action

abstract:
  We discuss the concept of the quantum action with the purpose to characterize
and quantitatively compute quantum chaos. As an example we consider in quantum
mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic
coupling - which is classically a chaotic system. We compare Poincar\'e
sections obtained from the quantum action with those from the classical action.


title: Systematic Analysis of Majorization in Quantum Algorithms

abstract:
  Motivated by the need to uncover some underlying mathematical structure of
optimal quantum computation, we carry out a systematic analysis of a wide
variety of quantum algorithms from the majorization theory point of view. We
conclude that step-by-step majorization is found in the known instances of fast
and efficient algorithms, namely in the quantum Fourier transform, in Grover's
algorithm, in the hidden affine function problem, in searching by quantum
adiabatic evolution and in deterministic quantum walks in continuous time
solving a classically hard problem. On the other hand, the optimal quantum
algorithm for parity determination, which does not provide any computational
speed-up, does not show step-by-step majorization. Lack of both speed-up and
step-by-step majorization is also a feature of the adiabatic quantum algorithm
solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum
algorithm for the hidden affine function problem does not make use of any
entanglement while it does obey majorization. All the above results give
support to a step-by-step Majorization Principle necessary for optimal quantum
computation.


title: Determinism beneath Quantum Mechanics

abstract:
  Contrary to common belief, it is not difficult to construct deterministic
models where stochastic behavior is correctly described by quantum mechanical
amplitudes, in precise accordance with the Copenhagen-Bohr-Bohm doctrine. What
is difficult however is to obtain a Hamiltonian that is bounded from below, and
whose ground state is a vacuum that exhibits complicated vacuum fluctuations,
as in the real world.
  Beneath Quantum Mechanics, there may be a deterministic theory with (local)
information loss. This may lead to a sufficiently complex vacuum state, and to
an apparent non-locality in the relation between the deterministic
("ontological") states and the quantum states, of the kind needed to explain
away the Bell inequalities.
  Theories of this kind would not only be appealing from a philosophical point
of view, but may also be essential for understanding causality at Planckian
distance scales.


title:
A common algebraic description for probabilistic and quantum
  computations

abstract:
  We study the computational complexity of the problem SFT (Sum-free Formula
partial Trace): given a tensor formula F over a subsemiring of the complex
field (C,+,.) plus a positive integer k, under the restrictions that all inputs
are column vectors of L2-norm 1 and norm-preserving square matrices, and that
the output matrix is a column vector, decide whether the k-partial trace of
$F\dagg{F}$ is superior to 1/2. The k-partial trace of a matrix is the sum of
its lowermost k diagonal elements. We also consider the promise version of this
problem, where the 1/2 threshold is an isolated cutpoint. We show how to encode
a quantum or reversible gate array into a tensor formula which satisfies the
above conditions, and vice-versa; we use this to show that the promise version
of SFT is complete for the class BPP for formulas over the semiring (Q^+,+,.)
of the positive rational numbers, for BQP in the case of formulas defined over
the field (Q,+,.), and for P in the case of formulas defined over the Boolean
semiring, all under logspace-uniform reducibility. This suggests that the
difference between probabilistic and quantum polynomial-time computers may
ultimately lie in the possibility, in the latter case, of having destructive
interference between computations occuring in parallel.


title: Parity Effects in Spin Decoherence

abstract:
  We demonstrate that decoherence of many-spin systems can drastically differ
from decoherence of single-spin systems. The difference originates at the most
basic level, being determined by parity of the central system, i.e. by whether
the system comprises even or odd number of spin-1/2 entities. Therefore, it is
very likely that similar distinction between the central spin systems of even
and odd parity is important in many other situations. Our consideration
clarifies the physical origin of the unusual two-step decoherence found
previously in the two-spin systems.


title: The Power of LOCCq State Transformations

abstract:
  Reversible state transformations under entanglement non-increasing operations
give rise to entanglement measures. It is well known that asymptotic local
operations and classical communication (LOCC) are required to get a simple
operational measure of bipartite pure state entanglement. For bipartite mixed
states and multipartite pure states it is likely that a more powerful class of
operations will be needed. To this end \cite{BPRST01} have defined more
powerful versions of state transformations (or reducibilities), namely LOCCq
(asymptotic LOCC with a sublinear amount of quantum communication) and CLOCC
(asymptotic LOCC with catalysis). In this paper we show that {\em LOCCq state
transformations are only as powerful as asymptotic LOCC state transformations}
for multipartite pure states. We first generalize the concept of entanglement
gambling from two parties to multiple parties: any pure multipartite entangled
state can be transformed to an EPR pair shared by some pair of parties and that
any irreducible $m$ $(m\ge 2)$ party pure state can be used to create any other
state (pure or mixed), using only local operations and classical communication
(LOCC). We then use this tool to prove the result. We mention some applications
of multipartite entanglement gambling to multipartite distillability and to
characterizations of multipartite minimal entanglement generating sets. Finally
we discuss generalizations of this result to mixed states by defining the class
of {\em cat distillable states}.


title:
Quantum Measurement Problem and Systems Selfdescription in Operators
  Algebras Formalism

abstract:
  Quantum Measurement problem studied in Information Theory approach of systems
selfdescription which exploits the information acquisition incompleteness for
the arbitrary information system. The studied model of measuring system (MS)
consist of measured state S environment E and observer $O$ processing input S
signal.
  $O$ considered as the quantum object which interaction with S,E obeys to
Schrodinger equation (SE). MS incomplete or restricted states for $O$ derived
by the algebraic QM formalism which exploits Segal and $C^*$-algebras. From
Segal theorem for systems subalgebras it's shown that such restricted states
$V^O=|O_j> < O_j|$ describes the classical random 'pointer' outcomes $O_j$
observed by $O$ in the individual events. The 'preferred' basis $|O_j>$ defined
by $O$ state decoherence via $O$ - E interactions.


title: Tripartite GHZ state generation with trapped ion in an optical cavity

abstract:
  We present a single step scheme to generate, experimentally, maximally
entangled tripartite GHZ state in a single ion, using trapped ion interacting
simultaneously with a resonant external laser field and red sideband tuned
quantized cavity field. Besides the simplicity of execution and short operation
time, GHZ state generation is reduction free.
  Pacs: 03.67.-a, 42.50.-p, 03.67.Dd


title: p-Mechanics as a Physical Theory. An Introduction

abstract:
  The paper provides an introduction into p-mechanics, which is a consistent
physical theory suitable for a simultaneous description of classical and
quantum mechanics. p-Mechanics naturally provides a common ground for several
different approaches to quantisation (geometric, Weyl, coherent states,
Berezin, deformation, Moyal, etc.) and has a potential for expansions into
field and string theories. The backbone of p-mechanics is solely the
representation theory of the Heisenberg group. Keywords: Classical mechanics,
quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg
group, orbit method, deformation quantisation, symplectic group, representation
theory, metaplectic representation, Berezin quantisation, Weyl quantisation,
Segal--Bargmann--Fock space, coherent states, wavelet transform, contextual
interpretation, string theory, field theory.

categories: quant-ph math-ph math.FA math.MP math.RT


title: Putting a Spin on the Aharonov-Bohm Oscillations

abstract:
  An experiment that shows the modulation of the Aharonov-Bohm oscillations of
magneto-resistance in a mesoscopic ring is described. Possible theoretical
explanations of this modulation due to the interaction of the electron spin
with the magnetic and electric fields are considered.


title: Wigner Centennial: His Function, and Its Environmental Decoherence

abstract:
  In 1983, Wigner outlined a modified Schr\"odinger--von-Neumann equation of
motion for macroobjects, to describe their typical coupling to the environment.
This equation has become a principal model of environmental decoherence which
is beleived responsible for the emergence ofclassicality in macroscopic quantum
systems. Typically, this happens gradually and asymptotically after a certain
characteristic decoherence time. For the Wigner-function, however, one can
prove that it evolves perfectly into a classical (non-negative) phase space
distribution after a finite time of decoherence.


title: Quantum dissipative systems from theory of continuous measurements

abstract:
  We apply the restricted-path-integral (RPI) theory of non-minimally
disturbing continuous measurements for correct description of frictional
Brownian motion. The resulting master equation is automatically of the Lindblad
form, so that the difficulties typical of other approaches do not exist. In the
special case of harmonic oscillator the known familiar master equation
describing its frictionally driven Brownian motion is obtained. A thermal
reservoir as a measuring environment is considered.


title:
Entanglement-Assisted Coherent Control in Nonreactive Diatom-Diatom
  Scattering

abstract:
  Intriguing quantum effects that result from entangled molecular rovibrational
states are shown to provide a novel means for controlling both differential and
total collision cross sections in identical particle diatom-diatom scattering.
Computational results on elastic and inelastic scattering of para--H$_2$ and
para--H$_2$ are presented, with the collision energy ranging from 400 cm$^{-1}$
to the ultracold regime. The experimental realization and possible extension to
other systems are discussed.


title: When is Quantum Decoherence Dynamics Classical?

abstract:
  A direct classical analog of quantum decoherence is introduced. Similarities
and differences between decoherence dynamics examined quantum mechanically and
classically are exposed via a second-order perturbative treatment and via a
strong decoherence theory, showing a strong dependence on the nature of the
system-environment coupling. For example, for the traditionally assumed linear
coupling, the classical and quantum results are shown to be in exact agreement.


title:
Stochastic Schr\"odinger evolution and symmetric K\"ahler manifolds of
  low dimension

abstract:
  We consider the manifold-valued, stochastic extension of the Schr\"odinger
equation introduced by Hughston (Proc.Roy.Soc.Lond. A452 (1996) 953) in a
manifestly covariant, differential-geometric framework, and examine the
resulting quantum evolution on some specific examples of K\"ahler manifolds
with many symmetries. We find conditions on the curvature for the evolution to
be a `collapse process' in the sense of Brody and Hughston (Proc.Roy.Soc.Lond.
A458 (2002) 1117) or, more generally, a `reduction process', and give examples
that satisfy these conditions. For some of these examples, we show that the
L\"uders projection postulate admits a consistent interpretation and remains
valid in the nonlinear regime.


title:
Non-adiabatic holonomy operators in classical and quantum completely
  integrable systems

abstract:
  Given a completely integrable system, we associate to any connection on its
invariant tori fibred over a parameter manifold the classical and quantum
holonomy operator (generalized Berry's phase factor), without any adiabatic
approximation.

categories: quant-ph math-ph math.DS math.MP nlin.SI


title: Exact two-qubit universal quantum circuit

abstract:
  We provide an analytic way to implement any arbitrary two-qubit unitary
operation, given an entangling two-qubit gate together with local gates. This
is shown to provide explicit construction of a universal quantum circuit that
exactly simulates arbitrary two-qubit operations in SU(4). Each block in this
circuit is given in a closed form solution. We also provide a uniform upper
bound of the applications of the given entangling gates, and find that exactly
half of all the Controlled-Unitary gates satisfy the same upper bound as the
CNOT gate. These results allow for the efficient implementation of operations
in SU(4) required for both quantum computation and quantum simulation.


title: Spin: The Classical to Quantum Connection

abstract:
  We show there exists an exact and continuous gauge transformation between the
Hamilton-Jacobi equation of classical mechanics, and the time-dependent
Schrodinger equation of quantum mechanics. The transformation parameter is
spin-dependent, and is a function of the quantum potential of Bohmian
mechanics.


title: Off-diagonal mixed state phases in unitary evolution

abstract:
  Off-diagonal mixed state phases based upon a concept of orthogonality adapted
to unitary evolution and a proper normalisation condition are introduced. Some
particular instances are analysed and parallel transport leading to the
off-diagonal mixed state geometric phase is delineated. A complete experimental
realisation of the off-diagonal mixed state geometric phases in the qubit case
using polarisation-entangled two-photon interferometry is proposed.


title:
Quantum continuous measurements, dynamical role of information and
  restricted path integrals

abstract:
  The restricted-path-integral (RPI) theory of continuous quantum measurements
including the evolution of the measured systems and phenomenon of decoherence
is reviewed. The measured system is considered as an open quantum system but
without usage of any model of the measurement (of the measuring medium or the
system's environment). The propagator of a measured system (conditioned by the
measurement readout) is presented by RPI. In the important special case of
monitoring an observable the propagator and the system's wave function satisfy
Schroedinger equation with a complex Hamiltonian (depending on the measurement
readout). Going over to the non-selective description of the measurement leads
to the Lindblad master equation. In case of non-minimally disturbing
measurements this gives theory of dissipative systems avoiding difficulties of
other approaches. The whole theory is deduced from first principles of quantum
mechanics. This proves that quantum mechanics includes theory of measurements
and is therefore conceptually closed.


title:
Stable nondegenerate optical parametric oscillation at degenerate
  frequencies in Na:KTP

abstract:
  We report the realization of a light source specifically designed for the
generation of bright continuous-variable entangled beams and for
Heisenberg-limited inteferometry. The source is a nondegenerate, single-mode,
continuous-wave optical parametric oscillator in Na:KTP, operated at frequency
degeneracy and just above threshold, which is also of interest for the study of
critical fluctuations at the transition point. The residual
frequency-difference jitter is $\pm$ 150 kHz for a 3 MHz cold cavity half-width
at half maximum. We observe 4 dB of photon-number-difference squeezing at 200
kHz. The Na:KTP crystal is noncritically phase-matched for a 532 nm pump and
polarization crosstalk is therefore practically nonexistent.


title: Entanglement in SU(2)-invariant quantum spin systems

abstract:
  We analyze the entanglement of SU(2)-invariant density matrices of two spins
$\vec S_{1}$, $\vec S_{2}$ using the Peres-Horodecki criterion. Such density
matrices arise from thermal equilibrium states of isotropic spin systems. The
partial transpose of such a state has the same multiplet structure and
degeneracies as the original matrix with eigenvalue of largest multiplicity
being non-negative. The case $S_{1}=S$, $S_{2}=1/2$ can be solved completely
and is discussed in detail with respect to isotropic Heisenberg spin models.
Moreover, in this case the Peres-Horodecki ciriterion turns out to be a
sufficient condition for non-separability. We also characterize SU(2)-invariant
states of two spins of length 1.


title: Geometric phase and quantum potential

abstract:
  We show that the geometric phase of Levy-Leblond arises from a low of
parallel transport for wave functions and point out that this phase belongs to
a new class of geometric phases due to the presence of a quantum potential.


title:
Efficient Quantum State Tomography for Quantum Information Processing
  using a two-dimensional Fourier Transform Technique

abstract:
  A new method of quantum state tomography for quantum information processing
is described. The method based on two-dimensional Fourier transform technique
involves detection of all the off-diagonal elements of the density matrix in a
two-dimensional experiment. All the diagonal elements are detected in another
one-dimensional experiment. The method is efficient and applicable to a wide
range of spin systems. The proposed method is explained using a 2 qubit system
and demonstrated by tomographing arbitrary complex density matrices of 2 and 4
qubit systems using simulations.


title:
On the equivalence of the CH and CHSH inequalities for two three-level
  systems

abstract:
  In this paper we show a Clauser-Horne (CH) inequality for two three-level
quantum systems or qutrits, alternative to the CH inequality given by
Kaszlikowski et al. [PRA 65, 032118 (2002)]. In contrast to this latter CH
inequality, the new one is shown to be equivalent to the
Clauser-Horne-Shimony-Holt (CHSH) inequality for two qutrits given by Collins
et al. [PRL 88, 040404 (2002)]. Both the CH and CHSH inequalities exhibit the
strongest resistance to noise for a nonmaximally entangled state for the case
of two von Neumann measurements per site, as first shown by Acin et al. [PRA
65, 052325 (2002)]. This equivalence, however, breaks down when one takes into
account the less-than-perfect quantum efficiency of detectors. Indeed, for the
noiseless case, the threshold quantum efficiency above which there is no local
and realistic description of the experiment for the optimal choice of
measurements is found to be 0.814 for the CH inequality, whereas it is equal to
0.828 for the CHSH inequality.


title:
Teleportation of a Bose-Einstein condensate state by controlled elastic
  collisions

abstract:
  A protocol for teleportation of the state of a Bose-Einstein condensate
trapped in a three-well potential is developed. The protocol uses hard-sphere
cross-collision between the condensate modes as a means of generating
entanglement. As Bell state measurement, it is proposed that a homodyne
detection of the condensate quadrature is performed through Josephson coupling
of the condensate mode to another mode in a neighbouring well.


title:
Dynamical disappearance of superposition states in the thermodynamic
  limit

abstract:
  It is shown that a macroscopic superposition state of radiation, strongly
interacting with an ensemble of two-level atoms, is removed generating a
coherent state describing a classical radiation field, when the thermodynamic
limit is taken on the unitary evolution obtained by the Schroedinger equation.
Decoherence appears as a dynamical effect in agreement with a recent proposal
[M. Frasca, Phys. Lett. A 283, 271 (2001)]. To prove that this effect is quite
general, we show that this same behavior appears when a superposition of two
Fock number states is also considered. Higher order corrections are computed
showing that this result tends to become exact in the thermodynamic limit. It
appears as a genuine example of intrinsic collapse of the wave function.


title: Bi-partite mode entanglement of bosonic condensates on tunneling graph

abstract:
  We study a set of $L$ spatial bosonic modes localized on a graph $\Gamma.$
The particles are allowed to tunnel from vertex to vertex by hopping along the
edges of $\Gamma.$ We analyze how, in the exact many-body eigenstates of the
system i.e., Bose-Einstein condensates over single-particle eigenfunctions, the
bi-partite quantum entanglement of a lattice vertex with respect to the rest of
the graph depends on the topology of $\Gamma.$


title:
Fundamental limitation on qubit operations due to the Bloch-Siegert
  Oscillation

abstract:
  We show that if the Rabi frequency is comparable to the Bohr frequency so
that the rotating wave approximation is inappropriate, an extra oscillation is
present with the Rabi oscillation. We discuss how the sensitivity of the degree
of excitation to the phase of the field may pose severe constraints on precise
rotations of quantum bits involving low-frequency transitions. We present a
scheme for observing this effect in an atomic beam.