title: Analysis of dephasing mechanisms in a standing wave dipole trap

abstract:
  We study in detail the mechanisms causing dephasing of hyperfine coherences
of cesium atoms confined by a far off-resonant standing wave optical dipole
trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey
spectroscopy and spin echo techniques, we measure the reversible and
irreversible dephasing times of the ground state coherences. We present an
analytical model to interpret the experimental data and identify the
homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and
detect the atomic hyperfine state is applied at the level of a single atom as
well as for ensembles of up to 50 atoms.


title:
Correlated Quantum Memory: Manipulating Atomic Entanglement via
  Electromagnetically Induced Transparency

abstract:
  We propose a feasible scheme of quantum state storage and manipulation via
electromagnetically induced transparency (EIT) in flexibly $united$
multi-ensembles of three-level atoms. For different atomic array
configurations, one can properly steer the signal and the control lights to
generate different forms of atomic entanglement within the framework of linear
optics. These results shed new light on designing the versatile quantum memory
devices by using, e.g., an atomic grid.


title:
Anharmonic effects on a phonon number measurement of a quantum
  mesoscopic mechanical oscillator

abstract:
  We generalize a proposal for detecting single phonon transitions in a single
nanoelectromechanical system (NEMS) to include the intrinsic anharmonicity of
each mechanical oscillator. In this scheme two NEMS oscillators are coupled via
a term quadratic in the amplitude of oscillation for each oscillator. One NEMS
oscillator is driven and strongly damped and becomes a transducer for phonon
number in the other measured oscillator. We derive the conditions for this
measurement scheme to be quantum limited and find a condition on the size of
the anharmonicity. We also derive the relation between the phase diffusion
back-action noise due to number measurement and the localization time for the
measured system to enter a phonon number eigenstate. We relate both these time
scales to the strength of the measured signal, which is an induced current
proportional to the position of the readout oscillator.


title: An Application of Quantum Finite Automata to Interactive Proof Systems

abstract:
  Quantum finite automata have been studied intensively since their
introduction in late 1990s as a natural model of a quantum computer with
finite-dimensional quantum memory space. This paper seeks their direct
application to interactive proof systems in which a mighty quantum prover
communicates with a quantum-automaton verifier through a common communication
cell. Our quantum interactive proof systems are juxtaposed to
Dwork-Stockmeyer's classical interactive proof systems whose verifiers are
two-way probabilistic automata. We demonstrate strengths and weaknesses of our
systems and further study how various restrictions on the behaviors of
quantum-automaton verifiers affect the power of quantum interactive proof
systems.


title:
Shape invariant potentials in SUSY quantum mechanics and periodic orbit
  theory

abstract:
  We examine shape invariant potentials (excluding those that are obtained by
scaling) in supersymmetric quantum mechanics from the stand-point of periodic
orbit theory. An exact trace formula for the quantum spectra of such potentials
is derived. Based on this result, and Barclay's functional relationship for
such potentials, we present a new derivation of the result that the lowest
order SWKB quantisation rule is exact.


title:
Deutsch-Jozsa Algorithm Revisited in the Domain of Cryptographically
  Significant Boolean Functions

abstract:
  Boolean functions are important building blocks in cryptography for their
wide application in both stream and block cipher systems. For cryptanalysis of
such systems one tries to find out linear functions that are correlated to the
Boolean functions used in the crypto system. Let $f$ be an $n$-variable Boolean
function and its Walsh spectra is denoted by $W_f(\omega)$ at the point $\omega
\in \{0, 1\}^n$. The Boolean function is available in the form of an oracle. We
like to find an $\omega$ such that $W_f(\omega) \neq 0$ as this will provide
one of the linear functions which are correlated to $f$. We show that the
quantum algorithm proposed by Deutsch and Jozsa (1992) solves the above
mentioned problem in constant time. However, the best known classical algorithm
to solve this problem requires exponential time in $n$. We also analyse certain
classes of cryptographically significant Boolean functions and highlight how
the basic Deutsch-Jozsa algorithm performs on them.


title: Quantum algorithm to distinguish Boolean functions of different weights

abstract:
  We exploit Grover operator of database search algorithm for weight decision
algorithm. In this research, weight decision problem is to find an exact weight
w from given two weights as w1 and w2 where w1+w2=1 and 0<w1<w2<1. Firstly, if
a Boolean function is given and when weights are {1/4,3/4}, we can find w with
only one application of Grover operator. Secondly, if we apply k many times of
Grover operator, we can decide w from the set of weights
{sin^2(\frac{k}{2k+1}\frac{\pi}{2}) cos^2(\frac{k}{2k+1}\frac{\pi}{2})}.
Finally, by changing the last two Grover operators with two phase conditions,
we can decide w from given any set of two weights. To decide w with a sure
success, if the quantum algorithm requires O(k) Grover steps, then the best
known classical algorithm requires \Omega(k^s) steps where s>2. Hence the
quantum algorithm achieves at least quadratic speedup.


title:
Manipulating Synchronous Optical Signals with a Double $\Lambda $ Atomic
  Ensemble

abstract:
  We analyze a double $\Lambda $ atomic configuration interacting with two
signal beams and two control beams. Because of the quantum interference between
the two $\Lambda $ channels, the four fields are phase-matched in
electromagnetically induced transparency. Our numerical simulation shows that
this system is able to manipulate synchronous optical signals, such as
generation of optical twin signals, data correction, signal transfer and
amplification in the atomic storage.


title: On the 'Polarized distances between quantum states and observables'

abstract:
  The scheme for construction of distances, presented in the previous paper
quant-ph/0005087, v.1 (Ref. 1) is amended. The formulation of Proposition 1 of
Ref. 1 does not ensure the triangle inequality, therefore some of the
functionals D(a,b) in Ref. 1 are in fact quasi-distances. In this note we
formulate sufficient conditions for a functional D(a,b) of the (squared) form
D(a,b)^2 = f(a)^2 + f(b)^2 - 2f(a)f(b)g(a,b) to be a distance and provide some
examples of such distances. A one parameter generalization of a bounded
distance of the (squared) form D(a,b)^2 = D_0^2 (1 - g(a,b)), which includes
the known Bures-Uhlmann and Hilbert-Schmidt distances between quantum states,
is established.


title: Efficiency of Deterministic Entanglement Transformation

abstract:
  We prove that sufficiently many copies of a bipartite entangled pure state
can always be transformed into some copies of another one with certainty by
local quantum operations and classical communication. The efficiency of such a
transformation is characterized by deterministic entanglement exchange rate,
and it is proved to be always positive and bounded from top by the infimum of
the ratios of Renyi's entropies of source state and target state. A careful
analysis shows that the deterministic entanglement exchange rate cannot be
increased even in the presence of catalysts. As an application, we show that
there can be two incomparable states with deterministic entanglement exchange
rate strictly exceeding 1.


title: Local Fault-tolerant Quantum Computation

abstract:
  We analyze and study the effects of locality on the fault-tolerance threshold
for quantum computation. We analytically estimate how the threshold will depend
on a scale parameter r which estimates the scale-up in the size of the circuit
due to encoding. We carry out a detailed semi-numerical threshold analysis for
concatenated coding using the 7-qubit CSS code in the local and `nonlocal'
setting. First, we find that the threshold in the local model for the [[7,1,3]]
code has a 1/r dependence, which is in correspondence with our analytical
estimate. Second, the threshold, beyond the 1/r dependence, does not depend too
strongly on the noise levels for transporting qubits. Beyond these results, we
find that it is important to look at more than one level of concatenation in
order to estimate the threshold and that it may be beneficial in certain
places, like in the transportation of qubits, to do error correction only
infrequently.


title: Stabilizing qubit coherence via tracking-control

abstract:
  We consider the problem of stabilizing the coherence of a single qubit
subject to Markovian decoherence, via the application of a control Hamiltonian,
without any additional resources. In this case neither quantum error
correction/avoidance, nor dynamical decoupling applies. We show that using
tracking-control, i.e., the conditioning of the control field on the state of
the qubit, it is possible to maintain coherence for finite time durations,
until the control field diverges.


title:
Searching for Decoherence-Free Subspaces in Cavity Quantum
  Electrodynamics

abstract:
  We construct a model which describes a recently performed experiment (Phys.
Rev. A 64, 050301(R) (2001)) in which an entangled state between two modes of a
single cavity is built. Environmental effects are taken into account and the
results agree with the experimental findings. Moreover the model predicts, for
different conditions of the same experiment, a decoherence-free subspace. These
conditions are analyzed and slightly different experiments suggested in order
to test its viability.


title:
Continuous variable tangle, monogamy inequality, and entanglement
  sharing in Gaussian states of continuous variable systems

abstract:
  For continuous-variable systems, we introduce a measure of entanglement, the
continuous variable tangle ({\em contangle}), with the purpose of quantifying
the distributed (shared) entanglement in multimode, multipartite Gaussian
states. This is achieved by a proper convex roof extension of the squared
logarithmic negativity. We prove that the contangle satisfies the
Coffman-Kundu-Wootters monogamy inequality in all three--mode Gaussian states,
and in all fully symmetric $N$--mode Gaussian states, for arbitrary $N$. For
three--mode pure states we prove that the residual entanglement is a genuine
tripartite entanglement monotone under Gaussian local operations and classical
communication. We show that pure, symmetric three--mode Gaussian states allow a
promiscuous entanglement sharing, having both maximum tripartite residual
entanglement and maximum couplewise entanglement between any pair of modes.
These states are thus simultaneous continuous-variable analogs of both the GHZ
and the $W$ states of three qubits: in continuous-variable systems monogamy
does not prevent promiscuity, and the inequivalence between different classes
of maximally entangled states, holding for systems of three or more qubits, is
removed.

categories: quant-ph cond-mat.other math-ph math.MP physics.optics


title: Comparing causality principles

abstract:
  The principle of common cause is discussed as a possible fundamental
principle of physics. Some revisions of Reichenbach's formulation of the
principle are given, which lead to a version given by Bell. Various similar
forms are compared and some equivalence results proved. The further problems of
causality in a quantal system, and indeterministic causal structure, are
addressed, with a view to defining a causality principle applicable to quantum
gravity.


title: Quantum state transformations and the Schubert calculus

abstract:
  Recent developments in mathematics have provided powerful tools for comparing
the eigenvalues of matrices related to each other via a moment map. In this
paper we survey some of the more concrete aspects of the approach with a
particular focus on applications to quantum information theory. After
discussing the connection between Horn's Problem and Nielsen's Theorem, we move
on to characterizing the eigenvalues of the partial trace of a matrix.


title: The Quantum Geometric Phase between Orthogonal States

abstract:
  We show that the geometric phase between any two states, including orthogonal
states, can be computed and measured using the notion of projective
measurement, and we show that a topological number can be extracted in the
geometric phase change in an infinitesimal loop near an orthogonal state. Also,
the Pancharatnam phase change during the passage through an orthogonal state is
shown to be either $\pi$ or zero (mod $2\pi$). All the off-diagonal geometric
phases can be obtained from the projective geometric phase calculated with our
generalized connection.


title: Asymmetric phase-covariant d-dimensional cloning

abstract:
  We consider cloning transformations of d-dimensional states of the form
e^{i\phi_0}|0> + e^{i\phi_1}|1> +...+ e^{i\phi_{d-1}}|d-1> that are covariant
with respect to rotations of the phases \phi_i's. The optimal cloning maps are
easily obtained using a well-defined general characterization of
state-dependent 1 -> 2 cloning transformations in arbitrary dimensions. Our
results apply to symmetric as well as asymmetric cloners, so that the balance
between the fidelity of the two clones can be analyzed.


title:
A dressing of zero-range potentials and electron-molecule scattering
  problem at Ramsauer-Townsend minimum

abstract:
  A dressing technique is used to improve zero range potential (ZRP) model. We
consider a Darboux transformation starting with a ZRP, the result of the
"dressing" gives a potential with non-zero range that depends on a seed
solution parameters. Concepts of the partial waves and partial phases for
non-spherical potential are used in order to perform Darboux transformation.
The problem of scattering on the regular X$_{\hbox{n}}$ and YX$_{\hbox{n}}$
structures is studied. The results of the low-energy electron-molecule
scattering on the dressed ZRPs are illustrated by model calculation for the
configuration and parameters of the silane ($\hbox{SiH}_4$) molecule.
\center{Key words: low-energy scattering, multiple scattering,
Ramsauer-Townsend minimum, silane, zero range potential.


title: Momentum Jumps in Quasi-2D Ballistic Systems

abstract:
  It is shown that the depopulation of magnetoelectric subbands of ballistic
electrons in quasi-2D systems, due to an increased magnetic field parallel to
the 2D electron gas plane, produces a momentum jump of the ballistic electrons
in a direction transverse to the magnetic field. The present technological
achievements allow the observation of this new phenomenon, which can be used to
implement qubit states or electron switches


title: Casimir force between dispersive magnetodielectrics

abstract:
  We extend our approach to the Casimir effect between absorbing dielectric
multilayers [M. S. Tomas, Phys. Rev. A 66, 052103 (2002)] to magnetodielectric
systems. The resulting expression for the force is used to numerically explore
the effect of the medium dispersion on the attractive/repulsive force in a
metal-magnetodielectric system described by the Drude-Lorentz permittivities
and permeabilities.


title: The optimal cloning of quantum coherent states is non-Gaussian

abstract:
  We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.


title: Bell Inequalities for Graph States

abstract:
  We investigate the non-local properties of graph states. To this aim, we
derive a family of Bell inequalities which require three measurement settings
for each party and are maximally violated by graph states. In turn, for each
graph state there is an inequality maximally violated only by that state. We
show that for certain types of graph states the violation of these inequalities
increases exponentially with the number of qubits. We also discuss connections
to other entanglement properties such as the positivity of the partial
transpose or the geometric measure of entanglement.


abstract:
  We present a variation on a gedanken experiment of Hardy [Phys. Rev. Lett. 68
(1992) 2981] that allows, for the first time, a Hardy-type nonlocality proof
for two maximally entangled particles in a four-dimensional Hilbert space.


title: Quantum Mechanics

abstract:
  I consider in this book a formulation of Quantum Mechanics. Usually QM is
formulated based on the notion of time and space, both of which are thought a
priori given quantities or notions. However, when we try to define the notion
of velocity or momentum, we encounter a difficulty as we will see in chapter 1.
The problem is that if the notion of time is given a priori, the velocity is
definitely determined when given a position, which contradicts the uncertainty
principle of Heisenberg. We then set the basis of QM on the notion of position
and momentum operators as in chapter 2. Time of a local system then is defined
approximately as a ratio $|x|/|v|$ between the space coordinate $x$ and the
velocity $v$. In this formulation of QM, we can keep the uncertainty principle,
and time is a quantity that does not have precise values unlike the usually
supposed notion of time has. The feature of local time is that it is a time
proper to each local system, which is defined as a finite set of quantum
mechanical particles. We now have an infinite number of local times that are
unique and proper to each local system. Based on the notion of local time, the
motion inside a local system is described by the usual Schr\"odinger equation.
We investigate such motion in a given local system in part II. This is a usual
quantum mechanics. After some excursion of the investigation of local motion,
we consider in part III the relative relation or motion between plural local
systems. In the final part IV, we will prove that there is at least one
Universe wave function $\phi$ in which all local systems have local motions and
thus local times. This concludes our formulation of Quantum Mechanics.


title: Controlled phase gate for solid-state charge qubits

abstract:
  We describe a mechanism for realizing a controlled phase gate for solid-state
charge qubits. By augmenting the positionally defined qubit with an auxiliary
state, and changing the charge distribution in the three-dot system, we are
able to effectively switch the Coulombic interaction, effecting an entangling
gate. We consider two architectures, and numerically investigate their
robustness to gate noise.


title:
Multiplicativity of Maximal p-Norms in Werner-Holevo channels for $1 \le
  p \le 2$

abstract:
  Recently, King and Ruskai [1] conjectured that the maximal p-norm of the
Werner--Holevo channel is multiplicative for all $1\le p \le 2$. In this paper
we prove this conjecture. Our proof relies on certain convexity and
monotonicity properties of the p--norm.


title:
Energy-time entanglement preservation in plasmon-assisted light
  transmission

abstract:
  We report on experimental evidences of the preservation of energy-time
entanglement for extraordinary plasmonic light transmission through
sub-wavelength metallic hole arrays, and for long range surface plasmon
polaritons. Plasmons are shown to coherently exist at two different times
separated by much more than the plasmons lifetime. This kind of entanglement
involving light and matter is expected to be useful for future processing and
storing of quantum information.


title:
About phase transitions in Bose gases at constant density and constant
  pressure

abstract:
  The phase transitions in Bose gases at constant volume and constant pressure
are considered. New results for the chemical potential, the effective
Landau-Ginzburg free energy and the equation of state of the Bose condensate in
ideal Bose gases with a general form of the energy spectrum are presented.
Unresolved problems are discussed.


title: Quantum circuits with uniformly controlled one-qubit gates

abstract:
  Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.


title:
Solution of the Schroedinger equation with one and two dimensional
  double-well potentials

abstract:
  The Schroedinger equation with one and two dimensional potentials are solved
in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger
equation for various asymmetric double-well potentials have been determined and
the eigenstates are expressed in terms of the orthogonal polynomials. The
solution of the double-well potential in two dimension have been analyzed.


title: Realizations of the osp(2,1) Superalgebra and Related Physical Systems

abstract:
  Eigenvalues and eigenfunction of two-boson 2x2 Hamiltonians in the framework
of the superalgebra osp(2,1) are determined by presenting a similarity
transformation. The Hamiltonians include two bosons and one fermion have been
transformed in the form of the one variable differential equations and the
conditions for its solvability have been discussed. It is observed that the
Hamiltonians of the various physical systems can be written in terms of the
generators of the osp(2,1) superalgebra and under some certain conditions their
eigenstates can exactly be obtained. In particular, the procedure given here is
useful in determining eigenstates of the Jaynes-Cummings Hamiltonians.


title: Spin Precession and Quantum Vacuum

abstract:
  The effect of quantum vacuum on spin precession is investigated. The
radiation reaction is obtained and the time of spin flip
  (up state to down state) or spontaneous decay, is calculated.


title: Bypassing Pauli's theorem

abstract:
  We define a quantum-mechanical time operator that is selfadjoint and
compatible with the energy operator having a spectrum bounded from below. On
their common domain, the operators of time and energy satisfy the expected
canonical commutation relation. Pauli's theorem is bypassed because the
correspondence between time and energy is not given by the standard Fourier
transformation, but by a variant thereof known as the holomorphic Fourier
transformation.


title: The Significance of Information in Quantum Theory

abstract:
  We propose a system of information-theoretic axioms from which we derive the
formalism of quantum theory. Part I is devoted to the conceptual foundations of
the information-theoretic approach. We argue that this approach belongs to the
epistemological framework depicted as a loop of existences. In Part II we
derive the quantum formalism from information-theoretic axioms and we analyze
the twofold role of observer as physical system and as informational agent.
Quantum logical techniques are then introduced, and we prove theorems
reconstructing elements of the formalism. In Part III, we introduce the
formalism of C*-algebras and give it an information theoretic interpretation.
We analyze the conceptual underpinnings of the theory of modular automorphisms
and we give an information-theoretic justification for the emergence of time in
the algebraic approach. We conclude by giving a list of open questions,
including topics in cognitive science, decision theory, and information
technology.


title: Experimental demonstration of quantum memory for light

abstract:
  The information carrier of today's communications, a weak pulse of light, is
an intrinsically quantum object. As a consequence, complete information about
the pulse cannot, even in principle, be perfectly recorded in a classical
memory. In the field of quantum information this has led to a long standing
challenge: how to achieve a high-fidelity transfer of an independently prepared
quantum state of light onto the atomic quantum state? Here we propose and
experimentally demonstrate a protocol for such quantum memory based on atomic
ensembles. We demonstrate for the first time a recording of an externally
provided quantum state of light onto the atomic quantum memory with a fidelity
up to 70%, significantly higher than that for the classical recording. Quantum
storage of light is achieved in three steps: an interaction of light with
atoms, the subsequent measurement on the transmitted light, and the feedback
onto the atoms conditioned on the measurement result. Density of recorded
states 33% higher than that for the best classical recording of light on atoms
is achieved. A quantum memory lifetime of up to 4 msec is demonstrated.


title: Unambiguous discrimination of mixed quantum states

abstract:
  In this paper, we consider the problem of unambiguous discrimination between
a set of mixed quantum states. We first divide the density matrix of each mixed
state into two parts by the fact that it comes from ensemble of pure quantum
states. The first part will not contribute anything to the discrimination, the
second part has support space linearly independent to each other. Then the
problem we consider can be reduced to a problem in which the strategy of set
discrimination can be used in designing measurements to discriminate mixed
states unambiguously. We find a necessary and sufficient condition of
unambiguous mixed state discrimination, and also point out that searching the
optimal success probability of unambiguous discrimination is mathematically the
well-known semi-definite programming problem. A upper bound of the optimal
success probability is also presented. Finally, We generalize the concept of
set discrimination to mixed state and point out that the problem of
discriminating it unambiguously is equivalent to that of unambiguously
discriminating mixed states.


title:
W state generation and effect of cavity photons on the purification of
  dot-like single quantum well excitons

abstract:
  A scheme of three-particle entanglement purification is presented in this
work. The physical system undertaken for investigation is dot-like single
quantum well excitons independently coupled through a single microcavity mode.
The theoretical framework for the proposed scheme is based on the quantum jump
approach for analyzing the progress of the trible-exciton entanglement as a
series of conditional measurement has been taken on the cavity field state. We
first investigate how cavity photon affects the purity of the double-exciton
state and the purification efficiency in two-particle protocol. Then we extend
the two-particle case and conclude that the three-exciton state can be purified
into W state, which involves the one-photon-trapping phenomenon, with a high
yield. Finally, an achievable setup for purification using only modest and
presently feasible technologies is also proposed.


title: Beating the PNS attack in practical quantum cryptography

abstract:
  In practical quantum key distribution, weak coherent state is often used and
the channel transmittance can be very small therefore the protocol could be
totally insecure under the photon-number-splitting attack. We propose an
efficient method to verify the upper bound of the fraction of counts caused by
multi-photon pluses transmitted from Alice to Bob, given whatever type of Eve's
action. The protocol simply uses two coherent states for the signal pulses and
vacuum for decoy pulse. Our verified upper bound is sufficiently tight for QKD
with very lossy channel, in both asymptotic case and non-asymptotic case. The
coherent states with mean photon number from 0.2 to 0.5 can be used in
practical quantum cryptography. We show that so far our protocol is the $only$
decoy-state protocol that really works for currently existing set-ups.


title: Counterfactual reasoning in time-symmetric quantum mechanics

abstract:
  A qualification is suggested for the counterfactual reasoning involved in
some aspects of time-symmetric quantum theory (which involves ensembles
selected by both the initial and final states). The qualification is that the
counterfactual reasoning should only apply to times when the quantum system has
been subjected to physical interactions which place it in a ``measurement-ready
condition" for the unperformed experiment on which the counterfactual reasoning
is based. The defining characteristic of a "measurement-ready condition" is
that a quantum system could be found to have the counterfactually ascribed
property without direct physical interaction with the eigenstate corresponding
to that property.


title:
Hybrid noiseless subsystems for quantum communication over optical
  fibers

abstract:
  We derive the general structure of noiseless subsystems for optical radiation
contained in a sequence of pulses undergoing collective depolarization in an
optical fiber. This result is used to identify optimal ways to implement
quantum communication over a collectively depolarizing channel, which in
general combine various degrees of freedom, such as polarization and phase,
into joint hybrid schemes for protecting quantum coherence.


title: Quantizing the damped harmonic oscillator

abstract:
  We consider the Fermi quantization of the classical damped harmonic
oscillator (dho). In past work on the subject, authors double the phase space
of the dho in order to close the system at each moment in time. For an
infinite-dimensional phase space, this method requires one to construct a
representation of the CAR algebra for each time. We show that unitary dilation
of the contraction semigroup governing the dynamics of the system is a logical
extension of the doubling procedure, and it allows one to avoid the
mathematical difficulties encountered with the previous method.


title: Bundle Theory of Improper Spin Transformations

abstract:
  {\it We first give a geometrical description of the action of the parity
operator ($\hat{P}$) on non relativistic spin ${{1}\over{2}}$ Pauli spinors in
terms of bundle theory. The relevant bundle, $SU(2)\odot \Z_2\to O(3)$, is a
non trivial extension of the universal covering group $SU(2)\to SO(3)$.
$\hat{P}$ is the non relativistic limit of the corresponding Dirac matrix
operator ${\cal P}=i\gamma_0$ and obeys $\hat{P}^2=-1$. Then, from the direct
product of O(3) by $\Z_2$, naturally induced by the structure of the galilean
group, we identify, in its double cover, the time reversal operator ($\hat{T}$)
acting on spinors, and its product with $\hat{P}$. Both, $\hat{P}$ and
$\hat{T}$, generate the group $\Z_4 \times \Z_2$. As in the case of parity,
$\hat{T}$ is the non relativistic limit of the corresponding Dirac matrix
operator ${\cal T}=\gamma^3 \gamma^1$, and obeys $\hat{T}^2=-1$.}


title: Filtering and Control in Quantum Optics

abstract:
  In this thesis we study continuously observed open quantum systems from the
point of view of quantum filtering theory. The conditioned state of the open
system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich
equation in classical filtering theory. The thesis consists out of four
chapters. The first chapter is a brief introduction to quantum probability
theory and quantum stochastic calculus. The second chapter is a description of
a photon counting experiment in continuous time within the framework of Davies
and Srinivas. The third chapter focusses on the derivation of the quantum
filtering or Belavkin equation from the quantum stochastic differential
equation governing the interaction between the open system and its environment,
the electromagnetic field. The fourth chapter shows how the quantum filtering
equation can be used to control quantum systems.


title:
Experimental Generation of Large Quadrature EPR Entanglement with a
  Self-Phase-Locked Type II OPO Below Threshold

abstract:
  We study theoretically and experimentally the quantum properties of a type II
frequency degenerate optical parametric oscillator below threshold with a
quarter-wave plate inserted inside the cavity which induces a linear coupling
between the orthogonally polarized signal and idler fields. This original
device provides a good insight into general properties of two-mode gaussian
states, illustrated in terms of covariance matrix. We report on the
experimental generation of two-mode squeezed vacuum on non-orthogonal
quadratures depending on the plate angle. After a simple operation, the
entanglement is maximized and put into standard form, \textit{i.e.} quantum
correlations and anti-correlations on orthogonal quadratures. A half-sum of
squeezed variances as low as $0.33 \pm 0.02$, well below the unit limit for
inseparability, is obtained and the entanglement measured by the entropy of
formation.


title: Semi-groups and time operators for quantum unstable systems

abstract:
  We use spectral projections of time operator in the Liouville space for
simple quantum scattering systems in order to define a space of unstable
particle states evolving under a contractive semi-group. This space includes
purely exponentially decaying states that correspond to complex eigenvalues of
this semi-group. The construction provides a probabilistic interpretation of
the resonant states characterized in terms of the Hardy class.


title: Quantifying the resource of sharing a reference frame

abstract:
  We define a new quantity called refbit, which allows one to quantify the
resource of sharing a reference frame in quantum communication protocols. By
considering both asymptotic and nonasymptotic protocols we find relations
between refbits and other communication resources. We also consider the same
resources in encoded, reference-frame independent, form. This allows one to
rephrase and unify previous work on phase references, reference frames, and
superselection rules.


title: Doppler effect and frequency-shift in optics

abstract:
  A critical review of frequency-shift phenomena a la Doppler effect is
presented. The importance of Fermi's theory of 1932 is pointed out, and it is
argued that there exists a gap in our understanding of this phenomena at a
fundamental level. Alternative mechanism in terms of photon number oscillations
is suggested for polarization changing experiments. The physical reality of
single photon is revisited, and a possible experimental scheme to test the
alternative mechanism is suggested.


title: Orthocomplementation and compound systems

abstract:
  In their 1936 founding paper on quantum logic, Birkhoff and von Neumann
postulated that the lattice describing the experimental propositions concerning
a quantum system is orthocomplemented. We prove that this postulate fails for
the lattice L_sep describing a compound system consisting of so called
separated quantum systems. By separated we mean two systems prepared in
different ``rooms'' of the lab, and before any interaction takes place. In that
case the state of the compound system is necessarily a product state. As a
consequence, Dirac's superposition principle fails, and therefore L_sep cannot
satisfy all Piron's axioms. In previous works, assuming that L_sep is
orthocomplemented, it was argued that L_sep is not orthomodular and fails to
have the covering property. Here we prove that L_sep cannot admit and
orthocomplementation. Moreover, we propose a natural model for L_sep which has
the covering property.


title:
Criteria for the entanglement of composite systems of identical
  particles

abstract:
  We identify a general criterion for detecting entanglement of pure bipartite
quantum states describing a system of two identical particles. Such a criterion
is based both on the consideration of the Slater-Schmidt number of the
fermionic and bosonic analog of the Schmidt decomposition and on the evaluation
of the von Neumann entropy of the one-particle reduced statistical operators.


title:
Random Quantum Circuits and Pseudo-Random Operators: Theory and
  Applications

abstract:
  Pseudo-random operators consist of sets of operators that exhibit many of the
important statistical features of uniformly distributed random operators. Such
pseudo-random sets of operators are most useful whey they may be parameterized
and generated on a quantum processor in a way that requires exponentially fewer
resources than direct implementation of the uniformly random set. Efficient
pseudo-random operators can overcome the exponential cost of random operators
required for quantum communication tasks such as super-dense coding of quantum
states and approximately secure quantum data-hiding, and enable efficient
stochastic methods for noise estimation on prototype quantum processors. This
paper summarizes some recently published work demonstrating a random circuit
method for the implementation of pseudo-random unitary operators on a quantum
processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further
elaborates the theory and applications of pseudo-random states and operators.


title:
Exact solution of position dependent mass Schroedinger equation by
  supersymmetric quantum mechanics

abstract:
  A supersymmetric technique for the solution of the effective mass Schr\"{o}%
dinger equation is proposed. Exact solutions of the Schroedinger equation
corresponding to a number of potentials are obtained. The potentials are fully
isospectral with the original potentials. The conditions for the shape
invariance of the potentials are discussed.


title: Exactly and Quasi-Exactly Solvable two-mode Bosonic Hamiltonians

abstract:
  We develop a method to determine the eigenvalues and eigenfunctions of
two-boson Hamiltonians include a wide class of quantum optical models. The
quantum Hamiltonians have been transformed in the form of the one variable
differential equation and the conditions for its solvability have been
discussed. Applicability of the method is demonstrated on some simple physical
systems.


title:
Local versus non-local information in quantum information theory:
  formalism and phenomena

abstract:
  In spite of many results in quantum information theory, the complex nature of
compound systems is far from being clear. In general the information is a
mixture of local, and non-local ("quantum") information. To make this point
more clear, we develop and investigate the quantum information processing
paradigm in which parties sharing a multipartite state distill local
information. The amount of information which is lost because the parties must
use a classical communication channel is the deficit. This scheme can be viewed
as complementary to the notion of distilling entanglement. After reviewing the
paradigm, we show that the upper bound for the deficit is given by the relative
entropy distance to so-called psuedo-classically correlated states; the lower
bound is the relative entropy of entanglement. This implies, in particular,
that any entangled state is informationally nonlocal i.e. has nonzero deficit.
We also apply the paradigm to defining the thermodynamical cost of erasing
entanglement. We show the cost is bounded from below by relative entropy of
entanglement. We demonstrate the existence of several other non-local
phenomena. For example,we prove the existence of a form of non-locality without
entanglement and with distinguishability. We analyze the deficit for several
classes of multipartite pure states and obtain that in contrast to the GHZ
state, the Aharonov state is extremely nonlocal (and in fact can be thought of
as quasi-nonlocalisable). We also show that there do not exist states, for
which the deficit is strictly equal to the whole informational content (bound
local information). We then discuss complementary features of information in
distributed quantum systems. Finally we discuss the physical and theoretical
meaning of the results and pose many open questions.


title:
On the quantum, classical and total amount of correlations in a quantum
  state

abstract:
  We give an operational definition of the quantum, classical and total amount
of correlations in a bipartite quantum state. We argue that these quantities
can be defined via the amount of work (noise) that is required to erase
(destroy) the correlations: for the total correlation, we have to erase
completely, for the quantum correlation one has to erase until a separable
state is obtained, and the classical correlation is the maximal correlation
left after erasing the quantum correlations.
  In particular, we show that the total amount of correlations is equal to the
quantum mutual information, thus providing it with a direct operational
interpretation for the first time. As a byproduct, we obtain a direct,
operational and elementary proof of strong subadditivity of quantum entropy.


title: Quantum State Transfer Between Matter and Light

abstract:
  We report on the coherent quantum state transfer from a two-level atomic
system to a single photon. Entanglement between a single photon (signal) and a
two-component ensemble of cold rubidium atoms is used to project the quantum
memory element (the atomic ensemble) onto any desired state by measuring the
signal in a suitable basis. The atomic qubit is read out by stimulating
directional emission of a single photon (idler) from the (entangled) collective
state of the ensemble. Faithful atomic memory preparation and read-out are
verified by the observed correlations between the signal and the idler photons.
These results enable implementation of distributed quantum networking.


title: Multiphoton path entanglement by non-local bunching

abstract:
  Multiphoton path entanglement is created without applying post-selection, by
manipulating the state of stimulated parametric down-conversion. A specific
measurement on one of the two output spatial modes leads to the non-local
bunching of the photons of the other mode, forming the desired multiphoton path
entangled state. We present experimental results for the case of a heralded
two-photon path entangled state and show how to extend this scheme to higher
photon numbers.


title:
Single photo-electron trapping, storage, and detection in a one-electron
  quantum dot

abstract:
  There has been considerable progress in electro-statically emptying, and
re-filling, quantum dots with individual electrons. Typically the quantum dot
is defined by electrostatic gates on a GaAs/AlGaAs modulation doped
heterostructure. We report the filling of such a quantum dot by a single
photo-electron, originating from an individual photon. The electrostatic dot
can be emptied and reset in a controlled fashion before the arrival of each
photon. The trapped photo-electron is detected by a point contact transistor
integrated adjacent to the electrostatic potential trap. Each stored
photo-electron causes a persistent negative step in the transistor channel
current. Such a controllable, benign, single photo-electron detector could
allow for information transfer between flying photon qubits and stored electron
qubits.


title:
Spontaneous Collapse of Unstable Quantum Superposition State: A
  Single-Particle Model of Modified Quantum Dynamics

abstract:
  We propose a modified dynamics of quantum mechanics, in which classical
mechanics of a point mass derives intrinsically in a massive limit of a
single-particle model. On the premise that a position basis plays a special
role in wavefunction collapse, we deduce to formalize spontaneous localization
of wavefunction on the analogy drawn from thermodynamics, in which a
characteristic energy scale and a time scale are introduced to separate quantum
and classical regimes.


title: Generation of Two-Flavor Vortex Atom Laser from a Five-State Medium

abstract:
  Two-flavor atom laser in a vortex state is obtained and analyzed via
electromagnetically induced transparency (EIT) technique in a five-level $M$
type system by using two probe lights with $\pm z$-directional orbital angular
momentum $\pm l\hbar$, respectively. Together with the original transfer
technique of quantum states from light to matter waves, the present result can
be extended to generate continuous two-flavor vortex atom laser with
non-classical atoms.


title: Multiple copy 2-state discrimination with individual measurements

abstract:
  We address the problem of non-orthogonal two-state discrimination when
multiple copies of the unknown state are available. We give the optimal
strategy when only fixed individual measurements are allowed and show that its
error probability saturates the collective (lower) bound asymptotically. We
also give the optimal strategy when adaptivity of individual von Neumann
measurements is allowed (which requires classical communication), and show that
the corresponding error probability is exactly equal to the collective one for
any number of copies. We show that this strategy can be regarded as Bayesian
updating.


title: An alternate model for protective measurements of two-level systems

abstract:
  In this article we propose an alternate model for the so called {\it
protective measurements}, more appropriately {\it adiabatic measurements} of a
spin 1/2 system where the {\it apparatus} is also a quantum system with a {\em
finite dimensional Hilbert space}. This circumvents several technical as well
as conceptual issues that arise when dealing with an infinite dimensional
Hilbert space as in the analysis of conventional Stern-Gerlach experiment. Here
also it is demonstrated that the response of the detector is continuous and it
{\it directly} measures {\em expectation values without altering the state of
the system}(when the unknown original state is a {\it nondegenerate eigenstate
of the system Hamiltonian}, in the limit of {\em ideal} adiabatic conditions.
We have also computed the corrections arising out of the inevitable departures
from ideal adiabaticity i.e the time of measurement being large but finite. To
overcome the {\em conceptual} difficulties with a {\it quantum apparatus}, we
have simulated a {\it classical apparatus} as a {\em large} assembly of
spin-1/2 systems. We end this article with a conclusion and a discussion of
some future issues.


title: Mesoscopic Fluctuations of the Loschmidt Echo

abstract:
  We investigate the time-dependent variance of the fidelity with which an
initial narrow wavepacket is reconstructed after its dynamics is time-reversed
with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we
show that the variance first rises algebraically up to a critical time $t_c$,
after which it decays. To leading order in the effective Planck's constant
$\hbar_{\rm eff}$, this decay is given by the sum of a classical term $\simeq
\exp[-2 \lambda t]$, a quantum term $\simeq 2 \hbar_{\rm eff} \exp[-\Gamma t]$
and a mixed term $\simeq 2 \exp[-(\Gamma+\lambda)t]$. Compared to the behavior
of the average fidelity, this allows for the extraction of the classical
Lyapunov exponent $\lambda$ in a larger parameter range. Our results are
confirmed by numerical simulations.


title: Quantum information with continuous variables

abstract:
  Quantum information is a rapidly advancing area of interdisciplinary
research. It may lead to real-world applications for communication and
computation unavailable without the exploitation of quantum properties such as
nonorthogonality or entanglement. We review the progress in quantum information
based on continuous quantum variables, with emphasis on quantum optical
implementations in terms of the quadrature amplitudes of the electromagnetic
field.


title:
Roughness correction to the Casimir force : Beyond the Proximity Force
  Approximation

abstract:
  We calculate the roughness correction to the Casimir effect in the parallel
plates geometry for metallic plates described by the plasma model. The
calculation is perturbative in the roughness amplitude with arbitrary values
for the plasma wavelength, the plate separation and the roughness correlation
length. The correction is found to be always larger than the result obtained in
the Proximity Force Approximation.


title: Constructing N-qubit entanglement monotones from anti-linear operators

abstract:
  We present a method to construct entanglement measures for pure states of
multipartite qubit systems. The key element of our approach is an antilinear
operator that we call {\em comb} in reference to the {\em hairy-ball theorem}.
For qubits (or spin 1/2) the combs are automatically invariant under
$SL(2,\CC)$. This implies that the {\em filters} obtained from the combs are
entanglement monotones by construction. We give alternative formulae for the
concurrence and the 3-tangle as expectation values of certain antilinear
operators. As an application we discuss inequivalent types of genuine
four-qubit entanglement.


title: Semiclassical limit of the entanglement in closed pure systems

abstract:
  We discuss the semiclassical limit of the entanglement for the class of
closed pure systems. By means of analytical and numerical calculations we
obtain two main results: (i) the short-time entanglement does not depend on
Planck's constant and (ii) the long-time entanglement increases as more
semiclassical regimes are attained. On one hand, this result is in contrast
with the idea that the entanglement should be destroyed when the macroscopic
limit is reached. On the other hand, it emphasizes the role played by
decoherence in the process of emergence of the classical world. We also found
that, for Gaussian initial states, the entanglement dynamics may be described
by an entirely classical entropy in the semiclassical limit.


title: Zero-curvature solutions of the one-dimensional Schrodinger equation

abstract:
  We discuss special k=sqrt{2m(E-V(x))/\hbar^2}=0 (i. e. zero-curvature)
solutions of the one-dimensional Schrodinger equation in several model systems
which have been used as idealized versions of various quantum well structures.
We consider infinite well plus Dirac delta function cases (where E=V(x)=0) and
piecewise-constant potentials, such as asymmetric infinite wells (where
E=V(x)=V_0>0). We also construct supersymmetric partner potentials for several
of the zero-energy solutions in these cases. One application of zero-curvature
solutions in the infinite well plus delta-function case is the construction of
`designer' wavefunctions, namely zero-energy wavefunctions of essentially
arbitrary shape, obtained through the proper placement and choice of strength
of the delta-functions.


title: Computing Spin Networks

abstract:
  We expand a set of notions recently introduced providing the general setting
for a universal representation of the quantum structure on which quantum
information stands. The dynamical evolution process associated with generic
quantum information manipulation is based on the (re)coupling theory of SU(2)
angular momenta. Such scheme automatically incorporates all the essential
features that make quantum information encoding much more efficient than
classical: it is fully discrete; it deals with inherently entangled states,
naturally endowed with a tensor product structure; it allows for generic
encoding patterns. The model proposed can be thought of as the non-Boolean
generalization of the quantum circuit model, with unitary gates expressed in
terms of 3nj coefficients connecting inequivalent binary coupling schemes of
n+1 angular momentum variables, as well as Wigner rotations in the eigenspace
of the total angular momentum. A crucial role is played by elementary j-gates
(6j symbols) which satisfy algebraic identities that make the structure of the
model similar to "state sum models", employed in discretizing Topological
Quantum Field Theories and quantum gravity. The spin network simulator can thus
be viewed also as a Combinatorial QFT model for computation. The semiclassical
limit (large j's) is discussed.


title: Liquid state NMR simulations of quantum many-body problems

abstract:
  Recently developed quantum algorithms suggest that in principle, quantum
computers can solve problems such as simulation of physical systems more
efficiently than classical computers. Much remains to be done to implement
these conceptual ideas into actual quantum computers. As a small-scale
demonstration of their capability, we simulate a simple many-fermion problem,
the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR).
We carefully designed our experiment so that the resource requirement would
scale up polynomially with the size of the quantum system to be simulated. The
experimental results allow us to assess the limits of the degree of quantum
control attained in these kinds of experiments. The simulation of other
physical systems, with different particle statistics, is also discussed.


title:
Efficient decoupling schemes with bounded controls based on Eulerian
  orthogonal arrays

abstract:
  The task of decoupling, i.e., removing unwanted interactions in a system
Hamiltonian and/or couplings with an environment (decoherence), plays an
important role in controlling quantum systems. There are many efficient
decoupling schemes based on combinatorial concepts like orthogonal arrays,
difference schemes and Hadamard matrices. So far these (combinatorial)
decoupling schemes have relied on the ability to effect sequences of
instantaneous, arbitrarily strong control Hamiltonians (bang-bang controls). To
overcome the shortcomings of bang-bang control Viola and Knill proposed a
method called Eulerian decoupling that allows the use of bounded-strength
controls for decoupling. However, their method was not directly designed to
take advantage of the composite structure of multipartite quantum systems. In
this paper we define a combinatorial structure called an Eulerian orthogonal
array. It merges the desirable properties of orthogonal arrays and Eulerian
cycles in Cayley graphs (that are the basis of Eulerian decoupling). We show
that this structure gives rise to decoupling schemes with bounded-strength
control Hamiltonians that can be applied to composite quantum systems with few
body Hamiltonians and special couplings with the environment. Furthermore, we
show how to construct Eulerian orthogonal arrays having good parameters in
order to obtain efficient decoupling schemes.


title:
A new class of quasi-exactly solvable potentials with position dependent
  mass

abstract:
  A new class of quasi exactly solvable potentials with a variable mass in the
Schroedinger equation is presented. We have derived a general expression for
the potentials also including Natanzon confluent potentials. The general
solution of the Schroedinger equation is determined and the eigenstates are
expressed in terms of the orthogonal polynomials.


title: Symmetries of the Jahn Teller System and their Solvability

abstract:
  We present a method of obtaining the quasi exact solution of the Jahn Teller
systems in the framework of osp(2,2) superalgebra. The hamiltonian have been
solved in the Bargmann-Fock space by obtaining an expression as linear and
bilinear combinations of the generators of osp(2,2). In particulare, we have
discussed quasi exact solvability of Exe Jahn-Teller Hamiltonian.


title:
Toward high-precision values of the self energy of non-S states in
  hydrogen and hydrogen-like ions

abstract:
  The method and status of a study to provide numerical, high-precision values
of the self-energy level shift in hydrogen and hydrogen-like ions is described.
Graphs of the self energy in hydrogen-like ions with nuclear charge number
between 20 and 110 are given for a large number of states. The self-energy is
the largest contribution of Quantum Electrodynamics (QED) to the energy levels
of these atomic systems. These results greatly expand the number of levels for
which the self energy is known with a controlled and high precision.
Applications include the adjustment of the Rydberg constant and atomic
calculations that take into account QED effects.


title:
Distinguishing two single-mode Gaussian states by homodyne detection: An
  information-theoretic approach

abstract:
  It is known that the quantum fidelity, as a measure of the closeness of two
quantum states, is operationally equivalent to the minimal overlap of the
probability distributions of the two states over all possible POVMs; the POVM
realizing the minimum is optimal. We consider the ability of homodyne detection
to distinguish two single-mode Gaussian states, and investigate to what extent
it is optimal in this information-theoretic sense. We completely identify the
conditions under which homodyne detection makes an optimal distinction between
two single-mode Gaussian states of the same mean, and show that if the Gaussian
states are pure, they are always optimally distinguished.


title:
Single-photon generation and simultaneous observation of wave and
  particle properties

abstract:
  We describe an experiment that generates single photons on demand and
measures properties accounted to both particle- and wave-like features of
light. The measurement is performed by exploiting data that are sampled
simultaneously in a single experimental run.


title: Transport of quantum noise through random media

abstract:
  We present an experimental study of the propagation of quantum noise in a
multiple scattering random medium. Both static and dynamic scattering
measurements are performed: the total transmission of noise is related to the
mean free path for scattering, while the noise frequency correlation function
determines the diffusion constant. The quantum noise observables are found to
scale markedly differently with scattering parameters compared to classical
noise observables. The measurements are explained with a full quantum model of
multiple scattering.


title:
Decoherence suppression for oscillator-assisted geometric quantum gates
  via symmetrization

abstract:
  We propose a novel symmetrization procedure to beat decoherence for
oscillator-assisted quantum gate operations. The enacted symmetry is related to
the global geometric features of qubits transformation based on ancillary
oscillator modes, e.g. phonons in an ion-trap system. It is shown that the
devised multi-circuit symmetrized evolution endows the system with a two-fold
resilience against decoherence: insensitivity to thermal fluctuations and
quantum dissipation.


title:
Nonadiabatic decoherence control of qubits strongly coupled to continuum
  edge

abstract:
  We propose a method for controlling the decoherence of a driven qubit that is
strongly coupled to a reservoir, when the qubit resonance frequency is close to
a continuum edge of the reservoir spectum. This strong-coupling regime is
outside the scope of existing methods of decoherence control. We demonstate
that an appropriate sequence of nearly abrupt changes of the resonance
frequency can protect the qubit state from decay and decoherence more
effectively than the intuitively obvious alternative, which is to fix the
resonance well within a forbidden bandgap of the reservoir spectrum, as far as
possible from the continuum edge. The "counterintuitive" nonadiabatic method
outlined here can outperform its adiabatic counterparts in maintaining a high
fidelity of quantum logic operations. The remarkable effectiveness of the
proposed method, which requires much lower rates of frequency changes than
previously proposed control methods, is due to the ability of appropriately
alternating detunings from the continuum edge to augment the interference of
the emitted and back-scattered quanta, thereby helping to stabilize the qubit
state against decay. Applications to the control of decoherence near the edge
of radiative, vibrational an photoionization continua are discussed.


title: Asymptotically Optimal Quantum Circuits for d-level Systems

abstract:
  As a qubit is a two-level quantum system whose state space is spanned by |0>,
|1>, so a qudit is a d-level quantum system whose state space is spanned by
|0>,...,|d-1>. Quantum computation has stimulated much recent interest in
algorithms factoring unitary evolutions of an n-qubit state space into
component two-particle unitary evolutions. In the absence of symmetry, Shende,
Markov and Bullock use Sard's theorem to prove that at least C 4^n two-qubit
unitary evolutions are required, while Vartiainen, Moettoenen, and Salomaa
(VMS) use the QR matrix factorization and Gray codes in an optimal order
construction involving two-particle evolutions. In this work, we note that
Sard's theorem demands C d^{2n} two-qudit unitary evolutions to construct a
generic (symmetry-less) n-qudit evolution. However, the VMS result applied to
virtual-qubits only recovers optimal order in the case that d is a power of
two. We further construct a QR decomposition for d-multi-level quantum logics,
proving a sharp asymptotic of Theta(d^{2n}) two-qudit gates and thus closing
the complexity question for all d-level systems (d finite.) Gray codes are not
required, and the optimal Theta(d^{2n}) asymptotic also applies to gate
libraries where two-qudit interactions are restricted by a choice of certain
architectures.


title:
Qubits in phase space: Wigner function approach to quantum error
  correction and the mean king problem

abstract:
  We analyze and further develop a new method to represent the quantum state of
a system of $n$ qubits in a phase space grid of $N\times N$ points (where
$N=2^n$). The method, which was recently proposed by Wootters and co--workers
(Gibbons {\it et al.}, quant-ph/0401155), is based on the use of the elements
of the finite field $GF(2^n)$ to label the phase space axes. We present a
self--contained overview of the method, we give new insights on some of its
features and we apply it to investigate problems which are of interest for
quantum information theory: We analyze the phase space representation of
stabilizer states and quantum error correction codes and present a phase space
solution to the so--called ``mean king problem''.


title: Validity of Quantum Adiabatic Theorem

abstract:
  The consistency of quantum adiabatic theorem has been doubted recently. It is
shown in the present paper that the difference between the adiabatic solution
and the exact solution to the Schrodinger equation with a slowly changing
driving Hamiltonian is small; while the difference between their time
derivatives is not small. This explains why substituting the adiabatic solution
back into Schrodinger equation leads to "inconsisitency" of the adiabatic
theorem. Physics is determined completely by the state vector, and not by its
time drivative. Therefore the quantum adiabatic theorem is physically correct.


title: Entanglement of large atomic samples: a Gaussian state analysis

abstract:
  We present a Gaussian state analysis of the entanglement generation between
two macroscopic atomic ensembles due the continuous probing of collective spin
variables by optical Faraday rotation. The evolution of the mean values and the
variances of the atomic variables is determined and the entanglement is
characterized by the Gaussian entanglement of formation (GEoF) and the
logarithmic negativity. The effects of induced opposite Larmor rotation of the
samples and of light absorption and atomic decay are analyzed in detail.


title: Mutually Unbiased Bases and The Complementarity Polytope

abstract:
  A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope
in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a
geometrical object such a polytope exists for all values of N, while it is
unknown whether it can be made to lie within the body of density matrices
unless N=p^k, where p is prime. We investigate the polytope in order to see if
some values of N are geometrically singled out. One such feature is found: It
is possible to select N^2 facets in such a way that their centers form a
regular simplex if and only if there exists an affine plane of order N. Affine
planes of order N are known to exist if N=p^k; perhaps they do not exist
otherwise. However, the link to the existence of MUBs--if any--remains to be
found.


title:
The Loschmidt echo in classically chaotic systems: Quantum chaos,
  irreversibility and decoherence

abstract:
  The Loschmidt echo (LE) is a measure of the sensitivity of quantum mechanics
to perturbations in the evolution operator. It is defined as the overlap of two
wave functions evolved from the same initial state but with slightly different
Hamiltonians. Thus, it also serves as a quantification of irreversibility in
quantum mechanics.
  In this thesis the LE is studied in systems that have a classical counterpart
with dynamical instability, that is, classically chaotic. An analytical
treatment that makes use of the semiclassical approximation is presented. It is
shown that, under certain regime of the parameters, the LE decays
exponentially. Furthermore, for strong enough perturbations, the decay rate is
given by the Lyapunov exponent of the classical system. Some particularly
interesting examples are given.
  The analytical results are supported by thorough numerical studies. In
addition, some regimes not accessible to the theory are explored, showing that
the LE and its Lyapunov regime present the same form of universality ascribed
to classical chaos. In a sense, this is evidence that the LE is a robust
temporal signature of chaos in the quantum realm.
  Finally, the relation between the LE and the quantum to classical transition
is explored, in particular with the theory of decoherence. Using two different
approaches, a semiclassical approximation to Wigner functions and a master
equation for the LE, it is shown that the decoherence rate and the decay rate
of the LE are equal. The relationship between these quantities results mutually
beneficial, in terms of the broader resources of decoherence theory and of the
possible experimental realization of the LE.


title: Bell's inequality tests: from photons to B-mesons

abstract:
  We analyse the recent claim that a violation of a Bell's inequality has been
observed in the $B$--meson system [A. Go, {\em Journal of Modern Optics} {\bf
51} (2004) 991]. The results of this experiment are a convincing proof of
quantum entanglement in $B$--meson pairs similar to that shown by polarization
entangled photon pairs. However, we conclude that the tested inequality is not
a genuine Bell's inequality and thus cannot discriminate between quantum
mechanics and local realistic approaches.


title: Fault-tolerant Quantum Communication with Minimal Physical Requirements

abstract:
  We describe a novel protocol for a quantum repeater which enables long
distance quantum communication through realistic, lossy photonic channels.
Contrary to previous proposals, our protocol incorporates active purification
of arbitrary errors at each step of the protocol using only two qubits at each
repeater station. Because of these minimal physical requirements, the present
protocol can be realized in simple physical systems such as solid-state single
photon emitters. As an example, we show how nitrogen vacancy color centers in
diamond can be used to implement the protocol, using the nuclear and electronic
spin to form the two qubits.


title: Entanglement tensor for a general pure multipartite quantum state

abstract:
  We propose an entanglement tensor to compute the entanglement of a general
pure multipartite quantum state. We compare the ensuing tensor with the
concurrence for bipartite state and apply the tensor measure to some
interesting examples of entangled three-qubit and four-qubit states. It is
shown that in defining the degree of entanglement of a multi-partite state, one
needs to make assumptions about the willingness of the parties to cooperate. We
also discuss the degree of entanglement of the multi-qubit
$\ket{W_{M}}$-states.


title: Atomic quantum memory: cavity vs single pass schemes

abstract:
  This paper presents a quantum mechanical treatment for both atomic and field
fluctuations of an atomic ensemble interacting with propagating fields, either
in Electromagnetically Induced Transparency or in a Raman situation. The atomic
spin noise spectra and the outgoing field spectra are calculated in both
situations. For suitable parameters both EIT and Raman schemes efficiently
preserve the quantum state of the incident probe field in the transfer process
with the atoms, although a single pass scheme is shown to be intrinsically less
efficient than a cavity scheme.


title: Hartman effect and non-locality in quantum networks

abstract:
  We study the phase time for various quantum mechanical networks having
potential barriers in its arms to find the generic presence of Hartman effect.
In such systems it is possible to control the `super arrival' time in one of
the arms by changing parameters on another, spatially separated from it. This
is yet another quantum nonlocal effect. Negative time delays (time advancement)
and `ultra Hartman effect' with negative saturation times have been observed in
some parameter regimes.


title:
A systematic study on the exact solution of the position dependent mass
  Schroedinger equation

abstract:
  An algebraic method of constructing potentials for which the Schroedinger
equation with position dependent mass can be solved exactly is presented. A
general form of the generators of su(1,1) algebra has been employed with a
unified approach to the problem. Our systematic approach reproduces a number of
earlier results and also leads to some novelties. We show that the solutions of
the Schroedinger equation with position dependent mass are free from the choice
of parameters for position dependent mass. Two classes of potentials are
constructed that include almost all exactly solvable potentials.


title: Resonant and non-resonant Tunneling through a double barrier

abstract:
  An explicit expression is obtained for the phase-time corresponding to
tunneling of a (non-relativistic) particle through two rectangular barriers,
both in the case of resonant and in the case of non-resonant tunneling. It is
shown that the behavior of the transmission coefficient and of the tunneling
phase-time near a resonance is given by expressions with "Breit-Wigner type"
denominators. By contrast, it is shown that, when the tunneling probability is
low (but not negligible), the non-resonant tunneling time depends on the
barrier width and on the distance between the barriers only in a very weak
(exponentially decreasing) way: This can imply in various cases, as well-known,
the highly Superluminal tunneling associated with the so-called "generalized
Hartman Effect"; but we are now able to improve and modify the mathematical
description of such an effect, and to compare more in detail our results with
the experimental data for non-resonant tunneling of photons. Finally, as a
second example, the tunneling phase-time is calculated, and compared with the
available experimental results, in the case of the quantum-mechanical tunneling
of neutrons through two barrier-filters at the resonance energy of the set-up.


title: Pure State Correlations: Chords in Phase Space

abstract:
  The intensity of the overlap of a quantum state with all its phase space
translations defines its quantum correlations. In the case of pure states,
these are invariant with respect to Fourier transformation. The overlaps
themselves are here studied in terms of the Wigner function and its Fourier
transform, i.e., the characteristic function or chord function. Unlike the
Wigner function, the chord function need not be real, but eventual symmetry
with respect to reflections about a phase space point may relate these
representations. Semiclassical approximations for the "classical-like" region
of small chords and for large chords are derived. These lead to an
interpretation of the Fourier invariance in terms of conjugate chords. The
interrelation of large and small (sub-Planck) phase space structures previously
noted in the literature are thus reinterpreted.


title: Scattering and bound states for a class of non-central potentials

abstract:
  We obtain L2-series solutions of the nonrelativistic three-dimensional wave
equation for a large class of non-central potentials that includes, as special
cases, the Aharonov-Bohm, Hartmann, and magnetic monopole potentials. It also
includes contributions from the potential term, cos(theta)/r^2 (in spherical
coordinates). The solutions obtained are for all energies, the discrete (for
bound states) as well as the continuous (for scattering states). The L2 bases
of the solution space are chosen such that the matrix representation of the
wave operator is tridiagonal. The expansion coefficients of the radial and
angular components of the wavefunction are written in terms of orthogonal
polynomials satisfying three-term recursion relations resulting from the matrix
wave equation.


title:
Dynamical Symmetry and Quantum Information Processing with
  Electromagnetically Induced Transparency

abstract:
  We study in detail the interesting dynamical symmetry and its applications in
various atomic systems with electromagnetically induced transparency (EIT) in
this paper. By discovering the symmetrical Lie group of various atomic systems,
such as single-atomic-ensemble composed of complex $m$-level $(m>3)$ atoms, and
$two$-atomic-ensemble and even multi-atomic-ensemble system composed of of
$three$-level atoms etc., one can obtain the general definition of dark-state
polaritons (DSPs), and then the dark-states of these different systems. The
symmetrical properties of the multi-level system and multi-atomic-ensemble
system are shown to be dependent on some characteristic parameters of the EIT
system. Furthermore, a controllable scheme to generate quantum entanglement
between lights or atoms via quantized DSPs theory is discussed and the
robustness of this scheme is analyzed by confirming the validity of adiabatic
passage conditions in this paper.


title: Spin Squeezing via One-Axis Twisting with Coherent Light

abstract:
  We propose a new method of spin squeezing of atomic spin, based on the
interactions between atoms and off-resonant light which are known as
paramagnetic Faraday rotation and fictitious magnetic field of light. Since the
projection process, squeezed light, or special interactions among the atoms are
not required in this method, it can be widely applied to many systems. The
attainable range of the squeezing parameter is S^{-2/5}, where S is the total
spin, which is limited by additional fluctuations imposed by coherent light and
the spherical nature of the spin distribution.


title:
Implementation of projective measurements with linear optics and
  continuous photon counting

abstract:
  We investigate the possibility of implementing a given projection measurement
using linear optics and arbitrarily fast feedforward based on the continuous
detection of photons. In particular, we systematically derive the so-called
Dolinar scheme that achieves the minimum error discrimination of binary
coherent states. Moreover, we show that the Dolinar-type approach can also be
applied to projection measurements in the regime of photonic-qubit signals. Our
results demonstrate that for implementing a projection measurement with linear
optics, in principle, unit success probability may be approached even without
the use of expensive entangled auxiliary states, as they are needed in all
known (near-)deterministic linear-optics proposals.


title:
Complexity of multivariate Feynman-Kac path integration in randomized
  and quantum settings

abstract:
  The Feynman-Kac path integration problem was studied in the worst case
setting by Plaskota et al. (J. Comp. Phys. 164 (2000) 335) for the univariate
case and by Kwas and Li (J. Comp. 19 (2003) 730) for the multivariate case with
d space variables. In this paper we consider the multivariate Feynman-Kac path
integration problem in the randomized and quantum settings. For smooth
multivariate functions, it was proven in Kwas and Li (2003) that the classical
worst case complexity suffers from the curse of dimensionality in d. We show
that in both the randomized and quantum settings the curse of dimensionality is
vanquished, i.e., the number of function evaluations and/or quantum queries
required to compute an e-approximation has a bound independent of d and
depending polynomially on 1/e. The exponents of these polynomials are at most 2
in the randomized setting and at most 1 in the quantum setting. Hence we have
exponential speedup over the classical worst case setting and quadratic speedup
of the quantum setting over the randomized setting. However, both the
randomized and quantum algorithms presented here still require extensive
precomputing, similar to the algorithms of Plaskota et al. (2000) and Kwas and
Li(2003).


title:
A complementarity-based approach to phase in finite-dimensional quantum
  systems

abstract:
  We develop a comprehensive theory of phase for finite-dimensional quantum
systems. The only physical requirement we impose is that phase is complementary
to amplitude. To implement this complementarity we use the notion of mutually
unbiased bases, which exist for dimensions that are powers of a prime. For a
d-dimensional system (qudit) we explicitly construct d+1 classes of maximally
commuting operators, each one consisting of d-1 operators. One of this class
consists of diagonal operators that represent amplitudes (or inversions). By
the finite Fourier transform, it is mapped onto ladder operators that can be
appropriately interpreted as phase variables. We discuss the examples of qubits
and qutrits, and show how these results generalize previous approaches.


title: On the torque on birefringent plates induced by quantum fluctuations

abstract:
  We present detailed numerical calculations of the mechanical torque induced
by quantum fluctuations on two parallel birefringent plates with in plane
optical anisotropy, separated by either vacuum or a liquid (ethanol). The
torque is found to vary as $\sin(2\theta)$, where $\theta$ represents the angle
between the two optical axes, and its magnitude rapidly increases with
decreasing plate separation $d$. For a 40 $\mu$m diameter disk, made out of
either quartz or calcite, kept parallel to a Barium Titanate plate at $d\simeq
100$ nm, the maximum torque (at $\theta={\pi\over 4}$) is of the order of
$\simeq 10^{-19}$ N$\cdot$m. We propose an experiment to observe this torque
when the Barium Titanate plate is immersed in ethanol and the other
birefringent disk is placed on top of it. In this case the retarded van der
Waals (or Casimir-Lifshitz) force between the two birefringent slabs is
repulsive. The disk would float parallel to the plate at a distance where its
net weight is counterbalanced by the retarded van der Waals repulsion, free to
rotate in response to very small driving torques.


title: Adiabatic state preparation in a cavity

abstract:
  The paper discusses the single-mode Jaynes-Cummings model with time dependent
parameters. Solvable models for two-level systems are utilized to consider the
changes in the photon distribution affected by the passage of atoms through the
cavity. It is suggested that such systems may be used as filters to modify the
photon distribution. The effect can be enhanced by repeatedly sending new atoms
through the cavity. We show that such filters can cut out either small or large
photon numbers. It is also shown that the method can be used to narrow down
photon distributions and in this way achieve highly non-classical
sub-Poissonian states. Some limitations and applications of the method are
presented.


title: Crucial Role of Quantum Entanglement in Bulk Properties of Solids

abstract:
  We demonstrate that the magnetic susceptibility of strongly alternating
antiferromagnetic spin-1/2 chains is an entanglement witness. Specifically,
magnetic susceptibility of copper nitrate (CN) measured in 1963 (Berger et al.,
Phys. Rev. 132, 1057 (1963)) cannot be described without presence of
entanglement. A detailed analysis of the spin correlations in CN as obtained
from neutron scattering experiments (Xu et al., Phys. Rev. Lett. 84, 4465
(2000)) provides microscopic support for this interpretation. We present a
quantitative analysis resulting in the critical temperature of 5K in both,
completely independent, experiments below which entanglement exists.


title: Multipartite Nonlocal Quantum Correlations Resistant to Imperfections

abstract:
  We use techniques for lower bounds on communication to derive necessary
conditions in terms of detector efficiency or amount of super-luminal
communication for being able to reproduce with classical local hidden-variable
theories the quantum correlations occurring in EPR-type experiments in the
presence of noise. We apply our method to an example involving n parties
sharing a GHZ-type state on which they carry out measurements and show that for
local-hidden variable theories, the amount of super-luminal classical
communication c and the detector efficiency eta are constrained by eta 2^(-c/n)
= O(n^(-1/6)) even for constant general error probability epsilon = O(1).


title:
Realization of decoherence-free subspace using Multiple-Quantum
  coherences

abstract:
  This letter presents a two-dimensional nuclear magnetic resonance(NMR)
approach for constructing a two-logical-qubit decoherence-free subspace (DFS)
based on the fact that the three protons in a CH3 spin system can not be
resolved in one-dimension NMR spectroscopy, but to a certain extent, can be
distinguished by two-dimensional multiple-quantum NMR. We used four noisy
physical nuclear spins, including three protons and one carbon in the CH3 spin
system, to generate two decoherence-free logical quantum bits. It made full use
of the unaddressed spins which could not be used in one-dimensional spectrum.
Furthermore, we have experimentally demonstrated such an approach. Our
experimental results have shown that our DFS can protect against far more types
of decoherence than the one composed of four noisy physical qubits all with
different chemical shifts. More importantly, this idea may provide new insights
into extending qubit systems in the sense that it effectively utilizes the
magnetically equivalent nuclei.


title: Does Quantum Mechanics allow for Infinite Parallelism?

abstract:
  Recent works have independently suggested that Quantum Mechanics might permit
for procedures that transcend the power of Turing Machines as well as of
`standard' Quantum Computers. These approaches rely on and indicate that
Quantum Mechanics seems to support some infinite variant of classical parallel
computing. We compare this new one with other attempts towards hypercomputation
by separating 1) its principal computing capabilities from 2) realizability
issues. The first are shown to coincide with recursive enumerability; the
second are considered in analogy to `existence' in mathematical logic.


title: Efficient polarization squeezing in optical fibers

abstract:
  We report on a novel and efficient source of polarization squeezing using a
single pass through an optical fiber. Simply passing this Kerr squeezed beam
through a carefully aligned lambda/2 waveplate and splitting it on a
polarization beam splitter, we find polarization squeezing of up to 5.1 +/- 0.3
dB. The experimental setup allows for the direct measurement of the squeezing
angle.


title:
Experimental Simulation of a Pairing Hamiltonian on an NMR Quantum
  Computer

abstract:
  We have developed a concrete quantum simulation scheme and experimentally
simulated a pairing model on an NMR quantum computer. The design of our
experiment includes choosing an appropriate initial state in order to make our
scheme scalable in near future, and the accomplishment of our experiment makes
use of twice Fourier transforms so that our method is applicable to other
physical models. Our results show that the experimental simulation can give the
spectrum of the simulated Hamiltonian. Consequently, the potential power of a
quantum computer on the simulation of complex physical systems is verified.


title:
Exact solutions of the Schrodinger equation with non central potential
  by Nikiforov Uvarov method

abstract:
  The general solutions of Schrodinger equation for non central potential are
obtained by using Nikiforov Uvarov method. The Schrodinger equation with
general non central potential is separated into radial and angular parts and
energy eigenvalues and eigenfunctions for these potentials are derived
analytically. Non central potential is reduced to Coulomb and Hartmann
potential by making special selections, and the obtained solutions are compared
with the solutions of Coulomb and Hartmann ring shaped potentials given in
literature.


title: Cluster States From Heisenberg Interaction

abstract:
  We show that a special type of entangled states, cluster states, can be
created with Heisenberg interactions and local rotations in 2d steps where d is
the dimension of the lattice. We find that, by tuning the coupling strengths,
anisotropic exchange interactions can also be employed to create cluster
states. Finally, we propose electron spins in quantum dots as a possible
realization of a one-way quantum computer based on cluster states.


title: Decoherence and the quantum-classical limit in the presence of chaos

abstract:
  We investigate how decoherence affects the short-time separation between
quantum and classical dynamics for classically chaotic systems, within the
framework of a specific model. For a wide range of parameters, the distance
between the corresponding phase-space distributions depends on a single
parameter $\chi$ that relates an effective Planck constant $\hbar_{\rm eff}$,
the Lyapunov coeffficient, and the diffusion constant. This distance peaks at a
time that depends logarithmically on $\hbar_{\rm eff}$, in agreement with
previous estimations of the separation time for Hamiltonian systems. However,
for $\chi\lesssim 1$, the separation remains small, going down with $\hbar_{\rm
eff}^2$, so the concept of separation time loses its meaning.


title: The Cat nRules

abstract:
  The nRules that are developed in another paper are applied to two versions of
the Schrodinger cat experiment. In version I the initially conscious cat is
made unconscious by a mechanism that is initiated by a radioactive decay. In
version II the initially unconscious cat is awakened by a mechanism that is
initiated by a radioactive decay. In both cases an observer is permitted to
check the statues of the cat at any time during the experiment. In all cases
the nRules correctly and unambiguously predict the conscious experience of the
cat and the observer. Keywords: brain states of observer, stochastic choice,
state reduction, wave collapse.


title: Family of Concurrence Monotones and its Applications

abstract:
  We extend the definition of concurrence into a family of entanglement
monotones, which we call concurrence monotones. We discuss their properties and
advantages as computational manageable measures of entanglement, and show that
for pure bipartite states all measures of entanglement can be written as
functions of the concurrence monotones. We then show that the concurrence
monotones provide bounds on quantum information tasks. As an example, we
discuss their applications to remote entanglement distributions (RED) such as
entanglement swapping and remote preparation of bipartite entangled states
(RPBES). We prove a powerful theorem which states what kind of (possibly mixed)
bipartite states or distributions of bipartite states can not be remotely
prepared. The theorem establishes an upper bound on the amount of
$G$-concurrence (one member in the concurrence family) that can be created
between two single-qudit nodes of quantum networks by means of tripartite RED.
For pure bipartite states the bound on the $G$-concurrence can always be
saturated by RPBES.


title:
Cooling of Nanomechanical Resonator Based on Periodical Coupling to
  Cooper Pair Box

abstract:
  We propose and study an active cooling mechanism for the nanomechanical
resonator (NAMR) based on periodical coupling to a Cooper pair box (CPB), which
is implemented by a designed series of magnetic flux pluses threading through
the CPB. When the initial phonon number of the NAMR is not too large, this
cooling protocol is efficient in decreasing the phonon number by two to three
orders of magnitude. Our proposal is theoretically universal in cooling various
boson systems of single mode. It can be specifically generalized to prepare the
nonclassical state of the NAMR.


title:
Universal quantum computation with electron spins in quantum dots based
  on superpositions of spacetime paths and Coulomb blockade

abstract:
  Using electrostatic gates to control the electron positions, we present a new
controlled-NOT gate based on quantum dots. The qubit states are chosen to be
the spin states of an excess conductor electron in the quantum dot; and the
main ingredients of our scheme are the superpositions of space-time paths of
electrons and the effect of Coulomb blockade. All operations are performed only
on individual quantum dots and are based on fundamental interactions. Without
resorting to spin-spin terms or other assumed interactions, the scheme can be
realized with a dedicated circuit and a necessary number of quantum dots. Gate
fidelity of the quantum computation is also presented.


title:
Some Physical Appearances of Vector Coherent States and CS Related to
  Degenerate Hamiltonians

abstract:
  In the spirit of some earlier work on the construction of vector coherent
states over matrix domains, we compute here such states associated to some
physical Hamiltonians. In particular, we construct vector coherent states of
the Gazeau-Klauder type. As a related problem, we also suggest a way to handle
degeneracies in the Hamiltonian for building coherent states. Specific physical
Hamiltonians studied include a single photon mode interacting with a pair of
fermions, a Hamiltonian involving a single boson and a single fermion, a
charged particle in a three dimensional harmonic force field and the case of a
two-dimensional electron placed in a constant magnetic field, orthogonal to the
plane which contains the electron. In this last example, an interesting modular
structure emerges for two underlying von Neumann algebras, related to opposite
directions of the magnetic field. This leads to the existence of coherent
states built out of KMS states for the system.

categories: quant-ph math-ph math.MP physics.atom-ph


title:
PT and non-PT-Symmetric Solutions of the Schrodinger Equation for the
  Generalized Woods-Saxon Potential

abstract:
  We investigate complex PT and non-PT-symmetric forms of the generalized
Woods- Saxon potential. We also look for exact solutions of the Schrodinger
equation for the PT and/or non-PT-symmetric potentials of the kind mentioned
above. Nikiforov-Uvarov method is used to obtain their energy eigenvalues and
associated eigenfunctions.


title:
Eigenvalues and Eigenfunctions of Woods Saxon Potential in PT Symmetric
  Quantum Mechanics

abstract:
  Using the Nikiforov Uvarov method, we obtained the eigenvalues and
eigenfunctions of the Woods Saxon potential with the negative energy levels
based on the mathematical approach. According to the PT Symmetric quantum
mechanics, we exactly solved the time independent Shcrodinger equation for the
same potential. Results are obtained for the s states.


title: Scattering model for quantum random walk on the hypercube

abstract:
  We elaborate on a model of quantum random walk proposed by Hillery et. al.,
and Jeong et. al., which uses the multiports for quantum "coin tossing". The
dynamics of this model is analyzed for the case when the multiports are
arranged on the hypercube. If the hypercube is attached to semi-infinite lines,
then it can act as a scattering potential, which can be reduced to a quantum
walk on the line with non-unitary evolution. We also show how this model can be
implemented using simple quantum gates.


title: Multicomplementary operators via finite Fourier transform

abstract:
  A complete set of d+1 mutually unbiased bases exists in a Hilbert spaces of
dimension d, whenever d is a power of a prime. We discuss a simple construction
of d+1 disjoint classes (each one having d-1 commuting operators) such that the
corresponding eigenstates form sets of unbiased bases. Such a construction
works properly for prime dimension. We investigate an alternative construction
in which the real numbers that label the classes are replaced by a finite field
having d elements. One of these classes is diagonal, and can be mapped to
cyclic operators by means of the finite Fourier transform, which allows one to
understand complementarity in a similar way as for the position-momentum pair
in standard quantum mechanics. The relevant examples of two and three qubits
and two qutrits are discussed in detail.


title: The Theory Experiment Connection: Rn Space and Inflationary Cosmology

abstract:
  Based on a discussion of the theory experiment connection, it is proposed to
tighten the connection by replacing the real and complex number basis of
physical theories by sets R_{n},C_{n} of length 2n finite binary string
numbers. The form of the numbers in R_{n} is based on the infinite hierarchy of
2n figure outputs from measurements of any physical quantity with an infinite
range (distance, energy, etc.). A space and time based on these numbers is
described. It corresponds to an infinite sequence of spherical scale sections
R_{n,e} (e an integer). Each section has the same number of points but the size
increases exponentially with increasing e. The sections converge towards an
origin which is a space singularity. Iteration of an order preserving
transformation, F_{<} or its inverse shows exponential expansion or contraction
of the space with the origin as a source or sink of space points. The
suitability of R_{n} space as a framework for inflationary cosmology is based
on a constant iteration rate for F_{<} and time dependent e and n=n(t). At t=0
all space is restricted to a region of scale sections R_{n_{0},e} with n_{0}
(small) and e\leq e_{0} (negative). Inflation, which occurs naturally, is
stopped automatically at time t_{I} by increasing n from n_{0} to n_{I}>>n_{0}.
Here n_{I} is such that the outermost \Delta scale sections of R_{n_{0}} space,
which are moving at velocities >c at time t_{I}, are contained in the scale
section R_{n_{I},0} of R_{n_{I}} space. This is needed if R_{n_{I},0} space is
to be similar to the usual R space. Hubble expansion and the redshift are
accounted for by a continuing slow increase in n. Comparison with experimental
data suggests that the rate of increase must be at least one n unit every 30-60
million years.


title: Nonlinear optics with stationary pulses of light

abstract:
  We show that the recently demonstrated technique for generating stationary
pulses of light [Nature {\bf 426}, 638 (2003)] can be extended to localize
optical pulses in all three spatial dimensions in a resonant atomic medium.
This method can be used to dramatically enhance the nonlinear interaction
between weak optical pulses. In particular, we show that an efficient Kerr-like
interaction between two pulses can be implemented as a sequence of several
purely linear optical processes. The resulting process may enable coherent
interactions between single photon pulses.


title: Experimental studies of light propagation and storage

abstract:
  We report on an experimental study of light pulse propagation and storage in
a Rb atomic vapor for different pulse durations, magnetic fields, and atomic
densities, and for two different isotopes. The results have been analyzed and
compared with previous studies.


title:
Exact Solutions of the Duffin Kemmer Petiau Equation for the Deformed
  Hulthen Potential

abstract:
  Using the Nikiforov Uvarov method, an application of the relativistic Duffin
Kemmer Petiau equation in the presence of a deformed Hulthen potential is
presented for spin zero particles. We derived the first order coupled
differential radial equations which enable the energy eigenvalues as well as
the full wavefunctions to be evaluated by using of the Nikiforov Uvarov method
that can be written in terms of the hypergeometric polynomials.


title: Realisation of Hardy's Thought Experiment

abstract:
  We present an experimental realisation of Hardy's thought experiment [Phys.
Rev. Lett. {\bf 68}, 2981 (1992)], using photons. The experiment consists of a
pair of Mach-Zehnder interferometers that interact through photon bunching at a
beam splitter. A striking contradiction is created between the predictions of
quantum mechanics and local hidden variable based theories. The contradiction
relies on non-maximally entangled position states of two particles.


title:
Description of quantum dynamics of open systems based on collision-like
  models

abstract:
  Master equations in the Lindblad form describe evolution of open quantum
systems that is completely positive and simultaneously has a semigroup
property. We analyze a possibility to derive this type of master equations from
an intrinsically discrete dynamics that is modelled as a sequence of collisions
between a given quantum system (a qubit) with particles that form the
environment. In order to illustrate our approach we analyze in detail how a
process of an exponential decay and a process of decoherence can be derived
from a collision-like model in which particular collisions are described by
SWAP and controlled-NOT interactions, respectively.


title:
Stasistically constrained operator associated with additivity of
  communication channel

abstract:
  Additivity of quantum communication channel is discussed in terms of Poisson
process to show it is additive in probability. Poisson process is shown to be
responsible for entanglement which is a rare event.