title:
Models of measurement for quantum fields and for classical continuous
  random fields

abstract:
  A quantum field model for an experiment describes thermal fluctuations
explicitly and quantum fluctuations implicitly, whereas a comparable continuous
random field model would describe both thermal and quantum fluctuations
explicitly. An ideal classical measurement does not affect the results of later
measurements, in contrast to ideal quantum measurements, but we can describe
the consequences of the thermal and quantum fluctuations of classically
non-ideal measurement apparatuses explicitly. Some details of continuous random
fields and of Bell inequalities for random fields will be discussed.


title: Techniques for the Synthesis of Reversible Toffoli Networks

abstract:
  This paper presents novel techniques for the synthesis of reversible networks
of Toffoli gates, as well as improvements to previous methods. Gate count and
technology oriented cost metrics are used. Our synthesis techniques are
independent of the cost metrics. Two new iterative synthesis procedure
employing Reed-Muller spectra are introduced and shown to complement earlier
synthesis approaches. The template simplification suggested in earlier work is
enhanced through introduction of a faster and more efficient template
application algorithm, updated (shorter) classification of the templates, and
presentation of the new templates of sizes 7 and 9. A novel ``resynthesis''
approach is introduced wherein a sequence of gates is chosen from a network,
and the reversible specification it realizes is resynthesized as an independent
problem in hopes of reducing the network cost. Empirical results are presented
to show that the methods are effective both in terms of the realization of all
3x3 reversible functions and larger reversible benchmark specifications.


title: Quantitative entanglement witnesses

abstract:
  Entanglement witnesses provide tools to detect entanglement in experimental
situations without the need of having full tomographic knowledge about the
state. If one estimates in an experiment an expectation value smaller than
zero, one can directly infer that the state has been entangled, or specifically
multi-partite entangled, in the first place. In this article, we emphasize that
all these tests - based on the very same data - give rise to quantitative
estimates in terms of entanglement measures: "If a test is strongly violated,
one can also infer that the state was quantitatively very much entangled". We
consider various measures of entanglement, including the negativity, the
entanglement of formation, and the robustness of entanglement, in the bipartite
and multipartite setting. As examples, we discuss several experiments in the
context of quantum state preparation that have recently been performed.


title: Description of resonances within the rigged Hilbert space

abstract:
  The spectrum of a quantum system has in general bound, scattering and
resonant parts. The Hilbert space includes only the bound and scattering
spectra, and discards the resonances. One must therefore enlarge the Hilbert
space to a rigged Hilbert space, within which the physical bound, scattering
and resonance spectra are included on the same footing. In these lectures, I
will explain how this is done.


title:
Quantum mechanics as a consistency condition on initial and final
  boundary conditions

abstract:
  If the block universe view is correct, the future and the past have similar
status and one would expect physical theories to involve final as well as
initial boundary conditions. A plausible consistency condition between the
initial and final boundary conditions in non-relativistic quantum mechanics
leads to the idea that the properties of macroscopic quantum systems,
relevantly measuring instruments, are uniquely determined by the boundary
conditions. An important element in reaching that conclusion is that
preparations and measurements belong in a special class because they involve
many subsystems, at least some of which do not form superpositions of their
physical properties before the boundary conditions are imposed. It is suggested
that the primary role of the formalism of standard quantum mechanics is to
provide the consistency condition on the boundary conditions rather than the
properties of quantum systems. Expressions are proposed for assigning a set of
(unmeasured) physical properties to a quantum system at all times. The physical
properties avoid the logical inconsistencies implied by the no-go theorems
because they are assigned differently from standard quantum mechanics. Since
measurement outcomes are determined by the boundary conditions, they help
determine, rather than are determined by, the physical properties of quantum
systems.


title: Stark shift control of single optical centers in diamond

abstract:
  Lifetime limited optical excitation lines of single nitrogen vacancy (NV)
defect centers in diamond have been observed at liquid helium temperature. They
display unprecedented spectral stability over many seconds and excitation
cycles. Spectral tuning of the spin selective optical resonances was performed
via the application of an external electric field (i.e. the Stark shift). A
rich variety of Stark shifts were observed including linear as well as
quadratic components. The ability to tune the excitation lines of single NV
centers has potential applications in quantum information processing.


title: Quantized Rotation of Atoms From Photons with Orbital Angular Momentum

abstract:
  We demonstrate the coherent transfer of the orbital angular momentum of a
photon to an atom in quantized units of hbar, using a 2-photon stimulated Raman
process with Laguerre-Gaussian beams to generate an atomic vortex state in a
Bose-Einstein condensate of sodium atoms. We show that the process is coherent
by creating superpositions of different vortex states, where the relative phase
between the states is determined by the relative phases of the optical fields.
Furthermore, we create vortices of charge 2 by transferring to each atom the
orbital angular momentum of two photons.


title:
Anomalies in experimental data for the EPR-Bohm experiment: Are both
  classical and quantum mechanics wrong?

abstract:
  We analyze anomalies in data to test the violation of Bell's inequality for
the EPR-Bohm experiment. We found that the experimental correlations for photon
polarization have an intriguing property. In the experimental data there are
visible non-negligible deviations of probabilities $P_{++}^{\rm{exp}}(\alpha,
\beta), P_{+-}^{\rm{exp}}(\alpha, \beta), P_{-+}^{\rm{exp}}(\alpha, \beta),
P_{--}^{\rm{exp}}(\alpha, \beta) $ from the predictions of quantum mechanics,
namely, $P_{++}(\alpha, \beta)=P_{--}(\alpha, \beta)=
{1/2}\cos^2(\alpha-\beta)$ and $P_{+-}=P_{-+}(\alpha,
\beta)={1/2}\sin^2(\alpha-\beta).$ However, in some mysterious way those
deviations compensate each other and finally the correlation
$E^{\rm{exp}}(\alpha, \beta)= P_{++}^{\rm{exp}}(\alpha, \beta)-
P_{+-}^{\rm{exp}}(\alpha, \beta)- P_{-+}^{\rm{exp}}(\alpha, \beta)+
P_{--}^{\rm{exp}}(\alpha, \beta)$ is in the complete agreement with the
QM-prediction, namely, $E(\alpha, \beta)= P_{++}(\alpha, \beta)- P_{+-}(\alpha,
\beta)- P_{-+}(\alpha, \beta)+ P_{--}(\alpha, \beta)= \cos 2(\alpha-\beta).$
Therefore such anomalies play no role in the Bell's inequality framework.
Nevertheless, other linear combinations of experimental probabilities do not
have such a compensation property. There can be found non-negligible deviations
from predictions of quantum mechanics. Thus neither classical nor quantum model
can pass the whole family of statistical tests given by all possible linear
combinations of the EPR-Bohm probabilities. Does it mean that both models are
wrong?


title:
The one-way communication complexity of the Boolean Hidden Matching
  Problem

abstract:
  We give a tight lower bound of Omega(\sqrt{n}) for the randomized one-way
communication complexity of the Boolean Hidden Matching Problem [BJK04]. Since
there is a quantum one-way communication complexity protocol of O(\log n)
qubits for this problem, we obtain an exponential separation of quantum and
classical one-way communication complexity for partial functions. A similar
result was independently obtained by Gavinsky, Kempe, de Wolf [GKdW06]. Our
lower bound is obtained by Fourier analysis, using the Fourier coefficients
inequality of Kahn Kalai and Linial [KKL88].


title:
Exponential Separation of Quantum and Classical One-Way Communication
  Complexity for a Boolean Function

abstract:
  We give an exponential separation between one-way quantum and classical
communication complexity for a Boolean function. Earlier such a separation was
known only for a relation. A very similar result was obtained earlier but
independently by Kerenidis and Raz [KR06]. Our version of the result gives an
example in the bounded storage model of cryptography, where the key is secure
if the adversary has a certain amount of classical storage, but is completely
insecure if he has a similar amount of quantum storage.


title:
Universal quantum computation in deocoherence-free subspace with neutral
  atoms

abstract:
  We show how realistic cavity-assisted interaction between neutral atoms and
coherent optical pulses, and measurement techniques, combined with optical
transportation of atoms, allow for a universal set of quantum gates acting on
decoherence-free subspace (DFS) in deterministic way. The logical qubits are
immunized to the dominant source of decoherece--dephasing; while, the
influences of additional errors are shown by numerical simulations. We analyze
the performance and stability of all required operations and emphasize that all
techniques we use are feasible with current experimental technology.


title:
Quasi-exact solutions for two interacting electrons in two-dimensional
  anisotropic dots

abstract:
  We present an analysis of the two-dimensional Schrodinger equation for two
electrons interacting via Coulombic force and confined in an anizotropic
harmonic potential. The separable case of wy = 2wx is studied particularly
carefully. The closed-form expressions for bound-state energies and the
corresponding eigenfunctions are found at some particular values of wx. For
highly-accurate determination of energy levels at other values of wx, we apply
an efficient scheme based on the Frobenius expansion.

categories: quant-ph cond-mat.mtrl-sci cond-mat.str-el math-ph math.MP


title: Long-distance quantum key distribution in optical fiber

abstract:
  Use of low-noise detectors can both increase the secret bit rate of
long-distance quantum key distribution (QKD) and dramatically extend the length
of a fibre optic link over which secure key can be distributed. Previous work
has demonstrated use of ultra-low-noise transition-edge sensors (TESs) in a QKD
system with transmission over 50 km. In this work, we demonstrate the potential
of the TESs by successfully generating error-corrected, privacy-amplified key
over 148.7 km of dark optical fibre at a mean photon number mu = 0.1, or 184.6
km of dark optical fibre at a mean photon number of 0.5. We have also exchanged
secret key over 67.5 km that is secure against powerful photon-number-splitting
attacks.


title: Electrical detection of 31P spin quantum states

abstract:
  In recent years, a variety of solid-state qubits has been realized, including
quantum dots, superconducting tunnel junctions and point defects. Due to its
potential compatibility with existing microelectronics, the proposal by Kane
based on phosphorus donors in Si has also been pursued intensively. A key issue
of this concept is the readout of the P quantum state. While electrical
measurements of magnetic resonance have been performed on single spins, the
statistical nature of these experiments based on random telegraph noise
measurements has impeded the readout of single spin states. In this letter, we
demonstrate the measurement of the spin state of P donor electrons in silicon
and the observation of Rabi flops by purely electric means, accomplished by
coherent manipulation of spin-dependent charge carrier recombination between
the P donor and paramagnetic localized states at the Si/SiO2 interface via
pulsed electrically detected magnetic resonance. The electron spin information
is shown to be coupled through the hyperfine interaction with the P nucleus,
which demonstrates the feasibility of a recombination-based readout of nuclear
spins.


title:
All-Fiber Source of Polarization-Entangled Photon Pairs Based on a Novel
  Birefringence Compensated Scheme

abstract:
  We propose a new all-fiber source of polarization-entangled photon pairs for
quantum communications. Fiber birefringence is compensated using Faraday
rotator mirror, resulting in enhanced stability against random polarization
drifts compared to existing schemes.


title: Interference of quantum channels in single photon interferometer

abstract:
  We experimently demonstrate the interference of dephasing quantum channel
using single photon Mach-Zender interferometer. We extract the information
inaccessible to the technology of quantum tomography. Further, We introduce the
application of our results in quantum key distribution.


title: Galilean and Dynamical Invariance of Entanglement in Particle Scattering

abstract:
  Particle systems admit a variety of tensor product structures (TPSs)
depending on the algebra of observables chosen for analysis. Global symmetry
transformations and dynamical transformations may be resolved into local
unitary operators with respect to certain TPSs and not with respect to others.
Symmetry-invariant and dynamical-invariant TPSs are defined and various notions
of entanglement are considered for scattering states.


title: Free-Space distribution of entanglement and single photons over 144 km

abstract:
  Quantum Entanglement is the essence of quantum physics and inspires
fundamental questions about the principles of nature. Moreover it is also the
basis for emerging technologies of quantum information processing such as
quantum cryptography, quantum teleportation and quantum computation. Bell's
discovery, that correlations measured on entangled quantum systems are at
variance with a local realistic picture led to a flurry of experiments
confirming the quantum predictions. However, it is still experimentally
undecided whether quantum entanglement can survive global distances, as
predicted by quantum theory. Here we report the violation of the
Clauser-Horne-Shimony-Holt (CHSH) inequality measured by two observers
separated by 144 km between the Canary Islands of La Palma and Tenerife via an
optical free-space link using the Optical Ground Station (OGS) of the European
Space Agency (ESA). Furthermore we used the entangled pairs to generate a
quantum cryptographic key under experimental conditions and constraints
characteristic for a Space-to-ground experiment. The distance in our experiment
exceeds all previous free-space experiments by more than one order of magnitude
and exploits the limit for ground-based free-space communication; significantly
longer distances can only be reached using air- or space-based platforms. The
range achieved thereby demonstrates the feasibility of quantum communication in
space, involving satellites or the International Space Station (ISS).


title:
Generation of a High-Visibility Four-Photon Entangled State and
  Realization of a Four-Party Quantum Communication Complexity Scenario

abstract:
  We obtain a four-photon polarization-entangled state with a visibility as
high as (95.35\pm 0.45)% directly from a single down-conversion source. A
success probability of (81.54\pm 1.38)% is observed by applying this entangled
state to realize a four-party quantum communication complexity scenario (QCCS),
which comfortably surpass the classical limit of 50%. As a comparison, two
Einstein-Podolsky-Rosen (EPR) pairs are shown to implement the scenario with a
success probability of (73.89\pm 1.33)%. This four-photon state can be used to
fulfill decoherence-free quantum information processing and other advanced
quantum communication schemes.


title: Spectroscopic observation of the rotational Doppler effect

abstract:
  We report on the first spectroscopic observation of the rotational Doppler
shift associated with light beams carrying orbital angular momentum. The effect
is evidenced as the broadening of a Hanle/EIT coherence resonance on Rb vapor
when the two incident Laguerre-Gaussian laser beams have opposite topological
charges. The observations closely agree with theoretical predictions.


title:
Implementations of quantum and classical gates with linear optical
  devices and photon number quantum non-demolition measurement for polarization
  encoded qubits

abstract:
  Aiming the construction of quantum computers and quantum communication
systems based on optical devices, in this work we present possible
implementations of quantum and classical CNOTs gates, as well an optical setup
for generation and distribution of bipartite entangled states, using linear
optical devices and photon number quantum non-demolition measurement.


title: Long distance decoy state quantum key distribution in optical fiber

abstract:
  The theoretical existence of photon-number-splitting attacks creates a
security loophole for most quantum key distribution (QKD) demonstrations that
use a highly attenuated laser source. Using ultra-low-noise, high-efficiency
transition-edge sensor photodetectors, we have implemented the first version of
a decoy-state protocol that incorporates finite statistics without the use of
Gaussian approximations in a one-way QKD system, enabling the creation of
secure keys immune to photon-number-splitting attacks and highly resistant to
Trojan horse attacks over 107 km of optical fiber.


title: Three-party qutrit-state sharing

abstract:
  A three-party scheme for securely sharing an arbitrary unknown single-qutrit
state is presented. Using a general Greenberger-Horne-Zeilinger (GHZ) state as
the quantum channel among the three parties, the quantum information (i.e., the
qutrit state) from the sender can be split in such a way that the information
can be recovered if and only if both receivers collaborate. Moreover, the
generation of the scheme to multi-party case is also sketched.


title: Symmetries and noise in quantum walk

abstract:
  We study some discrete symmetries of unbiased (Hadamard) and biased quantum
walk on a line, which are shown to hold even when the quantum walker is
subjected to environmental effects. The noise models considered in order to
account for these effects are the phase flip, bit flip and generalized
amplitude damping channels. The numerical solutions are obtained by evolving
the density matrix, but the persistence of the symmetries in the presence of
noise is proved using the quantum trajectories approach. We also briefly extend
these studies to quantum walk on a cycle. These investigations can be relevant
to the implementation of quantum walks in various known physical systems. We
discuss the implementation in the case of NMR quantum information processor and
ultra cold atoms.


title: Linear Optical Implemention of a Quantum Network for Quantum Estimation

abstract:
  We present a scheme for simulating the quantum network of quantum estimation
proposed by A. K. Ekert et al. [Phys. Rev. Lett. 88, 217901 (2002)]. We
experimentally implement the scheme with linear optical elements. We perform
overlap measurements of two single-qubit states and entanglement-witness
measurements of some two-qubit states. In addition, it can also be used for
entanglement quantification for some kinds of states. From the other
perspective, we physically realize the positive but not completely positive
map, transposition.


title:
Correlation criteria for Bell type inequalities and entanglement
  detection

abstract:
  We provide a novel criterion for identifying quantum correlation, which
allows us to find connections between Bell type inequalities, entanglement
detection, and correlation. We utilize the criterion to construct witness
operators that can detect genuine multi-qubit entanglement with fewer local
measurements. The connection between identifications of quantum correlation and
Mermin's inequality is discussed. Detection of genuine four-level tripartite
entanglement with two local measurement settings is shown in the same manner.
Further, through the criterion of quantum correlation, we derive a new Bell
inequality for arbitrary high-dimensional bipartite systems, which requires
fewer analyses of the measured outcomes.


title: A family of many-body models which are exactly solvable analytically

abstract:
  We present a family of many-body models which are exactly solvable
analytically. The models are an extended n-body interaction
Lipkin-Meshkov-Glick model which considers spin-flip terms which are associated
with the interaction of an external classical field which coherently
manipulates the state of the system in order to, for example, process quantum
information. The models also describe a two-mode Bose-Einstein condensate with
a Josephson-type interaction which includes n-particle elastic and inelastic
collisions. One of the models corresponds to the canonical two-mode
Bose-Einstein Hamitonian plus a term which we argue must be considered in the
description of the two-mode condensate. Intriguingly, this extra term allows
for an exact and analytical solution of the two-particle collision two-mode BEC
problem. Our results open up an arena to study many-body system properties
analytically.


title: Joint Probabilities Reproducing Three EPR Experiments On Two Qubits

abstract:
  An eight parameter family of the most general nonnegative quadruple
probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3
pairs of analyser settings are used. It is a simultaneous representation of 3
Bohr-incompatible experimental configurations valid for arbitrary quantum
states.


title: Efimov states and their Fano resonances in a neutron-rich nucleus

abstract:
  Asymmetric resonances in elastic n+$^{19}$C scattering are attributed to
Efimov states of such neutron-rich nuclei, that is, three-body bound states of
the n+n+$^{18}$C system when none of the pairs is bound or some of them only
weakly bound. By fitting to the general resonance shape described by Fano, we
extract resonance position, width, and the "Fano profile index". While Efimov
states have been discussed extensively in many areas of physics, there is only
one very recent experimental observation in trimers of cesium atoms. The
conjunction that we present of the Efimov and Fano phenomena may lead to
experimental realization in nuclei.


title: Experimental Violation of Bell Inequality beyond Cirel'son's Bound

abstract:
  The correlations between two qubits belonging to a three-qubit system can
violate the Clauser-Horne-Shimony-Holt-Bell inequality beyond Cirel'son's bound
[A. Cabello, Phys. Rev. Lett. 88, 060403 (2002)]. We experimentally demonstrate
such a violation by 7 standard deviations by using a three-photon
polarization-entangled Greenberger-Horne-Zeilinger state produced by Type-II
spontaneous parametric down-conversion. In addition, using part of our results,
we obtain a violation of the Mermin inequality by 39 standard deviations.


title:
Separability criteria based on the Bloch representation of density
  matrices

abstract:
  We study the separability of bipartite quantum systems in arbitrary
dimensions using the Bloch representation of their density matrix. This
approach enables us to find an alternative characterization of the separability
problem, from which we derive a necessary condition and sufficient conditions
for separability. For a certain class of states the necessary condition and a
sufficient condition turn out to be equivalent, therefore yielding a necessary
and sufficient condition. The proofs of the sufficient conditions are
constructive, thus providing decompositions in pure product states for the
states that satisfy them. We provide examples that show the ability of these
conditions to detect entanglement. In particular, the necessary condition is
proved to be strong enough to detect bound entangled states.


title:
The transition from ontic potentiality to actualization of states in
  quantum mechanical approach to reality: The Proof of a Mathematical Theorem
  to Support It

abstract:
  It is given a preliminary discussion on the ontic nature of quantum states to
be intended as potentialities and on the central role of spin to be considered
as the basic essence of quantum mechanical reality. The possible fundamental
role of potentialities and of spin is evidenced in the framework of physical as
well as of biological reality. After such preliminary deepening, using a
quantum like scheme delineated on the basis of an algebraic structure, it is
given for the first time mathematical demonstration of the transition from
potentiality of states to their actualization as basic mechanism of our
reality.


title:
Towards quantum computing with single atoms and optical cavities on atom
  chips

abstract:
  We report on recent developments in the integration of optical
microresonators into atom chips and describe some fabrication and
implementation challenges. We also review theoretical proposals for quantum
computing with single atoms based on the observation of photons leaking through
the cavity mirrors. The use of measurements to generate entanglement can result
in simpler, more robust and scalable quantum computing architectures. Indeed,
we show that quantum computing with atom-cavity systems is feasible even in the
presence of relatively large spontaneous decay rates and finite photon detector
efficiencies.


title: Manifestations of quantum holonomy in interferometry

abstract:
  Abelian and non-Abelian geometric phases, known as quantum holonomies, have
attracted considerable attention in the past. Here, we show that it is possible
to associate nonequivalent holonomies to discrete sequences of subspaces in a
Hilbert space. We consider two such holonomies that arise naturally in
interferometer settings. For sequences approximating smooth paths in the base
(Grassmann) manifold, these holonomies both approach the standard holonomy. In
the one-dimensional case the two types of holonomies are Abelian and coincide
with Pancharatnam's geometric phase factor. The theory is illustrated with a
model example of projective measurements involving angular momentum coherent
states.


title: Fast cooling of trapped ions using the dynamical Stark shift gate

abstract:
  A laser cooling scheme for trapped ions is presented which is based on the
fast dynamical Stark shift gate, described in [Jonathan etal, PRA 62, 042307].
Since this cooling method does not contain an off resonant carrier transition,
low final temperatures are achieved even in traveling wave light field. The
proposed method may operate in either pulsed or continuous mode and is also
suitable for ion traps using microwave addressing in strong magnetic field
gradients.


title:
New uncertainty relations for tomographic entropy: Application to
  squeezed states and solitons

abstract:
  Using the tomographic probability distribution (symplectic tomogram)
describing the quantum state (instead of the wave function or density matrix)
and properties of recently introduced tomographic entropy associated with the
probability distribution, the new uncertainty relation for the tomographic
entropy is obtained. Examples of the entropic uncertainty relation for squeezed
states and solitons of the Bose--Einstein condensate are considered.


title: Second Quantization and Bogoliubov Approximation

abstract:
  Recent experiments with trapped alkali atoms have drawn enormous interest to
the theoretical studies concerning Bose-Einstein condensation. The purpose of
this paper is to review one of the approaches to study bosonic matter at zero
temperature, namely the Bogoliubov approximation. Review of a necessary tool,
the second quantization, will also be made.


title: Quantum Separability of the vacuum for Scalar Fields with a Boundary

abstract:
  Using the Green's function approach we investigate separability of the vacuum
state of a massless scalar field with a single Dirichlet boundary. Separability
is demonstrated using the positive partial transpose criterion for effective
two-mode Gaussian states of collective operators. In contrast to the vacuum
energy, entanglement of the vacuum is not modified by the presence of the
boundary.


title: Quantum geometry and quantum algorithms

abstract:
  Motivated by algorithmic problems arising in quantum field theories whose
dynamical variables are geometric in nature, we provide a quantum algorithm
that efficiently approximates the colored Jones polynomial. The construction is
based on the complete solution of Chern-Simons topological quantum field theory
and its connection to Wess-Zumino-Witten conformal field theory. The colored
Jones polynomial is expressed as the expectation value of the evolution of the
q-deformed spin-network quantum automaton. A quantum circuit is constructed
capable of simulating the automaton and hence of computing such expectation
value. The latter is efficiently approximated using a standard sampling
procedure in quantum computation.


title: Permutation groups, minimal degrees and quantum computing

abstract:
  We study permutation groups of given minimal degree without the classical
primitivity assumption. We provide sharp upper bounds on the order of a
permutation group of minimal degree m and on the number of its elements of any
given support. These results contribute to the foundations of a non-commutative
coding theory.
  A main application of our results concerns the Hidden Subgroup Problem for
the symmetric group in Quantum Computing. We completely characterize the hidden
subgroups of the symmetric group that can be distinguished from identity with
weak Quantum Fourier Sampling, showing these are exactly the subgroups with
bounded minimal degree. This implies that the weak standard method for the
symmetric group has no advantage whatsoever over classical exhaustive search.


title:
Radiation-pressure cooling and optomechanical instability of a
  micro-mirror

abstract:
  Recent experimental progress in table-top experiments or gravitational-wave
interferometers has enlightened the unique displacement sensitivity offered by
optical interferometry. As the mirrors move in response to radiation pressure,
higher power operation, though crucial for further sensitivity enhancement,
will however increase quantum effects of radiation pressure, or even jeopardize
the stable operation of the detuned cavities proposed for next-generation
interferometers. The appearance of such optomechanical instabilities is the
result of the nonlinear interplay between the motion of the mirrors and the
optical field dynamics. In a detuned cavity indeed, the displacements of the
mirror are coupled to intensity fluctuations, which modifies the effective
dynamics of the mirror. Such "optical spring" effects have already been
demonstrated on the mechanical damping of an electromagnetic waveguide with a
moving wall, on the resonance frequency of a specially designed flexure
oscillator, and through the optomechanical instability of a silica
micro-toroidal resonator. We present here an experiment where a
micro-mechanical resonator is used as a mirror in a very high-finesse optical
cavity and its displacements monitored with an unprecedented sensitivity. By
detuning the cavity, we have observed a drastic cooling of the micro-resonator
by intracavity radiation pressure, down to an effective temperature of 10 K. We
have also obtained an efficient heating for an opposite detuning, up to the
observation of a radiation-pressure induced instability of the resonator.
Further experimental progress and cryogenic operation may lead to the
experimental observation of the quantum ground state of a mechanical resonator,
either by passive or active cooling techniques.


title: Quantum information processing via a lossy bus

abstract:
  We describe a method to perform two qubit measurements and logic operations
on pairs of qubits which each interact with a harmonic oscillator degree of
freedom (the \emph{bus}), but do not directly interact with one another. Our
scheme uses only weak interactions between the qubit and the bus, homodyne
measurements, and single qubit operations. In contrast to earlier schemes, the
technique presented here is extremely robust to photon loss in the bus mode,
and can function with high fidelity even when the rate of photon loss is
comparable to the strength of the qubit-bus coupling.


title:
Single-Shot Generation and Detection of a Two-Photon Generalized
  Binomial State in a Cavity

abstract:
  A "quasi-deterministic" scheme to generate a two-photon generalized binomial
state in a single-mode high-Q cavity is proposed. We also suggest a single-shot
scheme to measure the generated state based on a probe two-level atom that
"reads" the cavity field. The possibility of implementing the schemes is
discussed.


title: Non-statistical Weak Measurements

abstract:
  Non-statistical weak measurements yield weak values that are outside the
range of eigenvalues and are not rare, suggesting that weak values are a
property of every pre-and-post-selected ensemble. They also extend the
applicability and valid regime of weak values.


title:
Univariate Functions for the Hilbert-Schmidt Volumes of the Real and
  Complex Separable Two-Qubit Systems

abstract:
  The (complex) two-qubit systems comprise a 15-dimensional convex set and the
real two-qubit systems, a 9-dimensional convex set. While formulas for the
Hilbert-Schmidt volumes of these two sets are known -- owing to recent
important work of Sommers and Zyczkowski (J. Phys. A {36}, 10115 [2003]) --
formulas have not been so far obtained for the volumes of the separable
subsets. We reduce these two problems to the determination of certain functions
of a single variable.


title: Nonlocality and entanglement in a strange system

abstract:
  We show that the relation between nonlocality and entanglement is subtler
than one naively expects. In order to do this we consider the neutral kaon
system--which is oscillating in time (particle--antiparticle mixing) and
decaying--and describe it as an open quantum system. We consider a Bell--CHSH
inequality and show a novel violation for non--maximally entangled states.
Considering the change of purity and entanglement in time we find that, despite
the fact that only two degrees of freedom at a certain time can be measured,
the neutral kaon system does not behave like a bipartite qubit system.


title:
On parallel composition of zero-knowledge proofs with black-box quantum
  simulators

abstract:
  Let L be a language decided by a constant-round quantum Arthur-Merlin (QAM)
protocol with negligible soundness error and all but possibly the last message
being classical. We prove that if this protocol is zero knowledge with a
black-box, quantum simulator S, then L in BQP. Our result also applies to any
language having a three-round quantum interactive proof (QIP), with all but
possibly the last message being classical, with negligible soundness error and
a black-box quantum simulator.
  These results in particular make it unlikely that certain protocols can be
composed in parallel in order to reduce soundness error, while maintaining zero
knowledge with a black-box quantum simulator. They generalize analogous
classical results of Goldreich and Krawczyk (1990).
  Our proof goes via a reduction to quantum black-box search. We show that the
existence of a black-box quantum simulator for such protocols when L notin BQP
would imply an impossibly-good quantum search algorithm.


title:
Single-photon source characterization with infrared-sensitive
  superconducting single-photon detectors

abstract:
  Single-photon sources and detectors are key enabling technologies in quantum
information processing. Nanowire-based superconducting single-photon detectors
(SSPDs) offer single-photon detection from the visible well into the infrared
with low dark counts, low jitter and short dead times. We report on the high
fidelity characterization (via antibunching and spontaneous emission lifetime
measurements) of a cavity-coupled single-photon source at 902 nm using a pair
of SSPDs. The twin SSPD scheme reported here is well-suited to the
characterization of single-photon sources at telecom wavelengths (1310 nm, 1550
nm).


title: Single-atom as a macroscopic entanglement source

abstract:
  We discuss the generation of a macroscopic entangled state in a single atom
cavity-QED system. The three-level atom in a cascade configuration interacts
dispersively with two classical coherent fields inside a doubly resonant
cavity. We show that a macroscopic entangled state between these two cavity
modes can be generated under large detuning conditions. The entanglement
persists even under the presence of cavity losses.


title: Hawking effects on the entanglement near the Schwarzschild black hole

abstract:
  Hawking radiation effects on an entangled pair near the event horizon of a
Schwarzschild black hole are investigated. The Hawking radiation was found to
degrade both the quantum coherence of the entangled state and the mutual
correlations of the entangled pair. When the black hole evaporated completely,
the measure of entanglement vanished, but the classical correlation between the
entangled pair still remained.


title: Inclusion of non-idealities in the continuous photodetection model

abstract:
  Some non-ideal effects as non-unit quantum efficiency, dark counts, dead time
and cavity losses that occur in experiments are incorporated within the
continuous photodetection model by using the analytical quantum trajectories
approach. We show that in standard photocounting experiments the validity of
the model can be verified, and the formal expression for the quantum jump
superoperator can also be checked.


title: The Chernoff lower bound for symmetric quantum hypothesis testing

abstract:
  We consider symmetric hypothesis testing in quantum statistics, where the
hypotheses are density operators on a finite-dimensional complex Hilbert space,
representing states of a finite quantum system. We prove a lower bound on the
asymptotic rate exponents of Bayesian error probabilities. The bound represents
a quantum extension of the Chernoff bound, which gives the best asymptotically
achievable error exponent in classical discrimination between two probability
measures on a finite set. In our framework, the classical result is reproduced
if the two hypothetic density operators commute. Recently, it has been shown
elsewhere [Phys. Rev. Lett. 98 (2007) 160504] that the lower bound is
achievable also in the generic quantum (noncommutative) case. This implies that
our result is one part of the definitive quantum Chernoff bound.


title:
Optimization of segmented linear Paul traps and transport of stored
  particles

abstract:
  Single ions held in linear Paul traps are promising candidates for a future
quantum computer. Here, we discuss a two-layer microstructured segmented linear
ion trap. The radial and axial potentials are obtained from numeric field
simulations and the geometry of the trap is optimized. As the trap electrodes
are segmented in the axial direction, the trap allows the transport of ions
between different spatial regions. Starting with realistic numerically obtained
axial potentials, we optimize the transport of an ion such that the motional
degrees of freedom are not excited, even though the transport speed far exceeds
the adiabatic regime. In our optimization we achieve a transport within roughly
two oscillation periods in the axial trap potential compared to typical
adiabatic transports that take of the order 100 oscillations. Furthermore
heating due to quantum mechanical effects is estimated and suppression
strategies are proposed.


title: Quantum coherence and population trapping in three-photon processes

abstract:
  The spectroscopic properties of a single, tightly trapped atom are studied,
when the electronic levels are coupled by three laser fields in an $N$-shaped
configuration of levels, whereby a $\Lambda$-type level system is weakly
coupled to a metastable state. We show that depending on the laser frequencies
the response can be tuned from coherent population trapping at two-photon
resonance to novel behaviour at three photon resonance, where the metastable
state can get almost unit occupation in a wide range of parameters. For certain
parameter regimes the system switches spontaneously between dissipative and
coherent dynamics over long time scales.


title: Slipped non-Positive Reduced Dynamics and Entanglement

abstract:
  Non-positive Markov approximations are sometimes used to describe the
dynamics of qubits in weak interaction with suitable environments; the
appearance of negative probabilities is avoided by assuming that the transient
regime eliminates from the possible initial conditions those qubit states which
would otherwise be mapped out of the Bloch sphere by the subsequent Markovian
time-evolution. By means of a simple model, we discuss some physical
inconsistencies of this approach in relation to entanglement; in particular, we
show that slipped non-positive reduced dynamics might create entanglement
through a purely local action.


title:
Entanglement by linear SU(2) transformations: generation and evolution
  of quantum vortex states

abstract:
  We consider the evolution of a two-mode system of bosons under the action of
a Hamiltonian that generates linear SU(2) transformations. The Hamiltonian is
generic in that it represents a host of entanglement mechanisms, which can thus
be treated in a unified way. We start by solving the quantum dynamics
analytically when the system is initially in a Fock state. We show how the two
modes get entangled by evolution to produce a coherent superposition of vortex
states in general, and a single vortex state under certain conditions. The
degree of entanglement between the modes is measured by finding the explicit
analytical dependence of the Von Neumann entropy on the system parameters. The
reduced state of each mode is analyzed by means of its correlation function and
spatial coherence function. Remarkably, our analysis is shown to be equally as
valid for a variety of initial states that can be prepared from a two-mode Fock
state via a unitary transformation and for which the results can be obtained by
mere inspection of the corresponding results for an initial Fock state. As an
example, we consider a quantum vortex as the initial state and also find
conditions for its revival and charge conjugation. While studying the evolution
of the initial vortex state, we have encountered and explained an interesting
situation in which the entropy of the system does not evolve whereas its wave
function does. Although the modal concept has been used throughout the paper,
it is important to note that the theory is equally applicable for a
two-particle system in which each particle is represented by its bosonic
creation and annihilation operators.


title:
Nonadiabatic Transitions for a Decaying Two-Level-System: Geometrical
  and Dynamical Contributions

abstract:
  We study the Landau-Zener Problem for a decaying two-level-system described
by a non-hermitean Hamiltonian, depending analytically on time. Use of a
super-adiabatic basis allows to calculate the non-adiabatic transition
probability P in the slow-sweep limit, without specifying the Hamiltonian
explicitly. It is found that P consists of a ``dynamical'' and a
``geometrical'' factors. The former is determined by the complex adiabatic
eigenvalues E_(t), only, whereas the latter solely requires the knowledge of
\alpha_(+-)(t), the ratio of the components of each of the adiabatic
eigenstates. Both factors can be split into a universal one, depending only on
the complex level crossing points, and a nonuniversal one, involving the full
time dependence of E_(+-)(t). This general result is applied to the
Akulin-Schleich model where the initial upper level is damped with damping
constant $\gamma$. For analytic power-law sweeps we find that Stueckelberg
oscillations of P exist for gamma smaller than a critical value gamma_c and
disappear for gamma > gamma_c. A physical interpretation of this behavior will
be presented by use of a damped harmonic oscillator.


title:
Universality in an Information-theoretic Motivated Nonlinear Schrodinger
  Equation

abstract:
  Using perturbative methods, we analyse a nonlinear generalisation of
Schrodinger's equation that had previously been obtained through
information-theoretic arguments. We obtain analytical expressions for the
leading correction, in terms of the nonlinearity scale, to the energy
eigenvalues of the linear Schrodinger equation in the presence of an external
potential and observe some generic features. In one space dimension these are:
(i) For nodeless ground states, the energy shifts are subleading in the
nonlinearity parameter compared to the shifts for the excited states, (ii) the
shifts for the excited states are due predominantly to contribution from the
nodes of the unperturbed wavefunctions and (iii) the energy shifts for excited
states are positive for small values of a regulating parameter and negative at
large values, vanishing at a universal critical value that is not manifest in
the equation. Some of these features hold true for higher dimensional problems.
We also study two exactly solved nonlinear Schrodinger equations so as to
contrast our observations. Finally, we comment on the possible significance of
our results if the nonlinearity is physically realised.


title: Klein paradox for bound states - A puzzling phenomenon

abstract:
  While Klein paradox is often encountered in the context of scattering of
relativistic particles at a potential barrier, we presently discuss a puzzling
situation that arises with the Klein-Gordon equation for bound states. With the
usual minimal coupling procedure of introducing the interaction potential, a
paradoxical situation arises when the 'hill' becomes a 'well', simulating a
bound-state like situation. The phenomenal phenomenon for bound states is
contrary to the conventional wisdom of quantum mechanics and is analogous to
the well-known Klein paradox, a generic property of relativistic wave
equations.
  PACs Nos. 03.65.Ge, 03.65.Pm


title: How to Extract Entanglement from a Piece of Solid or a Bunch of Neutrons

abstract:
  We review how to obtain spin entangled pairs of fermions from a Fermi gas. An
experiment with neutrons is proposed in order to get such pairs.


title: Unconditional security at a low cost

abstract:
  By simulating four quantum key distribution (QKD) experiments and analyzing
one decoy-state QKD experiment, we compare two data post-processing schemes
based on security against individual attack by L\"{u}tkenhaus, and
unconditional security analysis by Gottesman-Lo-L\"{u}tkenhaus-Preskill. Our
results show that these two schemes yield close performances. Since the Holy
Grail of QKD is its unconditional security, we conclude that one is better off
considering unconditional security, rather than restricting to individual
attacks.


title: Relation between quantum tunneling times for bosons

abstract: This paper has been withdrawn by the authors


title:
Proposed experiment to test the non-locality hypothesis in transient
  light-interference phenomena

abstract:
  The transient phenomena of the Mach-Zender interferometer are discussed. To
test the non-locality hypothesis, a single mode laser with a large coherence
length is used. The behavior of a photon and its wave packets in the paths of
the interferometer are discussed. Coherent photons have wave packets that
overlap, thus their interference pattern is influenced by the overlap of the
wave packets of other photons in transient phenomena. The proposed transient
light-interference experiment will provide experimental data testing the
non-locality hypothesis.


title: Limitations on entropic Bell inequalities

abstract:
  The derivation of Bell inequalities in terms of quantum statistical
(thermodynamic) entropies is considered. Inequalities of the Wigner form are
derived but shown to be extremely limiting in their applicability due to the
nature of the density matrices involved. This also helps to identify a
limitation in the Cerf-Adami inequalities.


title:
Analysis of an experimental quantum logic gate by complementary
  classical operations

abstract:
  Quantum logic gates can perform calculations much more efficiently than their
classical counterparts. However, the level of control needed to obtain a
reliable quantum operation is correspondingly higher. In order to evaluate the
performance of experimental quantum gates, it is therefore necessary to
identify the essential features that indicate quantum coherent operation. In
this paper, we show that an efficient characterization of an experimental
device can be obtained by investigating the classical logic operations on a
pair of complementary basis sets. It is then possible to obtain reliable
predictions about the quantum coherent operations of the gate such as
entanglement generation and Bell state discrimination even without performing
these operations directly.


title:
Witnessing Entanglement with Second-Order Interference and Stokes
  Parameters

abstract:
  We propose to use Stokes parameter as an entanglement witness for correlated
EPR mixed states of light. Such states can be generated with a beam splitter
acting on two mixed squeezed states of light. Stokes witness operators are
closely related to the Hanbury-Brown and Twiss interference and can be used to
test entanglement in balanced homodyne experiments involving fluctuations of
quantum quadratures of the electric field.


title: Quantum information becomes classical when distributed to many users

abstract:
  Any physical transformation that equally distributes quantum information over
a large number M of users can be approximated by a classical broadcasting of
measurement outcomes. The accuracy of the approximation is at least of the
order 1/M. In particular, quantum cloning of pure and mixed states can be
approximated via quantum state estimation. As an example, for optimal qubit
cloning with 10 output copies, a single user has error probability p > 0.45 in
distinguishing classical from quantum output--a value close to the error
probability of the random guess.


title: A Bell Theorem with no locality assumption

abstract:
  We prove here a version of Bell Theorem that does not assume locality. As a
consequence classical realism, and not locality, is the common source of the
violation by nature of all Bell Inequalities.


title:
Joint Spectrum Mapping of Polarization Entanglement in Spontaneous
  Parametric Down-conversion

abstract:
  Polarization-entangled photon pairs can be efficiently prepared into pure
Bell states with a high fidelity via type-II spontaneous parametric
down-conversion (SPDC) of narrow-band pump light. However, the use of
femtosecond pump pulses to generate multi-photon states with precise timing
often requires spectral filtering to maintain a high quality of polarization
entanglement. This typically reduces the efficiency of photon pair collection.
We experimentally map the polarization correlations of photon pairs from such a
source over a range of down-converted wavelengths with a high spectral
resolution and find strong polarization correlations everywhere. A spectrally
dependent imbalance between contributions from the two possible decay paths of
SPDC is identified as the reason for a reduction in entanglement quality
observed with femtosecond pump pulses. Our spectral measurements allow to
predict the polarization correlations for arbitrary filter profiles when the
frequency degree of freedom of the photon pairs is ignored.


title: Simplification of additivity conjecture in quantum information theory

abstract:
  We simplify some conjectures in quantum information theory; the additivity of
minimal output entropy, the multiplicativity of maximal output p-norm and the
superadditivity of convex closure of output entropy. We construct a unital
channel for a given channel so that they share the above additivity properties;
we can reduce the conjectures for all channels to those for unital channels.


title: Questions and Physical Reality -Simple Philosophical considerations-

abstract:
  We argue, through some philosophical considerations, on (i)dependent or (ii)
an independent existence of physical reality underlying quantum states.
According these simple considerations, we conclude that is impossible to have a
clear independent existence of physical reality, we need to search the reasons
in the relationship between our questions (the observers) and the consequent
answers (always estimated by the same observers). Finally, we infer that every
theory is affected by our "questions", so we cannot speak about an
unconditional and independent theory underlying physical reality. Plan of the
paper. The existence of physical reality underlying quantum states: (i) it
before bit,(ii)it without bit,(iii)it from bit.


title: Measuring Multipartite Concurrence with a Single Factorizable Observable

abstract:
  We show that, for any composite system with an arbitrary number of
finite-dimensional subsystems, it is possible to directly measure the
multipartite concurrence of pure states by detecting only one single
factorizable observable, provided that two copies of the composite state are
available. This result can be immediately put into practice in trapped-ion and
entangled-photon experiments.


title: Entanglement, quantum phase transitions and quantum algorithms

abstract:
  The work that we present in this thesis tries to be at the crossover of
quantum information science, quantum many-body physics, and quantum field
theory. We use tools from these three fields to analyze problems that arise in
the interdisciplinary intersection. More concretely, in Chapter 1 we consider
the irreversibility of renormalization group flows from a quantum information
perspective by using majorization theory and conformal field theory. In Chapter
2 we compute the entanglement of a single copy of a bipartite quantum system
for a variety of models by using techniques from conformal field theory and
Toeplitz matrices. The entanglement entropy of the so-called
Lipkin-Meshkov-Glick model is computed in Chapter 3, showing analogies with
that of (1+1)-dimensional quantum systems. In Chapter 4 we apply the ideas of
scaling of quantum correlations in quantum phase transitions to the study of
quantum algorithms, focusing on Shor's factorization algorithm and quantum
algorithms by adiabatic evolution solving an NP-complete and the searching
problems. Also, in Chapter 5 we use techniques originally inspired by
condensed-matter physics to develop classical simulations, using the so-called
matrix product states, of an adiabatic quantum algorithm. Finally, in Chapter 6
we consider the behavior of some families of quantum algorithms from the
perspective of majorization theory. The structure within each Chapter is such
that the last section always summarizes the basic results. Some general
conclusions and possible future directions are briefly discussed in Chapter 7.
Appendix A, Appendix B and Appendix C respectively deal with some basic notions
on majorization theory, conformal field theory, and classical complexity
theory.


title: State Discrimination with Post-Measurement Information

abstract:
  We introduce a new state discrimination problem in which we are given
additional information about the state after the measurement, or more
generally, after a quantum memory bound applies. In particular, the following
special case plays an important role in quantum cryptographic protocols in the
bounded storage model: Given a string x encoded in an unknown basis chosen from
a set of mutually unbiased bases, you may perform any measurement, but then
store at most q qubits of quantum information. Later on, you learn which basis
was used. How well can you compute a function f(x) of x, given the initial
measurement outcome, the q qubits and the additional basis information? We
first show a lower bound on the success probability for any balanced function,
and any number of mutually unbiased bases, beating the naive strategy of simply
guessing the basis. We then show that for two bases, any Boolean function f(x)
can be computed perfectly if you are allowed to store just a single qubit,
independent of the number of possible input strings x. However, we show how to
construct three bases, such that you need to store all qubits in order to
compute f(x) perfectly. We then investigate how much advantage the additional
basis information can give for a Boolean function. To this end, we prove
optimal bounds for the success probability for the AND and the XOR function for
up to three mutually unbiased bases. Our result shows that the gap in success
probability can be maximal: without the basis information, you can never do
better than guessing the basis, but with this information, you can compute f(x)
perfectly. We also exhibit an example where the extra information does not give
any advantage at all.


title:
Security of coherent state quantum cryptography in the presence of
  Gaussian noise

abstract:
  We investigate the security against collective attacks of a continuous
variable quantum key distribution scheme in the asymptotic key limit for a
realistic setting. The quantum channel connecting the two honest parties is
assumed to be lossy and imposes Gaussian noise on the observed quadrature
distributions. Secret key rates are given for direct and reverse reconciliation
schemes including postselection in the collective attack scenario. The effect
of a non-ideal error correction and two-way communication in the classical
post-processing step is also taken into account.


title: On the quantum chromatic number of a graph

abstract:
  We investigate the notion of quantum chromatic number of a graph, which is
the minimal number of colours necessary in a protocol in which two separated
provers can convince an interrogator with certainty that they have a colouring
of the graph.
  After discussing this notion from first principles, we go on to establish
relations with the clique number and orthogonal representations of the graph.
We also prove several general facts about this graph parameter and find large
separations between the clique number and the quantum chromatic number by
looking at random graphs.
  Finally, we show that there can be no separation between classical and
quantum chromatic number if the latter is 2, nor if it is 3 in a restricted
quantum model; on the other hand, we exhibit a graph on 18 vertices and 44
edges with chromatic number 5 and quantum chromatic number 4.


title:
Adiabatic quantum algorithms as quantum phase transitions: first versus
  second order

abstract:
  In the continuum limit (large number of qubits), adiabatic quantum algorithms
display a remarkable similarity to sweeps through quantum phase transitions. We
find that transitions of second or higher order are advantageous in comparison
to those of first order. With this insight, we propose a novel adiabatic
quantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact
cover), which is significantly faster than previous proposals according to
numerical simulations (up to 20 qubits). These findings suggest that adiabatic
quantum algorithms can solve NP-complete problems such as 3-SAT much faster
than the Grover search routine (yielding a quadratic enhancement), possibly
even with an exponential speed-up. PACS: 03.67.-a, 03.67.Lx, 73.43.Nq,
64.70.-p.


title: Postselection threshold against biased noise

abstract:
  The highest current estimates for the amount of noise a quantum computer can
tolerate are based on fault-tolerance schemes relying heavily on postselecting
on no detected errors. However, there has been no proof that these schemes give
even a positive tolerable noise threshold. A technique to prove a positive
threshold, for probabilistic noise models, is presented. The main idea is to
maintain strong control over the distribution of errors in the quantum state at
all times. This distribution has correlations which conceivably could grow out
of control with postselection. But in fact, the error distribution can be
written as a mixture of nearby distributions each satisfying strong
independence properties, so there are no correlations for postselection to
amplify.


title: Classical search algorithm with resonances in $\sqrt{N}$ cycles

abstract:
  In this work we use the wave equation to obtain a classical analog of the
quantum search algorithm and we verify that the essence of search algorithms
resides in the establishment of resonances between the initial and the serched
states. In particular we show that, within a set of $N$ vibration modes, it is
possible to excite the searched mode in a number of steps proportional to
$\sqrt N$.


title:
Damped Population Oscillation in a Spontaneously Decaying Two-Level Atom
  Coupled to a Monochromatic Field

abstract:
  We investigate the time evolution of atomic population in a two-level atom
driven by a monochromatic radiation field, taking spontaneous emission into
account. The Rabi oscillation exhibits amplitude damping in time caused by
spontaneous emission. We show that the semiclassical master equation leads in
general to an overestimation of the damping rate and that a correct
quantitative description of the damped Rabi oscillation can thus be obtained
only with a full quantum mechanical theory.


title: Reduced coherence in double-slit diffraction of neutrons

abstract:
  In diffraction experiments with particle beams, several effects lead to a
fringe visibility reduction of the interference pattern. We theoretically
describe the intensity one can measure in a double-slit setup and compare the
results with the experimental data obtained with cold neutrons. Our conclusion
is that for cold neutrons the fringe visibility reduction is due not to
decoherence, but to initial incoherence.


title:
Statistical analysis on testing of an entangled state based on Poisson
  distribution framework

abstract:
  A hypothesis testing scheme for entanglement has been formulated based on the
Poisson distribution framework instead of the POVM framework. Three designs
were proposed to test the entangled states in this framework. The designs were
evaluated in terms of the asymptotic variance. It has been shown that the
optimal time allocation between the coincidence and anti-coincidence
measurement bases improves the conventional testing method. The test can be
further improved by optimizing the time allocation between the anti-coincidence
bases.


title: Impossibility of Probabilistic splitting of quantum information

abstract:
  We know that we cannot split the information encoded in two non-orthogonal
qubits into complementary parts deterministically. Here we show that each of
the copies of the state randomly selected from a set of non orthogonal linearly
independent states, splitting of quantum information can not be done even
probabilistically. Here in this work we also show that under certain restricted
conditions, we can probabilistically split the quantum information encoded in a
qubit.


title:
Quamtumness, Generalized Spherical 2-Design and Symmetric
  Informationally Complete POVM

abstract:
  C. A. Fuchs and M. Sasaki defined the quantumness of a set of quantum states
in \cite{Quantumness}, which is closely related to the fidelity loss in
transmission of the quantum states through a classical channel. In
\cite{Fuchs}, Fuchs showed that in $d$-dimensional Hilbert space, minimum
quantumness is $\frac{2}{d+1}$, and this can be achieved by all rays in the
space. He left an open problem, asking whether fewer than $d^2$ states can
achieve this bound. Recently, in a different context, A. J. Scott introduced a
concept of generalized $t$-design in \cite{GenSphet}, which is a natural
generalization of spherical $t$-design. In this paper, we show that the lower
bound on the quantumness can be achieved if and only if the states form a
generalized 2-design. As a corollary, we show that this bound can be only
achieved if the number of states are larger or equal to $d^2$, answering the
open problem. Furthermore, we also show that the minimal set of such ensemble
is Symmetric Informationally Complete POVM(SIC-POVM). This leads to an
equivalence relation between SIC-POVM and minimal set of ensemble achieving
minimal quantumness.


title: Quantum mechanics is a relativity theory

abstract:
  Non-relativistic quantum mechanics is shown to emerge from classical
mechanics through the requirement of a relativity principle based on special
transformations acting on position and momentum uncertainties. These
transformations keep the Heisenberg inequalities invariant and form a group.
They are related to dilatations of space variables provided the quantum
potential is added to the classical Hamiltonian functional. The Schr\"odinger
equation appears to have a nonunitary and nonlinear companion acting in another
time variable. Evolution in this time seems related to the state vector
reduction.


title: Search via Quantum Walk

abstract:
  We propose a new method for designing quantum search algorithms for finding a
"marked" element in the state space of a classical Markov chain. The algorithm
is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of
the Markov chain. The main new idea is to apply quantum phase estimation to the
quantum walk in order to implement an approximate reflection operator. This
operator is then used in an amplitude amplification scheme. As a result we
considerably expand the scope of the previous approaches of Ambainis (2004) and
Szegedy (2004). Our algorithm combines the benefits of these approaches in
terms of being able to find marked elements, incurring the smaller cost of the
two, and being applicable to a larger class of Markov chains. In addition, it
is conceptually simple and avoids some technical difficulties in the previous
analyses of several algorithms based on quantum walk.


title: Catalytic quantum error correction

abstract:
  We develop the theory of entanglement-assisted quantum error correcting
(EAQEC) codes, a generalization of the stabilizer formalism to the setting in
which the sender and receiver have access to pre-shared entanglement.
Conventional stabilizer codes are equivalent to dual-containing symplectic
codes. In contrast, EAQEC codes do not require the dual-containing condition,
which greatly simplifies their construction. We show how any quaternary
classical code can be made into a EAQEC code. In particular, efficient modern
codes, like LDPC codes, which attain the Shannon capacity, can be made into
EAQEC codes attaining the hashing bound. In a quantum computation setting,
EAQEC codes give rise to catalytic quantum codes which maintain a region of
inherited noiseless qubits.
  We also give an alternative construction of EAQEC codes by making classical
entanglement assisted codes coherent.


title:
On the Security of Y-00 under Fast Correlation and Other Attacks on the
  Key

abstract:
  The potential weakness of the Y-00 direct encryption protocol when the
encryption box ENC in Y-00 is not chosen properly is demonstrated in a fast
correlation attack by S. Donnet et al in Phys. Lett. A 35, 6 (2006) 406-410. In
this paper, we show how this weakness can be eliminated with a proper design of
ENC. In particular, we present a Y-00 configuration that is more secure than
AES under known-plaintext attack. It is also shown that under any
ciphertext-only attack, full information-theoretic security on the Y-00 seed
key is obtained for any ENC when proper deliberate signal randomization is
employed.


title: Efficiently implementable codes for quantum key expansion

abstract:
  The Shor-Preskill proof of the security of the BB84 quantum key distribution
protocol relies on the theoretical existence of good classical error-correcting
codes with the ``dual-containing'' property. A practical implementation of BB84
thus requires explicit and efficiently decodable constructions of such codes,
which are not known. On the other hand, modern coding theory abounds with
non-dual-containing codes with excellent performance and efficient decoding
algorithms. We show that the dual-containing constraint can be lifted at a
small price: instead of a key distribution protocol, an efficiently
implementable key expansion protocol is obtained, capable of increasing the
size of a pre-shared key by a constant factor.


title:
Security of quantum key distribution protocol with two-way classical
  communication assisted by one-time pad encryption

abstract:
  In this paper, we consider a quantum key distribution protocol (QKD) with
two-way classical communication that is assisted by one-time pad encryption. We
propose a two-way preprocessing that uses one-time pad encryption by previously
shared secret key, and the net key rate of the QKD with proposed preprocessing
exceeds the key rate of the QKD without it. The preprocessing is reduced to the
entanglement distillation protocol with two-way classical communication and
previously shared EPR pairs (two-way breeding protocol), and the security of
QKD with the preprocessing is guaranteed in the same way as Shor and Preskill's
arguments.


title: Arrival Time in Relativistic Quantum Mechanics

abstract:
  Relativistic free-motion time-of-arrival theory for massive spin-1/2
particles is systematically developed. Contrary to the nonrelativistic
time-of-arrival operator studied thoroughly in previous literatures, the
relativistic time-of-arrival operator possesses self-adjoint extensions because
of the particle-antiparticle symmetry. The nonrelativistic limit of our theory
is in agreement with the nonrelativistic time-of-arrival theory.


title:
Unconditional optimality of Gaussian attacks against continuous-variable
  QKD

abstract:
  A fully general approach to the security analysis of continuous-variable
quantum key distribution (CV-QKD) is presented. Provided that the quantum
channel is estimated via the covariance matrix of the quadratures, Gaussian
attacks are shown to be optimal against all eavesdropping strategies, including
collective and coherent attacks. The proof is made strikingly simple by
combining a physical model of measurement, an entanglement-based description of
CV-QKD, and a recent powerful result on the extremality of Gaussian states
[Phys. Rev. Lett. 96, 080502 (2006)].


title: Exact Casimir interaction between eccentric cylinders

abstract:
  The Casimir force is the ultimate background in ongoing searches of
extra-gravitational forces in the micrometer range. Eccentric cylinders offer
favorable experimental conditions for such measurements as spurious
gravitational and electrostatic effects can be minimized. Here we report on the
evaluation of the exact Casimir interaction between perfectly conducting
eccentric cylinders using a mode summation technique, and study different
limiting cases of relevance for Casimir force measurements, with potential
implications for the understanding of mechanical properties of nanotubes.


title:
Optimality of Gaussian Attacks in Continuous Variable Quantum
  Cryptography

abstract:
  We analyze the asymptotic security of the family of Gaussian modulated
Quantum Key Distribution protocols for Continuous Variables systems. We prove
that the Gaussian unitary attack is optimal for all the considered bounds on
the key rate when the first and second momenta of the canonical variables
involved are known by the honest parties.


title: Quantum measurements without sums

abstract:
  Sums play a prominent role in the formalisms of quantum mechanics, be it for
mixing and superposing states, or for composing state spaces. Surprisingly, a
conceptual analysis of quantum measurement seems to suggest that quantum
mechanics can be done without direct sums, expressed entirely in terms of the
tensor product. The corresponding axioms define classical spaces as objects
that allow copying and deleting data. Indeed, the information exchange between
the quantum and the classical worlds is essentially determined by their
distinct capabilities to copy and delete data. The sums turn out to be an
implicit implementation of this capabilities. Realizing it through explicit
axioms not only dispenses with the unnecessary structural baggage, but also
allows a simple and intuitive graphical calculus. In category-theoretic terms,
classical data types are dagger-compact Frobenius algebras, and quantum spectra
underlying quantum measurements are Eilenberg-Moore coalgebras induced by these
Frobenius algebras.


title: Two interacting spins in external fields. Four-level systems

abstract:
  In the present article, we consider the so-called two-spin equation that
describes four-level quantum systems. Recently, these systems attract attention
due to their relation to the problem of quantum computation. We study general
properties of the two-spin equation and show that the problem for certain
external backgrounds can be identified with the problem of one spin in an
appropriate background. This allows one to generate a number of exact solutions
for two-spin equations on the basis of already known exact solutions of the
one-spin equation. Besides, we present some exact solutions for the two-spin
equation with an external background different for each spin but having the
same direction. We study the eigenvalue problem for a time-independent spin
interaction and a time-independent external background. A possible analogue of
the Rabi problem for the two-spin equation is defined. We present its exact
solution and demonstrate the existence of magnetic resonances in two specific
frequencies, one of them coinciding with the Rabi frequency, and the other
depending on the rotating field magnitude. The resonance that corresponds to
the second frequency is suppressed with respect to the first one.


title: Quantum Control of a Single Qubit

abstract:
  Measurements in quantum mechanics cannot perfectly distinguish all states and
necessarily disturb the measured system. We present and analyse a proposal to
demonstrate fundamental limits on quantum control of a single qubit arising
from these properties of quantum measurements. We consider a qubit prepared in
one of two non-orthogonal states and subsequently subjected to dephasing noise.
The task is to use measurement and feedback control to attempt to correct the
state of the qubit. We demonstrate that projective measurements are not optimal
for this task, and that there exists a non-projective measurement with an
optimum measurement strength which achieves the best trade-off between gaining
information about the system and disturbing it through measurement back-action.
We study the performance of a quantum control scheme that makes use of this
weak measurement followed by feedback control, and demonstrate that it realises
the optimal recovery from noise for this system. We contrast this approach with
various classically inspired control schemes.


title: The one dimensional Hydrogen atom revisited

abstract:
  The one dimensional Schroedinger hydrogen atom is an interesting mathematical
and physical problem to study bound states, eigenfunctions and quantum
degeneracy issues. This 1D physical system gave rise to some intriguing
controversy over more than four decades. Presently, still no definite consensus
seems to have been reached. We reanalyzed this apparently controversial
problem, approaching it from a Fourier transform representation method combined
with some fundamental (basic) ideas found in self-adjoint extensions of
symmetric operators. In disagreement with some previous claims, we found that
the complete Balmer energy spectrum is obtained together with an odd parity set
of eigenfunctions. Closed form solutions in both coordinate and momentum spaces
were obtained. No twofold degeneracy was observed as predicted by the
degeneracy theorem in one dimension, though it does not necessarily have to
hold for potentials with singularities. No ground state with infinite energy
exists since the corresponding eigenfunction does not satisfy the Schroedinger
equation at the origin.


title: Time Optimal Unitary Operations

abstract:
  Extending our previous work on time optimal quantum state evolution, we
formulate a variational principle for the time optimal unitary operation, which
has direct relevance to quantum computation. We demonstrate our method with
three examples, i.e. the swap of qubits, the quantum Fourier transform and the
entangler gate, by choosing a two-qubit anisotropic Heisenberg model.


title:
Local Distinguishability of Orthogonal Quantum States and Generators of
  SU(N)

abstract:
  We investigate the possibility of distinguishing a set of mutually orthogonal
multipartite quantum states by local operations and classical communication
(LOCC). We connect this problem with generators of SU(N) and present a new
condition that is necessary for a set of orthogonal states to be locally
distinguishable. We show that even in multipartite cases there exists a
systematic way to check whether the presented condition is satisfied for a
given set of orthogonal states. Based on the proposed checking method, we find
that LOCC cannot distinguish three mutually orthogonal states in which two of
them are GHZ-like states.


title: Entanglement quantification through local observable correlations

abstract:
  We present a significantly improved scheme of entanglement detection inspired
by local uncertainty relations for a system consisting of two qubits.
Developing the underlying idea of local uncertainty relations, namely
correlations, we demonstrate that it's possible to define a measure which is
invariant under local unitary transformations and which is based only on local
measurements. It is quite simple to implement experimentally and it allows
entanglement quantification in a certain range for mixed states and exactly for
pure states, without first obtaining full knowledge (e.g. through tomography)
of the state.


title: Secret quantum communication of a reference frame

abstract:
  We propose quantum cryptographic protocols to secretly communicate a
reference frame- unspeakable information in the sense it cannot be encoded into
a string of bits. Two distant parties can secretly align their Cartesian axes
by exchanging N spin 1/2 particles, achieving the optimal accuracy 1/N. A
possible eavesdropper cannot gain any information without being detected.


title:
Efficient Photoionization-Loading of Trapped Cadmium Ions with Ultrafast
  Pulses

abstract:
  Atomic cadmium ions are loaded into radiofrequency ion traps by
photoionization of atoms in a cadmium vapor with ultrafast laser pulses. The
photoionization is driven through an intermediate atomic resonance with a
frequency-quadrupled mode-locked Ti:Sapphire laser that produces pulses of
either 100 fsec or 1 psec duration at a central wavelength of 229 nm. The large
bandwidth of the pulses photoionizes all velocity classes of the Cd vapor,
resulting in high loading efficiencies compared to previous ion trap loading
techniques. Measured loading rates are compared with a simple theoretical
model, and we conclude that this technique can potentially ionize every atom
traversing the laser beam within the trapping volume. This may allow the
operation of ion traps with lower levels of background pressures and less trap
electrode surface contamination. The technique and laser system reported here
should be applicable to loading most laser-cooled ion species.


title: Universal Mixing of Quantum Walk on Graphs

abstract:
  We study the set of probability distributions visited by a continuous-time
quantum walk on graphs. An edge-weighted graph G is universal mixing if the
instantaneous or average probability distribution of the quantum walk on G
ranges over all probability distributions on the vertices as the weights are
varied over non-negative reals. The graph is uniform mixing if it visits the
uniform distribution. Our results include the following:
  (a) All weighted complete multipartite graphs are instantaneous universal
mixing. This is in contrast to the fact that no unweighted complete
multipartite graphs are uniform mixing (except for the four-cycle).
  (b) The weighted claw or star graph is a minimally connected instantaneous
universal mixing graph. In fact, as a corollary, the unweighted claw is
instantaneous uniform mixing. This adds a new family of uniform mixing graphs
to a list that so far contains only the hypercubes.
  (c) Any weighted graph is average almost-uniform mixing unless its spectral
type is sublinear in the size of the graph. This provides a nearly tight
characterization for average uniform mixing on circulant graphs.
  (d) No weighted graphs are average universal mixing. This shows that weights
do not help to achieve average universal mixing, unlike the instantaneous case.
  Our proofs exploit the spectra of the underlying weighted graphs and path
collapsing arguments.


title: Quantum Error Correcting Subsystems are Unitarily Recoverable Subsystems

abstract:
  We show that every correctable subsystem for an arbitrary noise operation can
be recovered by a unitary operation, where the notion of recovery is more
relaxed than the notion of correction insofar as it does not protect the
subsystem from subsequent iterations of the noise. We also demonstrate that in
the case of unital noise operations one can identify a subset of all
correctable subsystems -- those that can be corrected by a single unitary
operation -- as the noiseless subsystems for the composition of the noise
operation with its dual. Using the recently developed structure theory for
noiseless subsystems, the identification of such unitarily correctable
subsystems is reduced to an algebraic exercise.


title: On derivation of Wigner distribution function

abstract:
  Wigner distribution function has much importance in quantum statistical
mechanics. It finds applications in various disciplines of physics including
condense matter, quantum optics, to name but a few. Wigner distribution
function is introduced by E. Wigner in 1932. However, there is no analytical
derivation of Wigner distribution function in the literatures, to date. In this
paper, a simple analytical derivation of Wigner distribution function is
presented. Our derivation is based on two assumptions, these are A) by taking
the integral of Wigner distribution function, with respect to configuration
space, the momentum space distribution function is obtained B) WDF is real.
Similarly, and in addition to Wigner distribution function, the distribution
function of Sobouti-Nasiri, which is imaginary, is also derived.


title: Quantum Interference of Photon Pairs from Two Trapped Atomic Ions

abstract:
  We collect the fluorescence from two trapped atomic ions, and measure quantum
interference between photons emitted from the ions. The interference of two
photons is a crucial component of schemes to entangle atomic qubits based on a
photonic coupling. The ability to preserve the generated entanglement and to
repeat the experiment with the same ions is necessary to implement entangling
quantum gates between atomic qubits, and allows the implementation of protocols
to efficiently scale to larger numbers of atomic qubits.


title: Some Non-Perturbative and Non-Linear Effects in Laser-Atom Interaction

abstract:
  We show that if the laser is intense enough, it may always ionize an atom or
induce transitions between discrete energy levels of the atom, no matter what
is its frequency. It means in the quantum transition of an atom interacting
with an intense laser of circular frequency $\omega$, the energy difference
between the initial and the final states of the atom is not necessarily being
an integer multiple of the quantum energy $\hbar\omega$. The absorption spectra
become continuous. The Bohr condition is violated. The energy of photoelectrons
becomes light intensity dependent in the intense laser photoelectric effect.
The transition probabilities and cross sections of photo-excitations and
photo-ionizations are laser intensity dependent, showing that these processes
cannot be reduced to the results of interactions between the atom and separate
individual photons, they are rather the processes of the atom interacting with
the laser as a whole. The interaction of photons on atoms are not simply
additive. The effects are non-perturbative and non-linear. Some numerical
results for processes between hydrogen atom and intense circularly polarized
laser, illustrating the non-perturbative and non-linear character of the
atom-laser interaction, are given.


title: Locality and the Greenberger-Horne-Zeilinger Theorem

abstract:
  In all local realistic theories worked out till now, locality is considered
as a basic assumption. Most people in the field consider the inconsistency
between local realistic theories and quantum mechanics to be a result of
non-local nature of quantum mechanics. In this Paper, we derive the
Greenberger-Horne-Zeilinger type theorem for particles with instantaneous
(non-local) interactions at the hidden-variable level. Then, we show that the
previous contradiction still exists between quantum mechanics and non-local
hidden variable models.


title: On the classification of pure multipartite states

abstract: This paper has been withdrawn by the author due to an error.


title: Excitation and Entanglement Transfer Near Quantum Critical Points

abstract:
  Recently, there has been growing interest in employing condensed matter
systems such as quantum spin or harmonic chains as quantum channels for short
distance communication. Many properties of such chains are determined by the
spectral gap between their ground and excited states. In particular this gap
vanishes at critical points of quantum phase transitions. In this article we
study the relation between the transfer speed and quality of such a system and
the size of its spectral gap. We find that the transfer is almost perfect but
slow for large spectral gaps and fast but rather inefficient for small gaps.


title: Entanglement generation by Fock-state filtration

abstract:
  We demonstrate a Fock-state filter which is capable of preferentially
blocking single photons over photon pairs. The large conditional nonlinearities
are based on higher-order quantum interference, using linear optics, an ancilla
photon, and measurement. We demonstrate that the filter acts coherently by
using it to convert unentangled photon pairs to a path-entangled state. We
quantify the degree of entanglement by transforming the path information to
polarisation information, applying quantum state tomography we measure a tangle
of T=(20+/-9)%.


title: Purifying and Reversible Physical Processes

abstract:
  Starting from the observation that reversible processes cannot increase the
purity of any input state, we study deterministic physical processes, which map
a set of states to a set of pure states. Such a process must map any state to
the same pure output, if purity is demanded for the input set of all states.
But otherwise, when the input set is restricted, it is possible to find
non-trivial purifying processes. For the most restricted case of only two input
states, we completely characterize the output of any such map. We furthermore
consider maps, which combine the property of purity and reversibility on a set
of states, and we derive necessary and sufficient conditions on sets, which
permit such processes.


title:
Effective Mass Schrodinger Equation for Exactly Solvable Class of
  One-Dimensional Potentials

abstract:
  We deal with the exact solutions of Schrodinger equation characterized by
position-dependent effective mass via point canonical transformations. The
Morse, Poschl-Teller and Hulthen type potentials are considered respectively.
With the choice of position-dependent mass forms, exactly solvable target
potentials are constructed. Their energy of the bound states and corresponding
wavefunctions are determined exactly.


title:
Demonstrating multipartite entanglement of single-particle W states:
  linear optical schemes

abstract:
  We present two linear optical schemes using nonideal photodetectors to
demonstrate inseparability of W-type N-partite entangled states containing only
a single photon. First, we show that the pairwise entanglement of arbitrary two
modes chosen from N optical modes can be detected using the method proposed by
Nha and Kim [Phys. Rev. A 74, 012317 (2006)], thereby suggesting the full
inseparability among N parties. In particular, this scheme is found to succeed
for any nonzero quantum efficiency of photodetectors. Second, we consider a
quantum teleportation network using linear optics without auxiliary modes. The
conditional teleportation can be optimized by a suitable choice of the
transmittance of the beam splitter in the Bell measurement. Specifically, we
identify the conditions under which maximum fidelity larger than classical
bound 2/3 is achieved only in cooperation with other parties. We also
investigate the case of on-off photodetectors that cannot discriminate the
number of detected photons.


title:
Entanglement and Symmetry: A Case Study in Superselection Rules,
  Reference Frames, and Beyond

abstract:
  This paper concentrates on a particular example of a constraint imposed by
superselection rules (SSRs): that which applies when the parties (Alice and
Bob) cannot distinguish among certain quantum objects they have. This arises
naturally in the context of ensemble quantum information processing such as in
liquid NMR. We discuss how a SSR for the symmetric group can be applied, and
show how the extractable entanglement can be calculated analytically in certain
cases, with a maximum bipartite entanglement in an ensemble of N Bell-state
pairs scaling as log(N) as N goes to infinity . We discuss the apparent
disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement
for other sorts of superselection rules, and show that the disparity disappears
when the correct notion of applying the symmetric group SSR to multiple copies
is used. Next we discuss reference frames in the context of this SSR, showing
the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502
(2004)]. The action of a reference frame can be regarded as the analog of
activation in mixed-state entanglement. We also discuss the analog of
distillation: there exist states such that one copy can act as an imperfect
reference frame for another copy. Finally we present an example of a stronger
operational constraint, that operations must be non-collective as well as
symmetric. Even under this stronger constraint we nevertheless show that
Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble
of N Bell-state pairs no matter how large N is. This last work is a
generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].


title:
Is efficiency of classical simulations of quantum dynamics related to
  integrability?

abstract:
  Efficiency of time-evolution of quantum observables, and thermal states of
quenched hamiltonians, is studied using time-dependent density matrix
renormalization group method in a family of generic quantum spin chains which
undergo a transition from integrable to non-integrable - quantum chaotic case
as control parameters are varied. Quantum states (observables) are represented
in terms of matrix-product-operators with rank D_\epsilon(t), such that
evolution of a long chain is accurate within fidelity error \epsilon up to time
t. We find that rank generally increases exponentially, D_\epsilon(t) \propto
\exp(const t), unless the system is integrable in which case we find polynomial
increase.


title: Entanglement witnesses and a loophole problem

abstract:
  We consider a possible detector-efficiency loophole in experiments that
detect entanglement via the local measurement of witness operators. Here, only
local properties of the detectors are known. We derive a general threshold for
the detector efficiencies which guarantees that a negative expectation value of
a witness is due to entanglement, rather than to erroneous detectors. This
threshold depends on the local decomposition of the witness and its measured
expectation value. For two-qubit witnesses we find the local operator
decomposition that is optimal with respect to closing the loophole.


title: Quantum phase transitions and quantum fidelity in free fermion graphs

abstract:
  In this paper we analyze the ground state phase diagram of a class of
fermionic Hamiltonians by looking at the fidelity of ground states
corresponding to slightly different Hamiltonian parameters. The Hamiltonians
under investigation can be considered as the variable range generalization of
the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the
XY spin-chain in a transverse magnetic field. Under periodic boundary
conditions, the matrices of the problem become circulant and the models are
exactly solvable. Their free-ends counterparts are instead analyzed
numerically. In particular, we focus on the long range model corresponding to a
fully connected directed graph, providing asymptotic results in the
thermodynamic limit, as well as the finite-size scaling analysis of the second
order quantum phase transitions of the system. A strict relation between
fidelity and single particle spectrum is demonstrated, and a peculiar gapful
transition due to the long range nature of the coupling is found. A comparison
between fidelity and another transition marker borrowed from quantum
information i.e., single site entanglement, is also considered.


title:
Classical simulation versus universality in measurement based quantum
  computation

abstract:
  We investigate for which resource states an efficient classical simulation of
measurement based quantum computation is possible. We show that the
Schmidt--rank width, a measure recently introduced to assess universality of
resource states, plays a crucial role in also this context. We relate
Schmidt--rank width to the optimal description of states in terms of tree
tensor networks and show that an efficient classical simulation of measurement
based quantum computation is possible for all states with logarithmically
bounded Schmidt--rank width (with respect to the system size). For graph states
where the Schmidt--rank width scales in this way, we efficiently construct the
optimal tree tensor network descriptions, and provide several examples. We
highlight parallels in the efficient description of complex systems in quantum
information theory and graph theory.


title: Lorentz transformations that entangle spins and entangle momenta

abstract:
  Simple examples are presented of Lorentz transformations that entangle the
spins and momenta of two particles with positive mass and spin 1/2. They apply
to indistinguishable particles, produce maximal entanglement from finite
Lorentz transformations of states for finite momenta, and describe entanglement
of spins produced together with entanglement of momenta. From the entanglements
considered, no sum of entanglements is found to be unchanged.


title: The K-way negativities as entanglement measures

abstract:
  A classification of N-partite states, based on K-way negativities (K=2 to N),
is proposed. The K-way partial transpose with respect to a subsystem is defined
so as to shift the focus to K-way coherences instead of K subsystems of the
composite system. For an N-partite system, the fraction of K-way negativity
contributing to global negativity, is obtained. After minimizing K-way
negativities through local unitary qubit rotations, a combined analysis of
2-way, 3-way and global negativities is shown to provide distinct measures of
genuine tripartite, W-state like and bipartite entanglement, for three qubit
composite system. To illustrate the point, entanglement of three qubit GHZ
class states, W-class states, three boson state and noisy states is analysed.
While genuine N-partite entanglement of a composite system is generated by
N-way coherences, N-partite entanglement in general can be present due to
(K<N)-way coherences as well.


title: Several Classes of Concatenated Quantum Codes: Constructions and Bounds

abstract:
  In this paper we present several classes of asymptotically good concatenated
quantum codes and derive lower bounds on the minimum distance and rate of the
codes. We compare these bounds with the best-known bound of
Ashikhmin--Litsyn--Tsfasman and Matsumoto. We also give a polynomial-time
decoding algorithm for the codes that can decode up to one fourth of the lower
bound on the minimum distance of the codes.


title: Simulation of bipartite qudit correlations

abstract:
  We present a protocol to simulate the quantum correlations of an arbitrary
bipartite state, when the parties perform a measurement according to two
traceless binary observables. We show that $\log(d)$ bits of classical
communication is enough on average, where $d$ is the dimension of both systems.
To obtain this result, we use the sampling approach for simulating the quantum
correlations. We discuss how to use this method in the case of qudits.


title:
Spin qubits in double quantum dots - entanglement versus the Kondo
  effect

abstract:
  We investigate the competition between pair entanglement of two spin qubits
in double quantum dots attached to leads with various topologies and the
separate entanglement of each spin with nearby electrodes. Universal behavior
of entanglement is demonstrated in dependence on the mutual interactions
between the spin qubits, the coupling to their environment, temperature and
magnetic field. As a consequence of quantum phase transition an abrupt switch
between fully entangled and unentangled states takes place when the dots are
coupled in parallel.


title: Interaction-free measurement with an imperfect absorber

abstract:
  In this paper, we consider interaction-free measurement (IFM) with imperfect
interaction. In the IFM proposed by Kwiat et al., we assume that interaction
between an absorbing object and a probe photon is imperfect, so that the photon
is absorbed with probability 1-\eta (0\leq\eta\leq 1) and it passes by the
object without being absorbed with probability \eta when it approaches close to
the object. We derive the success probability P that we can find the object
without the photon absorbed under the imperfect interaction as a power series
in 1/N, and show the following result: Even if the interaction between the
object and the photon is imperfect, we can let the success probability P of the
IFM get close to unity arbitrarily by making the reflectivity of the beam
splitter larger and increasing the number of the beam splitters. Moreover, we
obtain an approximating equation of P for large N from the derived power series
in 1/N.