title:
When are correlations quantum? -- Verification and quantification of
  entanglement by simple measurements

abstract:
  The verification and quantification of experimentally created entanglement by
simple measurements, especially between distant particles, is an important
basic task in quantum processing. When composite systems are subjected to local
measurements the measurement data will exhibit correlations, whether these
systems are classical or quantum. Therefore, the observation of correlations in
the classical measurement record does not automatically imply the presence of
quantum correlations in the system under investigation. In this work we explore
the question of when correlations, or other measurement data, are sufficient to
guarantee the existence of a certain amount of quantum correlations in the
system and when additional information, such as the degree of purity of the
system, is needed to do so. Various measurement settings are discussed, both
numerically and analytically. Exact results and lower bounds on the least
entanglement consistent with the observations are presented. The approach is
suitable both for the bi-partite and the multi-partite setting.


title:
Physical implementation of holonomic quantum computation in
  decoherence-free subspaces with trapped ions

abstract:
  We propose a feasible scheme to achieve holonomic quantum computation in a
decoherence-free subspace (DFS) with trapped ions. By the application of
appropriate bichromatic laser fields on the designated ions, we are able to
construct two noncommutable single-qubit gates and one controlled-phase gate
using the holonomic scenario in the encoded DFS.


title: Variational collocation on finite intervals

abstract:
  In this paper we study a new family of sinc--like functions, defined on an
interval of finite width. These functions, which we call ``little sinc'', are
orthogonal and share many of the properties of the sinc functions. We show that
the little sinc functions supplemented with a variational approach enable one
to obtain accurate results for a variety of problems. We apply them to the
interpolation of functions on finite domain and to the solution of the
Schr\"odinger equation, and compare the performance of present approach with
others.


title: Probability distributions and Gleason's Theorem

abstract:
  We discuss concrete examples for frame functions and their associated density
operators, as well as for non-Gleason type probability measures.


title: Generalization of Quantum Error Correction via the Heisenberg Picture

abstract:
  We show that the theory of operator quantum error correction can be naturally
generalized by allowing constraints not only on states but also on observables.
The resulting theory describes the correction of algebras of observables (and
may therefore suitably be called ``operator algebra quantum error
correction''). In particular, the approach provides a framework for the
correction of hybrid quantum-classical information and it does not require the
state to be entirely in one of the corresponding subspaces or subsystems. We
discuss applications to quantum teleportation and to the study of information
flows in quantum interactions.


title: POVMs and Naimark's theorem without sums

abstract:
  We provide a definition of POVM in terms of abstract tensor structure only.
It is justified in two distinct manners. i. At this abstract level we are still
able to prove Naimark's theorem, hence establishing a bijective correspondence
between abstract POVMs and abstract projective measurements on an extended
system, and this proof is moreover purely graphical. ii. Our definition
coincides with the usual one for the particular case of the Hilbert space
tensor product. We also point to a very useful normal form result for the
classical object structure introduced in quant-ph/0608035.

categories: quant-ph math-ph math.CT math.MP math.QA


title: Comment on a paper by Lapaire and Sipe

abstract:
  In a recent paper [quant-ph/0607008] Lapaire and Sipe argue that one can
discuss interference experiments using entangled photons in terms of single
photon wave functions. Furthermore, they argue that contrary to the claim of
the authors of the postponed compensation experiment [2], the single photon
wave functions overlap on the beam splitter when interference is observed. In
this comment, we show that the claim in [2] is correct and we argue that the
idea of single photon wave functions in entangled states is misleading.


title: Optimal estimation of qubit states with continuous time measurements

abstract:
  We propose an adaptive, two steps strategy, for the estimation of mixed qubit
states. We show that the strategy is optimal in a local minimax sense for the
trace norm distance as well as other locally quadratic figures of merit. Local
minimax optimality means that given $n$ identical qubits, there exists no
estimator which can perform better than the proposed estimator on a
neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is
asymptotically Bayesian optimal for a large class of prior distributions.
  We present a physical implementation of the optimal estimation strategy based
on continuous time measurements in a field that couples with the qubits.
  The crucial ingredient of the result is the concept of local asymptotic
normality (or LAN) for qubits. This means that, for large $n$, the statistical
model described by $n$ identically prepared qubits is locally equivalent to a
model with only a classical Gaussian distribution and a Gaussian state of a
quantum harmonic oscillator.
  The term `local' refers to a shrinking neighborhood around a fixed state
$\rho_{0}$. An essential result is that the neighborhood radius can be chosen
arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by
which we first localize the state within a smaller neighborhood of radius
$n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.


title: Finite Controllability of Infinite-Dimensional Quantum Systems

abstract:
  Quantum phenomena of interest in connection with applications to computation
and communication almost always involve generating specific transfers between
eigenstates, and their linear superpositions. For some quantum systems, such as
spin systems, the quantum evolution equation (the Schr\"{o}dinger equation) is
finite-dimensional and old results on controllability of systems defined on on
Lie groups and quotient spaces provide most of what is needed insofar as
controllability of non-dissipative systems is concerned. However, in an
infinite-dimensional setting, controlling the evolution of quantum systems
often presents difficulties, both conceptual and technical. In this paper we
present a systematic approach to a class of such problems for which it is
possible to avoid some of the technical issues. In particular, we analyze
controllability for infinite-dimensional bilinear systems under assumptions
that make controllability possible using trajectories lying in a nested family
of pre-defined subspaces. This result, which we call the Finite Controllability
Theorem, provides a set of sufficient conditions for controllability in an
infinite-dimensional setting. We consider specific physical systems that are of
interest for quantum computing, and provide insights into the types of quantum
operations (gates) that may be developed.


title: Spectral statistics for scaling quantum graphs

abstract:
  The explicit solution to the spectral problem of quantum graphs is used to
obtain the exact distributions of several spectral statistics, such as the
oscillations of the quantum momentum eigenvalues around the average, $\delta
k_{n}=k_{n}-\bar k_{n}$, and the nearest neighbor separations,
$s_{n}=k_{n}-k_{n-1}$.


title:
Universal potential barrier penetration by initially confined
  wavepackets

abstract:
  The dynamics of an initially sharp-boundary wavepacket in the presence of an
arbitrary potential barrier are investigated. It is shown that the penetration
through the barrier is universal in the sense that it depends only on the
values of the wavefunction and its derivatives at the boundary. The dependence
on the derivatives vanishes at long distances from the barrier, where the
dynamics are governed solely by the initial value of the wavefunction at the
boundary.


title: Laser Noise Reduction in Air

abstract:
  Fluctuations of the white-light supercontinuum produced by ultrashort laser
pulses in selfguided filaments (spatio-temporal solitons) in air are
investigated. We demonstrate that correlations exist within the white-light
supercontinuum, and that they can be used to significantly reduce the laser
intensity noise by filtering the spectrum. More precisely, the fundamental
wavelength is anticorrelated with the wings of the continuum, while conjugated
wavelength pairs on both sides of the continuum are strongly correlated.
Spectral filtering of the continuum reduces the laser intensity noise by 1.2
dB, showing that fluctuations are rejected to the edges of the spectrum.


title: Understanding Long-Distance Quantum Correlations

abstract:
  The interpretation of quantum mechanics (or, for that matter, of any physical
theory) consists in answering the question: How can the world be for the theory
to be true? That question is especially pressing in the case of the
long-distance correlations predicted by Einstein, Podolsky and Rosen, and
rather convincingly established during the past decades in various
laboratories. I will review four different approaches to the understanding of
long-distance quantum correlations: (i) the Copenhagen interpretation and some
of its modern variants; (ii) Bohmian mechanics of spin-carrying particles;
(iii) Cramer's transactional interpretation; and (iv) the Hess-Philipp analysis
of extended parameter spaces.


title: Multipartite purification protocols: upper and optimal bounds

abstract:
  A method for producing an upper bound for all multipartite purification
protocols is devised, based on knowing the optimal protocol for purifying
bipartite states. When applied to a range of noise models, both local and
correlated, the optimality of certain protocols can be demonstrated for a
variety of graph and valence bond states.


title: A generalization of boson normal ordering

abstract:
  In this paper we define generalizations of boson normal ordering. These are
based on the number of contractions whose vertices are next to each other in
the linear representation of the boson operator function. Our main motivation
is to shed further light onto the combinatorics arising from algebraic and Fock
space properties of boson operators.


title: Quantum metrology at the Heisenberg limit with ion traps

abstract:
  Sub-Planck phase-space structures in the Wigner function of the motional
degree of freedom of a trapped ion can be used to perform weak force
measurements with Heisenberg-limited sensitivity. We propose methods to
engineer the Hamiltonian of the trapped ion to generate states with such small
scale structures, and we show how to use them in quantum metrology
applications.


title:
Path Integral Approach for Superintegrable Potentials on Spaces of
  Non-constant Curvature: I. Darboux Spaces DI and DII

abstract:
  In this paper the Feynman path integral technique is applied for
superintegrable potentials on two-dimensional spaces of non-constant curvature:
these spaces are Darboux spaces D_I and D_II, respectively. On D_I there are
three and on D_II four such potentials, respectively. We are able to evaluate
the path integral in most of the separating coordinate systems, leading to
expressions for the Green functions, the discrete and continuous
wave-functions, and the discrete energy-spectra. In some cases, however, the
discrete spectrum cannot be stated explicitly, because it is either determined
by a transcendental equation involving parabolic cylinder functions (Darboux
space I), or by a higher order polynomial equation. The solutions on D_I in
particular show that superintegrable systems are not necessarily degenerate. We
can also show how the limiting cases of flat space (constant curvature zero)
and the two-dimensional hyperboloid (constant negative curvature) emerge.


title: A three grating electron interferometer

abstract:
  We report the observation of fringes from a three grating electron
interferometer. Interference fringes have been observed at low energies ranging
from 6 keV to 10 keV. Contrasts of up to 25% are recorded and exceed the
maximal contrast of the classical equivalent, Moire deflectometer. This type of
interferometer could serve as a separate beam Mach-Zehnder interferometer for
low energy electron interferometry experiments.


title: Quantum universality by state distillation

abstract:
  Quantum universality can be achieved using classically controlled stabilizer
operations and repeated preparation of certain ancilla states. Which ancilla
states suffice for universality? This "magic states distillation" question is
closely related to quantum fault tolerance. Lower bounds on the noise tolerable
on the ancilla help give lower bounds on the tolerable noise rate threshold for
fault-tolerant computation. Upper bounds show the limits of threshold
upper-bound arguments based on the Gottesman-Knill theorem.
  We extend the range of single-qubit mixed states that are known to give
universality, by using a simple parity-checking operation. For applications to
proving threshold lower bounds, certain practical stability characteristics are
often required, and we also show a stable distillation procedure.
  No distillation upper bounds are known beyond those given by the
Gottesman-Knill theorem. One might ask whether distillation upper bounds reduce
to upper bounds for single-qubit ancilla states. For multi-qubit pure states
and previously considered two-qubit ancilla states, the answer is yes. However,
we exhibit two-qubit mixed states that are not mixtures of stabilizer states,
but for which every postselected stabilizer reduction from two qubits to one
outputs a mixture of stabilizer states. Distilling such states would require
true multi-qubit state distillation methods.


title: Doubly constrained bounds on the entanglement of formation

abstract:
  We derive bounds on the entanglement of formation of states of a 4xN
bipartite system using two entanglement monotones constructed from operational
separability criteria. The bounds are used simultaneously as constraints on the
entanglement of formation. One monotone is the negativity, which is based on
the Peres positive-partial-transpose criterion. For the other, we formulate a
monotone based on a separability criterion introduced by Breuer (H.-P. Breuer,
e-print quant-ph/0605036).


title: POVMs: a small but important step beyond standard quantum mechanics

abstract:
  It is the purpose of the present contribution to demonstrate that the
generalization of the concept of a quantum mechanical observable from the
Hermitian operator of standard quantum mechanics to a positive operator-valued
measure is not a peripheral issue, allegedly to be understood in terms of a
trivial nonideality of practical measurement procedures, but that this
generalization touches the very core of quantum mechanics, viz. complementarity
and violation of the Bell inequalities.


title:
VIP: An Experiment to Search for a Violation of the Pauli Exclusion
  Principle

abstract:
  The Pauli Exclusion Principle is a basic principle of Quantum Mechanics, and
its validity has never been seriously challenged. However, given its
fundamental standing, it is very important to check it as thoroughly as
possible. Here we describe the VIP (VIolation of the Pauli exclusion principle)
experiment, an improved version of the Ramberg and Snow experiment (E. Ramberg
and G. Snow, {\it Phys. Lett. B} {\bf 238}, 438 (1990)); VIP has just completed
the installation at the Gran Sasso underground laboratory, and aims to test the
Pauli Exclusion Principle for electrons with unprecedented accuracy, down to
$\beta^2/2 \approx 10^{-30} - 10^{-31}$. We report preliminary experimental
results and briefly discuss some of the implications of a possible violation.


title:
Efficient coherent internal state transfer in trapped ions using
  Stimulated Raman Adiabatic Passage

abstract:
  We demonstrate experimentally how the process of Stimulated Raman Adiabatic
Passage (STIRAP) can be utilized for efficient coherent internal state transfer
in single trapped and laser-cooled $^{40}$Ca$^+$ ions. The transfer from the
D$_{3/2}$ to the D$_{5/2}$ state, is detected by a fluorescence measurement
revealing the population not transfered to the D$_{5/2}$ state. A coherent
population transfer efficiency at the level of 95 % in a setup allowing for the
internal state detection of individual ions in a string has been obtained.


title:
The Convex Closure of the Output Entropy of Infinite Dimensional
  Channels and the Additivity Problem

abstract:
  The continuity properties of the convex closure of the output entropy of
infinite dimensional channels and their applications to the additivity problem
are considered.
  The main result of this paper is the statement that the superadditivity of
the convex closure of the output entropy for all finite dimensional channels
implies the superadditivity of the convex closure of the output entropy for all
infinite dimensional channels, which provides the analogous statements for the
strong superadditivity of the EoF and for the additivity of the minimal output
entropy.
  The above result also provides infinite dimensional generalization of Shor's
theorem stated equivalence of different additivity properties.
  The superadditivity of the convex closure of the output entropy (and hence
the additivity of the minimal output entropy) for two infinite dimensional
channels with one of them a direct sum of noiseless and entanglement-breaking
channels are derived from the corresponding finite dimensional results.
  In the context of the additivity problem some observations concerning
complementary infinite dimensional channels are considered.


title: An ansatz for the eigenstates in PT-symmetric quantum mechanics

abstract:
  We suggest a general ansatz for the energy-eigenstates when a complex
one-dimensional PT-symmetric potential possesses real discrete spectrum.
Several interesting features of PT-symmetric quantum mechanics have been
brought out using this ansatz.


title: Sum Uncertainty Relation in Quantum Theory

abstract:
  We prove a new sum uncertainty relation in quantum theory which states that
the uncertainty in the sum of two or more observables is always less than or
equal to the sum of the uncertainties in corresponding observables. This shows
that the quantum mechanical uncertainty in any observable is a convex function.
We prove that if we have a finite number $N$ of identically prepared quantum
systems, then a joint measurement of any observable gives an error $\sqrt N$
less than that of the individual measurements. This has application in quantum
metrology that aims to give better precision in the parameter estimation.
Furthermore, this proves that a quantum system evolves slowly under the action
of a sum Hamiltonian than the sum of individuals, even if they are
non-commuting.


title: A gauge theory of quantum mechanics

abstract:
  An Abelian gerbe is constructed over classical phase space. The 2-cocycles
defining the gerbe are given by Feynman path integrals whose integrands contain
the exponential of the Poincare-Cartan form. The U(1) gauge group on the gerbe
has a natural interpretation as the invariance group of the Schroedinger
equation on phase space.


title: Spectrum of coherent backscattering of light by two atoms

abstract:
  We study theoretically inelastic spectrum of coherent backscattering of laser
light by two atoms. For an intense laser field, there are frequency domains of
not only constructive but also destructive (self-)interference of the inelastic
photons. We interpret the emergent spectral features using the dressed states
and considering coherent backscattering as a kind of the pump-probe experiment.


title:
Study of the Distillability of Werner States Using Entanglement
  Witnesses and Robust Semidefinite Programs

abstract:
  We use Robust Semidefinite Programs and Entanglement Witnesses to study the
distillability of Werner states. We perform exact numerical calculations which
show 2-undistillability in a region of the state space which was previously
conjectured to be undistillable. We also introduce bases which yield
interesting expressions for the {\em distillability witnesses} and for a tensor
product of Werner states with arbitrary number of copies.


title:
Coalitions in the quantum Minority game: classical cheats and quantum
  bullies

abstract:
  In a one-off Minority game, when a group of players agree to collaborate they
gain an advantage over the remaining players. We consider the advantage
obtained in a quantum Minority game by a coalition sharing an initially
entangled state versus that obtained by a coalition that uses classical
communication to arrive at an optimal group strategy. In a model of the quantum
Minority game where the final measurement basis is randomized, quantum
coalitions outperform classical ones when carried out by up to four players,
but an unrestricted amount of classical communication is better for larger
coalition sizes.


title:
Coupled Ito equations of continuous quantum state measurement, and
  estimation

abstract:
  We discuss a non-linear stochastic master equation that governs the
time-evolution of the estimated quantum state. Its differential evolution
corresponds to the infinitesimal updates that depend on the time-continuous
measurement of the true quantum state. The new stochastic master equation
couples to the two standard stochastic differential equations of
time-continuous quantum measurement. For the first time, we can prove that the
calculated estimate almost always converges to the true state, also at
low-efficiency measurements. We show that our single-state theory can be
adapted to weak continuous ensemble measurements as well.


title: Entanglement fidelity of quantum memories

abstract:
  We introduce a figure of merit for a quantum memory which measures the
preservation of entanglement between a qubit stored in and retrieved from the
memory and an auxiliary qubit. We consider a general quantum memory system
consisting of a medium of two level absorbers, with the qubit to be stored
encoded in a single photon. We derive an analytic expression for our figure of
merit taking into account Gaussian fluctuations in the Hamiltonian parameters,
which for example model inhomogeneous broadening and storage time dephasing.
Finally we specialize to the case of an atomic quantum memory where
fluctuations arise predominantly from Doppler broadening and motional
dephasing.


title:
Uniform semiclassical approximations of the nonlinear Schroedinger
  equation by a Painleve mapping

abstract:
  A useful semiclassical method to calculate eigenfunctions of the Schroedinger
equation is the mapping to a well-known ordinary differential equation, as for
example Airy's equation. In this paper we generalize the mapping procedure to
the nonlinear Schroedinger equation or Gross-Pitaevskii equation describing the
macroscopic wave function of a Bose-Einstein condensate. The nonlinear
Schroedinger equation is mapped to the second Painleve equation, which is one
of the best-known differential equations with a cubic nonlinearity. A
quantization condition is derived from the connection formulae of these
functions. Comparison with numerically exact results for a harmonic trap
demonstrates the benefit of the mapping method. Finally we discuss the
influence of a shallow periodic potential on bright soliton solutions by a
mapping to a constant potential.


title: Causality, Joint measurement and Tsirelson's bound

abstract:
  Tsirelson showed that $2\sqrt{2}$ is the maximum value that CHSH expression
can take for quantum-correlations [B. S.Tsirelson, Lett. Math. Phys, 4 (1980)
93]. This bound simply follows from the algebra of observables. Recently by
exploiting the physical structure of quantum mechanics like unitarity and
linearity, Buhrman and Massar [H. Buhrman and S.Massar, Phys. Rev. A, 72 (2005)
052103] have established that violation of Tsirelson's bound in quantum
mechanics will imply signalling. We prove the same with the help of realistic
joint measurement in quantum mechanics and a Bell's inequality which has been
derived under the assumption of existence of joint measurement and no
signalling condition.


title: The Bounded Storage Model in The Presence of a Quantum Adversary

abstract:
  An extractor is a function E that is used to extract randomness. Given an
imperfect random source X and a uniform seed Y, the output E(X,Y) is close to
uniform. We study properties of such functions in the presence of prior quantum
information about X, with a particular focus on cryptographic applications. We
prove that certain extractors are suitable for key expansion in the bounded
storage model where the adversary has a limited amount of quantum memory. For
extractors with one-bit output we show that the extracted bit is essentially
equally secure as in the case where the adversary has classical resources. We
prove the security of certain constructions that output multiple bits in the
bounded storage model.


title:
A study of the bound states for square potential wells with
  position-dependent mass

abstract:
  A square potential well with position-dependent mass is studied for bound
states. Applying appropriate matching conditions, a transcendental equation is
derived for the energy eigenvalues. Numerical results are presented graphically
and the variation of the energy of the bound states are calculated as a
function of the well-width and mass.


title:
Optical parametric oscillation under injection of orbital angular
  momentum

abstract:
  We present a theoretical model for the spatial mode dynamics of an optical
parametric oscillator under injection of orbital angular momentum. This process
is then interpreted in terms of an interesting picture based on a Poincare
representation of first order spatial modes. The spatial properties of the
down-converted fields can be easily understood from their symmetries in this
geometric representation. By considering the adiabatic mode conversion of the
injected signal, we also predict the occurrence of a geometric phase
conjugation in the down-converted beams. An experimental setup to measure this
effect is proposed.


title: Slow-light solitons revisited

abstract:
  We investigate propagation of slow-light solitons in atomic media described
by the nonlinear $\Lambda$-model. Under a physical assumption, appropriate to
the slow light propagation, we reduce the $\Lambda$-scheme to a simplified
nonlinear model, which is also relevant to 2D dilatonic gravity. Exact
solutions describing various regimes of stopping slow-light solitons can then
be readily derived.


title:
Implementation of qutrit-based quantum information processing via
  state-dependent forces on trapped ions

abstract:
  We propose a scheme to realize quantum logic and entanglement for qutrit
systems via state-dependent forces on trapped ions. By exploiting the laser-ion
coupling in the presence of Coulomb interactions, the set of quantum gate
operations including the conditional phase shifts on two qutrits as well as
arbitrary SU(3) rotations on single qutrits are derived for universal quantum
manipulation. As an illustration, we demonstrate in detail how these gate
resources could be used to generate the maximally entangled state of two
qutrits. Besides being insensitive to vibrational heating of the trapped ions,
the present scheme is also shown to be scalable through designing appropriately
the pulse configuration of the laser-ion interactions.


title: Quantum Partial Search of a Database with Several Target Items

abstract:
  We consider a database separated into blocks. Blocks containing target items
are called target blocks. Blocks without target items are called non-target
blocks. We consider a case, when each target block has the same number of
target items. We present a fast quantum algorithm, which finds one of the
target blocks. Our algorithm is based on Grover-Radhakrishnan algorithm of
partial search. We minimize the number of queries to the oracle.


title: Multiuser quantum communication networks

abstract:
  We study a quantum state transfer between spins interacting with an arbitrary
network of spins coupled by uniform XX interactions. It is shown that in such a
system under fairly general conditions, we can expect a nearly perfect transfer
of states. Then we analyze a generalization of this model to the case of many
network users, where the sender can choose which party he wants to communicate
with by appropriately tuning his local magnetic field. We also remark that a
similar idea can be used to create an entanglement between several spins
coupled to the network.


title: Factorization of Dephasing Process in Quantum Open System

abstract:
  The fluctuation-dissipation relation is well known for the quantum open
system with energy dissipation. In this paper a similar underlying relation is
found between the bath fluctuation and the dephasing of the quantum open
system, of which energy is conserved, but the information is leaking into the
bath. To obtain this relation we revisit the universal, but simple dephasing
model with quantum non-demolition interaction between the bath and the open
system. Then we show that the decoherence factor describing the dephasing
process is factorized into two parts, to indicate the two sources of dephasing,
the vacuum quantum fluctuation and the thermal excitations defined in the
initial state of finite temperature.


title: Controlled splitting of an atomic wave packet

abstract:
  We propose a simple scheme capable of adiabatically splitting an atomic wave
packet using two independent translating traps. Implemented with optical dipole
traps, our scheme allows a high degree of flexibility for atom interferometry
arrangements and highlights its potential as an efficient and high fidelity
atom optical beam splitter.


title:
100 km secure differential phase shift quantum key distribution with low
  jitter up-conversion detectors

abstract:
  We present a quantum key distribution experiment in which keys that were
secure against all individual eavesdropping attacks allowed by quantum
mechanics were distributed over 100 km of optical fiber. We implemented the
differential phase shift quantum key distribution protocol and used low timing
jitter 1.55 um single-photon detectors based on frequency up-conversion in
periodically poled lithium niobate waveguides and silicon avalanche
photodiodes. Based on the security analysis of the protocol against general
individual attacks, we generated secure keys at a practical rate of 166 bit/s
over 100 km of fiber. The use of the low jitter detectors also increased the
sifted key generation rate to 2 Mbit/s over 10 km of fiber.


title:
Preparation of cluster states and W states with superconducting-
  quantum-interference-device qubits in cavity QED

abstract:
  We propose schemes to create cluster states and W states by many
superconducting-quantum-interference-device (SQUID) qubits in cavities under
the influence of the cavity decay. Our schemes do not require auxiliary qubits,
and the excited levels are only virtually coupled throughout the scheme, which
could much reduce the experimental challenge. We consider the cavity decay in
our model and analytically demonstrate its detrimental influence on the
prepared entangled states.


title: Gate-level simulation of logical state preparation

abstract:
  Quantum error correction and fault-tolerant quantum computation are two
fundamental concepts which make quantum computing feasible. While providing a
theoretical means with which to ensure the arbitrary accuracy of any quantum
circuit, fault-tolerant error correction is predicated upon the robust
preparation of logical states. An optimal direct circuit and a more complex
fault-tolerant circuit for the preparation of the [[7,1,3]] Steane logical-zero
are simulated in the presence of discrete quantum errors to quantify the regime
within which fault-tolerant preparation of logical states is preferred.


title: Retrodictive fidelities for pure state postselectors

abstract:
  Two measures of fidelity are proposed for postselecting devices, the
retrodictive conditional probability that the state in the measurement arm is
the one indicated by the detectors, and the probability that the device
produces the state that it would produce if working perfectly. The first is the
natural quantity that one wishes to maximise to improve the device operation.
The second corresponds more closely with the accurate operation of the device
than the more usual overlap-based fidelity. The results are particularly
applicable to the types of state preparation and logic gate operation in linear
optical quantum computing.


title: Phase Dynamics of Two Entangled Qubits

abstract:
  We make a geometric study of the phases acquired by a general pure bipartite
two level system after a cyclic unitary evolution. The geometric representation
of the two particle Hilbert space makes use of Hopf fibrations. It allows for a
simple description of the dynamics of the entangled state's phase during the
whole evolution. The global phase after a cyclic evolution is always an entire
multiple of $\pi$ for all bipartite states, a result that does not depend on
the degree of entanglement. There are three different types of phases combining
themselves so as to result in the $n \pi$ global phase. They can be identified
as dynamical, geometrical and topological. Each one of them can be easily
identified using the presented geometric description. The interplay between
them depends on the initial state and on its trajectory and the results
obtained are shown to be in connection to those on mixed states phases.


title: Quantum levitation by left-handed metamaterials

abstract:
  Left-handed metamaterials make perfect lenses that image classical
electromagnetic fields with significantly higher resolution than the
diffraction limit. Here we consider the quantum physics of such devices. We
show that the Casimir force of two conducting plates may turn from attraction
to repulsion if a perfect lens is sandwiched between them. For optical
left-handed metamaterials this repulsive force of the quantum vacuum may
levitate ultra-thin mirrors.


title: Formulation of the uncertainty relations in terms of the Renyi entropies

abstract:
  Quantum mechanical uncertainty relations for position and momentum are
expressed in the form of inequalities involving the Renyi entropies. The proof
of these inequalities requires the use of the exact expression for the
(p,q)-norm of the Fourier transformation derived by Babenko and Beckner.
Analogous uncertainty relations are derived for angle and angular momentum and
also for a pair of complementary observables in N-level systems. All these
uncertainty relations become more attractive when expressed in terms of the
symmetrized Renyi entropies.


title: Quantum fractals on n-spheres. Clifford Algebra approach

abstract:
  Using the Clifford algebra formalism we extend the quantum jumps algorithm of
the Event Enhanced Quantum Theory (EEQT) to convex state figures other than
those stemming from convex hulls of complex projective spaces that form the
basis for the standard quantum theory. We study quantum jumps on n-dimensional
spheres, jumps that are induced by symmetric configurations of non-commuting
state monitoring detectors. The detectors cause quantum jumps via geometrically
induced conformal maps (Mobius transformations) and realize iterated function
systems (IFS) with fractal attractors located on n-dimensional spheres. We also
extend the formalism to mixed states, represented by "density matrices". As a
numerical illustration we study quantum fractals on the circle, two--sphere
(octahedron), and on three-dimensional sphere (hypercube-tesseract, 24 cell,
600 cell,and 120 cell). The invariant measure on the attractor is approximated
by the powers of the Markov operator. In the appendices we calculate the
Radon-Nikodym derivative of the SO(n+1) invariant measure on S^n under
SO(1,n+1) transformations and discuss the Hamilton's "icossian calculus" as
well as its application to quaternionic realization of the binary icosahedral
group that is at the basis of the 600 cell and its dual, the 120 cell. As a
by-product of this work we obtain several Clifford algebraic results, such as a
characterization of positive elements in a Clifford algebra Cl(n+1) as
generalized Lorentz boosts, and their action as Moebius transformation on
n-sphere, and a decomposition of any element of Spin^+(1,n+1) into a boost and
a rotation, including the explicit formula for the pullback of the O(n+1)
invariant Riemannian metric with respect to the associated Mobius
transformation.


title: Dispersion forces in macroscopic quantum electrodynamics

abstract:
  The description of dispersion forces within the framework of macroscopic
quantum electrodynamics in linear, dispersing, and absorbing media combines the
benefits of approaches based on normal-mode techniques of standard quantum
electrodynamics and methods based on linear response theory in a natural way.
It renders generally valid expressions for both the forces between bodies and
the forces on atoms in the presence of bodies, while showing very clearly the
intimate relation between the different types of dispersion forces. By
considering examples, the influence of various factors like form, size,
electric and magnetic properties, or intervening media on the forces is
addressed. Since the approach based on macroscopic quantum electrodynamics does
not only apply to equilibrium systems, it can be used to investigate dynamical
effects such as the temporal evolution of forces on arbitrarily excited atoms.


title: Decoherence of Anyonic Charge in Interferometry Measurements

abstract:
  We examine interferometric measurements of the topological charge of
(non-Abelian) anyons. The target's topological charge is measured from its
effect on the interference of probe particles sent through the interferometer.
We find that superpositions of distinct anyonic charges a and a' in the target
decohere (exponentially in the number of probes particles used) when the probes
have nontrivial monodromy with the charges that may be fused with a to give a'.


title: Ontological Models for Quantum Mechanics and the Kochen-Specker theorem

abstract:
  Certain concrete "ontological models" for quantum mechanics (models in which
measurement outcomes are deterministic and quantum states are equivalent to
classical probability distributions over some space of `hidden variables') are
examined. The models are generalizations of Kochen and Specker's such model for
a single 2-dimensional system - in particular a model for a three dimensional
quantum system is considered in detail. Unfortunately, it appears the models do
not quite reproduce the quantum mechanical statistics. They do, however, come
close to doing so, and in as much as they simply involve probability
distributions over the complex projective space they do reproduce pretty much
everything else in quantum mechanics.
  The Kochen-Specker theorem is examined in the light of these models, and the
rather mild nature of the manifested contextuality is discussed.


title:
Entanglement in general two-mode continuous-variable states: local
  approach and mapping to a two-qubit system

abstract:
  We present a new approach to the analysis of entanglement in smooth bipartite
continuous-variable states. One or both parties perform projective filterings
via preliminary measurements to determine whether the system is located in some
region of space; we study the entanglement remaining after filtering. For small
regions, a two-mode system can be approximated by a pair of qubits and its
entanglement fully characterized, even for mixed states. Our approach may be
extended to any smooth bipartite pure state or two-mode mixed state, leading to
natural definitions of concurrence and negativity densities. For Gaussian
states both these quantities are constant throughout configuration space.


title: Repulsive Casimir Pistons

abstract:
  Casimir pistons are models in which finite Casimir forces can be calculated
without any suspect renormalizations. It has been suggested that such forces
are always attractive. We present three scenarios in which that is not true.
Two of these depend on mixing two types of boundary conditions. The other,
however, is a simple type of quantum graph in which the sign of the force
depends upon the number of edges.


title: Non-Markovian decoherence in the adiabatic quantum search algorithm

abstract:
  We consider an adiabatic quantum algorithm (Grover's search routine) weakly
coupled to a rather general environment, i.e., without using the Markov
approximation. Markovian errors generally require high-energy excitations (of
the reservoir) and tend to destroy the scalability of the adiabatic quantum
algorithm. We find that, under appropriate conditions (such as low
temperatures), the low-energy (i.e., non-Markovian) modes of the bath are most
important. Hence the scalability of the adiabatic quantum algorithm depends on
the infra-red behavior of the environment: a reasonably small coupling to the
three-dimensional electromagnetic field does not destroy the scaling behavior,
whereas phonons or localized degrees of freedom can be problematic. PACS:
03.67.Pp, 03.67.Lx, 03.67.-a, 03.65.Yz.


title: Dimensions of generic local orbits of multipartite quantum systems

abstract:
  We consider the action of the group of local unitary transformations, U(m) x
U(n), on the set of (mixed) states W of the bipartite m x n quantum system. We
prove that the generic U(m) x U(n)--orbits in W have dimension m^2+n^2-2. This
problem was mentioned (and left open) by Kus and Zyczkowski in their paper
Geometry of entangled states. The proof can be extended to the case of
arbitrary finite-dimensional multipartite quantum systems.


title:
The spin-statistics relation in nonrelativistic quantum mechanics and
  projective modules

abstract:
  In this work we consider non-relativistic quantum mechanics, obtained from a
classical configuration space Q of indistinguishable particles. Following an
approach proposed by one of the authors, wave functions are regarded as
elements of suitable projective modules over C(Q). We take furthermore into
account the G-Theory point of view, where the role of group action is
particularly emphasized. As an example illustrating the method, the case of two
particles is worked out in detail. Previous works aiming at a proof of a
spin-statistics theorem for non-relativistic quantum mechanics are
re-considered from the point of view of our approach, enabling us to clarify
several points.


title: Characterization of unwanted noise in realistic cavities

abstract:
  The problem of the description of absorption and scattering losses in high-Q
cavities is studied. The considerations are based on quantum noise theories,
hence the unwanted noise associated with scattering and absorption is taken
into account by introduction of additional damping and noise terms in the
quantum Langevin equations and input--output relations. Completeness conditions
for the description of the cavity models obtained in this way are studied and
corresponding replacement schemes are discussed.


title: Classical and quantum theory for Superluminal particle

abstract:
  As we all know, when the relative velocity of two inertial reference frames
$\sum$ and $\sum^{'}$ is less than the speed of light, the relations of
$x_{\mu}$ with $x_{\mu}^{'}$, a particle mass $m$ with its velocity $\upsilon$,
and a particle mass with its energy are all given by Einstein's special
relativity. In this paper, we will give new relation of $x_{\mu}$ and
$x_{\mu}^{'}$ when the relative velocity of $\sum$ and $\sum^{'}$ frame is
larger than the speed of light, and also we give the relation of a particle
mass $m$ with its velocity $\upsilon$, and a particle mass $m$ with its energy
$E$ when the particle velocity $v$ is larger than the speed of light.


title: Bounds on Quantum Correlations in Bell Inequality Experiments

abstract:
  Bell inequality violation is one of the most widely known manifestations of
entanglement in quantum mechanics; indicating that experiments on physically
separated quantum mechanical systems cannot be given a local realistic
description. However, despite the importance of Bell inequalities, it is not
known in general how to determine whether a given entangled state will violate
a Bell inequality. This is because one can choose to make many different
measurements on a quantum system to test any given Bell inequality and the
optimization over measurements is a high-dimensional variational problem. In
order to better understand this problem we present algorithms that provide, for
a given quantum state, both a lower bound and an upper bound on the maximal
expectation value of a Bell operator. Both bounds apply techniques from convex
optimization and the methodology for creating upper bounds allows them to be
systematically improved. In many cases these bounds determine measurements that
would demonstrate violation of the Bell inequality or provide a bound that
rules out the possibility of a violation. Examples are given to illustrate how
these algorithms can be used to conclude definitively if some quantum states
violate a given Bell inequality.


title: Coherent Acceleration of Material Wavepackets

abstract:
  We study the quantum dynamics of a material wavepacket bouncing off a
modulated atomic mirror in the presence of a gravitational field. We find the
occurrence of coherent accelerated dynamics for atoms. The acceleration takes
place for certain initial phase space data and within specific windows of
modulation strengths. The realization of the proposed acceleration scheme is
within the range of present day experimental possibilities.


title: Wave functions of linear systems

abstract:
  Complete analysis of quantum wave functions of linear systems in an arbitrary
number of dimensions is given. It is shown how one can construct a complete set
of stationary quantum states of an arbitrary linear system from purely
classical arguments. This construction is possible because for linear systems
classical dynamics carries the whole information about quantum dynamics.


title: New models of quantum games

abstract:
  In this work we propose and develop modified quantum games (zero and non-zero
sum) in which payoffs and strategies are entangled. For the games studied, Nash
and Pareto equilibriums are always obtained indicating that there are some
interesting cases where quantum games can be applied.


title: Computation with Unitaries and One Pure Qubit

abstract:
  We define a semantic complexity class based on the model of quantum computing
with just one pure qubit (as introduced by Knill and Laflamme) and discuss its
computational power in terms of the problem of estimating the trace of a large
unitary matrix. We show that this problem is complete for the complexity class,
and derive some further fundamental features of the class. We conclude with a
discussion of some associated open conjectures and new oracle separations
between classes.


title: High fidelity teleportation between light and atoms

abstract:
  We show how high fidelity quantum teleportation of light to atoms can be
achieved in the same setup as was used in the recent experiment [J. Sherson
et.al., quant-ph/0605095, accepted by Nature], where such an inter-species
quantum state transfer was demonstrated for the first time. Our improved
protocol takes advantage of the rich multimode entangled structure of the state
of atoms and scattered light and requires simple post-processing of homodyne
detection signals and squeezed light in order to achieve fidelities up to 90%
(85%) for teleportation of coherent (qubit) states under realistic experimental
conditions. The remaining limitation is due to atomic decoherence and light
losses.


title:
Generation and Suppression of Decoherence in Artificial Environment for
  Qubit System

abstract:
  It is known that a quantum system with finite degrees of freedom can simulate
a composite of a system and an environment if the state of the hypothetical
environment is randomized by external manipulation. We show theoretically that
any phase decoherence phenomena of a single qubit can be simulated with a
two-qubit system and demonstrate experimentally two examples: one is phase
decoherence of a single qubit in a transmission line, and the other is that in
a quantum memory. We perform NMR experiments employing a two-spin molecule and
clearly measure decoherence for both cases. We also prove experimentally that
the bang-bang control efficiently suppresses decoherence.


title:
Decoherence problem in quantum state transfer via an engineered spin
  chain

abstract:
  A perfect quantum state transfer(QST) has been shown in an engineered spin
chain with "always-on interaction". Here, we consider a more realistic problem
for such a protocol, the quantum decoherence induced by a spatially distributed
environment, which is universally modeled as a bath of harmonic oscillators. By
making use of the irreducible tensor method in angular momentum theory, we
investigate the effect of decoherence on the efficiency of QST for both cases
at zero and finite temperatures. We not only show the generic exponential decay
of QST efficiency as the number of sites increase, but also find some
counterintuitive effect, the QST can be enhanced as temperature increase.


title:
Multimode uncertainty relations and separability of continuous variable
  states

abstract:
  A multimode uncertainty relation (generalising the Robertson-Schroedinger
relation) is derived as a necessary constraint on the second moments of n pairs
of canonical operators. In turn, necessary conditions for the separability of
multimode continuous variable states under (m+n)-mode bipartitions are derived
from the uncertainty relation. These conditions are proven to be necessary and
sufficient for (1+n)-mode Gaussian states and for (m+n)-mode bisymmetric
Gaussian states.


title: Implementation of multipartite unitary operations with limited resources

abstract:
  A general method for implementing weakly entangling multipartite unitary
operations using a small amount of entanglement and classical communication is
presented. For the simple Hamiltonian \sigma_z\otimes\sigma_z this method
requires less entanglement than previously known methods. In addition,
compression of multiple operations is applied to reduce the average
communication required.


title: The certainty principle (review)

abstract:
  The certainty principle (2005) allowed to conceptualize from the more
fundamental grounds both the Heisenberg uncertainty principle (1927) and the
Mandelshtam-Tamm relation (1945). In this review I give detailed explanation
and discussion of the certainty principle, oriented to all physicists, both
theorists and experimenters.


title: Entanglement versus energy in the entanglement transfer problem

abstract:
  We study the relation between energy and entanglement in an entanglement
transfer problem. We first analyze the general setup of two entangled qubits (a
and b) exchanging this entanglement with two other independent qubits (A and
B). Qubit a (b) interacts with qubit A (B) via a spin exchange-like unitary
evolution. A physical realization of this scenario could be the problem of
two-level atoms transferring entanglement to resonant cavities via independent
Jaynes-Cummings interactions. We study the dynamics of entanglement and energy
for the second pair of qubits (tracing out the originally entangled ones) and
show that these quantities are closely related. For example, the allowed
quantum states occupy a restricted area in a phase diagram entanglement vs.
energy. Moreover the curve which bounds this area is exactly the one followed
if both interactions are equal and the entire four qubit system is isolated. We
also consider the case when the target pair of qubits is subjected to losses
and can spontaneously decay.


title: 1951 Lectures on Advanced Quantum Mechanics Second Edition

abstract:
  The legendary 1951 Dyson Lectures on Advanced Quantum Mechanics are finally
LaTeXed, with thorough annotations and an index as an added bonus. See the
Typist's Afterward preceding the backmatter for an explanation of this new
version, and for the historical context see the website:
http://hrst.mit.edu/hrs/renormalization/dyson51-intro/ as well as the author's
website at the Princeton Institute for Advanced Study:
http://www.sns.ias.edu/~dyson/


title: Useful entanglement from the Pauli principle

abstract:
  We address the question whether identical-particle entanglement is a useful
resource for quantum information processing. We answer this question positively
by reporting a scheme to create entanglement using semiconductor quantum wells.
The Pauli exclusion principle forces quantum correlations between the spins of
two independent fermions in the conduction band. Selective electron-hole
recombination then transfers this entanglement to the polarization of emitted
photons, which can subsequently be used for quantum information tasks.


title: The Learnability of Quantum States

abstract:
  Traditional quantum state tomography requires a number of measurements that
grows exponentially with the number of qubits n. But using ideas from
computational learning theory, we show that "for most practical purposes" one
can learn a state using a number of measurements that grows only linearly with
n. Besides possible implications for experimental physics, our learning theorem
has two applications to quantum computing: first, a new simulation of quantum
one-way communication protocols, and second, the use of trusted classical
advice to verify untrusted quantum advice.


title: Analyzing the effectiveness of the quantum repeater

abstract:
  The communication distance of QKD is limited by exponential attenuation of
photons propagating through optical fibers. However, it has been shown that
introducing a quantum repeater can improve the order of the attenuation and is
useful for extending the communication distance of QKD when the repeater noise
is ignored. In this paper, we analyze the effectiveness of the quantum repeater
when taking the repeater noise into consideration. We analyze the effectiveness
also from the viewpoint of the security and show that QKD is secure even if a
quantum repeater is used.


title:
Efficient-phase-encoding protocols for continuous-variable quantum key
  distribution using coherent states and postselection

abstract:
  We propose efficient-phase-encoding protocols for continuous-variable quantum
key distribution using coherent states and postselection. By these phase
encodings, the probability of basis mismatch is reduced and total efficiency is
increased. We also propose mixed-state protocols by omitting a part of
classical communication steps in the efficient-phase-encoding protocols. The
omission implies a reduction of information to an eavesdropper and possibly
enhances the security of the protocols. We investigate the security of the
protocols against individual beam splitting attack.


title: Stabilizer state breeding

abstract:
  We present a breeding protocol that distills pure copies of any stabilizer
state from noisy copies and a pool of predistilled pure copies of the same
state, by means of local Clifford operations, Pauli measurements and classical
communication.


title: Strong Parallel Repetition Theorem for Quantum XOR Proof Systems

abstract:
  We consider a class of two-prover interactive proof systems where each prover
returns a single bit to the verifier and the verifier's verdict is a function
of the XOR of the two bits received. We show that, when the provers are allowed
to coordinate their behavior using a shared entangled quantum state, a perfect
parallel repetition theorem holds in the following sense. The prover's optimal
success probability for simultaneously playing a collection of XOR proof
systems is exactly the product of the individual optimal success probabilities.
This property is remarkable in view of the fact that, in the classical case
(where the provers can only utilize classical information), it does not hold.
The theorem is proved by analyzing parities of XOR proof systems using
semidefinite programming techniques, which we then relate to parallel
repetitions of XOR games via Fourier analysis.


title:
Numerical simulation of a Controlled-Controlled-Not (CCN) quantum gate
  in a chain of three interacting nuclear spins system

abstract:
  We present the study of a quantum Controlled-Controlled-Not gate, implemented
in a chain of three nuclear spins weakly Ising interacting between all of them,
that is, taking into account first and second neighbor spin interactions. This
implementation is done using a single resonant $\pi$-pulse on the initial state
of the system (digital and superposition). The fidelity parameter is used to
determine the behavior of the CCN quantum gate as a function of the ratio of
the second neighbor interaction coupling constant to the first neighbor
interaction coupling constant ($J'/J$). We found that for $J'/J\ge 0.02$ we can
have a well defined CCN quantum gate.


title:
Chain of nuclear spins system quantum computer taking into account
  second neighbor Ising spins interaction and numerical simulation of Shor
  factorization of N=4

abstract:
  For a one-dimensional chain of four nuclear spins (1/2) and taking into
account first and second neighbor interactions among the spin system, we make
the numerical simulation of Shor prime factorization algorithm of the integer
number N=4 to study the influence of the second neighbor interaction on the
performance of this algorithm. It is shown that the optimum Rabi's frequency to
control the non-resonant effects is dominated by the second neighbor
interaction coupling parameter ($J'$), and that a good Shor quantum
factorization is achieved for a ratio of second to first coupling constant of
$J'/J\ge 0.04$.


title:
Quantization of a one-dimensional time-dependent periodic system with
  Hamiltonian and constants of motion approaches

abstract:
  For a particle moving in a one-dimensional space an under a periodic external
force, its quantization is study using the Hamiltonian (generalized linear
momentum quantization) and constant of motion (velocity quantization)
approaches. it is shown a great difference on the quantization of both
approaches and the ambiguities arisen by using the quantization on the
constants of motion.


title: Projecting onto Qubit Irreps of Young Diagrams

abstract:
  Let K be the diagonal subgroup of U(2)^{(x)n}. We may view the one-qubit
state-space H_1 as a standard representation of U(2) and the n-qubit state
space H_n=(H_1)^{(x) n} as the n-fold tensor product of standard
representations. Representation theory then decomposes H_n into irreducible
subrepresentations of K parametrized by combinatorial objects known as Young
diagrams. We argue that n-1 classically controlled measurement circuits, each a
Fredkin-gate interferometer, may be used to form a projection operator onto a
random Young diagram irrep within H_n. For H_2, the two irreps happen to be
orthogonal and correspond to the symmetric and wedge product. The latter is
spanned by ket{Psi^-}, and the standard two-qubit swap interferometer requiring
a single Fredkin gate suffices in this case. In the n-qubit case, it is
possible to extract many copies of ket{Psi^-}. Thus applying this process using
nondestructive Fredkin interferometers allows for the creation of entangled
bits (e-bits) using fully mixed states and von Neumann measurements.


title: Separability and Entanglement of Identical Bosonic Systems

abstract:
  We investigate the separability of arbitrary $n$-dimensional multipartite
identical bosonic systems. An explicit relation between the dimension and the
separability is presented. In particular, for $n=3$, it is shown that the
property of PPT (positive partial transpose) and the separability are
equivalent for tripartite systems.


title: Effective error-suppression scheme for reversible quantum computer

abstract:
  We construct a new error-suppression scheme that makes use of the adjoint of
reversible quantum algorithms. For decoherence induced errors such as
depolarization, it is presented that provided the depolarization error
probability is less than 1, our scheme can exponentially reduce the final
output error rate to zero using a number of cycles, and the output state can be
coherently sent to another stage of quantum computation process. Besides,
experimental set-ups via optical approach have been proposed using Grover's
search algorithm as an example. Some further discussion on the benefits and
limitations of the scheme is given in the end.


title: Superbroadcasting and classical information

abstract:
  We address the problem of broadcasting N copies of a generic qubit state to
M>N copies by estimating its direction and preparing a suitable output state
according to the outcome of the estimate. This semiclassical broadcasting
protocol is more restrictive than a general one, since it requires an
intermediate step where classical information is extracted and processed.
However, we prove that a suboptimal superbroadcasting, namely broadcasting with
simultaneous purification of the local output states with respect to the input
ones, is possible. We show that in the asymptotic limit of $M \to \infty$ the
purification rate converges to the optimal one, proving the conjecture that
optimal broadcasting and state estimation are asymptotically equivalent. We
also show that it is possible to achieve superbroadcasting with simultaneous
inversion of the Bloch vector direction (universal NOT). We prove that in this
case the semiclassical procedure of state estimation and preparation turns out
to be optimal. We finally analyse semiclassical superbroadcasting in the
phase-covariant case.


title: Convergence theorems for quantum annealing

abstract:
  We prove several theorems to give sufficient conditions for convergence of
quantum annealing, which is a protocol to solve generic optimization problems
by quantum dynamics. In particular the property of strong ergodicity is proved
for the path-integral Monte Carlo implementation of quantum annealing for the
transverse Ising model under a power decay of the transverse field. This result
is to be compared with the much slower inverse-log decay of temperature in the
conventional simulated annealing. Similar results are proved for the Green's
function Monte Carlo approach. Optimization problems in continuous space of
particle configurations are also discussed.


title: Improving the efficiency of decoding quantum error correction code

abstract:
  To improve the efficiency of the encoding and the decoding is the important
problem in the quantum error correction. In a preceding work, a general
algorithm for decoding the stabilizer code is shown. This paper will show an
decoding which is more efficient for some codes. The proposed decoding as well
as the conventional decoding consists of the eigenvalue output step and the
entanglement dissolution step. The proposed decoding outputs a part of the
eigenvalues into a part of the code qubits in contrast to the conventional
method's outputting into the ancilla. Besides, the proposed decoding dissolves
a part of the entanglement in the eigenvalue output step in contrast to the
conventional method which does not dissolve in the eigenvalue output step. With
these improvements, the number of gates was reduced for some codes.


title: Communication Complexity Protocol for Q-trits

abstract:
  Consider a function where its entries are distributed among many parties.
Suppose each party is allowed to transmit only a limited amount of information
to a net. One can use a classical protocol to guess the value of the global
function. Is there a quantum protocol improving the results of all classical
protocols? Brukner et. al. showed the deep connection between such problems and
the theory of Bell's inequalities. Here we generalize the theory to trits.
There the best classical protocol fails whereas the quantum protocol yields the
correct answer.


title:
Enhancing the Violation of the Einstein-Podolsky-Rosen Local Realism by
  Quantum Hyper-entanglement

abstract:
  Mermin's observation [Phys. Rev. Lett. {\bf 65}, 1838 (1990)] that the
magnitude of the violation of local realism, defined as the ratio between the
quantum prediction and the classical bound, can grow exponentially with the
size of the system is demonstrated using two-photon hyper-entangled states
entangled in polarization and path degrees of freedom, and local measurements
of polarization and path simultaneously.


title:
How much entanglement can be generated between two atoms by detecting
  photons?

abstract:
  It is possible to achieve an arbitrary amount of entanglement between two
atoms using only spontaneously emitted photons, linear optics, single photon
sources and projective measurements. This is in contrast to all current
experimental proposals for entangling two atoms, which are fundamentally
restricted to one entanglement bit or ebit.


title: Collisional decoherence during writing and reading quantum states

abstract:
  Collisions, even though they do not limit the lifetime of quantum information
stored in ground state hyperfine coherences, may severely limit the fidelity
for quantum memory when they happen during the write and read process. This
imposes restrictions on the implementation of quantum processes in thermal
vapor cells and their performance as a quantum memory. We study the effect of
these collisions in our experiment.


title:
Unconditional Bell-type state generation for spatially separate trapped
  ions

abstract:
  We propose a scheme for generation of maximally entangled states involving
internal electronic degrees of freedom of two distant trapped ions, each of
them located in a cavity. This is achieved by using a single flying atom to
distribute entanglement. For certain specific interaction times, the proposed
scheme leads to the non-probabilistic generation of a perfect Bell-type state.
At the end of the protocol, the flying atom completely disentangles from the
rest of the system, leaving both ions in a Bell-type state. Moreover, the
scheme is insensitive to the cavity field state and cavity losses. We also
address the situation in which dephasing and dissipation must be taken into
account for the flying atom on its way from one cavity to the other, and
discuss the applicability of the resulting noisy channel for performing quantum
teleportation.


title:
Improved quantum algorithms for the ordered search problem via
  semidefinite programming

abstract:
  One of the most basic computational problems is the task of finding a desired
item in an ordered list of N items. While the best classical algorithm for this
problem uses log_2 N queries to the list, a quantum computer can solve the
problem using a constant factor fewer queries. However, the precise value of
this constant is unknown. By characterizing a class of quantum query algorithms
for ordered search in terms of a semidefinite program, we find new quantum
algorithms for small instances of the ordered search problem. Extending these
algorithms to arbitrarily large instances using recursion, we show that there
is an exact quantum ordered search algorithm using 4 log_{605} N \approx 0.433
log_2 N queries, which improves upon the previously best known exact algorithm.


title:
Linear optical setups for active and passive quantum error correction in
  polarization encoded qubits

abstract:
  In this work, we present active and passive linear optical setups for error
correction in quantum communication systems that employ polarization of
single-photon and mesoscopic coherent states. Applications in quantum
communication systems are described.


title: Transverse Entanglement Migration in Hilbert Space

abstract:
  We show that, although the amount of mutual entanglement of photons
propagating in free space is fixed, the type of correlations between the
photons that determine the entanglement can dramatically change during
propagation. We show that this amounts to a migration of entanglement in
Hilbert space, rather than real space. For the case of spontaneous parametric
down conversion, the migration of entanglement in transverse coordinates takes
place from modulus to phase of the bi-photon state and back again. We propose
an experiment to observe this migration in Hilbert space and to determine the
full entanglement.


title: Stochastic Resonance Phenomena in Quantum Many-Body Systems

abstract:
  We discuss stochastic resonance (SR) effects in driven coupled quantum
systems. We construct dynamical and information theoretic measures of the
system's response that exhibit a non-monotonic behaviour as a function of the
noise strength. We analyze the relation between lack of monotonicity in the
response and the presence of quantum correlations and identify parameter
regimes where the breakdown of a linear response can be linked to the presence
of entanglement. We also show that a chain of coupled spin systems can exhibit
an array-enhanced response, where the sensitivity of a single resonator is
enhanced as a result of nearest-neighbour coupling. These results enlarge the
domain where SR effects exist and should be observable in arrays of
superconducting qubits.


title: Two-party Models and the No-go Theorems

abstract:
  In this paper, we reconsider the communication model used in the no-go
theorems on the impossibility of quantum bit commitment and oblivious transfer.
We state that a macroscopic classical channel may not be replaced with a
quantum channel which is used in the reduced model proving the no-go theorems.
We show that in some restricted cases, the reduced model is insecure while the
original model with a classical channel is secure.


title: Bipartite Bell inequalities for hyperentangled states

abstract:
  We show that bipartite Bell inequalities based on the Einstein-Podolsky-Rosen
criterion for elements of reality and derived from the properties of some
hyperentangled states allow feasible experimental verifications of the fact
that quantum nonlocality grows exponentially with the size of the subsystems,
and Bell loophole-free tests with currently available photodetection
efficiencies.


title: Natural Philosophy and Quantum Theory

abstract:
  We attempt to show how relationalism might help in understanding Bell's
theorem. We also present an analogy with Darwinian evolution in order to
pedagogically hint at how one might go about using a theory in which one does
not even desire to explain correlations by invoking common causes.


title:
Single-experiment-detectable multipartite entanglement witness for
  ensemble quantum computing

abstract:
  In this paper we provide an operational method to detect multipartite
entanglement in ensemble-based quantum computing. This method is based on the
concept of entanglement witness. We decompose the entanglement witness for each
class of multipartite entanglement into nonlocal operations in addition to
local measurements. Individual single qubit measurements are performed
simultaneously, hence complete detection of entanglement is performed in a
single run experiment. This approach is particularly important for experiments
where it is operationally difficult to prepare several copies of an unknown
quantum state and in this sense the introduced scheme in this work is superior
to the generally used entanglement witnesses that require a number of
experiments and preparation of copies of quantum state.


title:
The effect of anisotropy and external magnetic filed on the thermal
  entanglement in a two-spin-qutrit system

abstract:
  We study the thermal entanglement in a two-spin-qutrit system with anisotropy
in the exchange coupling between two spins. We use the realignment criterion to
distinguish the entangled states, and the negativity for measuring the
entanglement in this system. We see that the anisotropy can provide an
additional parameter for enhancing the entanglement.


title:
Quantum States of Light Produced by a High-Gain Optical Parametric
  Amplifier for Use in Quantum Lithography

abstract:
  We present a theoretical analysis of the properties of an unseeded optical
parametic amplifier (OPA) used as the source of entangled photons for
applications in quantum lithography. We first study the dependence of the
excitation rate of a two-photon absorber on the intensity of the light leaving
the OPA. We find that the rate depends linearly on intensity only for output
beams so weak that they contain fewer than one photon per mode. We also study
the use of an N-photon absorber for arbitrary N as the recording medium to be
used with such a light source. We find that the contrast of the interference
pattern and the sharpness of the fringe maxima tend to increase with increasing
values of N, but that the density of fringes and thus the limiting resolution
does not increase with N. We conclude that the output of an unseeded OPA
exciting an N-photon absorber provides an attractive system in which to perform
quantum lithography.


title: Properties of nonfreeness: an entropy measure of electron correlation

abstract:
  "Nonfreeness" is the (negative of the) difference between the von Neumann
entropies of a given many-fermion state and the free state that has the same
1-particle statistics. It also equals the relative entropy of the two states in
question, i.e., it is the entropy of the given state relative to the
corresponding free state. The nonfreeness of a pure state is the same as its
"particle-hole symmetric correlation entropy", a variant of an established
measure of electron correlation. But nonfreeness is also defined for mixed
states, and this allows one to compare the nonfreeness of subsystems to the
nonfreeness of the whole. Nonfreeness of a part does not exceed that in the
whole; nonfreeness is additive over independent subsystems; and nonfreeness is
superadditive over subsystems that are independent on the 1-particle level.


title: Population-only decay map for n-qubit n-partite inseparability detection

abstract:
  We introduce a new positive linear map for a single qubit. This map is a
decay only in populations of a single-qubit density operator. It is shown that
an n-fold product of this map may be used for a detection of n-partite
inseparability of an n-qubit density operator (i.e., detection of impossibility
of representing a density operator in the form of a convex combination of
products of density operators of individual qubits). This product map is also
investigated in relation to a variant of the entanglement detection method
mentioned by Laskowski and Zukowski.


abstract:
  Mutually unbiased bases and discrete Wigner functions are closely, but not
uniquely related. Such a connection becomes more interesting when the Hilbert
space has a dimension that is a power of a prime $N=d^n$, which describes a
composite system of $n$ qudits. Hence, entanglement naturally enters the
picture. Although our results are general, we concentrate on the simplest
nontrivial example of dimension $N=8=2^3$. It is shown that the number of
fundamentally different Wigner functions is severely limited if one
simultaneously imposes translational covariance and that the generating
operators consist of rotations around two orthogonal axes, acting on the
individual qubits only.


title: Preventing Multipartite Disentanglement by Local Modulations

abstract:
  An entangled multipartite system coupled to a zero-temperature bath undergoes
rapid disentanglement in many realistic scenarios, due to local,
symmetry-breaking, differences in the particle-bath couplings. We show that
locally controlled perturbations, addressing each particle individually, can
impose a symmetry, and thus allow the existence of decoherence-free
multipartite entangled systems in zero-temperature environments.


title:
Universal Dynamical Control of Local Decoherence for Multipartite and
  Multilevel Systems

abstract:
  A unified theory is given of dynamically modified decay and decoherence of
field-driven multilevel multipartite entangled states that are weakly coupled
to zero-temperature baths or undergo random phase fluctuations. The theory
allows for arbitrary local differences in their coupling to the environment.
Due to such differences, the optimal driving-field modulation to ensure maximal
fidelity is found to substantially differ from conventional ``Bang-Bang'' or
$\pi$-phase flips of the single-qubit evolution.


title:
Transition of D- Level Quantum Systems Through Quantum Channels with
  Correlated Noise

abstract:
  Entanglement and entanglement-assisted are useful resources to enhance the
mutual information of the Pauli channels, when the noise on consecutive uses of
the channel has some partial correlations. In this Paper, we study
quantum-communication channels in $d$-dimensional systems and derive the mutual
information of the quantum channels for maximally entangled states and product
states coding with correlated noise. Then, we compare fidelity between these
states. Our results show that there exists a certain fidelity memory threshold
which depends on the dimension of the Hilbert space $(d)$ and the properties of
noisy channels. We calculate the classical capacity of a particular correlated
noisy channel and show that in order to achieve Holevo limit, we must use $d$
particles with $d$ degrees of freedom. Our results show that entanglement is a
useful means to enhance the mutual information. We choose a special
non-maximally entangled state and show that in the quasi-classical depolarizing
and quantum depolarizing channels, maximum classical capacity in the higher
memory channels is given by the maximally entangled state. Hence, our results
show that for high error channels in every degree of memory, maximally
entangled states have better mutual information.


title: Fermionic coherent states for pseudo-Hermitian two-level systems

abstract:
  We introduce creation and annihilation operators of pseudo-Hermitian fermions
for two-level systems described by pseudo-Hermitian Hamiltonian with real
eigenvalues. This allows the generalization of the fermionic coherent states
approach to such systems. Pseudo-fermionic coherent states are constructed as
eigenstates of two pseudo-fermion annihilation operators. These coherent states
form a bi-normal and bi-overcomplete system, and their evolution governed by
the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the
introduced pseudo-fermion operators the two-level system' Hamiltonian takes a
factorized form similar to that of a harmonic oscillator.


title: Determination of quantum-noise parameters of realistic cavities

abstract:
  A procedure is developed which allows one to measure all the parameters
occurring in a complete model [A.A. Semenov et al., Phys. Rev. A 74, 033803
(2006); quant-ph/0603043] of realistic leaky cavities with unwanted noise. The
method is based on the reflection of properly chosen test pulses by the cavity.


title:
Spontaneous absorption of an accelerated hydrogen atom near a conducting
  plane in vacuum

abstract:
  We study, in the multipolar coupling scheme, a uniformly accelerated
multilevel hydrogen atom in interaction with the quantum electromagnetic field
near a conducting boundary and separately calculate the contributions of the
vacuum fluctuation and radiation reaction to the rate of change of the mean
atomic energy. It is found that the perfect balance between the contributions
of vacuum fluctuations and radiation reaction that ensures the stability of
ground-state atoms is disturbed, making spontaneous transition of ground-state
atoms to excited states possible in vacuum with a conducting boundary. The
boundary-induced contribution is effectively a nonthermal correction, which
enhances or weakens the nonthermal effect already present in the unbounded
case, thus possibly making the effect easier to observe. An interesting feature
worth being noted is that the nonthermal corrections may vanish for atoms on
some particular trajectories.


title:
Exactly solvable associated Lame potentials and supersymmetric
  transformations

abstract:
  A systematic procedure to derive exact solutions of the associated Lame
equation for an arbitrary value of the energy is presented. Supersymmetric
transformations in which the seed solutions have factorization energies inside
the gaps are used to generate new exactly solvable potentials; some of them
exhibit an interesting property of periodicity defects.


title: Decoherence and Thermalization

abstract:
  We present a rigorous analysis of the phenomenon of decoherence for general
N-level systems coupled to reservoirs of free massless bosonic fields. We apply
our general results to the specific case of the qubit. Our approach does not
involve master equation approximations and applies to a wide variety of systems
which are not explicitly solvable.


title: Quantum phase gate and controlled entanglement with polar molecules

abstract:
  We propose an alternative scenario for the generation of entanglement between
rotational quantum states of two polar molecules. This entanglement arises from
dipole-dipole interaction, and is controlled by a sequence of laser pulses
simultaneously exciting both molecules. We study the efficiency of the process,
and discuss possible experimental implementations with cold molecules trapped
in optical lattices or in solid matrices. Finally, various entanglement
detection procedures are presented, and their suitability for these two
physical situations is analyzed.


title:
Deterministic unitary operations on time-bin qudits for quantum
  communication

abstract:
  We show for the first time how deterministic unitary operations on time-bin
qubits encoded in single photon pulses can be realized using fiber optics
components that are available with current technology. We also generalize this
result to operations on time-bin qudits, i.e. $d$-level systems, and show that
this can be done efficiently using 2$\times$2 beamsplitters and phase
modulators. Important benefits for experimental quantum communication are
highlighted. This work shows how to bridge the gap between current
proof-of-principle demonstrations and complete, deterministic experiments.


title:
Quantification of Continuous Variable Entanglement with only Two Types
  of Simple Measurements

abstract:
  Here we propose an experimental set-up in which it is possible to measure the
entanglement of a two-mode Gaussian state, be it pure or mixed, using only
simple linear optical devices. After a proper unitary manipulation of the
two-mode Gaussian state only number and purity measurements of just one of the
modes suffice to give us a complete and exact knowledge of the state's
entanglement.


title: Operational approach to the Uhlmann holonomy

abstract:
  We suggest a physical interpretation of the Uhlmann amplitude of a density
operator. Given this interpretation we propose an operational approach to
obtain the Uhlmann condition for parallelity. This allows us to realize
parallel transport along a sequence of density operators by an iterative
preparation procedure. At the final step the resulting Uhlmann holonomy can be
determined via interferometric measurements.


title: More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$

abstract:
  In this paper we revisit the isomorphism $SU(2)\otimes SU(2)\cong SO(4)$ to
apply to some subjects in Quantum Computation and Mathematical Physics.
  The unitary matrix $Q$ by Makhlin giving the isomorphism as an adjoint action
is studied and generalized from a different point of view. Some problems are
also presented.
  In particular, the homogeneous manifold $SU(2n)/SO(2n)$ which characterizes
entanglements in the case of $n=2$ is studied, and a clear-cut calculation of
the universal Yang-Mills action in (hep-th/0602204) is given for the abelian
case.


title:
Experimental Preparation of Quadripartite Cluster and GHZ Entangled
  States for Continuous Variables

abstract:
  The cluster states and Greenberger-Horne-Zeilinger (GHZ) states are two
different types of multipartite quantum entangled states. We present the first
experimental results generating continuous variable quadripartite cluster and
GHZ entangled states of electromagnetic fields. Utilizing four two-mode
squeezed states of light and linearly optical transformations, the two types of
entangled states for amplitude and phase quadratures of light are
experimentally produced. The combinations of the measured quadrature variances
prove the full inseparability of the generated four subsystems. The presented
experimental schemes show that the multipartite entanglement of continuous
variables can be deterministically generated with the relatively simple
implementation.


title:
Effect of exchange interaction on fidelity of quantum state transfer
  from a photon qubit to an electron-spin qubit

abstract:
  We analyzed the fidelity of the quantum state transfer (QST) from a
photon-polarization qubit to an electron-spin-polarization qubit in a
semiconductor quantum dot, with special attention to the exchange interaction
between the electron and the simultaneously created hole. In order to realize a
high-fidelity QST we had to separate the electron and hole as soon as possible,
since the electron-hole exchange interaction modifies the orientation of the
electron spin. Thus, we propose a double-dot structure to separate the electron
and hole quickly, and show that the fidelity of the QST can reach as high as
0.996 if the resonant tunneling condition is satisfied.


title: Squeezing in multi-mode nonlinear optical state truncation

abstract:
  In this paper, we show that multi-mode qubit states produced via nonlinear
optical state truncation driven by classical external pumpings exhibit
squeezing condition. We restrict our discussions to the two and three-mode
cases.


title: Subjective probability and quantum certainty

abstract:
  In the Bayesian approach to quantum mechanics, probabilities--and thus
quantum states--represent an agent's degrees of belief, rather than
corresponding to objective properties of physical systems. In this paper we
investigate the concept of certainty in quantum mechanics. Particularly, we
show how the probability-1 predictions derived from pure quantum states
highlight a fundamental difference between our Bayesian approach, on the one
hand, and Copenhagen and similar interpretations on the other. We first review
the main arguments for the general claim that probabilities always represent
degrees of belief. We then argue that a quantum state prepared by some physical
device always depends on an agent's prior beliefs, implying that the
probability-1 predictions derived from that state also depend on the agent's
prior beliefs. Quantum certainty is therefore always some agent's certainty.
Conversely, if facts about an experimental setup could imply agent-independent
certainty for a measurement outcome, as in many Copenhagen-like
interpretations, that outcome would effectively correspond to a preexisting
system property. The idea that measurement outcomes occurring with certainty
correspond to preexisting system properties is, however, in conflict with
locality. We emphasize this by giving a version of an argument of Stairs [A.
Stairs, Phil. Sci. 50, 578 (1983)], which applies the Kochen-Specker theorem to
an entangled bipartite system.


title:
Simulation of an entangled state in a chain of three nuclear spins
  system

abstract:
  We study the formation of an entangled state in a one-dimensional chain of
three nuclear spins system which interact weakly through the Ising type of
interaction and taking into account first and second neighbor interactions. We
can get this entangled state using two pulses ($\pi/2$ and $\pi$ pulses), and
we study the efficiency of getting this entangled state as a function of the
ratio of the second neighbor interaction coupling constant to the first
neighbor interaction coupling constant ($J'/J$). We found that for $J'/J\ge
0.04$, the entangled state is well defined.


title: Coherence and Entanglement in a Stern-Gerlach experiment

abstract:
  We give a simple example of the tight connection between entanglement and
coherence for pure bipartite systems showing the double role played by
entanglement; it allows for the creation of superpositions of macroscopic
objects but at the same time makes subsystems lose their quantum mechanical
coherence. For this we study the time evolution of the spin coherence in the
Stern-Gerlach (SG) experiment. We also show that, contrary to the naive
intuition, the spin coherence is lost before the two beams become separated in
the spatial coordinates.


title: Two-photon interaction between trapped ions and cavity fields

abstract:
  In this paper, we generalize the ordinary two-photon Jaynes-Cummings model
(TPJCM) by considering the atom (or ion) to be trapped in a simple harmonic
well. A typical setup would be an optical cavity containing a single ion in a
Paul trap. Due to the inclusion of atomic vibrational motion, the atom-field
coupling becomes highly nonlinear what brings out quite different behaviors for
the system dynamics when compared to the ordinary TPJCM. In particular, we
derive an effective two-photon Hamiltonian with dependence on the number
operator of the ion's center-of-mass motion. This dependence occurs both in the
cavity induced Stark-shifs and in the ion-field coupling, and its role in the
dynamics is illustrated by showing the time evolution of the probability of
occupation of the electronic levels for simple initial preparations of the
state of the system.


title:
Numerical simulation of Quantum Teleportation in a chain of three
  nuclear spins system taking into account second neighbor interaction

abstract:
  For a one-dimensional chain of three nuclear spins (one half), we make the
numerical simulation of quantum teleportation of a given state from one end of
the chain to the other end, taking into account first and second neighbor
interactions among the spins. It is shown that a well defined teleportation
protocol is achieved for a ratio of the first to second neighbor interaction
coupling constant of $J'/J\ge 0.04$. We also show that the optimum Rabi's
frequency to control the non-resonant effects is dominated by the second
neighbor interaction coupling parameter ($J'$).


title:
Quantum key distribution based on private states: unconditional security
  over untrusted channels with zero quantum capacity

abstract:
  We prove unconditional security for a quantum key distribution (QKD) protocol
based on distilling pbits (twisted ebits) [quant-ph/0309110] from an arbitrary
untrusted state that is claimed to contain distillable key. Our main result is
that we can verify security using only public communication -- via parameter
estimation of the given untrusted state. The technique applies even to bound
entangled states, thus extending QKD to the regime where the available quantum
channel has zero quantum capacity. We also show how to convert our
purification-based QKD schemes to prepare-measure schemes.


title: Visualization of superposition of macroscopically distinct states

abstract:
  We propose a method of visualizing superpositions of macroscopically distinct
states in many-body pure states. We introduce a visualization function, which
is a coarse-grained quasi joint probability density for two or more hermitian
additive operators. If a state contains superpositions of macroscopically
distinct states, one can visualize them by plotting the visualization function
for appropriately taken operators. We also explain how to efficiently find
appropriate operators for a given state. As examples, we visualize four states
containing superpositions of macroscopically distinct states: the ground state
of the XY model, that of the Heisenberg antiferromagnet, a state in Shor's
factoring algorithm, and a state in Grover's quantum search algorithm. Although
the visualization function can take negative values, it becomes non-negative
(hence becomes a coarse-grained joint probability density) if the
characteristic width of the coarse-graining function used in the visualization
function is sufficiently large.


title: Matrix Product State Representations

abstract:
  This work gives a detailed investigation of matrix product state (MPS)
representations for pure multipartite quantum states. We determine the freedom
in representations with and without translation symmetry, derive respective
canonical forms and provide efficient methods for obtaining them. Results on
frustration free Hamiltonians and the generation of MPS are extended, and the
use of the MPS-representation for classical simulations of quantum systems is
discussed.


title: Quantum estimation and the quantum central limit theorem

abstract:
  This paper gives a survey about quantum estimation. We also describes the
relation between the quantum central limit theorem and the asymptotic bound of
mean square error in quantum state estimation.


title: Unifying classical and quantum key distillation

abstract:
  Assume that two distant parties, Alice and Bob, as well as an adversary, Eve,
have access to (quantum) systems prepared jointly according to a tripartite
state. In addition, Alice and Bob can use local operations and authenticated
public classical communication. Their goal is to establish a key which is
unknown to Eve. We initiate the study of this scenario as a unification of two
standard scenarios: (i) key distillation (agreement) from classical
correlations and (ii) key distillation from pure tripartite quantum states.
  Firstly, we obtain generalisations of fundamental results related to
scenarios (i) and (ii), including upper bounds on the key rate. Moreover, based
on an embedding of classical distributions into quantum states, we are able to
find new connections between protocols and quantities in the standard scenarios
(i) and (ii).
  Secondly, we study specific properties of key distillation protocols. In
particular, we show that every protocol that makes use of pre-shared key can be
transformed into an equally efficient protocol which needs no pre-shared key.
This result is of practical significance as it applies to quantum key
distribution (QKD) protocols, but it also implies that the key rate cannot be
locked with information on Eve's side. Finally, we exhibit an arbitrarily large
separation between the key rate in the standard setting where Eve is equipped
with quantum memory and the key rate in a setting where Eve is only given
classical memory. This shows that assumptions on the nature of Eve's memory are
important in order to determine the correct security threshold in QKD.


title: Interference in discrete Wigner functions

abstract:
  We analyse some features of the class of discrete Wigner functions that was
recently introduced by Gibbons et al. to represent quantum states of systems
with power-of-prime dimensional Hilbert spaces [Phys. Rev. A 70, 062101
(2004)]. We consider "cat" states obtained as coherent superpositions of states
with positive Wigner function; for such states we show that the oscillations of
the discrete Wigner function typically spread over the entire discrete
phase-space (including the regions where the two interfering states are
localized). This is a generic property which is in sharp contrast with the
usual attributes of Wigner functions that make them useful candidates to
display the existence of quantum coherence through oscillations. However, it is
possible to find subsets of cat states with a natural phase-space
representation, in which the oscillatory regions remain localized. We show that
this can be done for interesting families of stabilizer states used in quantum
error-correcting codes, and illustrate this by analysing the phase-space
representation of the five-qubit error-correcting code.


title: On some entropic entanglement parameter

abstract:
  In this paper we present the quantity, which is an entanglement parameter.
Its origin is very intriguing, because its construction is motivated by
separability criteria based on uncertainty relation. We show that this quantity
is asymptotically continuous. We also find the lower and upper bounds for it.
Our entanglement parameter has the same feature as the coherent information:
both can be negative.
  There are also some classes of states for which these quantities coincide
with each other.


title: Entanglement and quantum interference

abstract:
  In the history of quantum mechanics, much has been written about the
double-slit experiment, and much debate as to its interpretation has ensued.
Indeed, to explain the interference patterns for sub-atomic particles,
explanations have been given not only in terms of the principle of
complementarity and wave-particle duality but also in terms of quantum
consciousness and parallel universes. In this paper, the topic will be
discussed from the perspective of spin-coupling in the hope of further
clarification. We will also suggest that this explanation allows for a realist
interpretation of the Afshar Experiment.


title:
Geometric Phase and Quantum Phase Transition in the Lipkin-Meshkov-Glick
  model

abstract:
  The relation between the geometric phase and quantum phase transition has
been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the
ability of geometric phase of the ground state to mark quantum phase transition
in this model. The possibility of the geometric phase or its derivatives as the
universal order parameter of characterizing quantum phase transitions has been
also discussed.


title:
Relaxation- and Decoherence-free subspaces in networks of weakly and
  strongly coupled resonators

abstract:
  We consider a network of interacting resonators and analyze the physical
ingredients that enable the emergence of relaxation-free and decoherence-free
subspaces. We investigate two different situations: i) when the whole network
interacts with a common reservoir and ii) when each resonator, strongly coupled
to each other, interacts with its own reservoir. Our main result is that both
subspaces are generated when all the resonators couple with the same group of
reservoir modes, thus building up a correlation (among these modes), which has
the potential to shield particular network states against relaxation and/or
decoherence.