title:
Violation of Locality Without Inequalities for Multiparticle Perfect
  Correlations

abstract:
  We prove that for a three-qubit system in the Greenberger-Horne-Zeilinger
(GHZ) state, locality per se is in conflict with the perfect GHZ correlations.
The proof does not in any way use the realism assumption and can lead to a
refutation of locality. We also provide inequalities that are imposed by
locality. The experimental confirmation of the present reasoning may imply a
genuine quantum nonlocality and will deepen our understanding of nonlocality of
nature.


abstract:
  Chains of Darboux transformations for the matrix Schroedinger equation are
considered. Matrix generalization of the well-known for the scalar equation
Crum-Krein formulas for the resulting action of such chains is given.


title: Second Order Darboux Displacements

abstract:
  The potentials for a one dimensional Schroedinger equation that are displaced
along the x axis under second order Darboux transformations, called 2-SUSY
invariant, are characterized in terms of a differential-difference equation.
The solutions of the Schroedinger equation with such potentials are given
analytically for any value of the energy. The method is illustrated by a
two-soliton potential. It is proven that a particular case of the periodic
Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the
corresponding Schroedinger equation equation are found for any value of the
energy. A simple analytic expression for a family of two-gap potentials is
derived.


title:
Entanglement Generation from Thermal Spin States via Unitary Beam
  Splitters

abstract:
  We suggest a method of generating distillable entanglement form mixed states
unitarily, by utilizing the flexibility of dimension od occupied Hilbert space.
We present a model of a thermal spin state entering a beam splitter generating
entanglement. It is the truncation of the state that allows for entanglement
generation. The output entanglement is investigated for different temperatures
and it is found that more randomness - in the form of higher temperature - is
better for this set up.


title:
Fungible dynamics: there are only two types of entangling multiple-qubit
  interactions

abstract:
  What interactions are sufficient to simulate arbitrary quantum dynamics in a
composite quantum system? It has been shown that all two-body Hamiltonian
evolutions can be simulated using \emph{any} fixed two-body entangling
$n$-qubit Hamiltonian and fast local unitaries. By \emph{entangling} we mean
that every qubit is coupled to every other qubit, if not directly, then
indirectly via intermediate qubits. We extend this study to the case where
interactions may involve more than two qubits at a time. We find necessary and
sufficient conditions for an arbitrary $n$-qubit Hamiltonian to be
\emph{dynamically universal}, that is, able to simulate any other Hamiltonian
acting on $n$ qubits, possibly in an inefficient manner. We prove that an
entangling Hamiltonian is dynamically universal if and only if it contains at
least one coupling term involving an \emph{even} number of interacting qubits.
For \emph{odd} entangling Hamiltonians, i.e., Hamiltonians with couplings that
involve only an odd number of qubits, we prove that dynamic universality is
possible on an encoded set of $n-1$ logical qubits. We further prove that an
odd entangling Hamiltonian can simulate any other odd Hamiltonian and classify
the algebras that such Hamiltonians generate. Thus, our results show that up to
local unitary operations, there are only two fundamentally different types of
entangling Hamiltonian on $n$ qubits. We also demonstrate that, provided the
number of qubits directly coupled by the Hamiltonian is bounded above by a
constant, our techniques can be made efficient.


title: Lower Bounds for Local Search by Quantum Arguments

abstract:
  The problem of finding a local minimum of a black-box function is central for
understanding local search as well as quantum adiabatic algorithms. For
functions on the Boolean hypercube {0,1}^n, we show a lower bound of
Omega(2^{n/4}/n) on the number of queries needed by a quantum computer to solve
this problem. More surprisingly, our approach, based on Ambainis' quantum
adversary method, also yields a lower bound of Omega(2^{n/2}/n^2) on the
problem's classical randomized query complexity. This improves and simplifies a
1983 result of Aldous. Finally, in both the randomized and quantum cases, we
give the first nontrivial lower bounds for finding local minima on grids of
constant dimension greater than 2.


title: A Lambda Calculus for Quantum Computation

abstract:
  The classical lambda calculus may be regarded both as a programming language
and as a formal algebraic system for reasoning about computation. It provides a
computational model equivalent to the Turing machine, and continues to be of
enormous benefit in the classical theory of computation. We propose that
quantum computation, like its classical counterpart, may benefit from a version
of the lambda calculus suitable for expressing and reasoning about quantum
algorithms. In this paper we develop a quantum lambda calculus as an
alternative model of quantum computation, which combines some of the benefits
of both the quantum Turing machine and the quantum circuit models. The calculus
turns out to be closely related to the linear lambda calculi used in the study
of Linear Logic. We set up a computational model and an equational proof system
for this calculus, and we argue that it is equivalent to the quantum Turing
machine.


title: Entanglement as precondition for secure quantum key distribution

abstract:
  We demonstrate that a necessary precondition for unconditionally secure
quantum key distribution is that sender and receiver can use the available
measurement results to prove the presence of entanglement in a quantum state
that is effectively distributed between them. One can thus systematically
search for entanglement using the class of entanglement witness operators that
can be constructed from the observed data. We apply such analysis to two
well-known quantum key distribution protocols, namely the 4-state protocol and
the 6-state protocol. As a special case, we show that, for some asymmetric
error patterns, the presence of entanglement can be proven even for error rates
above 25% (4-state protocol) and 33% (6-state protocol).


title: Intertwining technique for the one-dimensional stationary Dirac equation

abstract:
  The technique of differential intertwining operators (or Darboux
transformation operators) is systematically applied to the one-dimensional
Dirac equation.
  The following aspects are investigated: factorization of a polynomial of
Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation
operators, chains of transformations, and finally particular cases of
pseudoscalar and scalar potentials. The method is widely illustrated by
numerous examples.


title:
Scaling issues in ensemble implementations of the Deutsch-Jozsa
  algorithm

abstract:
  We discuss the ensemble version of the Deutsch-Jozsa (DJ) algorithm which
attempts to provide a "scalable" implementation on an expectation-value NMR
quantum computer. We show that this ensemble implementation of the DJ algorithm
is at best as efficient as the classical random algorithm. As soon as any
attempt is made to classify all possible functions with certainty, the
implementation requires an exponentially large number of molecules. The
discrepancies arise out of the interpretation of mixed state density matrices.


title:
Quantum Mechanical Ground State of Hydrogen Obtained from Classical
  Electrodynamics

abstract:
  The behavior of a classical charged point particle under the influence of
only a Coulombic binding potential and classical electromagnetic zero-point
radiation, is shown to yield agreement with the probability density
distribution of Schroedinger's wave equation for the ground state of hydrogen.
These results, obtained without any fitting parameters, again raise the
possibility that the main tenets of stochastic electrodynamics (SED) are
correct, thereby potentially providing a more fundamental basis of quantum
mechanics. The present methods should help propel yet deeper investigations
into SED.


title:
On a suggestion relating topological and quantum mechanical
  entanglements

abstract:
  We analyze a recent suggestion \cite{kauffman1,kauffman2} on a possible
relation between topological and quantum mechanical entanglements. We show that
a one to one correspondence does not exist, neither between topologically
linked diagrams and entangled states, nor between braid operators and quantum
entanglers. We also add a new dimension to the question of entangling
properties of unitary operators in general.


title: On the Quantum Phase Operator for Coherent States

abstract:
  In papers by Lynch [Phys. Rev. A41, 2841 (1990)] and Gerry and Urbanski
[Phys. Rev. A42, 662 (1990)] it has been argued that the phase-fluctuation
laser experiments of Gerhardt, B\"uchler and Lifkin [Phys. Lett. 49A, 119
(1974)] are in good agreement with the variance of the Pegg-Barnett phase
operator for a coherent state, even for a small number of photons. We argue
that this is not conclusive. In fact, we show that the variance of the phase in
fact depends on the relative phase between the phase of the coherent state and
the off-set phase $\phi_0$ of the Pegg-Barnett phase operator. This off-set
phase is replaced with the phase of a reference beam in an actual experiment
and we show that several choices of such a relative phase can be fitted to the
experimental data. We also discuss the Noh, Foug\`{e}res and Mandel [Phys.Rev.
A46, 2840 (1992)] relative phase experiment in terms of the Pegg-Barnett phase
taking post-selection conditions into account.


title: Source Field Effects and Wave Function Collapse

abstract:
  Detection of a material particle is accompanied by emission of
bremsstrahlung. Thus the dynamics of the energy loss of the particle is
determined by radiation reaction force. The description of radiation reaction
is a difficult problem still being subject of ongoing debates. There are
problems of runaway solutions, preacceleration already in classical description
of radiation reaction. Additional complications in quantum mechanical
description arise because of the infinite source field energy term in
hamiltonian for a point charge. There is still no general consensus on an
appropriate quantum mechanical description. Neither the achievements of the
radiation theory on the subject nor the problems associated with it are
sufficiently taken into account in context with measurement problem. Radiation
reaction doesn't effect free particle wave packets, but it favors stationary
states of the `wave function of the measured particle" in presence of a
potential gradient. We suggest therefore that radiation reaction may play a
significant role in the dynamics of the wave function collapse. keywords: wave
function collapse,interpretation,randomness, Jaynes Cummings dynamics,
spontaneous emission, source field effects, radiation reaction, quantum
measurement,decoherence


title: Discrete entanglement distribution with squeezed light

abstract:
  We show how one can entangle distant atoms by using squeezed light.
Entanglement is obtained in steady state, and can be increased by manipulating
the atoms locally. We study the effects of imperfections, and show how to scale
up the scheme to build a quantum network.


title: New exactly solvable periodic potentials for the Dirac equation

abstract:
  A new exactly solvable relativistic periodic potential is obtained by the
periodic extension of a well-known transparent scalar potential. It is found
that the energy band edges are determined by a transcendental equation which is
very similar to the corresponding equation for the Dirac Kronig-Penney model.
The solutions of the Dirac equation are expressed in terms of elementary
functions.


title: Analysis of the loss of coherence in interferometry with macromolecules

abstract:
  We provide a self-contained quantum description of the interference produced
by macromolecules diffracted by a grating, with particular reference to
fullerene interferometry experiments. We analyze the processes inducing loss of
coherence consisting in beam preparation (collimation setup and thermal spread
of the wavelengths of the macromolecules) and in environmental disturbances.
The results show a good agreement with experimental data published by
Zeilinger's group and highlight the analogy with optics. Our analysis gives
some hints for planning future experiments.


title: Observed Correlations in Minkowski Space

abstract:
  The author has proposed five rules that permit conscious observers to be
included in quantum mechanics. In the present paper, these rules are applied to
the observation of a non-local pair of correlated particles. Rule (4) again
prevents an anomalous result. Two different kinds of relativistic state
reduction are considered, where these differ in the way that they impose
boundary conditions in Minkowski space. In response to a problem that arises in
this context, we require the Lorentz invariance of stochastic hits. And
finally, it is claimed that the rules proposed by the author are themselves
relativistically covariant with some qualification. Key Words: brain states,
boundary conditions, consciousness, decoherence, macroscopic superposition,
probability current, von Neumann, wave collapse.


title:
Direct observation of non-classical photon statistics in parametric
  downconversion

abstract:
  We employ a high quantum efficiency photon number counter to determine the
photon number distribution of the output field from a parametric downconverter.
The raw photocount data directly demonstrates that the source is nonclassical
by forty standard deviations, and correcting for the quantum efficiency yields
a direct observation of oscillations in the photon number distribution.


title:
Entanglement between two superconducting qubits via interaction with
  non-classical radiation

abstract:
  We propose a scheme to physically interface superconducting nano-circuits and
quantum optics. We address the transfer of quantum information between systems
having different physical natures and defined in Hilbert spaces of different
dimensions. In particular, we investigate the transfer of the entanglement
initially in a non-classical state of a continuous-variable system to a pair of
superconducting charge qubits. This set-up is able to drive an initially
separable state of the qubits into an almost pure, highly entangled state
suitable for quantum information processing.


title: Nonlocal Properties and Local Invariants for Bipartite Systems

abstract:
  The nonlocal properties for a kind of generic N-dimensional bipartite quantum
systems are investigated. A complete set of invariants under local unitary
transformations is presented. It is shown that two generic density matrices are
locally equivalent if and only if all these invariants have equal values in
these density matrices.


title:
Measurement and Information Extraction in Complex Dynamics Quantum
  Computation

abstract:
  We address the problem related to the extraction of the information in the
simulation of complex dynamics quantum computation. Here we present an example
where important information can be extracted efficiently by means of quantum
simulations. We show how to extract efficiently the localization length, the
mean square deviation and the system characteristic frequency. We show how this
methods work on a dynamical model, the Sawtooth Map, that is characterized by
very different dynamical regimes: from near integrable to fully developed
chaos; it also exhibits quantum dynamical localization.


title: Scaling and renormalization in fault-tolerant quantum computers

abstract:
  This work is concerned with phrasing the concepts of fault-tolerant quantum
computation within the framework of disordered systems, Bernoulli site
percolation in particular. We show how the so-called "threshold theorems" on
the possibility of fault-tolerant quantum computation with constant error rate
can be cast as a renormalization (coarse-graining) of the site percolation
process describing the occurrence of errors during computation. We also use
percolation techniques to derive a trade-off between the complexity overhead of
the fault-tolerant circuit and the threshold error rate.


title: Inclusion relations among separability criteria

abstract:
  We revisit the application of different separability criteria by recourse to
an exhaustive Monte Carlo exploration involving the pertinent state-space of
pure and mixed states. The corresponding chain of implications of different
criteria is in such a way numerically elucidated. We also quantify, for a
bipartite system of arbitrary dimension, the proportion of states $\rho$ that
can be distilled according to a definite criterion. Our work can be regarded as
a complement to the recent review paper by B. Terhal [Theor. Comp. Sci. {\bf
287} (2002) 313]. Some questions posed there receive an answer here.


title:
Cavity QED and Quantum Computation in the Strong Coupling Regime II :
  Two Atoms Case

abstract:
  In this paper we study the behavior of (laser--cooled) m--atoms trapped in a
cavity interacting with a photon $...$ Cavity QED $...$ and attempt to solve
the Schr{\"o}dinger equation of this model in the strong coupling regime. In
the case of m = 2 we construct Bell--Schr{\" o}dinger cat states (in our
terminology) and obtain with such bases some unitary transformations by making
use of the rotating wave approximation under new resonance conditionscontaining
the Bessel functions, which will be applied to construct important quantum
logic gates in Quantum Computation. Moreover we propose in the case of m = 3 a
crucial problem to solve on Quantum Computation.


title: Wehrl entropy, Lieb conjecture and entanglement monotones

abstract:
  We propose to quantify the entanglement of pure states of $N \times N$
bipartite quantum system by defining its Husimi distribution with respect to
$SU(N)\times SU(N)$ coherent states. The Wehrl entropy is minimal if and only
if the pure state analyzed is separable. The excess of the Wehrl entropy is
shown to be equal to the subentropy of the mixed state obtained by partial
trace of the bipartite pure state. This quantity, as well as the generalized
(R{\'e}nyi) subentropies, are proved to be Schur--convex, so they are
entanglement monotones and may be used as alternative measures of entanglement.


title:
Quantum Stein's lemma revisited, inequalities for quantum entropies, and
  a concavity theorem of Lieb

abstract:
  We derive the monotonicity of the quantum relative entropy by an elementary
operational argument based on Stein's lemma in quantum hypothesis testing. For
the latter we present an elementary and short proof that requires the law of
large numbers only. Joint convexity of the quantum relative entropy is proven
too, resulting in a self-contained elementary version of Tropp's approach to
Lieb's concavity theorem, according to which the map tr(exp(h+log a)) is
concave in a on positive operators for self-adjoint h.


title: Separability conditions from entropic uncertainty relations

abstract:
  We derive a collection of separability conditions for bipartite systems of
dimensions d X d which is based on the entropic version of the uncertainty
relations. A detailed analysis of the two-qubit case is given by comparing the
new separability conditions with existing criteria.


title: Quantum-Mechanical Dualities from Classical Phase Space

abstract:
  The geometry of the classical phase space C of a finite number of degrees of
freedom determines the possible duality symmetries of the corresponding quantum
mechanics. Under duality we understand the relativity of the notion of a
quantum with respect to an observer on C. We illustrate this property
explicitly in the case when classical phase space is complex n-dimensional
projective space. We also provide some examples of classical dynamics that
exhibit these properties at the quantum level.


title: Scheme for preparation of W state via cavity QED

abstract:
  In this paper, we presented a physical scheme to generate the multi-cavity
maximally entangled W state via cavity QED. All the operations needed in this
scheme are to modulate the interaction time only once.


title: Entanglement distillation for atomic states via cavity QED

abstract:
  In this paper, we proposed a physical scheme to concentrate the non-maximally
entangled atomic pure states via cavity QED by using atomic collision in a
far-off-resonant cavity. The most distinctive advantage of our scheme is that
there is no excitation of cavity mode during the distillation procedure.
Therefore the requirement on the quality of cavity is greatly loosened.


title:
Superconducting Analogues of Quantum Optical Phenomena: Macroscopic
  Quantum Superpositions and Squeezing in a SQUID Ring

abstract:
  In this paper we explore the quantum behaviour of a SQUID ring which has a
significant Josephson coupling energy. We show that that the eigenfunctions of
the Hamiltonian for the ring can be used to create macroscopic quantum
superposition states of the ring. We also show that the ring potential may be
utilised to squeeze coherent states. With the SQUID ring as a strong contender
as a device for manipulating quantum information, such properties may be of
great utility in the future. However, as with all candidate systems for quantum
technologies, decoherence is a fundamental problem. In this paper we apply an
open systems approach to model the effect of coupling a quantum mechanical
SQUID ring to a thermal bath. We use this model to demonstrate the manner in
which decoherence affects the quantum states of the ring.


title: Quantum Cellular Automata from Lattice Field Theories

abstract:
  We apply the methods of lattice field theories to the quantization of
cellular automata. We discuss the quantization of five main categories of
cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot
using path integral and operator formalisms of lattice field theories. We show
that the quantization of supersymmetric cellular automata is related to
recently discussed string bit models of Thorn and Bergman and represents a link
of cellular automata theory to fundamental physics. We discuss spin and quantum
dot cellular automata for their importance in experimental realizations and
their use in quantum computation. Previous studies of quantum cellular automata
utilize the wave function values as cell contents and the discretized linear
Dirac equation as an update equation. We show that our approach to the
quantization of fermionic cellular automata includes this utilization as a
field equation, and in addition allows for nonlinearity through lattice field
interactions.


title:
A universal quantum circuit for two-qubit transformations with three
  CNOT gates

abstract:
  We consider the implementation of two-qubit unitary transformations by means
of CNOT gates and single-qubit unitary gates. We show, by means of an explicit
quantum circuit, that together with local gates three CNOT gates are necessary
and sufficient in order to implement an arbitrary unitary transformation of two
qubits. We also identify the subset of two-qubit gates that can be performed
with only two CNOT gates.


title: Overcoming Quantum Noise in Optical Fibers

abstract:
  Noise in optical Telecom fibers is an important limitation on optical quantum
data transmission. Unfortunately, the classically successful amplifiers (such
as EDFA) cannot be used in quantum communication because of the no-cloning
theorem. We propose a simple method to reduce quantum noise: the insertion of
phase-shifters and/or beam-splitters at regular distance intervals into a
fiber. We analyze in detail the case of qubits encoded into polarization states
of low-intensity light, which is of central importance to various quantum
information tasks, such as quantum cryptography and communication. We discuss
the experimental feasibility of our scheme and propose a simple experiment to
test our method.


title:
There is no first quantization - except in the de Broglie-Bohm
  interpretation

abstract:
  The relativistic effects of the integer-spin quantum field theory imply that
the wave functions describing a fixed number of particles do not admit the
usual probabilistic interpretation. Among several most popular interpretations
of quantum mechanics applied to first quantization, the only interpretation for
which this fact does not lead to a serious problem, and therefore the only
consistent interpretation of first quantization, is the de Broglie-Bohm
interpretation.


title: Stability of macroscopic entanglement under decoherence

abstract:
  We investigate the lifetime of macroscopic entanglement under the influence
of decoherence. For GHZ-type superposition states we find that the lifetime
decreases with the size of the system (i.e. the number of independent degrees
of freedom) and the effective number of subsystems that remain entangled
decreases with time. For a class of other states (e.g. cluster states),
however, we show that the lifetime of entanglement is independent of the size
of the system.


title:
Controlled creation of maximally entangled states using a SQUID ring
  coupled to an electromagnetic field

abstract:
  We present solutions of the time dependent Schrodinger equation for a SQUID
ring coupled to an electromagnetic field, both treated quantum mechanically. We
that show the SQUID ring can be used to create a maximally entangled state with
the em field that without dissipation remains constant in time. Using methods
familiar in quantum optics, we extend the model to include the effects of
coupling this system to a dissipative environment. With this model we show that
although such an environment makes a noticeable difference to the time
evolution of the system, it need not destroy the the entanglement of this
coupled system over time scales required for quantum technologies.


title: Extremal Quantum States in Coupled Systems

abstract:
  Let ${\cal H}_1,$ ${\cal H}_2$ be finite dimensional complex Hilbert spaces
describing the states of two finite level quantum systems. Suppose $\rho_i$ is
a state in ${\cal H}_i, i=1,2.$ Let ${\cal C} (\rho_1, \rho_2)$ be the convex
set of all states $\rho$ in ${\cal H} = {\cal H}_1 \otimes {\cal H}_2$ whose
marginal states in ${\cal H}_1$ and ${\cal H}_2$ are $\rho_1$ and $\rho_2$
respectively. Here we present a necessary and sufficient criterion for a $\rho$
in ${\cal C} (\rho_1, \rho_2)$ to be an extreme point. Such a condition
implies, in particular, that for a state $\rho$ to be an extreme point of
${\cal C} (\rho_1, \rho_2)$ it is necessary that the rank of $\rho$ does not
exceed $(d_1^2 + d_2^2 - 1)^{{1/2}},$ where $d_i = \dim {\cal H}_i, i=1,2.$
When ${\cal H}_1$ and ${\cal H}_2$ coincide with the 1-qubit Hilbert space
$\mathbb{C}^2$ with its standard orthonormal basis $\{|0 >, |1> \}$ and $\rho_1
= \rho_2 = {1/2} I$ it turns out that a state $\rho \in {\cal C} ({1/2}I,
{1/2}I)$ is extremal if and only if $\rho$ is of the form $|\Omega>< \Omega|$
where $| \Omega > = \frac{1}{\sqrt{2}} (|0> | \psi_0 > + |1 > | \psi_1 >),$
$\{| \psi_0 >, | \psi_1> \}$ being an arbitrary orthonormal basis of
$\mathbb{C}^2.$ In particular, the extremal states are the maximally entangled
states.


title: A Helium nanodrop bouncing off a wall

abstract:
  We investigate numerically the quantum collision between a stable Helium
nanodrop and an infinitely hard wall in one dimension. The scattering outcome
is compared to the same event omitting the quantum pressure. Only the quantum
process reflects the effect of diffraction of wave packets in space and time.


title:
Dipolar Relaxation in an ultra-cold Gas of magnetically trapped chromium
  atoms

abstract:
  We have investigated both theoretically and experimentally dipolar relaxation
in a gas of magnetically trapped chromium atoms. We have found that the large
magnetic moment of 6 $\mu_B$ results in an event rate coefficient for dipolar
relaxation processes of up to $3.2\cdot10^{-11}$ cm$^{3}$s$^{-1}$ at a magnetic
field of 44 G. We present a theoretical model based on pure dipolar coupling,
which predicts dipolar relaxation rates in agreement with our experimental
observations. This very general approach can be applied to a large variety of
dipolar gases.


title:
Entanglement of a Mesoscopic Field with an Atom induced by Photon
  Graininess in a Cavity

abstract:
  We observe that a mesoscopic field made of several tens of microwave photons
exhibits quantum features when interacting with a single Rydberg atom in a
high-Q cavity. The field is split into two components whose phases differ by an
angle inversely proportional to the square root of the average photon number.
The field and the atomic dipole are phase-entangled. These manifestations of
photon graininess vanish at the classical limit. This experiment opens the way
to studies of large Schrodinger cat states at the quantum-classical boundary.


title: Achievable efficiencies for probabilistically cloning the states

abstract:
  We present an example of quantum computational tasks whose performance is
enhanced if we distribute quantum information using quantum cloning.
Furthermore we give achievable efficiencies for probabilistic cloning the
quantum states used in implemented tasks for which cloning provides some
enhancement in performance.


title: Correlated imaging, quantum and classical

abstract:
  We analytically show that it is possible to perform coherent imaging by using
the classical correlation of two beams obtained by splitting incoherent thermal
radiation. The case of such two classically correlated beams is treated in
parallel with the configuration based on two entangled beams produced by
parametric down-conversion, and a basic analogy is pointed out. The results are
compared in a specific numerical example.


title: On an Argument of David Deutsch

abstract:
  We analyse an argument of Deutsch, which purports to show that the
deterministic part of classical quantum theory together with deterministic
axioms of classical decision theory, together imply that a rational decision
maker behaves as if the probabilistic part of quantum theory (Born's law) is
true. We uncover two missing assumptions in the argument, and show that the
argument also works for an instrumentalist who is prepared to accept that the
outcome of a quantum measurement is random in the frequentist sense: Born's law
is a consequence of functional and unitary invariance principles belonging to
the deterministic part of quantum mechanics. Unfortunately, it turns out that
after the necessary corrections we have done no more than give an easier proof
of Gleason's theorem under stronger assumptions. However, for some special
cases the proof method gives positive results while using different assumptions
to Gleason. This leads to the conjecture that the proof could be improved to
give the same conclusion as Gleason under unitary invariance together with a
much weaker functional invariance condition.


title: On Quantum Statistical Inference, I

abstract:
  Recent developments in the mathematical foundations of quantum mechanics have
brought the theory closer to that of classical probability and statistics. On
the other hand, the unique character of quantum physics sets many of the
questions addressed apart from those met classically in stochastics.
Furthermore, concurrent advances in experimental techniques and in the theory
of quantum computation have led to a strong interest in questions of quantum
information, in particular in the sense of the amount of information about
unknown parameters in given observational data or accessible through various
possible types of measurements. This scenery is outlined (with an audience of
statisticians and probabilists in mind).


title: Lower bounds on the complexity of simulating quantum gates

abstract:
  We give a simple proof of a formula for the minimal time required to simulate
a two-qubit unitary operation using a fixed two-qubit Hamiltonian together with
fast local unitaries. We also note that a related lower bound holds for
arbitrary n-qubit gates.


title: On Quantum Statistical Inference, II

abstract:
  Interest in problems of statistical inference connected to measurements of
quantum systems has recently increased substantially, in step with dramatic new
developments in experimental techniques for studying small quantum systems.
Furthermore, theoretical developments in the theory of quantum measurements
have brought the basic mathematical framework for the probability calculations
much closer to that of classical probability theory. The present paper reviews
this field and proposes and interrelates a number of new concepts for an
extension of classical statistical inference to the quantum context.


title: Characterizing entanglement with global and marginal entropic measures

abstract:
  We qualify the entanglement of arbitrary mixed states of bipartite quantum
systems by comparing global and marginal mixednesses quantified by different
entropic measures. For systems of two qubits we discriminate the class of
maximally entangled states with fixed marginal mixednesses, and determine an
analytical upper bound relating the entanglement of formation to the marginal
linear entropies. This result partially generalizes to mixed states the
quantification of entaglement with marginal mixednesses holding for pure
states. We identify a class of entangled states that, for fixed marginals, are
globally more mixed than product states when measured by the linear entropy.
Such states cannot be discriminated by the majorization criterion.

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


title:
Realism in Energy Transition Processes: an example from Bohmian Quantum
  Mechanics

abstract:
  In this paper we study in details a system of two weakly coupled harmonic
oscillators. This system may be viewed as a simple model for the interaction
between a photon and a photodetector. We obtain exact solutions for the general
case. We then compute approximate solutions for the case of a single photon
(where one oscillator is initially in its first excited state) reaching a
photodetector in its ground state (the other oscillator). The approximate
solutions represent the state of both the photon and the photodetector after
the interaction, which is not an eigenstate of the individual hamiltonians for
each particle, and therefore the energies for each particle do not exist in the
Copenhagen interpretation of Quantum Mechanics. We use the approximate
solutions that we obtained to compute bohmian trajectories and to study the
energy transfer between the two particles. We conclude that even using the
bohmian view the energy of each individual particle is not well defined, as the
nonlocal quantum potential is not negligible even after the coupling is turned
off.


title: Squeezing and entanglement in continous variable systems

abstract:
  Based on total variance of a pair of Einstein-Podolsky-Rosen (EPR) type
operators, the generalized EPR entangled states in continuous variable systems
are defined. We show that such entangled states must correspond with two-mode
squeezing states whether these states are Gaussian or not and whether they are
pure or not. With help of the relation between the total variance and the
entanglement, the degree of such entanglement is also defined. Through
analyzing some specific cases, we see that this method is very convenient and
easy in practical application. In addition, an entangled state with no
squeezing is studied, which reveals that there certainly exist something
unknown about entanglement in continuous variable systems.


title:
Nonrelativistic system of interacting particles in the model of the
  noncommutative operators of coordinates and momenta of different particles

abstract:
  It is shown that the Schr\"{o}dinger equation for a system of interacting
particles whose Compton wavelengths are of the same order of magnitude as the
system size is contradictory and is not strictly nonrelativistic, because it is
based on the implicit assumption that the velocity of propagation of
interactions is finite. In the framework of the model of the noncommutative
operators of coordinates and momenta of different particles, the equation for a
wave function which has no above-mentioned drawbacks is deduced. The
significant differences from solutions of the nonrelativistic Schr\"{o}dinger
equation for large values of the interaction constant are found, and the
comparison of analogous results for hydrogenlike atoms with experimental data
is carried out.


title: Tutorial Notes on One-Party and Two-Party Gaussian States

abstract:
  Gaussian states -- or, more generally, Gaussian operators -- play an
important role in Quantum Optics and Quantum Information Science, both in
discussions about conceptual issues and in practical applications. We describe,
in a tutorial manner, a systematic operator method for first characterizing
such states and then investigating their properties. The central numerical
quantities are the covariance matrix that specifies the characteristic function
of the state, and the closely related matrices associated with Wigner's and
Glauber's phase space functions. For pedagogical reasons, we restrict the
discussion to one-dimensional and two-dimensional Gaussian states, for which we
provide illustrating and instructive examples.


title: Quantum Teleportation with Atoms Trapped in Cavities

abstract:
  We propose a scheme to implement the quantum teleportation protocol with
single atoms trapped in cavities. The scheme is based on the adiabatic passage
and the polarization measurement. We show that it is possible to teleport the
internal state of an atom trapped in a cavity to an atom trapped in another
cavity with the success probability of 1/2 and the fidelity of 1. The scheme is
resistant to a number of considerable imperfections such as the violation of
the Lamb-Dicke condition, weak atom-cavity coupling, spontaneous emission, and
detection inefficiency.


title: A de Finetti Representation Theorem for Quantum Process Tomography

abstract:
  In quantum process tomography, it is possible to express the experimenter's
prior information as a sequence of quantum operations, i.e., trace-preserving
completely positive maps. In analogy to de Finetti's concept of exchangeability
for probability distributions, we give a definition of exchangeability for
sequences of quantum operations. We then state and prove a representation
theorem for such exchangeable sequences. The theorem leads to a simple
characterization of admissible priors for quantum process tomography and solves
to a Bayesian's satisfaction the problem of an unknown quantum operation.


title: Collective vs local measurements in qubit mixed state estimation

abstract:
  We discuss the problem of estimating a general (mixed) qubit state. We give
the optimal guess that can be inferred from any given set of measurements. For
collective measurements and for a large number $N$ of copies, we show that the
error in the estimation goes as 1/N. For local measurements we focus on the
simpler case of states lying on the equatorial plane of the Bloch sphere. We
show that standard tomographic techniques lead to an error proportional to
$1/N^{1/4}$, while with our optimal data processing it is proportional to
$1/N^{3/4}$.


title: Generalized Quantum Secret Sharing

abstract:
  We explore a generalization of quantum secret sharing (QSS) in which
classical shares play a complementary role to quantum shares, exploring further
consequences of an idea first studied by Nascimento, Mueller-Quade and Imai
(Phys. Rev. {\bf A64} 042311 (2001)). We examine three ways, termed inflation,
compression and twin-thresholding, by which the proportion of classical shares
can be augmented. This has the important application that it reduces quantum
(information processing) players by replacing them with their classical
counterparts, thereby making quantum secret sharing considerably easier and
less expensive to implement in a practical setting. In compression, a QSS
scheme is turned into an equivalent scheme with fewer quantum players,
compensated for by suitable classical shares. In inflation, a QSS scheme is
enlarged by adding only classical shares and players. In a twin-threshold
scheme, we invoke two separate thresholds for classical and quantum shares
based on the idea of information dilution.


title:
A Preliminar Evidence of Quantum Like Behavior in Measurements of Mental
  States

abstract:
  Experimental results presented in this paper supports the hypothesis on
quantum-like statistical behaviour of cognitive systems (at least human
beings). Our quantum-like approach gives the possibility to represent mental
states by Hilbert space vectors (complex amplitudes). Such a representation
induces huge reduction of information about a mental state. We realize an
approach that has no direct relation with reductionist quantum models and we
are not interested in statistical behavior of micro systems forming the macro
system of the brain. We describe only probabilistic features of cognitive
measurements. Our quantum-like approach describes statistics of measurements of
cognitive systems with the aim to ascertain if cognitive systems behave as
quantum-like systems where here quantum-like cognitive behavior means that
cognitive systems result to be very sensitive to changes of the context with
regard to the complex of the mental conditions.


title:
Quasi-paraxial theory for coupled unstable cavities I: formal
  development

abstract:
  We present a formal wave theory for the calculation of the spectrum and the
eigenmodes for a certain class of ray-chaotic optical cavities introduced by A.
Aiello, M. P. van Exter, and J. P. Woerdman [quant-ph/0307119].


title: An algebraic solution of driven single band tight binding dynamics

abstract:
  The dynamics of the driven tight binding model for Wannier-Stark systems is
formulated and solved using a dynamical algebra. This Lie algebraic approach is
very convenient for evaluating matrix elements and expectation values. It is
also shown that a dynamical invariant can be constructed. A classicalization of
the tight binding model is discussed as well as some illustrating examples of
Bloch oscillations and dynamical localization effects.


title:
Universal ultrabright source of entangled photon states: generation and
  tomographic analysis of Werner states and of Maximally Entangled Mixed States

abstract:
  A novel ultrabright parametric source of polarization entangled photon pairs
with striking spatial characteristics is reported. The distribution of the
output electromagnetic k-modes excited by Spontaneous Parametris Down
Conversion and coupled to the output detectors can be very broad. It could
coincide with the full set of phase-matched excited modes, at least in
principle. In this case a relevant conditional quasi-pure output state should
be realized. By these (approximate) states realized over a full
Entanglement-Ring output distribution, the non local properties of the
generated entanglement has been tested by standard Bell measurements and by
Ou-Mandel interferometry. A novel ''mode-patchwork'' technique based on the
quantum superposition principle is adopted to synthesize in a straightforward
and reliable way any kind of mixed-states, of large conceptual and
technological interest in modern Quantum Information. Tunable Werner states and
Maximally Entangled Mixed States (MEMS) have indeed been created by the new
technique and investigated by quantum tomography. A thorough study of the
entropic and nonlocal properties of these states has been undertaken
experimentally and theoretically, by a unifying variational approach.


title: Self testing quantum apparatus

abstract:
  We study a configuration of devices that includes (1) a source of some
unknown bipartite quantum state that is claimed to be the Bell state $\Phi^+$
and (2) two commuting but otherwise unknown measurement apparatus, one on each
side, that are each claimed to execute an orthogonal measurement at an angle
$\theta \in \{0, \pi/8, \pi/4\}$ that is chosen by the user. We show that, if
the nine distinct probability distributions that are generated by the self
checking configuration, one for each pair of angles, are consistent with the
specifications, the source and the two measurement apparatus are guaranteed to
be identical modulo some isomorphism to the claimed specifications. We discuss
the connection with quantum cryptography.


title:
Strong subadditivity inequality for quantum entropies and four-particle
  entanglement

abstract:
  Strong subadditivity inequality for a three-particle composite system is an
important inequality in quantum information theory which can be studied via a
four-particle entangled state. We use two three-level atoms in $\Lambda$
configuration interacting with a two-mode cavity and the Raman adiabatic
passage technique for the production of the four-particle entangled state.
Using this four-particle entanglement, we study for the first time various
aspects of the strong subadditivity inequality.


title: Information transfer through a one-atom micromaser

abstract:
  We consider a realistic model for the one-atom micromaser consisting of a
cavity maintained in a steady state by the streaming of two-level Rydberg atoms
passing one at a time through it. We show that it is possible to monitor the
robust entanglement generated between two successive experimental atoms passing
through the cavity by the control decoherence parameters. We calculate the
entanglement of formation of the joint two-atom state as a function of the
micromaser pump parameter. We find that this is in direct correspondence with
the difference of the Shannon entropy of the cavity photons before and after
the passage of the atoms for a reasonable range of dissipation parameters. It
is thus possible to demonstrate information transfer between the cavity and the
atoms through this set-up.


title: Qubit Rotation by STIRAP

abstract:
  We introduce a novel procedure for qubit rotation, alternative to the
commonly used method of Rabi oscillations of controlled pulse area. It is based
on the technique of Stimulated Raman Adiabatic Passage (STIRAP) and therefore
it is robust against fluctuations of experimental parameters. Furthermore, our
work shows that it is in principle possible to perform quantum logic operations
via stimulated Raman adiabatic passage. This opens up the search for a
completely new class of schemes to implement logic gates.


title:
Enhanced Nonlinear Generation in a Three-Level Medium with Spatially
  Dependent Coherence

abstract:
  We consider a method for efficient parametric generation of a laser pulse. A
single laser field is injected to a three-level medium which has two lower
states and one excited state. The lower states are prepared initially in a
position-dependent coherent superposition state. It is shown that by proper
choice of the position dependence of the superposition along the direction of
propagation, the incoming field can be converted completely to a new field.


title: Tomography of entangled massive particles

abstract:
  We report on tomographic means to study the stability of a qubit register
based on a string of trapped ions. In our experiment, two ions are held in a
linear Paul trap and are entangled deterministically by laser pulses that
couple their electronic and motional states. We reconstruct the density matrix
using single qubit rotations and subsequent measurements with near-unity
detection efficiency. This way, we characterize the created Bell states, the
states into which they subsequently decay, and we derive their entanglement,
applying different entanglement measures.


title: Quantized phase shifts and a dispersive universal quantum gate

abstract:
  A single 40Ca+ ion is trapped and laser cooled to its motional ground state.
Laser radiation which couples off-resonantly to a motional sideband of the
ion's S1/2 to D5/2 transition causes a phase shift proportional to the ion's
motional quantum state |n>. As the phase shift is conditional upon the ion's
motion, we are able to demonstrate a universal 2-qubit quantum gate operation
where the electronic target state {S,D} is flipped depending on the motional
qubit state |n>={|0>,|1>}. Finally, we discuss scaling properties of this
universal quantum gate for linear ion crystals and present numerical
simulations for the generation of a maximally entangled state of five ions.


title: Hyperentanglement-assisted Bell-state analysis

abstract:
  We propose a simple scheme for complete Bell-state measurement of photons
using hyperentangled states - entangled in multiple degrees of freedom. In
addition to hyperentanglement, our scheme requires only linear optics and
single photon detectors, and is realizable with current technology. At the cost
of additional classical communication, our Bell-state measurement can be
implemented non-locally. We discuss the possible application of these results
to quantum dense coding and quantum teleportation.


title: Dynamical Properties of the Delta Kicked Harmonic Oscillator

abstract:
  We propose an efficient procedure for numerically evolving the Delta Kicked
Harmonic Oscillator. The method allows for longer and more accurate simulations
of the system as well as a simple procedure for calculating the systems Floquet
eigenstates and quasi-energies. The method is used to examine the dynamical
behaviour of the system in cases where the ratio of the kicking frequency to
the systems natural frequency is both rational and irrational.


title: Suppression of Dephasing of Optically Trapped Atoms

abstract:
  Ultra-cold atoms trapped in an optical dipole trap and prepared in a coherent
superposition of their hyperfine ground states, decohere as they interact with
their environment. We demonstrate than the loss in coherence in an "echo"
experiment, which is caused by mechanisms such as Rayleigh scattering, can be
suppressed by the use of a new pulse sequence. We also show that the coherence
time is then limited by mixing to other vibrational levels in the trap and by
the finite lifetime of the internal quantum states of the atoms.


title:
Special reduction of density matrixes and entanglement between two
  bunches of particles

abstract:
  By using of a special reduction way of density matrices, in this Letter we
find the entanglement between two bunches of particles, its measure can be
represented by the entanglement of formation.


title: Atoms, dipole waves, and strongly focused light beams

abstract:
  We describe the resonant interaction of an atom with a strongly focused light
beam by expanding the field in multipole waves. For a classical field, or when
the field is described by a coherent state, we find that both intensity pattern
and photon statistics of the scattered light are fully determined by a small
set of parameters. One crucial parameter is the overlap of the field with the
appropriate dipole wave corresponding to the relevant dipole transition in the
atom. We calculate this overlap for a particular set of strongly focused
longitudinally polarized light beams, whose spot size is only $0.1\lambda^2$,
as discussed in S. Quabis, et al., Appl. Phys. B {\bf 72}, 109 (2001).


title: The chaotic chameleon

abstract:
  Various local hidden variables models for the singlet correlations exploit
the detection loophole, or other loopholes connected with post-selection on
coincident arrival times. I consider the connection with a probabilistic
simulation technique called rejection-sampling, and pose some natural questions
concerning what can be achieved and what cannot be achieved with local (or
distributed) rejection sampling. In particular a new and more serious loophole,
which we call the coincidence loophole, is introduced.


title: Manifold of density matrices

abstract:
  We show that the manifold of density matrices can be derived from CP^{N^2-1}
by the action of SU(N). We give some preliminary observations on the structure
of this manifold.


title:
Geometric measure of entanglement and applications to bipartite and
  multipartite quantum states

abstract:
  The degree to which a pure quantum state is entangled can be characterized by
the distance or angle to the nearest unentangled state. This geometric measure
of entanglement, already present in a number of settings (see Shimony 1995 and
Barnum and Linden 2001), is explored for bipartite and multipartite pure and
mixed states. The measure is determined analytically for arbitrary two-qubit
mixed states and for generalized Werner and isotropic states, and is also
applied to certain multipartite mixed states. In particular, a detailed
analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W
states. Along the way, we point out connections of the geometric measure of
entanglement with entanglement witnesses and with the Hartree approximation
method.


title: A Lattice Problem in Quantum NP

abstract:
  We consider coGapSVP_\sqrt{n}, a gap version of the shortest vector in a
lattice problem. This problem is known to be in AM\cap coNP but is not known to
be in NP or in MA. We prove that it lies inside QMA, the quantum analogue of
NP. This is the first non-trivial upper bound on the quantum complexity of a
lattice problem.
  The proof relies on two novel ideas. First, we give a new characterization of
QMA, called QMA+. Working with the QMA+ formulation allows us to circumvent a
problem which arises commonly in the context of QMA: the prover might use
entanglement between different copies of the same state in order to cheat. The
second idea involves using estimations of autocorrelation functions for
verification. We make the important observation that autocorrelation functions
are positive definite functions and using properties of such functions we
severely restrict the prover's possibility to cheat. We hope that these ideas
will lead to further developments in the field.


title: Superdense coding of quantum states

abstract:
  We describe a method to non-obliviously communicate a 2l-qubit quantum state
by physically transmitting l+o(l) qubits of communication, and by consuming l
ebits of entanglement and some shared random bits. In the non-oblivious
scenario, the sender has a classical description of the state to be
communicated. Our method can be used to communicate states that are pure or
entangled with the sender's system; l+o(l) and 3l+o(l) shared random bits are
sufficient respectively.


title:
On a Rigorous Proof of the Joos-Zeh Formula for Decoherence in a
  Two-Body Problem

abstract:
  We consider a simple one dimensional system consisting of two particles
interacting with a $\delta$-potential and we discuss a rigorous derivation of
the asymptotic wave function of the system in the limit of small mass ratio. We
apply the result to the explicit computation of the decoherence effect induced
by scattering in a concrete example of quantum evolution.


title:
Electromagnetically-induced transparency and light storing of a pair of
  pulses

abstract:
  Electromagnetically-induced transparency and light storing are studied in the
case of a medium of atoms in a double Lambda configuration, both in terms of
dark- and bright-state polatitons and atomic susceptibility. It is proven that
the medium can be made transparent simultaneously for two pulses following
their self-adjusting so that a condition for an adiabatic evolution has become
fulfilled. Analytic formulas are given for the shapes and phases of the
transmitted/stored pulses. The level of transparency can be regulated by
adjusting the heights and phases of the control fields.


title:
Sub and Super-Luminal Propagation of Intense Pulses in Media with
  Saturated and Reverse Absorption

abstract:
  We develop models for the propagation of intense pulses in solid state media
which can have either saturated absorption or exhibit reverse absorption . We
show that the experiments of Bigelow {\it et al.}[Phys. Rev. Lett. {\bf 90},
113903 (2003); Science {\bf 301}, 200 (2003).] on subluminal propagation in
Ruby and superluminal propagation in Alexandrite are well explained by
modelling them as three level and four level systems coupled to Maxwell
equations. We present results well beyond the traditional pump-probe approach.


title: Asymptotic estimation of shift parameter of a quantum state

abstract:
  We develop an asymptotic theory of estimation of a shift parameter in a pure
quantum state to study the relation between entangled and unentangled covariant
estimates in the analytically most transparent way. After recollecting basics
of estimation of shift parameter in Sec. 2, we study the structure of the
optimal covariant estimate in Sec. 3, showing how entanglement comes into play
for several independent trials. In Secs. 4,5 we give the asymptotics of the
performance of the optimal covariant estimate comparing it with the
``semiclassical'' unentangled covariant estimation in the regular case of
finite variance of the generator of the shift group. Sec. 6 is devoted to
covariant estimation in the case where the regularity assumption is violated.


title: Maser and Laser Action with One Atom

abstract:
  We present a theory which can explain the micromaser as well as its optical
counterpart, the microlaser, for appropriate values of dissipative parameters.
We show that, in both the the cases, the cavity radiation fields can have
sub-Poissonian photon statistics. We further analyse if it is possible to
attain a Fock state of the radiation field. The microlaser is precluded for
such analysics due to the damping of its lasing levels making transitions at
optical frequencies. Hence, we focus our attention on the micromaser and our
exact simulation of the dynamics shows that it is not possible to generate a
Fock state of the cavity radiation field.


title:
On the existence of physical transformations between sets of quantum
  states

abstract:
  Let A = {rho_1,...,rho_n} be a given set of quantum states. We consider the
problem of finding necessary and sufficient conditions on another set B =
{sigma_1,...,sigma_n} that guarantee the existence of a physical transformation
taking rho_i to sigma_i for all i. Uhlmann has given an elegant such condition
when both sets comprise pure states. We give a simple proof of this condition
and develop some consequences. Then we consider multi-probabilistic
transformations between sets of pure states which leads to conditions for the
problem of transformability between A and B when one set is pure and the other
is arbitrary.


title: Electron propagation in crossed magnetic and electric fields

abstract:
  Laser-atom interaction can be an efficient mechanism for the production of
coherent electrons. We analyze the dynamics of monoenergetic electrons in the
presence of uniform, perpendicular magnetic and electric fields. The Green
function technique is used to derive analytic results for the field--induced
quantum mechanical drift motion of i) single electrons and ii) a dilute Fermi
gas of electrons. The method yields the drift current and, at the same time it
allows us to quantitatively establish the broadening of the (magnetic) Landau
levels due to the electric field: Level number k is split into k+1 sublevels
that render the $k$th oscillator eigenstate in energy space. Adjacent Landau
levels will overlap if the electric field exceeds a critical strength. Our
observations are relevant for quantum Hall configurations whenever electric
field effects should be taken into account.


title:
Objective properties from subjective quantum states: Environment as a
  witness

abstract:
  We study the emergence of objective properties in open quantum systems. In
our analysis, the environment is promoted from a passive role of reservoir
selectively destroying quantum coherence, to an active role of amplifier
selectively proliferating information about the system. We show that only
preferred pointer states of the system can leave a redundant and therefore
easily detectable imprint on the environment. Observers who--as it is almost
always the case--discover the state of the system indirectly (by probing a
fraction of its environment) will find out only about the corresponding pointer
observable. Many observers can act in this fashion independently and without
perturbing the system: they will agree about the state of the system. In this
operational sense, preferred pointer states exist objectively.


title: Theory of output coupling for trapped fermionic atoms

abstract:
  We develop a dynamic theory of output coupling, for fermionic atoms initially
confined in a magnetic trap. We consider an exactly soluble one-dimensional
model, with a spatially localized delta-type coupling between the atoms in the
trap and a continuum of free-particle external modes. Two important special
cases are considered for the confinement potential: the infinite box and the
harmonic oscillator. We establish that in both cases a bound state of the
coupled system appears for any value of the coupling constant, implying that
the trap population does not vanish in the infinite-time limit. For weak
coupling, the energy spectrum of the outgoing beam exhibits peaks corresponding
to the initially occupied energy levels in the trap; the height of these peaks
increases with the energy. As the coupling gets stronger, the energy spectrum
is displaced towards dressed energies of the fermions in the trap. The
corresponding dressed states result from the coupling between the unperturbed
fermionic states in the trap, mediated by the coupling between these states and
the continuum. In the strong-coupling limit, there is a reinforcement of the
lowest-energy dressed mode, which contributes to the energy spectrum of the
outgoing beam more strongly than the other modes. This effect is especially
pronounced for the one-dimensional box, which indicates that the efficiency of
the mode-reinforcement mechanism depends on the steepness of the confinement
potential. In this case, a quasi-monochromatic anti-bunched atomic beam is
obtained. Results for a bosonic sample are also shown for comparison.


title: Simulating quantum Brownian motion with single trapped ions

abstract:
  We study the open system dynamics of a harmonic oscillator coupled with an
artificially engineered reservoir. We single out the reservoir and system
variables governing the passage between Lindblad type and non-Lindblad type
dynamics of the reduced system's oscillator. We demonstrate the existence of
conditions under which virtual exchanges of energy between system and reservoir
take place. We propose to use a single trapped ion coupled to engineered
reservoirs in order to simulate quantum Brownian motion.


title: Decay in a uniform field: an exactly solvable model

abstract:
  We investigate the time evolution of the decay (or ionization) probability of
a D-dimensional model atom (D=1,2,3) in the presence of a uniform (i.e., static
and homogeneous) background field. The model atom consists in a
non-relativistic point particle in the presence of a point-like attractive
well. It is shown that the model exhibits infinitely many resonances leading to
possible deviations from the naive exponential decay law of the non-decay (or
survival) probability of the initial atomic quantum state. Almost stable states
exist due to the presence of the attractive interaction, no matter how weak it
is. Analytic estimates as well as numerical evaluation of the decay rates are
explicitly given and discussed.

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


title: Quantum Computing of Poincare Recurrences and Periodic Orbits

abstract:
  Quantum algorithms are built enabling to find Poincar\'e recurrence times and
periodic orbits of classical dynamical systems. It is shown that exponential
gain compared to classical algorithms can be reached for a restricted class of
systems. Quadratic gain can be achieved for a larger set of dynamical systems.
The simplest cases can be implemented with small number of qubits.


title: Statistical Structures Underlying Quantum Mechanics and Social Science

abstract:
  Common observations of the unpredictability of human behavior and the
influence of one question on the answer to another suggest social science
experiments are probabilistic and may be mutually incompatible with one
another, characteristics attributed to quantum mechanics (as distinguished from
classical mechanics). This paper examines this superficial similarity in depth
using the Foulis-Randall Operational Statistics language. In contradistinction
to physics, social science deals with complex, open systems for which the set
of possible experiments is unknowable and outcome interference is a graded
phenomenon resulting from the ways the human brain processes information. It is
concluded that social science is, in some ways, "less classical" than quantum
mechanics, but that generalized "quantum" structures may provide appropriate
descriptions of social science experiments. Specific challenges to extending
"quantum" structures to social science are identified.


title: Towards a Neo-Copenhagen Interpretation of Quantum Mechanics

abstract:
  The Copenhagen interpretation is critically considered. A number of
ambiguities, inconsistencies and confusions are discussed. It is argued that it
is possible to purge the interpretation so as to obtain a consistent and
reasonable way to interpret the mathematical formalism of quantum mechanics,
which is in agreement with the way this theory is dealt with in experimental
practice. In particular, the essential role attributed by the Copenhagen
interpretation to measurement is acknowledged. For this reason it is proposed
to refer to it as a neo-Copenhagen interpretation.


title: Coherence control for qubits

abstract:
  We study the influence of an external driving field on the coherence
properties of a qubit under the influence of bit-flip noise. In the presence of
driving, two paradigmatic cases are considered: (i) a field that results for a
suitable choice of the parameters in so-called coherent destruction of
tunneling and (ii) one that commutes with the static qubit Hamiltonian. In each
case, we give for high-frequency driving a lower bound for the coherence time.
This reveals the conditions under which the external fields can be used for
coherence stabilization.


title: Strong Coupling Perturbation Theory in Quantum Mechanics

abstract:
  We present a full introduction to the recent devised perturbation theory for
strong coupling in quantum mechanics. In order to put the theory in a proper
historical perspective, the approach devised in quantum field theory is rapidly
presented, showing how it implies a kind of duality in perturbation theory,
from the start. The approach of renormalization group in perturbation theory is
then presented. This method permits to resum secularities in perturbation
theory and makes fully algorithmical the resummation, transforming the
perturbation calculations in a step by step computational procedure. The
general theorem on which is founded a proper application of the strong coupling
expansion, based on a result in the quantum adiabatic theory, is then exposed.
This theorem gives the leading order of a strong coupling expansion. Then,
after the introduction of the principle of duality in perturbation theory that
puts in a proper context the quantum field theory method, the resulting theory
of the strong coupling expansion and the free picture are presented. An
algorithm for the computation of the perturbation series is finally given. This
approach has a lot of applications in fields as quantum optics, condensed
matter and so on, extending the original expectations of the quantum field
theory method. So, we give some examples of application for a class of
two-level systems that, in recent years, proved to be extremely important. One
of the most interesting concepts that can be obtained in this way is that of a
Quantum Amplifier (QAMP) that permits to obtain an amplification to the
classical level of the quantum fluctuations of the ground state of a single
radiation mode.


title:
Decoherence in a Talbot Lau interferometer: the influence of molecular
  scattering

abstract:
  We study the interference of C70 fullerenes in a Talbot-Lau interferometer
with a large separation between the diffraction gratings. This permits the
observation of recurrences of the interference contrast both as a function of
the de Broglie wavelength and in dependence of the interaction with background
gases. We observe an exponential decrease of the fringe visibility with
increasing background pressure and find good quantitative agreement with the
predictions of decoherence theory. From this we extrapolate the limits of
matter wave interferometry and conclude that the influence of collisional
decoherence may be well under control in future experiments with proteins and
even larger objects.


title:
Low-lying spectra in anharmonic three-body oscillators with a strong
  short-range repulsion

abstract:
  Three-body Schroedinger equation is studied in one dimension. Its two-body
interactions are assumed composed of the long-range attraction (dominated by
the L-th-power potential) in superposition with a short-range repulsion
(dominated by the (-K)-th-power core) plus further subdominant power-law
components if necessary. This unsolvable and non-separable generalization of
Calogero model (which is a separable and solvable exception at L = K = 2) is
presented in polar Jacobi coordinates. We derive a set of trigonometric
identities for the potentials which generalizes the well known K=2 identity of
Calogero to all integers. This enables us to write down the related partial
differential Schroedinger equation in an amazingly compact form. As a
consequence, we are able to show that all these models become separable and
solvable in the limit of strong repulsion.


title:
Quantum Information processing by NMR: Preparation of pseudopure states
  and implementation of unitary operations in a single-qutrit system

abstract:
  Theoretical Quantum Information Processing (QIP) has matured from the use of
qubits to the use of qudits (systems having states> 2). Where as most of the
experimental implementations have been performed using qubits, little
experimental work has been carried out using qudits as yet. In this paper we
demonstrate experimental realization of a qutrit system by nuclear magnetic
resonance (NMR), utilizing deuterium (spin-1) nuclei partially oriented in
liquid crystalline phase. Preparation of pseudopure states and implementation
of unitary operations are demonstrated in this single-qutrit system, using
transition selective pulses.


title:
On linearity of separating multi-particle differential Schr\"odinger
  operators for identical particles

abstract:
  We show that hierarchies of differential Schroedinger operators for identical
particles which are separating for the usual (anti-)symmetric tensor product,
are necessarily linear, and offer some speculations on the source of quantum
linearity.


title: Classical Motion

abstract:
  Preciously given rules allow conscious systems to be included in quantum
mechanical systems. There rules are derived from the empirical experience of an
observer who witnesses a quantum mechanical interaction leading to the capture
of a single particle. In the present paper it is shown that purely classical
changes experienced by an observer are consistent with these rules. Three
different interactions are considered, two of which combine classical and
quantum mechanical changes. The previously given rules support all of these
cases. Key Words: brain states, conscious observer, detector, measurement,
probability current, state reduction, von Neumann, wave collapse.


title: Maximally entangled mixed states: Creation and concentration

abstract:
  Using correlated photons from parametric downconversion, we extend the
boundaries of experimentally accessible two-qubit Hilbert space. Specifically,
we have created and characterized maximally entangled mixed states (MEMS) that
lie above the Werner boundary in the linear entropy-tangle plane. In addition,
we demonstrate that such states can be efficiently concentrated, simultaneously
increasing both the purity and the degree of entanglement. We investigate a
previously unsuspected sensitivity imbalance in common state measures, i.e.,
the tangle, linear entropy, and fidelity.


title:
Orbits of quantum states and geometry of Bloch vectors for $N$-level
  systems

abstract:
  Physical constraints such as positivity endow the set of quantum states with
a rich geometry if the system dimension is greater than two. To shed some light
on the complicated structure of the set of quantum states, we consider a
stratification with strata given by unitary orbit manifolds, which can be
identified with flag manifolds. The results are applied to study the geometry
of the coherence vector for n-level quantum systems. It is shown that the
unitary orbits can be naturally identified with spheres in R^{n^2-1} only for
n=2. In higher dimensions the coherence vector only defines a non-surjective
embedding into a closed ball. A detailed analysis of the three-level case is
presented. Finally, a refined stratification in terms of symplectic orbits is
considered.


title:
Appearance and Stability of Anomalously Fluctuating States in Shor's
  Factoring Algorithm

abstract:
  We analyze quantum computers which perform Shor's factoring algorithm, paying
attention to asymptotic properties as the number L of qubits is increased.
Using numerical simulations and a general theory of the stabilities of
many-body quantum states, we show the following: Anomalously fluctuating states
(AFSs), which have anomalously large fluctuations of additive operators, appear
in various stages of the computation. For large L, they decohere at anomalously
great rates by weak noises that simulate noises in real systems. Decoherence of
some of the AFSs is fatal to the results of the computation, whereas
decoherence of some of the other AFSs does not have strong influence on the
results of the computation. When such a crucial AFS decoheres, the probability
of getting the correct computational result is reduced approximately
proportional to L^2. The reduction thus becomes anomalously large with
increasing L, even when the coupling constant to the noise is rather small.
Therefore, quantum computations should be improved in such a way that all AFSs
appearing in the algorithms do not decohere at such great rates in the existing
noises.


title: Optimal Quantum Circuits for General Two-Qubit Gates

abstract:
  In order to demonstrate non-trivial quantum computations experimentally, such
as the synthesis of arbitrary entangled states, it will be useful to understand
how to decompose a desired quantum computation into the shortest possible
sequence of one-qubit and two-qubit gates. We contribute to this effort by
providing a method to construct an optimal quantum circuit for a general
two-qubit gate that requires at most 3 CNOT gates and 15 elementary one-qubit
gates. Moreover, if the desired two-qubit gate corresponds to a purely real
unitary transformation, we provide a construction that requires at most 2 CNOTs
and 12 one-qubit gates. We then prove that these constructions are optimal with
respect to the family of CNOT, y-rotation, z-rotation, and phase gates.


title:
Quantum key distribution with unconditional security for all optical
  fiber network

abstract:
  In this paper, we present an efficient implementation method of physical
layer of Y-00 which can support a secure communication and a quantum key
distribution (more generally key expansion) by IMDD(intensity modulation/direct
detection) or FSK(frequency shift keying)optical fiber communication network.
Although the general proof of the security is not yet given, a brief sketch of
security analysis is shown, which involve an entanglement attack.


title: Measuring Polynomial Invariants of Multi-Party Quantum States

abstract:
  We present networks for directly estimating the polynomial invariants of
multi-party quantum states under local transformations. The structure of these
networks is closely related to the structure of the invariants themselves and
this lends a physical interpretation to these otherwise abstract mathematical
quantities. Specifically, our networks estimate the invariants under local
unitary (LU) transformations and under stochastic local operations and
classical communication (SLOCC). Our networks can estimate the LU invariants
for multi-party states, where each party can have a Hilbert space of arbitrary
dimension and the SLOCC invariants for multi-qubit states. We analyze the
statistical efficiency of our networks compared to methods based on estimating
the state coefficients and calculating the invariants.


title: Quantum Teleportation: from Pure to Mixed States and Standard to Optimal

abstract:
  Teleportation for pure states, mixed states with standard and optimal
protocols are introduced and investigated systematically. An explicit equation
governing the teleportation of finite dimensional quantum pure states by a
generally given non-local entangled state is presented. For the teleportation
of a mixed state with an arbitrary mixed state resource, an explicit expression
is obtained for the quantum channel associated with the standard teleportation
protocol. The corresponding transmission fidelity is calculated. It is shown
that the standard teleportation protocol is not optimal. The optimal quantum
teleportation is further studied, its fidelity is given and shown to be related
to the fully entangled fraction of the quantum resource, rather than the single
fraction as in the standard teleportation protocol.


title: Classical Communication Cost of Quantum Teleportation

abstract:
  Quantum teleportation schemes in which operations are performed before
establishing the quantum channel are not constrained by resource limits set in
H.K.Lo and Bennett et al. We compare the standard teleportation protocol to the
one proposed by Kak on the basis of the classical communication cost. Due to
its unique architecture we study the problems in implementing Kak teleportation
protocol.


title:
Measuring 4-local n-qubit observables could probabilistically solve
  PSPACE

abstract:
  We consider a hypothetical apparatus that implements measurements for
arbitrary 4-local quantum observables A on n qubits. The apparatus implements
the ``measurement algorithm'' after receiving a classical description of A. We
show that a few precise measurements, applied to a basis state would provide a
probabilistic solution of PSPACE problems. The error probability decreases
exponentially with the number of runs if the measurement accuracy is of the
order of the spectral gaps of A.
  Moreover, every decision problem which can be solved on a quantum computer in
T time steps can be encoded into a 4-local observable such that the solution
requires only measurements of accuracy O(1/T).
  Provided that BQP<>PSPACE, our result shows that efficient algorithms for
precise measurements of general 4-local observables cannot exist. We conjecture
that the class of physically existing interactions is large enough to allow the
conclusion that precise energy measurements for general many-particle systems
require control algorithms with high complexity.


title: Classical capacity of the lossy bosonic channel: the exact solution

abstract:
  The classical capacity of the lossy bosonic channel is calculated exactly. It
is shown that its Holevo information is not superadditive, and that a
coherent-state encoding achieves capacity. The capacity of far-field,
free-space optical communications is given as an example.


title: Generalized Hypergeometric Coherent States

abstract:
  We introduce a large class of holomorphic quantum states by choosing their
normalization functions to be given by generalized hypergeometric functions. We
call them generalized hypergeometric states in general, and generalized
hypergeometric coherent states in particular, if they allow a resolution of
unity. Depending on the domain of convergence of the generalized hypergeometric
functions, we distinguish generalized hypergeometric states on the plane, the
open unit disk, and the unit circle. All states are eigenstates of suitably
defined lowering operators. We then study their photon number statistics and
phase properties as revealed by the Husimi and Pegg-Barnett phase
distributions. On the basis of the generalized hypergeometric coherent states
we introduce generalized hypergeometric Husimi distributions and corresponding
phase distributions as well as new analytic representations of arbitrary
quantum states in Bargmann and Hardy spaces.


title: Entangling capacities of noisy two-qubit Hamiltonians

abstract:
  We show that intrinsic fluctuations in system control parameters impose
limits on the ability of two-qubit (exchange) Hamiltonians to generate
entanglement starting from mixed initial states. We find three classes for
Gaussian and Laplacian fluctuations. For the Ising and XYZ models there are
qualitatively distinct sharp entanglement-generation transitions, while the
class of Heisenberg, XY, and XXZ Hamiltonians is capable of generating
entanglement for any finite noise level. Our findings imply that exchange
Hamiltonians are surprisingly robust in their ability to generate entanglement
in the presence of noise, thus potentially reducing the need for quantum error
correction.


title:
Quantum time ordering and degeneracy. II: Coherent population transfer
  between degenerate states

abstract:
  We find conditions required to achieve complete population transfer, via
coherent population trapping, from an initial state to a designated final state
at a designated time in a degenerate $n$-state atom, where transitions are
caused by an external interaction. In systems with degenerate states there is
no time ordering. Analytic expressions have been found for transition
probabilities in a degenerate $n$-state atom interacting with a strong external
field that gives a common time dependence to all of the transition matrix
elements. Except for solving a simple $n^{th}$ order equation to determine
eigenvalues of dressed states, the method is entirely analytic. These
expressions may be used to control electron populations in degenerate $n$-state
atoms. Examples are given for $n=2$ and $n=3$.


title:
Eigenvector Approximation Leading to Exponential Speedup of Quantum
  Eigenvalue Calculation

abstract:
  We present an efficient method for preparing the initial state required by
the eigenvalue approximation quantum algorithm of Abrams and Lloyd. Our method
can be applied when solving continuous Hermitian eigenproblems, e.g., the
Schroedinger equation, on a discrete grid. We start with a classically obtained
eigenvector for a problem discretized on a coarse grid, and we efficiently
construct, quantum mechanically, an approximation of the same eigenvector on a
fine grid. We use this approximation as the initial state for the eigenvalue
estimation algorithm, and show the relationship between its success probability
and the size of the coarse grid.


title: Towards Lagrangian approach to quantum computations (revised)

abstract:
  In this work is discussed possibility and actuality of Lagrangian approach to
quantum computations. Finite-dimensional Hilbert spaces used in this area
provide some challenge for such consideration. The model discussed here can be
considered as an analogue of Weyl quantization of field theory via path
integral in L. D. Faddeev's approach. Weyl quantization is possible to use also
in finite-dimensional case, and some formulas may be simply rewritten with
change of integrals to finite sums. On the other hand, there are specific
difficulties relevant to finite case.


title: Time operator within projection evolution model

abstract:
  We apply the projection evolution approach to the particle detection process
and calculation of the detection moment. Influence of the essential system
properties on the evolution process is discussed. It is shown, that using only
the projection postulate in the evolution scheme allows to understand the time
as a kind of observable.


title:
Tensor of coherences parameterization of multiqubit density operators
  for entanglement characterization

abstract:
  For multiqubit densities, the tensor of coherences (or Stokes tensor) is a
real parameterization obtained by the juxtaposition of the affine Bloch vectors
of each qubit. While it maintains the tensorial structure of the underlying
space, it highlights the pattern of correlations, both classical and quantum,
between the subsystems and, due to the affine parameterization, it contains in
its components all reduced densities of all orders. The main purpose of our use
of this formalism is to deal with entanglement. For example, the detection of
bipartite entanglement is straightforward, as it is the synthesis of densities
having positive partial transposes between desired qubits. In addition, finding
explicit mixtures for families of separable states becomes a feasible issue for
few qubit symmetric densities (we compute it for Werner states) and, more
important, it provides some insight on the possible origin of entanglement for
such densities.


title: Teleportation with partially entangled states

abstract:
  The relations of antilinear maps, bipartite states and quantum channels is
summarized. Antilinear maps are applied to describe bipartite states and
entanglement. Teleportation is treated in this general formalism with an
emphasis on conditional schemes applying partially entangled pure states. It is
shown that in such schemes the entangled state shared by the parties, and those
measured by the sender should ``match'' each other.


title:
Commutative version of the k-local Hamiltonian problem and common
  eigenspace problem

abstract:
  We study the complexity of a problem "Common Eigenspace" -- verifying
consistency of eigenvalue equations for composite quantum systems. The input of
the problem is a family of pairwise commuting Hermitian operators H_1,...,H_r
on a Hilbert space (C^d)^{\otimes n} and a string of real numbers h_1,...,h_r.
The problem is to determine whether a common eigenspace specified by equalities
(H_a - h_a)|\psi>=0, a=1,...,r, has a positive dimension. We consider two
cases: (i) all operators H_a are k-local; (ii) all operators H_a are
factorized. It can be easily shown that both problems belong to the class QMA -
the quantum analogue of NP, and that some NP-complete problems can be reduced
to either (i) or (ii). A non-trivial question is whether the problems (i) or
(ii) belong to NP? We show that the answer is positive for some special values
of k and d. Also we prove that the problem (ii) can be reduced to its special
case, such that all operators H_a are factorized projectors and all h_a=0.


title:
Quantum error correcting codes and one-way quantum computing: Towards a
  quantum memory

abstract:
  For realizing a quantum memory we suggest to first encode quantum information
via a quantum error correcting code and then concatenate combined decoding and
re-encoding operations. This requires that the encoding and the decoding
operation can be performed faster than the typical decoherence time of the
underlying system. The computational model underlying the one-way quantum
computer, which has been introduced by Hans Briegel and Robert Raussendorf,
provides a suitable concept for a fast implementation of quantum error
correcting codes. It is shown explicitly in this article is how encoding and
decoding operations for stabilizer codes can be realized on a one-way quantum
computer. This is based on the graph code representation for stabilizer codes,
on the one hand, and the relation between cluster states and graph codes, on
the other hand.


title: Rule 4 Statistics

abstract:
  When a conscious observer is part of a quantum mechanical system, rule (4)
cuts off solutions to the Schrodinger equation. It is important to show that
this interruption of the Hamiltonian dynamics does not effect the statistical
predictions of the theory. The initial case considered is that of a two atom
radioactive source. It is found that when the predictions of standard (Born
rule) quantum theory are verified by using a particular experimental procedure,
the result is the same as that predicted by quantum theory qualified by rule
(4). This example is generalized, and the result is found to be the same.


title: Time-Resolved Two-Photon Quantum Interference

abstract:
  The interference of two independent single-photon pulses impinging on a beam
splitter is analysed in a generalised time-resolved manner. Different aspects
of the phenomenon are elaborated using different representations of the
single-photon wave packets, like the decomposition into single-frequency field
modes or spatio-temporal modes matching the photonic wave packets. Both
representations lead to equivalent results, and a photon-by-photon analysis
reveals that the quantum-mechanical two-photon interference can be interpreted
as a classical one-photon interference once a first photon is detected. A novel
time-dependent quantum-beat effect is predicted if the interfering photons have
different frequencies. The calculation also reveals that full two-photon fringe
visibility can be achieved under almost any circumstances by applying a
temporal filter to the signal.


title: Engineering squeezed states in high-Q cavities

abstract:
  While it has been possible to build fields in high-Q cavities with a high
degree of squeezing for some years, the engineering of arbitrary squeezed
states in these cavities has only recently been addressed [Phys. Rev. A 68,
061801(R) (2003)]. The present work examines the question of how to squeeze any
given cavity-field state and, particularly, how to generate the squeezed
displaced number state and the squeezed macroscopic quantum superposition in a
high-Q cavity.


title: Interpretation of "non-local" experiments using disentanglement

abstract:
  It is shown that a number of experiments designed to use entangled photon
pairs in order to demonstrate the viability of quantum "teleportation" can, in
fact, also be understood using disentanglement. Whether entangled or not, using
an ensemble approach, the experiments can be explained without any non-local
communication between Alice's photon and Bob's photon. Moreover, it is
emphasized that entanglement maintains a symmetry property between the two
photons that is absent in disentanglment, the symmetry being parity due to
phase conerence.


title: The next stage: quantum game theory

abstract:
  Recent development in quantum computation and quantum information theory
allows to extend the scope of game theory for the quantum world. The paper
presents the history, basic ideas and recent development in quantum game
theory. On grounds of the discussed material, we reason about possible future
development of quantum game theory and its impact on information processing and
the emerging information society.


title:
Is Pseudo-Hermitian Quantum Mechanics an Indefinite-Metric Quantum
  Theory?

abstract:
  With a view to eliminate an important misconception in some recent
publications, we give a brief review of the notion of a pseudo-Hermitian
operator, outline pseudo-Hermitian quantum mechanics, and discuss its basic
difference with the indefinite-metric quantum mechanics. In particular, we show
that the answer to the question posed in the title is a definite No.


title:
Reliability of Calderbank-Shor-Steane Codes and Security of Quantum Key
  Distribution

abstract:
  After Mayers (1996, 2001) gave a proof of the security of the
Bennett-Brassard 1984 (BB84) quantum key distribution protocol, Shor and
Preskill (2000) made a remarkable observation that a Calderbank-Shor-Steane
(CSS) code had been implicitly used in the BB84 protocol, and suggested its
security could be proven by bounding the fidelity, say F(n), of the
incorporated CSS code of length n in the form 1-F(n) <= exp[-n E+o(n)] for some
positive number E. This work presents such a number E=E(R) as a function of the
rate of a code R, and a threshold R' such that E(R)>0 whenever R < R', which is
larger than the achievable rate based on the Gilbert-Varshamov bound that is
essentially due to Shor and Preskill (2000). The codes in the present work are
robust against fluctuations of channel parameters, which fact is needed to
establish the security rigorously and was not proved for rates above the
Gilbert-Varshamov rate before in the literature. As a byproduct, the security
of a modified BB84 protocol against any joint (coherent) attacks is proved
quantitatively.


title:
Experimental Eavesdropping Attack against Ekert's Protocol based on
  Wigner's Inequality

abstract:
  We experimentally implemented an eavesdropping attack against the Ekert
protocol for quantum key distribution based on the Wigner inequality. We
demonstrate a serious lack of security of this protocol when the eavesdropper
gains total control of the source. In addition we tested a modified Wigner
inequality which should guarantee a secure quantum key distribution.


title: Measures of entanglement in multipartite bound entangled states

abstract:
  Bound entangled states are states that are entangled but from which no
entanglement can be distilled if all parties are allowed only local operations
and classical communication. However, in creating these states one needs
nonzero entanglement resources to start with. Here, the entanglement of two
distinct multipartite bound entangled states is determined analytically in
terms of a geometric measure of entanglement and a related quantity. The
results are compared with those for the negativity and the relative entropy of
entanglement.


title: A complete family of separability criteria

abstract:
  We introduce a new family of separability criteria that are based on the
existence of extensions of a bipartite quantum state $\rho$ to a larger number
of parties satisfying certain symmetry properties. It can be easily shown that
all separable states have the required extensions, so the non-existence of such
an extension for a particular state implies that the state is entangled. One of
the main advantages of this approach is that searching for the extension can be
cast as a convex optimization problem known as a semidefinite program (SDP).
Whenever an extension does not exist, the dual optimization constructs an
explicit entanglement witness for the particular state. These separability
tests can be ordered in a hierarchical structure whose first step corresponds
to the well-known Positive Partial Transpose (Peres-Horodecki) criterion, and
each test in the hierarchy is at least as powerful as the preceding one. This
hierarchy is complete, in the sense that any entangled state is guaranteed to
fail a test at some finite point in the hierarchy, thus showing it is
entangled. The entanglement witnesses corresponding to each step of the
hierarchy have well-defined and very interesting algebraic properties that in
turn allow for a characterization of the interior of the set of positive maps.
Coupled with some recent results on the computational complexity of the
separability problem, which has been shown to be NP-hard, this hierarchy of
tests gives a complete and also computationally and theoretically appealing
characterization of mixed bipartite entangled states.


title: Minimal Universal Two-qubit Quantum Circuits

abstract:
  We give quantum circuits that simulate an arbitrary two-qubit unitary
operator up to global phase. For several quantum gate libraries we prove that
gate counts are optimal in worst and average cases. Our lower and upper bounds
compare favorably to previously published results. Temporary storage is not
used because it tends to be expensive in physical implementations.
  For each gate library, best gate counts can be achieved by a single universal
circuit. To compute gate parameters in universal circuits, we only use
closed-form algebraic expressions, and in particular do not rely on matrix
exponentials. Our algorithm has been coded in C++.


title: Quantum games of asymmetric information

abstract:
  We investigate quantum games in which the information is asymmetrically
distributed among the players, and find the possibility of the quantum game
outperforming its classical counterpart depends strongly on not only the
entanglement, but also the informational asymmetry. What is more interesting,
when the information distribution is asymmetric, the contradictive impact of
the quantum entanglement on the profits is observed, which is not reported in
quantum games of symmetric information.


title: Lueders Theorem for Coherent-State POVMs

abstract:
  Lueders theorem states that two observables commute if measuring one of them
does not disturb the measurement outcomes of the other. We study measurements
which are described by continuous positive operator-valued measurements (or
POVMs) associated with coherent states on a Lie group. In general, operators
turn out to be invariant under the Lueders map if their P- and Q-symbols
coincide. For a spin corresponding to SU(2), the identity is shown to be the
only operator with this property. For a particle, a countable family of
linearly independent operators is identified which are invariant under the
Lueders map generated by the coherent states of the Heisenberg-Weyl group, H_3.
The Lueders map is also shown to implement the anti-normal ordering of creation
and annihilation operators of a particle.


title: Quantum logic network for probabilistic cloning the quantum states

abstract:
  We construct efficient quantum logic network for probabilistic cloning the
quantum states used in implemented tasks for which cloning provides some
enhancement in performance.


title:
Silver mean conjectures for 15-d volumes and 14-d hyperareas of the
  separable two-qubit systems

abstract:
  Extensive numerical integration results lead us to conjecture that the silver
mean, that is, s = \sqrt{2}-1 = .414214 plays a fundamental role in certain
geometries (those given by monotone metrics) imposable on the 15-dimensional
convex set of two-qubit systems. For example, we hypothesize that the volume of
separable two-qubit states, as measured in terms of (four times) the minimal
monotone or Bures metric is s/3, and 10s in terms of (four times) the Kubo-Mori
monotone metric. Also, we conjecture, in terms of (four times) the Bures
metric, that that part of the 14-dimensional boundary of separable states
consisting generically of rank-four 4 x 4 density matrices has volume
(``hyperarea'') 55s/39 and that part composed of rank-three density matrices,
43s/39, so the total boundary hyperarea would be 98s/39. While the Bures
probability of separability (0.07334) dominates that (0.050339) based on the
Wigner-Yanase metric (and all other monotone metrics) for rank-four states, the
Wigner-Yanase (0.18228) strongly dominates the Bures (0.03982) for the
rank-three states.