title:
Understanding Heisenberg's 'Magical' Paper of July 1925: a New Look at
  the Calculational Details

abstract:
  In July 1925 Heisenberg published a paper [Z. Phys. 33, 879-893 (1925)] which
ended the period of `the Old Quantum Theory' and ushered in the new era of
Quantum Mechanics. This epoch-making paper is generally regarded as being
difficult to follow, perhaps partly because Heisenberg provided few clues as to
how he arrived at the results which he reported. Here we give details of
calculations of the type which, we suggest, Heisenberg may have performed. We
take as a specific example one of the anharmonic oscillator problems considered
by Heisenberg, and use our reconstruction of his approach to solve it up to
second order in perturbation theory. We emphasize that the results are
precisely those obtained in standard quantum mechanics, and suggest that some
discussion of the approach - based on the direct computation of transition
amplitudes - could usefully be included in undergraduate courses in quantum
mechanics.


title: Continuous-variable quantum non-demolishing interaction at a distance

abstract:
  A feasible setup of continuous-variable (CV) quantum non-demolishing (QND)
interaction at a distance is proposed. If two distant experimentalists are able
to locally perform identical QND interactions then the proposed realization
requires only a single quantum channel and classical communication between
them. A possible implementation of the proposed setup in recent quantum optical
laboratories is discussed and an influence of Gaussian noise in the quantum
channel on a quality of the implementation is analyzed. An efficient
realization of the QND interaction at a distance can be a basic step to
possible distributed quantum CV experiments between the distant laboratories.


title: The Statistical Interpretation of Entangled States

abstract:
  Entangled EPR spin pairs can be treated using the statistical ensemble
interpretation of quantum mechanics. As such the singlet state results from an
ensemble of spin pairs each with an arbitrary axis of quantization. This axis
acts as a quantum mechanical hidden variable. If the spins lose coherence they
disentangle into a mixed state. Whether or not the EPR spin pairs retain
entanglement or disentangle, however, the statistical ensemble interpretation
resolves the EPR paradox and gives a mechanism for quantum "teleportation"
without the need for instantaneous action-at-a-distance.


title: Time as an operator/observable in nonrelativistic quantum mechanics

abstract:
  The nonrelativistic Schroedinger equation for motion of a structureless
particle in four-dimensional space-time entails a well-known expression for the
conserved four-vector field of local probability density and current that are
associated with a quantum state solution to the equation. Under the physical
assumption that each spatial, as well as the temporal, component of this
current is observable, the position in time becomes an operator and an
observable in that the weighted average value of the time of the particle's
crossing of a complete hyperplane can be simply defined: ... When the
space-time coordinates are (t,x,y,z), the paper analyzes in detail the case
that the hyperplane is of the type z=constant. Particles can cross such a
hyperplane in either direction, so it proves convenient to introduce an
indefinite metric, and correspondingly a sesquilinear inner product with
non-Hilbert space structure, for the space of quantum states on such a surface.
>... A detailed formalism for computing average crossing times on a z=constant
hyperplane, and average dwell times and delay times for a zone of interaction
between a pair of z=constant hyperplanes, is presented.


title: A conclusive experiment to throw more light on "light"

abstract:
  We describe a new realization of Ghose, Home, Agarwal experiment on wave
particle duality of light where some limitations of the former experiment,
realized by Mizobuchi and Ohtake, are overcome. Our results clearly indicate
that wave-particle complementarity must be understood between interference and
"whelcher weg" knowledge and not in a more general sense.


title:
Deriving Tight Bell Inequalities for 2 Parties with Many 2-valued
  Observables from Facets of Cut Polytopes

abstract:
  Relatively few families of Bell inequalities have previously been identified.
Some examples are the trivial, CHSH, I_{mm22}, and CGLMP inequalities. This
paper presents a large number of new families of tight Bell inequalities for
the case of many observables. For example, 44,368,793 inequivalent tight Bell
inequalities other than CHSH are obtained for the case of 2 parties each with
10 2-valued observables. This is accomplished by first establishing a
relationship between the Bell inequalities and the facets of the cut polytope,
a well studied object in polyhedral combinatorics. We then prove a theorem
allowing us to derive new facets of cut polytopes from facets of smaller
polytopes by a process derived from Fourier-Motzkin elimination, which we call
triangular elimination. These new facets in turn give new tight Bell
inequalities. We give additional results for projections, liftings, and the
complexity of membership testing for the associated Bell polytope.


title:
BB84 Quantum Key Distribution System based on Silica-Based Planar
  Lightwave Circuits

abstract:
  We constructed an optical interferometer for a Bennett-Brassard quantum key
distribution system using integrated optics based on planar lightwave circuit
technology, and tested its operation and stability. Experimental results show
that this interferometer is useful in implementing a practical quantum key
distribution system.


title: Einstein's Boxes

abstract:
  At the 1927 Solvay conference, Einstein presented a thought experiment
intended to demonstrate the incompleteness of the quantum mechanical
description of reality. In the following years, the thought experiment was
picked up and modified by Einstein, de Broglie, and several other commentators
into a simple scenario involving the splitting in half of the wave function of
a single particle in a box. In this paper we collect together several
formulations of this thought experiment from the existing literature; analyze
and assess it from the point of view of the Einstein-Bohr debates, the EPR
dilemma, and Bell's theorem; and generally lobby for Einstein's Boxes taking
its rightful place alongside similar but historically better-known quantum
mechanical thought experiments such as EPR and Schroedinger's Cat.


title: Quantum Mechanical Properties of Bessel Beams

abstract:
  Bessel beams are studied within the general framework of quantum optics. The
two modes of the electromagnetic field are quantized and the basic dynamical
operators are identified. The algebra of these operators is analyzed in detail;
it is shown that the operators that are usually associated to linear momentum,
orbital angular momentum and spin do not satisfy the algebra of the translation
and rotation group. In particular, what seems to be the spin is more similar to
the helicity. Some physical consequences of these results are examined.


title:
Storing and processing optical information with ultra-slow light in
  Bose-Einstein condensates

abstract:
  We theoretically explore coherent information transfer between ultra-slow
light pulses and Bose-Einstein condensates (BECs) and find that storing light
pulses in BECs, by switching off the coupling field, allows the coherent
condensate dynamics to process optical information. We develop a formalism,
applicable in both the weak and strong probe regimes, to analyze such
experiments and establish several new results. Investigating examples relevant
to Rb-87 experimental parameters we see a variety of novel two-component BEC
dynamics occur during the storage, including interference fringes, gentle
breathing excitations, and two-component solitons. We find the dynamics when
the levels |F=1, M_F=-1> and |F=2, M_F=+1> are well suited to designing
controlled processing of the information. By switching the coupling field back
on, the processed information is rewritten onto probe pulses which then
propagate out as slow light pulses. We calculate the fidelity of information
transfer between the atomic and light fields upon the switch-on and subsequent
output. The fidelity is affected both by absorption of small length scale
features and absorption of regions of the pulse stored near the condensate
edge. In the strong probe case, we find that when the oscillator strengths for
the two transitions are equal the fidelity is not strongly sensitive to the
probe strength, while when they are unequal the fidelity is worse for stronger
probes. Applications to distant communication between BECs, squeezed light
generation and quantum information are anticipated.


title:
Rotational Effects of Twisted Light on Atoms Beyond the Paraxial
  Approximation

abstract:
  The transition probability for the emission of a Bessel photon by an atomic
system is calculated within first order perturbation theory. We derive a closed
expression for the electromagnetic potentials beyond the paraxial approximation
that permits a systematic multipole approximation . The matrix elements between
center of mass and internal states are evaluated for some specially relevant
cases. This permits to clarify the feasibility of observing the rotational
effects of twisted light on atoms predicted by the calculations. It is shown
that the probability that the internal state of an atom acquires orbital
angular momentum from light is, in general, maximum for an atom located at the
axis of a Bessel mode. For a Gaussian packet, the relevant parameter is the
ratio of the spread of the atomic center of mass wave packet to the transversal
wavelength of the photon.


title:
New considerations on the separability of very noisy mixed states and
  implications for NMR quantum computing

abstract:
  We revise the problem first addressed by Braunstein and co-workers (Phys.
Rev. Lett. {\bf 83} (5) (1999) 1054) concerning the separability of very noisy
mixed states represented by general density matrices with the form
$\rho_\epsilon = (1-\epsilon)M_d+\epsilon\rho_1$. From a detailed numerical
analysis, it is shown that: (1) there exist infinite values in the interval
taken for the density matrix expansion coefficients, $-1\le
c_{\alpha_1,...,\alpha_N}\le 1$, which give rise to {\em non-physical density
matrices}, with trace equal to 1, but at least one {\em negative} eigenvalue;
(2) there exist entangled matrices outside the predicted entanglement region,
and (3) there exist separable matrices inside the same region. It is also shown
that the lower and upper bounds of $\epsilon$ depend on the coefficients of the
expansion of $\rho_1$ in the Pauli basis. If $\rho_{1}$ is hermitian with trace
equal to 1, but is allowed to have {\em negative} eigenvalues, it is shown that
$\rho_\epsilon$ can be entangled, even for two qubits.


title: One-dimensional inverse power reflectionless potentials

abstract:
  A condition, at which the one-dimensional inverse power potential becomes
reflectionless during propagation through it of a plane wave, is obtained on
the basis of SUSY QM methods. A scattering of a particle on spherically
symmetric inverse power potential is analysed with taking into account of the
reflectionless possibility.


title: Inconsistency in the application of the adiabatic theorem

abstract:
  The adiabatic theorem states that an initial eigenstate of a slowly varying
Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at
a later time. We show that a perfunctory application of this statement is
problematic if the change in eigenstate is significant, regardless of how
closely the evolution satisfies the requirements of the adiabatic theorem. We
also introduce an example of a two-level system with an exactly solvable
evolution to demonstrate the inapplicability of the adiabatic approximation for
a particular slowly varying Hamiltonian.


title: Euclidean Resonance: Application to Physical and Chemical Experiments

abstract:
  The phenomenon of Euclidean resonance (a strong enhancement of quantum
tunneling through a nonstationary potential barrier) is applied to
disintegration of atoms and molecules through tunnel barriers formed by applied
constant and time-dependent electric fields. There are two different channels
for such disintegration, electronic and ionic. The electronic mechanism is
associated with the ionization of a molecule into an electron and a positive
ion. The required frequencies are in a wide range between 100 MHz and infrared.
This mechanism may constitute a method of selective destruction of chemical
bonds. The ionic mechanism consists of dissociation of a molecule into two
ions. Since an ion is more massive than an electron, the necessary frequency is
about 1 MHz. This provides a theoretical possibility of a new method of isotope
separation by radio frequency waves.


title:
Generation and characterization of a source of wavelength division
  multiplexing quantum key distribution

abstract:
  Using spontaneous parametric down-conversion, photon pairs entangled in
frequency and polarization were generated. After frequency resolving the photon
pairs, the polarization correlations were measured on several polarization
basis, and it was confirmed that the frequency resolved photon pairs were
entangled in polarization, indicating the photon pairs can be used as a source
of wavelength division multiplexing quantum key distribution.


title:
Statistical Origin of Pseudo-Hermitian Supersymmetry and
  Pseudo-Hermitian Fermions

abstract:
  We show that the metric operator for a pseudo-supersymmetric Hamiltonian that
has at least one negative real eigenvalue is necessarily indefinite. We
introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras
and provide a pair of basic realizations of the algebra of N=2
pseudo-supersymmetric quantum mechanics in which pseudo-supersymmetry is
identified with either a boson-phermion or a boson-abnormal-phermion exchange
symmetry. We further establish the physical equivalence (non-equivalence) of
phermions (abnormal phermions) with ordinary fermions, describe the underlying
Lie algebras, and study multi-particle systems of abnormal phermions. The
latter provides a certain bosonization of multi-fermion systems.


title:
Logarithmic divergence of the block entanglement entropy for the
  ferromagnetic Heisenberg model

abstract:
  Recent studies have shown that logarithmic divergence of entanglement entropy
as function of size of a subsystem is a signature of criticality in quantum
models. We demonstrate that the ground state entanglement entropy of $ n$ sites
for ferromagnetic Heisenberg spin-1/2 chain of the length $L$ in a sector with
fixed magnetization $y$ per site grows as ${1/2}\log_{2} \frac{n(L-n)}{L}C(y)$,
where $C(y)=2\pi e({1/4}-y^{2})$


title: Experimental Quantum Coin Tossing

abstract:
  In this letter we present the first implementation of a quantum coin tossing
protocol. This protocol belongs to a class of ``two-party'' cryptographic
problems, where the communication partners distrust each other. As with a
number of such two-party protocols, the best implementation of the quantum coin
tossing requires qutrits. In this way, we have also performed the first
complete quantum communication protocol with qutrits. In our experiment the two
partners succeeded to remotely toss a row of coins using photons entangled in
the orbital angular momentum. We also show the experimental bounds of a
possible cheater and the ways of detecting him.


title: Noncommutative Spacetime and Quantum Mechanics

abstract:
  In this paper we will analyze the the status of gauge freedom in quantum
mechanics (QM) and quantum field theory (QFT). Along with this analysis
comparison with ordinary QFT will be given. We will show how the gauge freedom
problem is connected with the spacetime coordinates status - the very point at
which the difficulties of QM begin. A natural solution of the above mentioned
problem will be proposed in which we give a slightly more general form of QM
and QFT (in comparison to the ordinary QFT) with noncommutative structure of
spacetime playing fundamental role in it. We achieve it by reinterpretation of
the Bohr's complementarity principle on the one hand and by incorporation of
our gauge freedom analysis on the other. We will present a generalization of
the Bargmann's theory of exponents of ray representations. It will be given an
example involving time dependent gauge freedom describing non-relativistic
quantum particle in nonrelativistic gravitational field. In this example we
infer the most general Schroedinger equation and prove equality of the
(passive) inertial and the gravitational masses of quantum particle.


title: Intrinsic Entanglement Degradation by Multi-Mode Detection

abstract:
  Relations between photon scattering, entanglement and multi-mode detection
are investigated. We first establish a general framework in which one- and
two-photon elastic scattering processes can be discussed, then we focus on the
study of the intrinsic entanglement degradation caused by a multi-mode
detection. We show that any multi-mode scattered state cannot maximally violate
the Bell-CHSH inequality because of the momentum spread. The results presented
here have general validity and can be applied to both deterministic and random
scattering processes.


title: Observing Quantum Systems

abstract:
  An introduction to some basic ideas of the author's "quantum cybernetics" is
given, which depicts waves and "particles" as mutually dependent system
components, thus defining "organizationally closed systems" characterized by a
fundamental circular causality. According to this, a new derivation of quantum
theory's most fundamental equation, the Schroedinger equation, is presented.
Finally, it is shown that quantum systems can be described by what Heinz von
Foerster has called "nontrivial machines", whereas the corresponding classical
counterparts turn out to behave as "trivial machines".


title: Engineering superpositions of displaced number states of a trapped ion

abstract:
  We present a protocol that permits the generation of a subtle with
superposition with 2^(l+1) displaced number states on a circle in phase space
as target state for the center-of-mass motion of a trapped ion. Through a
sequence of 'l' cycles involving the application of laser pulses and
no-fluorescence measurements, explicit expressions for the total duration of
laser pulses employed in the sequence and probability of getting the ion in the
upper electronic state during the 'l' cycles are obtained and analyzed in
detail. Furthermore, assuming that the effective relaxation process of a
trapped ion can be described in the framework of the standard master equation
for the damped harmonic oscillator, we investigate the degradation of the
quantum interference effects inherent to superpositions via Wigner function.


title: Toward reconstruction of relative state formulation of quantum theory

abstract:
  In quantum theory, it is widely accepted that all experimental results must
agree with theoretical predictions based on the Copenhagen interpretation.
However the classical system in the Copenhagen interpretation has not been
defined yet. On the other hand, although ongoing research of decoherence is
trying to elucidate the emergence of the classical world, it cannot answer why
we observe one of eigenstates in observed system. These situations show that
the relation between what we observe and physical law has not been elucidated.
Here I elucidate the relation by developing Everett's suggestion. Further, from
this point of view, I point out that today's brain science falls into circular
argument because it is trying to assign what we observe in the brain to process
of the subjective perception, and I suggest the future research line in brain
science.


title: Coherent Destruction of Photon Emission from a Single Molecule Source

abstract:
  The behavior of a single molecule driven simultaneously by a laser and by an
electric radio frequency field is investigated using a non-Hermitian
Hamiltonian approach. Employing the renormalization group method for
differential equations we calculate the average waiting time for the first
photon emission event to occur, and determine the conditions for the
suppression and enhancement of photon emission. An abrupt transition from
localization-like behavior to delocalization behavior is found.


title: Explicit Form of Evolution Operator of Three Atoms Tavis-Cummings Model

abstract:
  In this letter the explicit form of evolution operator of three atoms
Tavis-Cummings model is given, which is a generalization of the paper
quant-ph/0403008.


title: Statistical properties of radiation fields in a compact space

abstract:
  We discuss radiation fields in a compact space of finite size instead of that
in a cavity for investigating the coupled atom-radiation field system.
Representations of $T(1)\times SO(4)$ group are used to give a formulation for
kinematics of the radiation fields. The explicit geometrical parameter
dependence of statistical properties of radiation fields is obtained. Results
show remarkable differences from that of the black-body radiation system in
free space.


title:
Quantum Information processing by NMR: Implementation of
  Inversion-on-equality gate, Parity gate and Fanout gate

abstract:
  While quantum information processing by nuclear magnetic resonance (NMR) with
small number of qubits is well established, implementation of lengthy
computations have proved to be difficult due to decoherence/relaxation. In such
circumstances, shallow circuits (circuits using parallel computation) may prove
to be realistic. Parity and fanout gates are essential to create shallow
circuits. In this article we implement inversion-on-equality gate, followed by
parity gate and fanout gate in 3-qubit systems by NMR, using evolution under
indirect exchange coupling Hamiltonian.


title: Minimum Renyi and Wehrl entropies at the output of bosonic channels

abstract:
  The minimum Renyi and Wehrl output entropies are found for bosonic channels
in which the signal photons are either randomly displaced by a Gaussian
distribution (classical-noise channel), or in which they are coupled to a
thermal environment through lossy propagation (thermal-noise channel). It is
shown that the Renyi output entropies of integer orders z>1 and the output
Wehrl entropy are minimized when the channel input is a coherent state.


title: Advances in decoherence control

abstract:
  I address the current status of dynamical decoupling techniques in terms of
required control resources and feasibility. Based on recent advances in both
improving the theoretical design and assessing the control performance for
specific noise models, I argue that significant progress may still be possible
on the road of implementing decoupling under realistic constraints.


title: Quantum Abacus

abstract:
  We show that the U(2) family of point interactions on a line can be utilized
to provide the U(2) family of qubit operations for quantum information
processing. Qubits are realized as localized states in either side of the point
interaction which represents a controllable gate. The manipulation of qubits
proceeds in a manner analogous to the operation of an abacus.
  Keywords: quantum computation, quantum contact interaction, quantum wire

categories: quant-ph cond-mat.mes-hall math-ph math.MP


title: Quantum Quandaries: a Category-Theoretic Perspective

abstract:
  General relativity may seem very different from quantum theory, but work on
quantum gravity has revealed a deep analogy between the two. General relativity
makes heavy use of the category nCob, whose objects are (n-1)-dimensional
manifolds representing "space" and whose morphisms are n-dimensional cobordisms
representing "spacetime". Quantum theory makes heavy use of the category Hilb,
whose objects are Hilbert spaces used to describe "states", and whose morphisms
are bounded linear operators used to describe "processes". Moreover, the
categories nCob and Hilb resemble each other far more than either resembles
Set, the category whose objects are sets and whose morphisms are functions. In
particular, both Hilb and nCob but not Set are *-categories with a noncartesian
monoidal structure. We show how this accounts for many of the famously puzzling
features of quantum theory: the failure of local realism, the impossibility of
duplicating quantum information, and so on. We argue that these features only
seem puzzling when we try to treat Hilb as analogous to Set rather than nCob,
so that quantum theory will make more sense when regarded as part of a theory
of spacetime.


title: Quantum Reality, Complex Numbers and the Meteorological Butterfly Effect

abstract:
  A not-too-technical version of the paper: "A Granular Permutation-based
Representation of Complex Numbers and Quaternions: Elements of a Realistic
Quantum Theory" - Proc. Roy. Soc.A (2004) 460, 1039-1055. The phrase
"meteorological butterfly effect" is introduced to illustrate, not the familiar
loss of predictability in low-dimensional chaos, but the much less familiar and
much more radical paradigm of the finite-time predictability horizon,
associated with upscale transfer of uncertainty in certain multi-scale systems.
This motivates a novel reinterpretation of unit complex numbers (and
quaternions) in terms of a family of self-similar permutation operators. A
realistic deterministic kinematic reformulation of the foundations of quantum
theory is given using this reinterpretation of complex numbers. Using a
property of the cosine function not normally encountered in physics, that it is
irrational for all dyadic rational angles between 0 and pi/2, this
reformulation is shown to have the emergent property of counterfactual
indefiniteness and is therefore not non-locally causal.


title: How does the entropy/information bound work ?

abstract:
  According to the universal entropy bound, the entropy (and hence information
capacity) of a complete weakly self-gravitating physical system can be bounded
exclusively in terms of its circumscribing radius and total gravitating energy.
The bound's correctness is supported by explicit statistical calculations of
entropy, gedanken experiments involving the generalized second law, and
Bousso's covariant holographic bound. On the other hand, it is not always
obvious in a particular example how the system avoids having too many states
for given energy, and hence violating the bound. We analyze in detail several
purported counterexamples of this type (involving systems made of massive
particles, systems at low temperature, systems with high degeneracy of the
lowest excited states, systems with degenerate ground states, or involving a
particle spectrum with proliferation of nearly massless species), and exhibit
in each case the mechanism behind the bound's efficacy.


title: Complementarity and quantum walks

abstract:
  We show that quantum walks interpolate between a coherent `wave walk' and a
random walk depending on how strongly the walker's coin state is measured;
i.e., the quantum walk exhibits the quintessentially quantum property of
complementarity, which is manifested as a trade-off between knowledge of which
path the walker takes vs the sharpness of the interference pattern. A physical
implementation of a quantum walk (the quantum quincunx) should thus have an
identifiable walker and the capacity to demonstrate the interpolation between
wave walk and random walk depending on the strength of measurement.


title: Does the wavefunction of the universe exist?

abstract:
  The overwhelming majority of scientists still takes it for granted that
classical mechanics (ClM) is nothing but a limiting case of quantum mechanics
(QM). Although some physicists restrict this belief to a generalized QM as
represented, e. g., by the algebra of observables, it will be shown in this
contribution that the view of ClM as a mere sub-set of QM is nevertheless
unfounded. The usual attempts to derive the laws of ClM from QM are either
insufficient or not universally applicable. The transition from traditional to
algebraic QM does not add any further insight. It is demonstrated that typical
constituents of the classical macroscopic world i) cannot be described
reasonably in terms of QM and/or ii) do not show up the typical quantum
behavior which manifests in the double-slit interference and in the
Einstein-Podolsky-Rosen correlations. Moreover, both attempts to recover ClM
from QM and approaches based on vacuum fluctuations are critically inspected,
and we arrive at the conclusion: QM does not comprehend ClM, i. e., a
wavefunction of the universe does not exist.


title: Quantum mechanics without quantum logic

abstract:
  We describe a scheme of quantum mechanics in which the Hilbert space and
linear operators are only secondary structures of the theory. As primary
structures we consider observables, elements of noncommutative algebra, and the
physical states, the nonlinear functionals on this algebra, which associate
with results of single measurement. We show that in such scheme the
mathematical apparatus of the standard quantum mechanics does not contradict a
hypothesis on existence of an objective local reality, a principle of a
causality and Kolmogorovian probability theory.


title:
An Equivalence of Entanglement-Assisted Transformation and Multiple-Copy
  Entanglement Transformation

abstract:
  We examine the powers of entanglement-assisted transformation and
multiple-copy entanglement transformation. First, we find a sufficient
condition of when a given catalyst is useful in producing another specific
target state. As an application of this condition, for any non-maximally
entangled bipartite pure state and any integer $n$ not less than 4, we are able
to explicitly construct a set of $n\times n$ quantum states which can be
produced by using the given state as a catalyst. Second, we prove that for any
positive integer $k$, entanglement-assisted transformation with $k\times
k$-dimensional catalysts is useful in producing a target state if and only if
multiple-copy entanglement transformation with $k$ copies of state is useful in
producing the same target. Moreover, a necessary and sufficient condition for
both of them is obtained in terms of the Schmidt coefficients of the target.
This equivalence of entanglement-assisted transformation and multiple-copy
entanglement transformation implies many interesting properties of entanglement
transformation. Furthermore, these results are generalized to the case of
probabilistic entanglement transformations.


title: Partial Recovery of Quantum Entanglement

abstract:
  Suppose Alice and Bob try to transform an entangled state shared between them
into another one by local operations and classical communications. Then in
general a certain amount of entanglement contained in the initial state will
decrease in the process of transformation. However, an interesting phenomenon
called partial entanglement recovery shows that it is possible to recover some
amount of entanglement by adding another entangled state and transforming the
two entangled states collectively.
  In this paper we are mainly concerned with the feasibility of partial
entanglement recovery. The basic problem we address is whether a given state is
useful in recovering entanglement lost in a specified transformation. In the
case where the source and target states of the original transformation satisfy
the strict majorization relation, a necessary and sufficient condition for
partial entanglement recovery is obtained. For the general case we give two
sufficient conditions. We also give an efficient algorithm for the feasibility
of partial entanglement recovery in polynomial time.
  As applications, we establish some interesting connections between partial
entanglement recovery and the generation of maximally entangled states, quantum
catalysis, mutual catalysis, and multiple-copy entanglement transformation.


title: Effective three-body interactions in triangular optical lattices

abstract:
  We demonstrate that a triangular optical lattice of two atomic species,
bosonic or fermionic, can be employed to generate a variety of novel spin-1/2
Hamiltonians. These include effective three-spin interactions resulting from
the possibility of atoms tunneling along two different paths. Such interactions
can be employed to simulate particular one or two dimensional physical systems
with ground states that possess a rich structure and undergo a variety of
quantum phase transitions. In addition, tunneling can be activated by employing
Raman transitions, thus creating an effective Hamiltonian that does not
preserve the number of atoms of each species. In the presence of external
electromagnetic fields, resulting in complex tunneling couplings, we obtain
effective Hamiltonians that break chiral symmetry. The ground states of these
Hamiltonians can be used for the physical implementation of geometrical or
topological objects.


title:
Multipartite continuous-variable entanglement from concurrent
  nonlinearities

abstract:
  We show theoretically that concurrent interactions in a second-order
nonlinear medium placed inside an optical resonator can generate multipartite
entanglement between the resonator modes. We show that there is a mathematical
connexion between this system and van Loock and Braunstein's proposal for
entangling N continuous quantum optical variables by interfering the outputs of
N degenerate optical parametric amplifiers (OPA) at a N-port beam splitter. Our
configuration, however, requires only one nondegenerate OPA and no
interferometer. In a preliminary experimental study, we observe the concurrence
of the appropriate interactions in periodically poled RbTiOAsO4.


title: Geometric Control Methods for Quantum Computations

abstract:
  The applications of geometric control theory methods on Lie groups and
homogeneous spaces to the theory of quantum computations are investigated.
These methods are shown to be very useful for the problem of constructing an
universal set of gates for quantum computations: the well-known result that the
set of all one-bit gates together with almost any one two-bit gate is universal
is considered from the control theory viewpoint.


title: Macroscopic objects in quantum mechanics: A combinatorial approach

abstract:
  Why we do not see large macroscopic objects in entangled states? There are
two ways to approach this question. The first is dynamic: the coupling of a
large object to its environment cause any entanglement to decrease
considerably. The second approach, which is discussed in this paper, puts the
stress on the difficulty to observe a large scale entanglement. As the number
of particles n grows we need an ever more precise knowledge of the state, and
an ever more carefully designed experiment, in order to recognize entanglement.
To develop this point we consider a family of observables, called witnesses,
which are designed to detect entanglement. A witness W distinguishes all the
separable (unentangled) states from some entangled states. If we normalize the
witness W to satisfy |tr(W\rho)| \leq 1 for all separable states \rho, then the
efficiency of W depends on the size of its maximal eigenvalue in absolute
value; that is, its operator norm ||W||. It is known that there are witnesses
on the space of n qbits for which ||W|| is exponential in n. However, we
conjecture that for a large majority of n-qbit witnesses ||W|| \leq O(\sqrt{n
logn}). Thus, in a non ideal measurement, which includes errors, the largest
eigenvalue of a typical witness lies below the threshold of detection. We prove
this conjecture for the family of extremal witnesses introduced by Werner and
Wolf (Phys. Rev. A 64, 032112 (2001)).


title: Gaussian quantum Monte Carlo methods for fermions

abstract:
  We introduce a new class of quantum Monte Carlo methods, based on a Gaussian
quantum operator representation of fermionic states. The methods enable
first-principles dynamical or equilibrium calculations in many-body Fermi
systems, and, combined with the existing Gaussian representation for bosons,
provide a unified method of simulating Bose-Fermi systems. As an application,
we calculate finite-temperature properties of the two dimensional Hubbard
model.


title: Ordering two-qubit states with concurrence and negativity

abstract:
  We study the ordering of two-qubit states with respect to the degree of
bipartite entanglement using the Wootters concurrence -- a measure of the
entanglement of formation, and the negativity -- a measure of the entanglement
cost under the positive-partial-transpose-preserving operations. For two-qubit
pure states, the negativity is the same as the concurrence. However, we
demonstrate analytically on simple examples of various mixtures of Bell and
separable states that the entanglement measures can impose different orderings
on the states. We show which states, in general, give the maximally different
predictions, (i) when one of the states has the concurrence greater but the
negativity smaller than those for the other state, and (ii) when the states are
entangled to the same degree according to one of the measures, but differently
according to the other.


title:
Quantum cloning at the light-atoms interface: copying a coherent light
  state into two atomic quantum memories

abstract:
  A scheme for the optimal Gaussian cloning of coherent light states at the
light-atoms interface is proposed. The distinct feature of this proposal is
that the clones are stored in an atomic quantum memory, which is important for
applications in quantum communication. The atomic quantum cloning machine
requires only a single passage of the light pulse through the atomic ensembles
followed by the measurement of a light quadrature and an appropriate feedback,
which renders the protocol experimentally feasible. An alternative protocol,
where one of the clones is carried by the outgoing light pulse, is discussed in
connection with quantum key distribution.


title: Quantum Information Processing with Trapped Neutral Atoms

abstract:
  Quantum information can be processed using large ensembles of ultracold and
trapped neutral atoms, building naturally on the techniques developed for
high-precision spectroscopy and metrology. This article reviews some of the
most important protocols for universal quantum logic with trapped neutrals, as
well as the history and state-of-the-art of experimental work to implement
these in the laboratory. Some general observations are made concerning the
different strategies for qubit encoding, transport and interaction, including
tradeoffs between decoherence rates and the likelihood of twoqubit gate errors.
These tradeoffs must be addressed through further refinements of logic
protocols and trapping technologies before one can undertake the design of a
generalpurpose neutral-atom quantum processor.


title:
A perturbative expansion of the evolution operator associated with
  time-dependent quantum Hamiltonians

abstract:
  A novel expansion -- which generalizes Magnus expansion -- of the evolution
operator associated with a (in general, time-dependent) perturbed Hamiltonian
is introduced. It is shown that it has a wide range of possible solutions that
can be fitted according to computational convenience. The time-independent and
the adiabatic case are studied in detail.


title:
Initial wave packets and the various power-law decreases of scattered
  wave packets at long times

abstract:
  The long time behavior of scattered wave packets $\psi (x,t)$ from a
finite-range potential is investigated, by assuming $\psi (x,t)$ to be
initially located outside the potential. It is then shown that $\psi (x,t)$ can
asymptotically decrease in the various power laws at long time, according to
its initial characteristics at small momentum. As an application, we consider
the square-barrier potential system and demonstrate that $\psi (x,t)$ exhibits
the asymptotic behavior $t^{-3/2}$, while another behavior like $t^{-5/2}$ can
also appear for another $\psi (x,t)$.


title: Steering Distillation by "Pulsed" and "Continuous" Measurements

abstract:
  A new systematic strategy for steering the distillation process for a quantum
system, that utilizes the so-called "pulsed" and "continuous" measurements on
another quantum system in interaction with the former, is proposed. The
distillation process characterized by the specific interaction between the two
systems and the "pulsed" measurements is shown to be controllable through the
"continuous" measurements, i.e., the quantum Zeno dynamics, providing an
effective recipe to prefix the target.


title:
Experimental Demonstration of a Quantum Circuit using Linear Optics
  Gates

abstract:
  One of the main advantages of an optical approach to quantum computing is the
fact that optical fibers can be used to connect the logic and memory devices to
form useful circuits, in analogy with the wires of a conventional computer.
Here we describe an experimental demonstration of a simple quantum circuit of
that kind in which two probabilistic exclusive-OR (XOR) logic gates were
combined to calculate the parity of three input qubits.


title: A quantum Fourier transform algorithm

abstract:
  Algorithms to compute the quantum Fourier transform over a cyclic group are
fundamental to many quantum algorithms. This paper describes such an algorithm
and gives a proof of its correctness, tightening some claimed performance
bounds given earlier. Exact bounds are given for the number of qubits needed to
achieve a desired tolerance, allowing simulation of the algorithm.


title: Classical Cryptosystems In A Quantum Setting

abstract:
  Encryption schemes attempt to provide a means for entities to communicate
confidentially over a public channel. Such schemes have been studied for
centuries, and their use has become widespread. However, developments in the
area of quantum computing indicate that many of the public key cryptosystems
currently in use could easily be broken if large-scale quantum computers become
technologically feasible. Further, encrypted messages captured and stored in
the past could also be decrypted by a future quantum attacker. Since
large-scale quantum computers may one day be developed, We need to prepare for
that eventuality by analysing modern cryptosystems with respect to attacks with
a quantum computer.
  In this thesis, submitted in fulfilment of the requirements for the degree of
Master of Mathematics in Combinatorics & Optimisation at the University of
Waterloo, we examine the quantum strengths and vulnerabilities of several of
the most popular classical public key cryptosystems.


title: On the Complexity of Quantum Languages

abstract:
  The standard inputs given to a quantum machine are classical binary strings.
In this view, any quantum complexity class is a collection of subsets of
$\{0,1\}^{*}$. However, a quantum machine can also accept quantum states as its
input. T. Yamakami has introduced a general framework for quantum operators and
inputs \cite{Yam02}. In this paper we present several quantum languages within
this model and by generalizing the complexity classes QMA and QCMA we analyze
the complexity of the introduced languages. We also discuss how to derive a
classical language from a given quantum language and as a result we introduce
new QCMA and QMA languages.


title:
Sub- and super-radiance over macroscopic distances using a perfect lens
  with negative refraction

abstract:
  Two atoms put at the foci of a perfect lens [J.B. Pendry, Phys. Ref. Lett.
85, 3966 (2000)] are shown to exhibit perfect sub- and super-radiance even over
macroscopic distances limited only by the propagation length in the free-space
decay time. If the left-handed material forming the perfect lens has nearly
constant negative refraction and vanishing absorption over a spectral range
larger than the natural linewidth, the imaginary part of the retarded
Greens-function between the two focal points is identical to the one at the
same spatial position and the atoms undergo a Markovian dynamics. Collective
decay rates and level shifts are calculated from the Greens-function of the
Veselago-Pendry lens and limitation as well as potential applications are
discussed.


title: NMR Techniques for Quantum Control and Computation

abstract:
  Fifty years of developments in nuclear magnetic resonance (NMR) have resulted
in an unrivaled degree of control of the dynamics of coupled two-level quantum
systems. This coherent control of nuclear spin dynamics has recently been taken
to a new level, motivated by the interest in quantum information processing.
NMR has been the workhorse for the experimental implementation of quantum
protocols, allowing exquisite control of systems up to seven qubits in size.
Here, we survey and summarize a broad variety of pulse control and tomographic
techniques which have been developed for and used in NMR quantum computation.
Many of these will be useful in other quantum systems now being considered for
implementation of quantum information processing tasks.


title: Dynamic optical bistability in resonantly enhanced Raman generation

abstract:
  We report observations of novel dynamic behavior in resonantly-enhanced
stimulated Raman scattering in Rb vapor. In particular, we demonstrate a
dynamic hysteresis of the Raman scattered optical field in response to changes
of the drive laser field intensity and/or frequency. This effect may be
described as a dynamic form of optical bistability resulting from the formation
and decay of atomic coherence. We have applied this phenomenon to the
realization of an all-optical switch.


title: The Generalised Liar Paradox: A Quantum Model and Interpretation

abstract:
  The formalism of abstracted quantum mechanics is applied in a model of the
generalized Liar Paradox. Here, the Liar Paradox, a consistently testable
configuration of logical truth properties, is considered a dynamic conceptual
entity in the cognitive sphere. Basically, the intrinsic contextuality of the
truth-value of the Liar Paradox is appropriately covered by the abstracted
quantum mechanical approach. The formal details of the model are explicited
here for the generalized case. We prove the possibility of constructing a
quantum model of the m-sentence generalizations of the Liar Paradox. This
includes (i) the truth-falsehood state of the m-Liar Paradox can be represented
by an embedded 2m-dimensional quantum vector in a (2m)^m dimensional complex
Hilbert space, with cognitive interactions corresponding to projections, (ii)
the construction of a continuous 'time' dynamics is possible: typical truth and
falsehood value oscillations are described by Schrodinger evolution, (iii)
Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value
by inference' projectors, (iv) time invariance of unmeasured state.


title: A Note on the Quantum Query Complexity of the Hidden Subgroup Problem

abstract:
  We are concerned with the Hidden Subgroup Problem for finite groups. We
present a simplified analysis of a quantum algorithm proposed by Hallgren,
Russell and Ta-Shma as well as a detailed proof of a lower bound on the
probability of success of the algorithm.


title: A Case for Applying an Abstracted Quantum Formalism to Cognition

abstract:
  This chapter outlines some of the highlights of efforts undertaken by our
group to describe the role of contextuality in the conceptualization of
conscious experience using generalized formalisms from quantum mechanics.


title: Entanglement bounds of tripartite squeezed thermal states

abstract:
  I propose the multi-mode squeezed thermal state based on the multi-mode pure
entangled state. The correlation matrix of the state is characterized by two
parameters. I then analysis the separable condition for this state, and
calculating the relative entropy of the state with respect to the same kind of
fully separable state in order to provide an upper bound of the relative
entropy of entanglement. The bound is compared with the other bounds which were
obtained with reduced state.


title:
State Property Systems and Closure Spaces: Extracting the Classical and
  Nonclassical Parts

abstract:
  We introduce classical properties using the concept of super selection rule,
i.e. two properties are separated by a superselection rule iff there do not
exist 'superposition states' related to these two properties. Then we show that
the classical properties of a state property system correspond exactly to the
clopen subsets of the corresponding closure space. Thus connected closure
spaces correspond precisely to state property systems for which the elements 0
and I are the only classical properties, the so called pure nonclassical state
property systems. The main result is a decomposition theorem, which allows us
to split a state property system into a number of 'pure nonclassical state
property systems' and a 'totally classical state property system'. This
decomposition theorem for a state property system is the translation of a
decomposition theorem for the corresponding closure space into its connected
components.


title:
Classicality and connectedness for state property systems and closure
  spaces

abstract:
  It has been shown that there is a categorical equivalence between the
category SPS of state property systems and the category Cl of closure spaces.
In this note we prove, using this equivalence between categories, that the
concept of connectedness for closure spaces can be used to formulate a
decomposition theorem, which allows us to split a state property system into a
number of 'pure nonclassical state property systems' and a 'totally classical
state property system'.


title: On the notion of phase in mechanics

abstract:
  The notion of phase plays an esential role in both classical and quantum
mechanics.But what is a phase? We show that if we define the notion of phase in
phase (!) space one can very easily and naturally recover the Heisenberg-Weyl
formalism; this is achieved using the properties of the Poincare-Cartan
invariant, and without making any quantum assumption.


title: Correction to the Casimir force due to the anomalous skin effect

abstract:
  The surface impedance approach is discussed in connection with the precise
calculation of the Casimir force between metallic plates. It allows to take
into account the nonlocal connection between the current density and electric
field inside of metals. In general, a material has to be described by two
impedances $Z_{s}(\omega,q)$ and $Z_{p}(\omega,q)$ corresponding to two
different polarization states. In contrast with the approximate Leontovich
impedance they depend not only on frequency $\omega$ but also on the wave
vector along the plate $q$. In this paper only the nonlocal effects happening
at frequencies $\omega<\omega_{p}$ (plasma frequency) are analyzed. We refer to
all of them as the anomalous skin effect. The impedances are calculated for the
propagating and evanescent fields in the Boltzmann approximation. It is found
that $Z_p$ significantly deviates from the local impedance as a result of the
Thomas-Fermi screening. The nonlocal correction to the Casimir force is
calculated at zero temperature. This correction is small but observable at
small separations between bodies. The same theory can be used to find more
significant nonlocal contribution at $\omega\sim\omega_p$ due to the plasmon
excitation.


title: The Wigner function associated to the Rogers-Szego polynomials

abstract:
  We show here that besides the well known Hermite polynomials, the q-deformed
harmonic oscillator algebra admits another function space associated to a
particular family of q-polynomials, namely the Rogers-Szego polynomials. Their
main properties are presented, the associated Wigner function is calculated and
its properties are discussed. It is shown that the angle probability density
obtained from the Wigner function is a well-behaved function defined in the
interval [-Pi,Pi), while the action probability only assumes integer values
greater or equal than zero. It is emphasized the fact that the width of the
angle probability density is governed by the free parameter q characterizing
the polynomial.


title:
Small Pseudo-Random Families of Matrices: Derandomizing Approximate
  Quantum Encryption

abstract:
  A quantum encryption scheme (also called private quantum channel, or state
randomization protocol) is a one-time pad for quantum messages. If two parties
share a classical random string, one of them can transmit a quantum state to
the other so that an eavesdropper gets little or no information about the state
being transmitted. Perfect encryption schemes leak no information at all about
the message. Approximate encryption schemes leak a non-zero (though small)
amount of information but require a shorter shared random key. Approximate
schemes with short keys have been shown to have a number of applications in
quantum cryptography and information theory.
  This paper provides the first deterministic, polynomial-time constructions of
quantum approximate encryption schemes with short keys. Previous constructions
(quant-ph/0307104) are probabilistic--that is, they show that if the operators
used for encryption are chosen at random, then with high probability the
resulting protocol will be a secure encryption scheme. Moreover, the resulting
protocol descriptions are exponentially long. Our protocols use keys of the
same length as (or better length than) the probabilistic constructions; to
encrypt $n$ qubits approximately, one needs $n+o(n)$ bits of shared key.
  An additional contribution of this paper is a connection between classical
combinatorial derandomization and constructions of pseudo-random matrix
families in a continuous space.


title: Consequences and Limits of Nonlocal Strategies

abstract:
  This paper investigates the powers and limitations of quantum entanglement in
the context of cooperative games of incomplete information. We give several
examples of such nonlocal games where strategies that make use of entanglement
outperform all possible classical strategies. One implication of these examples
is that entanglement can profoundly affect the soundness property of two-prover
interactive proof systems. We then establish limits on the probability with
which strategies making use of entanglement can win restricted types of
nonlocal games. These upper bounds may be regarded as generalizations of
Tsirelson-type inequalities, which place bounds on the extent to which quantum
information can allow for the violation of Bell inequalities. We also
investigate the amount of entanglement required by optimal and nearly optimal
quantum strategies for some games.


title:
Completely Positive Post-Markovian Master Equation via a Measurement
  Approach

abstract:
  A new post-Markovian quantum master equation is derived, that includes bath
memory effects via a phenomenologically introduced memory kernel k(t). The
derivation uses as a formal tool a probabilistic single-shot bath-measurement
process performed during the coupled system-bath evolution. The resulting
analytically solvable master equation interpolates between the exact
Nakajima-Zwanzig equation and the Markovian Lindblad equation. A necessary and
sufficient condition for complete positivity in terms of properties of k(t) is
presented, in addition to a prescription for the experimental determination of
k(t). The formalism is illustrated with examples.


title: Coincidence Subwavelength Interference by a Classical Thermal Light

abstract:
  We show that a thermal light random in transverse direction can perform
subwavelength double slit interference in a joint-intensity measurement. This
is the classical version of quantum lithography, and it can be explained with
the correlation of rays instead of the entanglement of photons.


title: Quantum entanglement theory in the presence of superselection rules

abstract:
  Superselection rules severly constrain the operations which can be
implemented on a distributed quantum system. While the restriction to local
operations and classical communication gives rise to entanglement as a nonlocal
resource, particle number conservation additionally confines the possible
operations and should give rise to a new resource. In [Phys. Rev. Lett. 92,
087904 (2004), quant-ph/0310124] we showed that this resource can be quantified
by a single additional number, the superselection induced variance (SiV)
without changing the concept of entanglement. In this paper, we give the
results on pure states in greater detail; additionally, we provide a discussion
of mixed state nonlocality with superselection rules where we consider both
formation and distillation. Finally, we demonstrate that SiV is indeed a
resource, i.e., that it captures how well a state can be used to overcome the
restrictions imposed by the superselection rule.


title:
Resonance-enhanced group delay times in an asymmetric single quantum
  barrier

abstract:
  It is shown that the transmission and reflection group delay times in an
asymmetric single quantum barrier are greatly enhanced by the transmission
resonance when the energy of incident particles is larger than the height of
the barrier. The resonant transmission group delay is of the order of the
quasibound state lifetime in the barrier region. The reflection group delay can
be either positive or negative, depending on the relative height of the
potential energies on the two sides of the barrier. Its magnitude is much
larger than the quasibound state lifetime. These predictions have been observed
in a microwave experiment by H. Spieker of Braunschweig University.


title:
Local control theory for unitary transformations: Application to quantum
  computing without leakage

abstract:
  We present a local optimal control strategy to produce desired unitary
transformations. Unitary transformations are central to all quantum
computational algorithms. Many realizations of quantum computation use a
submanifold of states, comprising the quantum register, coupled by an external
driving field to a collection of additional mediating excited states. Previous
attempts to apply control theory to induce unitary transformations on the
quantum register, while successful, produced pulses that drive the population
out of the computational register at intermediate times. Leakage of population
from the register is undesirable since often the states outside the register
are prone to decay and decoherence, and populating them causes a decrease in
the final fidelity. In this work we devise a local optimal control method for
achieving target unitary transformations on a quantum register, while avoiding
intermediate leakage out of the computational submanifold. The technique
exploits a phase locking of the field to the system such as to eliminate the
undesirable excitation. This method is then applied to produce an SU(6) Fourier
transform on the vibrational levels of the ground electronic state of the
Na$_2$ molecule. The emerging mechanism uses two photon resonances to create a
transformation on the quantum register while blocking one photon resonances to
excited states.


title: Computation by measurements: a unifying picture

abstract:
  The ability to perform a universal set of quantum operations based solely on
static resources and measurements presents us with a strikingly novel viewpoint
for thinking about quantum computation and its powers. We consider the two
major models for doing quantum computation by measurements that have hitherto
appeared in the literature and show that they are conceptually closely related
by demonstrating a systematic local mapping between them. This way we
effectively unify the two models, showing that they make use of interchangeable
primitives. With the tools developed for this mapping, we then construct more
resource-effective methods for performing computation within both models and
propose schemes for the construction of arbitrary graph states employing
two-qubit measurements alone.


title: Demonstration of conditional quantum phase shift between ions in a solid

abstract:
  Due to their potential for long coherence times, dopant ions have long been
considered promising candidates for scalable solid state quantum computing.
However, the demonstration of two qubit operation has proven to be problematic,
largely due to the difficulty of addressing closely spaced ions. Here we use
optically active ions and optical frequency addressing to demonstrate a
conditional phase shift between two qubits.


title:
Spin-orbit entanglement in time evolution of radial wave packets in
  hydrogenic systems

abstract:
  Time evolution of radial wave packets built from the eigenstates of Dirac
equation for a hydrogenic systems is considered. Radial wave packets are
constructed from the states of different $n$ quantum number and the same lowest
angular momentum. In general they exhibit a kind of breathing motion with
dispersion and (partial) revivals. Calculations show that for some particular
preparations of the wave packet one can observe interesting effects in spin
motion, coming from inherent entanglement of spin and orbital degrees of
freedom. These effects manifest themselves through some oscillations in the
mean values of spin operators and through changes of spatial probability
density carried by upper and lower components of the wave function. It is also
shown that the characteristic time scale of predicted effects (called
$T_{\mathrm{ls}}$) is for radial wave packets much smaller than in other cases,
reaching values comparable to (or even less than) the time scale for the wave
packet revival.


title:
Eavesdropping on the Bostroem-Filbinger Communication Protocol in Noisy
  Quantum Channel

abstract:
  We show an eavesdropping scheme on Bostr\UNICODE{0xf6}m-Felbinger
communication protocol (called ping-pong protocol) [Phys. Rev. Lett. 89, 187902
(2002)] in an ideal quantum channel. A measurement attack can be perfectly used
to eavesdrop Alice's information instead of a most general quantum operation
attack. In a noisy quantum channel, the direct communication is forbidden. We
present a quantum key distribution protocol based on the ping-pong protocol,
which can be used in a low noisy quantum channel. And we give a weak upper
bound on the bit-error ratio that the detection probability $d$ should be lower
than 0.11, which is a requirement criterion when we utilize the ping-pong
protocol in a real communication.


title: Passive Quantum Erasure for Neutral Kaons

abstract:
  Quantum marking and quantum erasure are discussed for the neutral kaon
system. Contrary to other two-level systems, strangeness and lifetime of a
neutral kaon state can be alternatively measured via an "active" or a "passive"
procedure. This offers new quantum erasure possibilities. In particular, the
operation of a quantum eraser in the "delayed choice" mode is clearly
illustrated.


title: Position Uncertainty Measures on the Sphere

abstract:
  Position uncertainty (delocalization) measures for a particle on the sphere
are proposed and illustrated on several examples of states. The new measures
are constructed using suitably the standard multiplication angle operator
variances. They are shown to depend solely on the state of the particle and to
obey uncertainty relations of the Schroedinger--Robertson type. A set of
Hermitian operators with continuous spectrum is pointed out the variances of
which are complementary to the longitudinal angle uncertainty measure.


title:
The nonlinear field theory I. The Dirac electron theory as approximation
  of the nonlinear electrodynamics

abstract:
  In the present paper it is shown that the Dirac electron theory is the
approximation of the special nonlinear electromagnetic field theory


title: Quantum Circuits for General Multiqubit Gates

abstract:
  We consider a generic elementary gate sequence which is needed to implement a
general quantum gate acting on n qubits -- a unitary transformation with 4^n
degrees of freedom. For synthesizing the gate sequence, a method based on the
so-called cosine-sine matrix decomposition is presented. The result is optimal
in the number of elementary one-qubit gates, 4^n, and scales more favorably
than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT
gates.


title: Operational formulation of homodyne detection

abstract:
  We obtain the standard quadrature-phase positive operator-valued measure
(POVM) for homodyne detection directly and rigorously from the POVM for photon
counting without directly employing the mean field approximation for the local
oscillator. In addition we obtain correction terms for the quadrature-phase
POVM that are applicable for relatively weak local oscillator field strengths
and typical signal states.


title: Ensemble teleportation

abstract:
  The possibility of teleportation is by sure the most interesting consequence
of quantum non-separability. So far, however, teleportation schemes have been
formulated by use of state vectors and considering individual entities only. In
the present article the feasibility of teleportation is examined on the basis
of the rigorous ensemble interpretation of quantum mechanics (not to be
confused with a mere treatment of noisy EPR pairs) leading to results which are
unexpected from the usual point of view.


title: Locational Qubit Realization with One-dimensional Contact Interactions

abstract:
  We show that the U(2) group structure of thin barriers can be adopted for
quantum information processing when used in combination with environmental
potential whose bouncing modes are profile preserving. Qubits are realized as
wave functions localized in either side of the barrier which divides the
one-dimensional system into two regions. It is argued that this model is a
theoretical prototype of a robust and scalable quantum computing device.
  Keywords: Quantum Computation, Quantum Wire, Quantum Contact Interaction


title: Observable Phase Entanglement

abstract:
  Quantum entanglement can manifest itself in the narrowing of wavepackets. We
define the phenomenon of phase entanglement and describe its effect on the
interpretation of spatial localization experiments.


title: Testing QM : the Uncertainty Principle

abstract:
  We propose the experimental test of the uncertainty principle. From
sub-quantum models it follows that the uncertainty principle may be not true on
short time intervals of the order of a picosecond. The positive result of this
experiment would signify the limits of QM.


title:
Classical simulation of Quantum Entanglement using Optical Transverse
  Modes in Multimode Waveguides

abstract:
  We discuss mode-entangled states based on the optical transverse modes of the
optical field propagating in multi-mode waveguides, which are classical analogs
of the quantum entangled states. The analogs are discussed in detail, including
the violation of the Bell inequality and the correlation properties of optical
pulses' group delays. The research on these analogs may be important, for it
not only provides useful insights into fundamental features of quantum
entanglement, but also yields new insights into quantum computation and quantum
communication.


title: Locking entanglement measures with a single qubit

abstract:
  We study the loss of entanglement of bipartite state subjected to discarding
or measurement of one qubit. Examining the behavior of different entanglement
measures, we find that entanglement of formation, entanglement cost, and
logarithmic negativity are lockable measures in that it can decrease
arbitrarily after measuring one qubit. We prove that any convex and
asymptotically non-continuous measure is lockable. As a consequence, all the
convex roof measures can be locked. Relative entropy of entanglement is shown
to be a non-lockable measure.


title: Non-local correlations as an information theoretic resource

abstract:
  It is well known that measurements performed on spatially separated entangled
quantum systems can give rise to correlations that are non-local, in the sense
that a Bell inequality is violated. They cannot, however, be used for
super-luminal signalling. It is also known that it is possible to write down
sets of ``super-quantum'' correlations that are more non-local than is allowed
by quantum mechanics, yet are still non-signalling. Viewed as an information
theoretic resource, super-quantum correlations are very powerful at reducing
the amount of communication needed for distributed computational tasks. An
intriguing question is why quantum mechanics does not allow these more powerful
correlations. We aim to shed light on the range of quantum possibilities by
placing them within a wider context. With this in mind, we investigate the set
of correlations that are constrained only by the no-signalling principle. These
correlations form a polytope, which contains the quantum correlations as a
(proper) subset. We determine the vertices of the no-signalling polytope in the
case that two observers each choose from two possible measurements with d
outcomes. We then consider how interconversions between different sorts of
correlations may be achieved. Finally, we consider some multipartite examples.


title:
Contribution a la recherche des equations de Mouvement en Mecanique
  quantique et a une interpretation deterministe

abstract:
  In this thesis, we present the deterministic approach of quantum mechanics
already presented in quant-ph/0103071 (Phys. lett. A 285 (2001) 27-33) of which
this thesis is the embryo.


title: Entanglement of distant electron interference experiments

abstract:
  Two electron interference experiments which are far from each other are
considered. They are irradiated with correlated nonclassical electromagnetic
fields, produced by the same source. The phase factors are in this case
operators, and their expectation values with respect to the density matrix of
the electromagnetic field quantify the observed electron fringes. The
correlated photons create correlations between the observed electron
intensities. Both cases of classically correlated (separable) and quantum
mechanically correlated (entangled) electromagnetic fields are considered. It
is shown that the induced correlation between the distant electron
interferences is sensitive to the nature of the correlation between the
irradiating photons.


title: Weakly-entangled states are dense and robust

abstract:
  Motivated by the mathematical definition of entanglement we undertake a
rigorous analysis of the separability and non-distillability properties in the
neighborhood of those three-qubit mixed states which are entangled and
completely bi-separable. Our results are not only restricted to this class of
quantum states, since they rest upon very general properties of mixed states
and Unextendible Product Bases for any possible number of parties. Robustness
against noise of the relevant properties of these states implies the
significance of their possible experimental realization, therefore being of
physical -and not exclusively mathematical- interest.


title: Exact solutions for universal holonomic quantum gates

abstract:
  We show how one can implement any local quantum gate on specific qubits in an
array of qubits by carrying adiabatically a Hamiltonian around a closed loop.
We find the exact form of the loop and the Hamiltonian for implementing general
one and two qubits gates. Our method is analytical and is not based on
numerical search in the space of all loops.


title: Sewing sound quantum flesh onto classical bones

abstract:
  Semiclassical transformation theory implies an integral representation for
stationary-state wave functions $\psi_m(q)$ in terms of angle-action variables
($\theta,J$). It is a particular solution of Schr\"{o}dinger's time-independent
equation when terms of order $\hbar^2$ and higher are omitted, but the
pre-exponential factor $A(q,\theta)$ in the integrand of this integral
representation does not possess the correct dependence on $q$. The origin of
the problem is identified: the standard unitarity condition invoked in
semiclassical transformation theory does not fix adequately in $A(q,\theta)$ a
factor which is a function of the action $J$ written in terms of $q$ and
$\theta$. A prescription for an improved choice of this factor, based on
succesfully reproducing the leading behaviour of wave functions in the vicinity
of potential minima, is outlined. Exact evaluation of the modified integral
representation via the Residue Theorem is possible. It yields wave functions
which are not, in general, orthogonal. However, closed-form results obtained
after Gram-Schmidt orthogonalization bear a striking resemblance to the exact
analytical expressions for the stationary-state wave functions of the various
potential models considered (namely, a P\"{o}schl-Teller oscillator and the
Morse oscillator).


title: Schroedinger equation for joint bidirectional motion in time

abstract:
  The conventional, time-dependent Schroedinger equation describes only
unidirectional time evolution of the state of a physical system, i.e., forward
or, less commonly, backward. This paper proposes a generalized quantum dynamics
for the description of joint, and interactive, forward and backward time
evolution within a physical system. [...] Three applications are studied: (1) a
formal theory of collisions in terms of perturbation theory; (2) a
relativistically invariant quantum field theory for a system that kinematically
comprises the direct sum of two quantized real scalar fields, such that one
field evolves forward and the other backward in time, and such that there is
dynamical coupling between the subfields; (3) an argument that in the latter
field theory, the dynamics predicts that in a range of values of the coupling
constants, the expectation value of the vacuum energy of the universe is forced
to be zero to high accuracy. [...]


title: Fault-Tolerant Postselected Quantum Computation: Threshold Analysis

abstract:
  The schemes for fault-tolerant postselected quantum computation given in
[Knill, Fault-Tolerant Postselected Quantum Computation: Schemes,
http://arxiv.org/abs/quant-ph/0402171] are analyzed to determine their
error-tolerance. The analysis is based on computer-assisted heuristics. It
indicates that if classical and quantum communication delays are negligible,
then scalable qubit-based quantum computation is possible with errors above 1%
per elementary quantum gate.


title:
Wave function collapses in a single spin magnetic resonance force
  microscopy

abstract:
  We study the effects of wave function collapses in the oscillating cantilever
driven adiabatic reversals (OSCAR) magnetic resonance force microscopy (MRFM)
technique. The quantum dynamics of the cantilever tip (CT) and the spin is
analyzed and simulated taking into account the magnetic noise on the spin. The
deviation of the spin from the direction of the effective magnetic field causes
a measurable shift of the frequency of the CT oscillations. We show that the
experimental study of this shift can reveal the information about the average
time interval between the consecutive collapses of the wave function


title: Local invariants of stabilizer codes

abstract:
  In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which
separate the orbits of multi-qubit density operators $\rho$ under the action of
the local unitary group was presented. We consider this family of invariants
for the class of those $\rho$ which are the projection operators describing
stabilizer codes and give a complete translation of these invariants into the
binary framework in which stabilizer codes are usually described. Such an
investigation of local invariants of quantum codes is of natural importance in
quantum coding theory, since locally equivalent codes have the same
error-correcting capabilities and local invariants are powerful tools to
explore their structure. Moreover, the present result is relevant in the
context of multipartite entanglement and the development of the
measurement-based model of quantum computation known as the one-way quantum
computer.


title: Realization of a photonic CNOT gate sufficient for quantum computation

abstract:
  We report the first experimental demonstration of a quantum controlled-NOT
gate for different photons, which is classically feed-forwardable. In the
experiment, we achieved this goal with the use only of linear optics, an
entangled ancillary pair of photons and post-selection. The techniques
developed in our experiment will be of significant importance for quantum
information processing with linear optics.


title: Induced Magnetic Monopole from Trapped $\Lambda$-Type Atom

abstract:
  We investigate the spatial motion of the trapped atom with the
electromagnetically induced transparency (EIT) configuration where the two Rabi
transitions are coupled to two classical light fields respectively with the
same detuning. When the internal degrees of freedom can be decoupled
adiabatically from the spatial motion of the center of mass via the
Born-Oppenheimer approximation, it is demonstrated that the lights of certain
profile can provide the atom with an effective field of magnetic monopole,
which is the so-called induced gauge field relevant to the Berry's phase. Such
an artificial magnetic monopole structure manifests itself in the
characterizing energy spectrum.


title:
Robust generation of entanglement in Bose-Einstein condensates by
  collective atomic recoil

abstract:
  We address the dynamics induced by collective atomic recoil in a
Bose-Einstein condensate in presence of radiation losses and atomic
decoherence. In particular, we focus on the linear regime of the lasing
mechanism, and analyze the effects of losses and decoherence on the generation
of entanglement. The dynamics is that of three bosons, two atomic modes
interacting with a single-mode radiation field, coupled with a bath of
oscillators. The resulting three-mode dissipative Master equation is solved
analytically in terms of the Wigner function. We examine in details the two
complementary limits of {\em high-Q cavity} and {\em bad-cavity}, the latter
corresponding to the so-called superradiant regime, both in the quasi-classical
and quantum regimes. We found that three-mode entanglement as well as two-mode
atom-atom and atom-radiation entanglement is generally robust against losses
and decoherence,thus making the present system a good candidate for the
experimental observation of entanglement in condensate systems. In particular,
steady-state entanglement may be obtained both between atoms with opposite
momenta and between atoms and photons.


title:
Strong continuous-variable entanglement in modulated quantum dissipative
  dynamics

abstract:
  We investigate the creation of entangled states of bright light beams obeying
the condition of strong Einstein-Podolsky-Rosen-like paradox criterion in
time-modulated quantum dissipative dynamics. Having in view the generation of
these states we propose a non-degenerate optical parametric oscillator(NOPO)
driven by an amplitude-modulated pump field. We develop semi-classical and
quantum theories of this device for all operational regimes concluding that,
contrary to ordinary NOPO, the continuous-variable entanglement becomes
approximately perfect for high level of modulation. Our analytical results are
in well agreement with numerical simulations.


title:
Interpolation of recurrence and hashing entanglement distillation
  protocols

abstract:
  We construct new entanglement distillation protocols by interpolating between
the recurrence and hashing protocols. This leads to asymptotic two-way
distillation protocols, resulting in an improvement of the distillation rate
for all mixed Bell diagonal entangled states, even for the ones with very high
fidelity. We also present a method how entanglement-assisted distillation
protocols can be converted into non-entanglement-assisted protocols with the
same yield.


title: Phase correlation of laser waves with arbitrary frequency spacing

abstract:
  The theoretically predicted correlation of laser phase fluctuations in
Lambda-type interaction schemes is experimentally demonstrated. We show, that
the mechanism of correlation in a Lambda scheme is restricted to high frequency
noise components, whereas in a double-$\Lambda$ scheme, due to the laser phase
locking in closed-loop interaction, it extends to all noise frequencies. In
this case the correlation is weakly sensitive to coherence losses. Thus the
double-Lambda scheme can be used to correlate e.m. fields with carrier
frequency differences beyond the GHz regime.


title: Matched detectors as definers of force

abstract:
  Although quantum states nicely express interference effects, outcomes of
experimental trials show no states directly; they indicate properties of
probability distributions for outcomes. We prove categorically that probability
distributions leave open a choice of quantum states and operators and
particles, resolvable only by a move beyond logic, which, inspired or not, can
be characterized as a guess. By recognizing guesswork as inescapable in
choosing quantum states and particles, we free up the use of particles as
theoretical inventions by which to describe experiments with devices, and
thereby replace the postulate of state reductions by a theorem. By using the
freedom to invent probe particles in modeling light detection, we develop a
quantum model of the balancing of a light-induced force, with application to
models and detecting devices by which to better distinguish one source of weak
light from another. Finally, we uncover a symmetry between entangled states and
entangled detectors, a dramatic example of how the judgment about what light
state is generated by a source depends on choosing how to model the detector of
that light.


title: Magnetic resonance in an elliptic magnetic field

abstract:
  The behaviour of a particle with a spin 1/2 and a dipole magnetic moment in a
time-varying magnetic field in the form $(h_0 cn(\omega t,k), h_0 sn(\omega
t,k), H_0 dn(\omega t,k))$, where $\omega$ is the driving field frequency, $t$
is the time, $h_0$ and $H_0$ are the field amplitudes, $cn$, $sn$, $dn$ are
Jacobi elliptic functions, $ k$ is the modulus of the elliptic functions has
been considered. The variation parameter $k$ from zero to 1 gives rise to a
wide set of functions from trigonometric shapes to exponential pulse shapes
modulating the field. The problem was reduced to the solution of general Heun'
equation. The exact solution of the wave function was found at resonance for
any $ k$. It has been shown that the transition probability in this case does
not depend on $k$. The present study may be useful for analysis interference
experiments, improving magnetic spectrometers and the field of quantum
computing.


title: Practical Quantum Key Distribution with Polarization-Entangled Photons

abstract:
  We present an entangled-state quantum cryptography system that operated for
the first time in a real world application scenario. The full key generation
protocol was performed in real time between two distributed embedded hardware
devices, which were connected by 1.45 km of optical fiber, installed for this
experiment in the Vienna sewage system. The generated quantum key was
immediately handed over and used by a secure communication application.


title:
The nonlinear field theory II. The field representation of the Dirac
  electron theory

abstract:
  The present paper is the continuation of the paper "Nonlinear field theory
I". In the paper it is shown that a fully correspondence between the quantum
and the nonlinear electromagnetic forms of the Dirac electron theory exists, so
that each element of the Dirac theory acquires the known electrodynamics
meaning and reversely


title: A universal ionization threshold for strongly driven Rydberg states

abstract:
  We observe a universal ionization threshold for microwave driven one-electron
Rydberg states of H, Li, Na, and Rb, in an {\em ab initio} numerical treatment
without adjustable parameters. This sheds new light on old experimental data,
and widens the scene for Anderson localization in light matter interaction.


title:
Decay of Quantum Correlations in Atom Optics Billiards with Chaotic and
  Mixed Dynamics

abstract:
  We perform echo spectroscopy on ultra cold atoms in atom optics billiards, to
study their quantum dynamics. The detuning of the trapping laser is used to
change the ``perturbation'', which causes a decay in the echo coherence. Two
different regimes are observed: First, a perturbative regime in which the decay
of echo coherence is non-monotonic and partial revivals of coherence are
observed. These revivals are more pronounced in traps with mixed dynamics as
compared to traps where the dynamics is fully chaotic. Next, for stronger
perturbations, the decay becomes monotonic and independent of the strength of
the perturbation. In this regime no clear distinction can be made between
chaotic traps and traps with mixed dynamics.


title:
A study on the shape of two-photon wavefunctions after the nonlinear
  interaction with a one-dimensional atom

abstract:
  We study the interaction of Gaussian one- and two-photon pulses with a single
two-level atom based on a one-dimensional model of pulse propagation to and
from the atom. The characteristic time scale of the atomic response is the
dipole relaxation time 1/Gamma. We therefore compare the effect of the
non-linear two-photon interaction for a long pulse length of 10/Gamma with a
short pulse of $1/\Gamma$. Our results indicate that the effect of the
non-linear interaction is particularly strong for the short pulse length of
1/Gamma.


title: Fine-grained entanglement loss along renormalization group flows

abstract:
  We explore entanglement loss along renormalization group trajectories as a
basic quantum information property underlying their irreversibility. This
analysis is carried out for the quantum Ising chain as a transverse magnetic
field is changed. We consider the ground-state entanglement between a large
block of spins and the rest of the chain. Entanglement loss is seen to follow
from a rigid reordering, satisfying the majorization relation, of the
eigenvalues of the reduced density matrix for the spin block. More generally,
our results indicate that it may be possible to prove the irreversibility along
RG trajectories from the properties of the vacuum only, without need to study
the whole hamiltonian.


title: An Analysis of Stapp's "A Bell-type theorem without hidden variables"

abstract:
  H. P. Stapp has proposed a number of demonstrations of a Bell-type theorem
which dispensed with an assumption of hidden variables, but relied only upon
locality together with an assumption that experimenters can choose freely which
of several incompatible observables to measure. In recent papers his strategy
has centered upon counterfactual conditionals. Stapp's paper in American
Journal of Physics, 2004, replies to objections raised against earlier
expositions of this strategy and proposes a simplified demonstration. The new
demonstration is criticized, several subtleties in the logic of counterfactuals
are pointed out, and the proofs of J. S. Bell and his followers are advocated.


title: On the Quantumness of a Hilbert Space

abstract:
  We derive an exact expression for the quantumness of a Hilbert space (defined
in quant-ph/0302092), and show that in composite Hilbert spaces the signal
states must contain at least some entangled states in order to achieve such a
sensitivity. Furthermore, we establish that the accessible fidelity for
symmetric informationally complete signal ensembles is equal to the
quantumness. Though spelling the most trouble for an eavesdropper because of
this, it turns out that the accessible fidelity is nevertheless easy for her to
achieve in this case: Any measurement consisting of rank-one POVM elements is
an optimal measurement, and the simple procedure of reproducing the projector
associated with the measurement outcome is an optimal output strategy. Two and
epsilon elevator stories are added for entertainment.


title: Superselection from canonical constraints

abstract:
  The evolution of both quantum and classical ensembles may be described via
the probability density P on configuration space, its canonical conjugate S,
and an_ensemble_ Hamiltonian H[P,S]. For quantum ensembles this evolution is,
of course, equivalent to the Schroedinger equation for the wavefunction, which
is linear. However, quite simple constraints on the canonical fields P and S
correspond to_nonlinear_ constraints on the wavefunction. Such constraints act
to prevent certain superpositions of wavefunctions from being realised, leading
to superselection-type rules. Examples leading to superselection for energy,
spin-direction and `classicality' are given. The canonical formulation of the
equations of motion, in terms of a probability density and its conjugate,
provides a universal language for describing classical and quantum ensembles on
both continuous and discrete configuration spaces, and is briefly reviewed in
an appendix.


title: Distribution of time-bin qubits over 50 km of optical fiber

abstract:
  We report experimental distribution of time-bin entangled qubits over 50 km
of optical fibers. Using actively stabilized preparation and measurement
devices we demonstrate violation of the CHSH Bell inequality by more than 15
standard deviations without removing the detector noise. In addition we report
a proof of principle experiment of quantum key distribution over 50 km of
optical fibers using entangled photon.


title:
Unifying Quantum Computation with Projective Measurements only and
  One-Way Quantum Computation

abstract:
  Quantum measurement is universal for quantum computation. Two models for
performing measurement-based quantum computation exist: the one-way quantum
computer was introduced by Briegel and Raussendorf, and quantum computation via
projective measurements only by Nielsen. The more recent development of this
second model is based on state transfers instead of teleportation. From this
development, a finite but approximate quantum universal family of observables
is exhibited, which includes only one two-qubit observable, while others are
one-qubit observables. In this article, an infinite but exact quantum universal
family of observables is proposed, including also only one two-qubit
observable.
  The rest of the paper is dedicated to compare these two models of
measurement-based quantum computation, i.e. one-way quantum computation and
quantum computation via projective measurements only. From this comparison,
which was initiated by Cirac and Verstraete, closer and more natural
connections appear between these two models. These close connections lead to a
unified view of measurement-based quantum computation.


title:
Lieb's simple proof of concavity of Tr A^p K^* B^(1-p) K and remarks on
  related inequalities

abstract:
  A simple, self-contained proof is presented for the concavity of the map
(A,B) --> Tr(A^p K^* B^(1-p) K). The author makes no claim to originality; this
note gives Lieb's original argument in its simplest, rather than its most
general, form. A sketch of the chain of implications from this result to
concavity of A --> Tr e^[K + log(A)] is then presented. An independent
elementary proof is given for the joint convexity of the map (A,B,X) --> Tr
\int X^* (A+ uI)^{-1} X (B+ uI)^{-1} du which plays a key role in entropy
inequalities.


title: 6th order robust pulses for quantum control

abstract:
  Composite pulse sequences designed for nuclear magnetic resonance experiments
are currently being applied in many quantum information processing
technologies.We present an analysis of a family of composite pulse sequences
used to address systematic pulse-length errors in the execution of quantum
gates. It has been demonstrated by Cummins et al. [Phys. Rev. A 67, 042308
(2003)] that for this family of composite pulse sequences, the fidelity of the
resulting unitary operation compared with the ideal unitary operation is
1+C*epsilon^6, where epsilon is the fractional error in the length of the
pulse. We derive an exact expression for the 6th order coefficient, C, and from
this deduce conditions under which this 6th order dependance is observed. We
also present new pulse sequences which achieve the same fidelity.


title: How to teach Quantum Mechanics

abstract:
  In the spirit and style of John S. Bell's well known paper on How to Teach
Special Relativity it is argued, that a ``Bohmian pedagogy''provides a very
useful tool to illustrate the relation between classical and quantum physics
and illuminates the peculiar features of the latter.


title:
Experimental demonstration of a non-destructive controlled-NOT quantum
  gate for two independent photon-qubits

abstract:
  Universal logic gates for two quantum bits (qubits) form an essential
ingredient of quantum information processing. However, the photons, one of the
best candidates for qubits, suffer from the lack of strong nonlinear coupling
required for quantum logic operations. Here we show how this drawback can be
overcome by reporting a proof-of-principle experimental demonstration of a
non-destructive controlled-NOT (CNOT) gate for two independent photons using
only linear optical elements in conjunction with single-photon sources and
conditional dynamics. Moreover, we have exploited the CNOT gate to discriminate
all the four Bell-states in a teleportation experiment.


title: On probability, indeterminism and quantum paradoxes

abstract:
  If the quantum mechanical description of reality is not complete and a hidden
variable theory is possible, what arises is the problem to explain where the
rates of the outcomes of statistical experiments come from, as already noticed
by Land\'e and Popper. In this paper this problem is investigated, and a new
"paradigm" about the nature of dynamical and statistical laws is proposed. This
paradigm proposes some concepts which contrast with the usual intuitive view of
evolution and of physical law, such as: initial conditions could play no
privileged role in determining the evolution of the universe; the statistical
distribution of the particles emitted by a source could depend on the future
interactions of the particles; indeterministic trajectories can be defined by
the least action principle.
  This paradigm is applied to the analysis of the two-slit experiment and of
the EPR paradox, and a coherent picture for these phenomena is proposed; this
new picture shows how the well known difficulties in completing the quantum
mechanical description of reality could be overcome.


title: Secure quantum channels with correlated twin laser beams

abstract:
  This work is the development and analysis of the recently proposed quantum
cryptographic protocol, based on the use of the two-mode coherently correlated
states. The protocol is supplied with the cryptographic control procedures. The
quantum noise influence on the channel error properties is examined. State
detection features are proposed.


title: Unified derivations of measurement-based schemes for quantum computation

abstract:
  We present unified, systematic derivations of schemes in the two known
measurement-based models of quantum computation. The first model (introduced by
Raussendorf and Briegel [Phys. Rev. Lett., 86, 5188 (2001)]) uses a fixed
entangled state, adaptive measurements on single qubits, and feedforward of the
measurement results. The second model (proposed by Nielsen [Phys. Lett. A, 308,
96 (2003)] and further simplified by Leung [Int. J. Quant. Inf., 2, 33 (2004)])
uses adaptive two-qubit measurements that can be applied to arbitrary pairs of
qubits, and feedforward of the measurement results. The underlying principle of
our derivations is a variant of teleportation introduced by Zhou, Leung, and
Chuang [Phys. Rev. A, 62, 052316 (2000)]. Our derivations unify these two
measurement-based models of quantum computation and provide significantly
simpler schemes.


title: Multi-partite quantum cryptographic protocols with noisy GHZ states

abstract:
  We propose a wide class of distillation schemes for multi-partite entangled
states that are CSS-states. Our proposal provides not only superior efficiency,
but also new insights on the connection between CSS-states and bipartite graph
states. We then apply our distillation schemes to the tri-partite case for
three cryptographic tasks--namely, (a) conference key agreement, (b) quantum
sharing of classical secrets and (c) third-man cryptography. Moreover, we
construct ``prepare-and-measure'' protocols for the above three cryptographic
tasks which can be implemented with the generation of only a single entangled
pair at a time. This gives significant simplification over previous
experimental implementations which require two entangled pairs generated
simultaneously. We also study the yields of those protocols and the threshold
values of the fidelity above which the protocols can function securely. Rather
surprisingly, our protocols will function securely even when the initial state
does not violate the standard Bell-inequalities for GHZ states.


title: Are All Particles Real?

abstract:
  In Bohmian mechanics elementary particles exist objectively, as point
particles moving according to a law determined by a wavefunction. In this
context, questions as to whether the particles of a certain species are
real--questions such as, Do photons exist? Electrons? Or just the quarks?--have
a clear meaning. We explain that, whatever the answer, there is a corresponding
Bohm-type theory, and no experiment can ever decide between these theories.
Another question that has a clear meaning is whether particles are
intrinsically distinguishable, i.e., whether particle world lines have labels
indicating the species. We discuss the intriguing possibility that the answer
is no, and particles are points--just points.


title:
Model for resonant photon creation in a cavity with time dependent
  conductivity

abstract:
  In an electromagnetic cavity, photons can be created from the vacuum state by
changing the cavity's properties with time. Using a simple model based on a
massless scalar field, we analyze resonant photon creation induced by the
time-dependent conductivity of a thin semiconductor film contained in the
cavity. This time dependence may be achieved by irradiating periodically the
film with short laser pulses. This setup offers several experimental advantages
over the case of moving mirrors.


title: An approximation to $\delta'$ couplings on graphs

abstract:
  We discuss a general parametrization for vertices of quantum graphs and show,
in particular, how the $\delta'_s$ and $\delta'$ coupling at an $n$ edge vertex
can be approximated by means of $n+1$ couplings of the $\delta$ type provided
the latter are properly scaled.