title:
Characterization of combinatorially independent permutation separability
  criteria

abstract:
  The so-called permutation separability criteria are simple operational
conditions that are necessary for separability of mixed states of multipartite
systems: (1) permute the indices of the density matrix and (2) check if the
trace norm of at least one of the resulting operators is greater than one. If
it is greater than one then the state is necessarily entangled. A shortcoming
of the permutation separability criteria is that many permutations give rise to
dependent separability criteria. Therefore, we introduce a necessary condition
for two permutations to yield independent criteria called combinatorical
independence. This condition basically means that the map corresponding to one
permutation cannot be obtained by concatenating the map corresponding to the
second permutation with a norm-preserving map. We characterize completely
combinatorically independent criteria, and determine simple permutations that
represent all independent criteria. The representatives can be visualized by
means of a simple graphical notation. They are composed of three basic
operations: partial transpose, and two types of so-called reshufflings. In
particular, for a four-partite system all criteria except one are composed of
partial transpose and only one type of reshuffling; the exceptional one
requires the second type of reshuffling. Furthermore, we show how to obtain
efficiently for every permutation a simple representative. This method allows
to check easily if two permutations are combinatorically equivalent or not.


title: Simple proof of fault tolerance in the graph-state model

abstract:
  We consider the problem of fault tolerance in the graph-state model of
quantum computation. Using the notion of composable simulations, we provide a
simple proof for the existence of an accuracy threshold for graph-state
computation by invoking the threshold theorem derived for quantum circuit
computation. Lower bounds for the threshold in the graph-state model are then
obtained from known bounds in the circuit model under the same noise process.


title: Entanglement in the scattering process by local impurity

abstract:
  We study entanglement in the scattering processes by fixed impurity and Kondo
impurity. The fixed impurity plays a role as spin state filter that is employed
to concentrate entanglement between the scattering particle and the
unscattering particle. One Kondo impurity can entangle two noninteracting
scattering particles while one scattering particle can entangle two separate
noninteracting Kondo impurities.


title: Entanglement manipulation by a local magnetic pulse

abstract:
  A scheme for controlling the entanglement of a two-qubit system by a local
magnetic pulse is proposed. We show that the entanglement of the two-qubit
system can be increased by sacrificing the coherence in ancillary degree of
freedom, which is induced by a local manipulation.


title:
Direct versus measurement assisted bipartite entanglement in multi-qubit
  systems and their dynamical generation in spin systems

abstract:
  We consider multi-qubit systems and relate quantitatively the problems of
generating cluster states with high value of concurrence of assistance, and
that of generating states with maximal bipartite entanglement. We prove an
upper bound for the concurrence of assistance. We consider dynamics of spin-1/2
systems that model qubits, with different couplings and possible presence of
magnetic field to investigate the appearance of the discussed entanglement
properties. We find that states with maximal bipartite entanglement can be
generated by an XY Hamiltonian, and their generation can be controlled by the
initial state of one of the spins. The same Hamiltonian is capable of creating
states with high concurrence of assistance with suitably chosen initial state.
We show that the production of graph states using the Ising Hamiltonian is
controllable via a single-qubit rotation of one spin-1/2 subsystem in the
initial multi-qubit state. We shown that the property of Ising dynamics to
convert a product state basis into a special maximally entangled basis is
temporally enhanced by the application of a suitable magnetic field. Similar
basis transformations are found to be feasible in the case of isotropic XY
couplings with magnetic field.


title: Comment on "On the temperature dependence of the Casimir effect"

abstract:
  Recently, Brevik et al. [Phys. Rev. E 71, 056101 (2005)] adduced arguments
against the traditional approach to the thermal Casimir force between real
metals and in favor of one of the alternative approaches. The latter assumes
zero contribution from the transverse electric mode at zero frequency in
qualitative disagreement with unity as given by the thermal quantum field
theory for ideal metals. Those authors claim that their approach is consistent
with experiments as well as with thermodynamics. We demonstrate that these
conclusions are incorrect. We show specifically that their results are
contradicted by four recent experiments and also violate the third law of
thermodynamics (the Nernst heat theorem).


title: Entanglement correlations, Bell inequalities, and the concurrence

abstract:
  Probabilities of measurement outcomes of two-particle entangled states give a
physically transparent interpretation of the concurrence and of the
I-concurrence as entanglement measures. The (I)-concurrence can thus be
measured experimentally. The tight connection between these measures and Bell
inequalities is highlighted.


title: Quantum Cooperation of Two Insects

abstract:
  The physical concept of quantum entanglement is brought to the biological
domain. We simulate the cooperation of two insects by hypothesizing that they
share a large number of quantum entangled spin-1/2 particles. Each of them
makes measurements on these particles to decide whether to execute certain
actions. In the first example, two ants must push a pebble, which may be too
heavy for one ant. In the second example, two distant butterflies must find
each other. In both examples the individuals make odour-guided random choices
of possible directions, followed by a quantum decision whether to push/fly or
to wait. With quantum entanglement the two ants can push the pebble up to twice
as far as independent ants, and the two butterflies may need as little as half
of the flight path of independent butterflies to find each other.


title: Dirac oscillators and quasi-exactly solvable operators

abstract:
  The Dirac equation is considered in the background of potentials of several
types, namely scalar and vector-potentials as well as "Dirac-oscillator"
potential or some of its generalisations. We investigate the radial Dirac
equation within a quite general spherically symmetric form for these potentials
and we analyse some exactly and quasi exactly solvable properties of the
underlying matricial linear operators.


title: No partial erasure of quantum information

abstract:
  In complete erasure any arbitrary pure quantum state is transformed to a
fixed pure state by irreversible operation. Here we ask if the process of
partial erasure of quantum information is possible by general quantum
operations, where partial erasure refers to reducing the dimension of the
parameter space that specifies the quantum state. Here we prove that quantum
information stored in qubits and qudits cannot be partially erased, even by
irreversible operations. The no-flipping theorem, which rules out the existence
of a universal NOT gate for an arbitrary qubit, emerges as a corollary to this
theorem. The `no partial erasure' theorem is shown to apply to spin and bosonic
coherent states, with the latter result showing that the `no partial erasure'
theorem applies to continuous variable quantum information schemes as well. The
no partial erasure theorem suggests an integrity principle that quantum
information is indivisible.


title: Approximate Quantum Error-Correcting Codes and Secret Sharing Schemes

abstract:
  It is a standard result in the theory of quantum error-correcting codes that
no code of length n can fix more than n/4 arbitrary errors, regardless of the
dimension of the coding and encoded Hilbert spaces. However, this bound only
applies to codes which recover the message exactly. Naively, one might expect
that correcting errors to very high fidelity would only allow small violations
of this bound. This intuition is incorrect: in this paper we describe quantum
error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors
with fidelity exponentially close to 1, at the price of increasing the size of
the registers (i.e., the coding alphabet). This demonstrates a sharp
distinction between exact and approximate quantum error correction. The codes
have the property that any $t$ components reveal no information about the
message, and so they can also be viewed as error-tolerant secret sharing
schemes.
  The construction has several interesting implications for cryptography and
quantum information theory. First, it suggests that secret sharing is a better
classical analogue to quantum error correction than is classical error
correction. Second, it highlights an error in a purported proof that verifiable
quantum secret sharing (VQSS) is impossible when the number of cheaters t is
n/4. More generally, the construction illustrates a difference between exact
and approximate requirements in quantum cryptography and (yet again) the
delicacy of security proofs and impossibility results in the quantum model.


title: Relations between cloning and the universal NOT from conservation laws

abstract:
  We discuss certain relations between cloning and the NOT operation that can
be derived from conservation laws alone. Those relations link the limitations
on cloning and the NOT operation possibly imposed by {\em other} laws of
Nature. Our result is quite general and holds both in classical and
quantum-mechanical worlds, for both optimal and suboptimal operations, and for
bosons as well as fermions.


title: A new local invariant for quantum gates

abstract:
  In this paper we study the properties of two-qubit gates. We review the most
common parameterizations for the local equivalence classes of two-qubit gates
and the connections between them. We then introduce a new discrete local
invariant, namely the number of local degrees of freedom that a gate can bind.
The value of this invariant is calculated analytically for all the local
equivalence classes of two-qubit gates. We find that almost all two-qubit gates
can bind the full six local degrees of freedom and are in this sense more
effective than the controlled-NOT gate, which only can bind four local degrees
of freedom.


title: Quantum walks and orbital states of a Weyl particle

abstract:
  The time-evolution equation of a one-dimensional quantum walker is exactly
mapped to the three-dimensional Weyl equation for a zero-mass particle with
spin 1/2, in which each wave number k of walker's wave function is mapped to a
point \vec{q}(k) in the three-dimensional momentum space and \vec{q}(k) makes a
planar orbit as k changes its value in [-\pi, \pi). The integration over k
providing the real-space wave function for a quantum walker corresponds to
considering an orbital state of a Weyl particle, which is defined as a
superposition (curvilinear integration) of the energy-momentum eigenstates of a
free Weyl equation along the orbit. Konno's novel distribution function of
quantum-walker's pseudo-velocities in the long-time limit is fully controlled
by the shape of the orbit and how the orbit is embedded in the
three-dimensional momentum space. The family of orbital states can be regarded
as a geometrical representation of the unitary group U(2) and the present study
will propose a new group-theoretical point of view for quantum-walk problems.

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


title: Robust and fragile Werner states in the collective dephasing

abstract:
  We investigate the concurrence and Bell violation of the standard Werner
state or Werner-like states in the presence of collective dephasing. It is
shown that the standard Werner state and certain kinds of Werner-like states
are robust against the collective dephasing, and some kinds of Werner-like
states is fragile and becomes completely disentangled in a finite-time. The
threshold time of complete disentanglement of the fragile Werner-like states is
given. The influence of external driving field on the finite-time
disentanglement of the standard Werner state or Werner-like states is
discussed. Furthermore, we present a simple method to control the stationary
state entanglement and Bell violation of two qubits. Finally, we show that the
theoretical calculations of fidelity based on the initial Werner state
assumption well agree with previous experimental results.


title:
Constraints of the Dynamic Equations and Lagrangian required by
  Superposition of Field

abstract:
  A general form of the dynamical equations of field is obtained on the
requirement this field is a superposable one; hence the constraint on the forms
of the Lagrangians is acquired. It shows this requirement requires the
continuous transformation group of the Lagrangians of field to be compact, and
that All Lagrangians of elementary particles, such as leptons, quarks, photons
and gluons, satisfy this requirement.The result of regarding this character as
a general property of physical field is discussed.


title:
Calculation of resonances in the Coulomb three-body system with two
  disintegration channels in the adiabatic hyperspherical approach

abstract:
  The method of calculation of the resonance characteristics is developed for
the metastable states of the Coulomb three-body (CTB) system with two
disintegration channels. The energy dependence of K-matrix in the resonance
region is calculated with the use of the stabilization method. Resonance
position and partial widths are obtained by fitting the numerically calculated
K(E)-matrix with the help of the generalized Breit-Wigner formula.


title: On Energy Expenditure per Unit of the Amount of Information

abstract:
  It is shown that for an equilibrium state of time-symmetric system of
non-relativistic strings the energy per unit of information transfer (storage,
processing) obeys the Bekenstein conjecture. The result is based on a theorem
due to A.Kholevo relating the physical entropy and the amount of information.
Interestingly, the energy in question is the difference between the ensemble
average of the energy and the Helmholtz free energy.


title:
Cosine and Sine Operators Related with Orthogonal Polynomial Sets on the
  Intervall [-1,1]

abstract:
  The quantization of phase is still an open problem. In the approach of
Susskind and Glogower so called cosine and sine operators play a fundamental
role. Their eigenstates in the Fock representation are related with the
Chebyshev polynomials of the second kind. Here we introduce more general cosine
and sine operators whose eigenfunctions in the Fock basis are related in a
similar way with arbitrary orthogonal polynomial sets on the intervall [-1,1].
To each polynomial set defined in terms of a weight function there corresponds
a pair of cosine and sine operators. Depending on the symmetry of the weight
function we distinguish generalized or extended operators. Their eigenstates
are used to define cosine and sine representations and probability
distributions. We consider also the inverse arccosine and arcsine operators and
use their eigenstates to define cosine-phase and sine-phase distributions,
respectively. Specific, numerical and graphical results are given for the
classical orthogonal polynomials and for particular Fock and coherent states.


title: Cloning quantum entanglement in arbitrary dimensions

abstract:
  We have found a quantum cloning machine that optimally duplicates the
entanglement of a pair of $d$-dimensional quantum systems. It maximizes the
entanglement of formation contained in the two copies of any
maximally-entangled input state, while preserving the separability of
unentangled input states. Moreover, it cannot increase the entanglement of
formation of all isotropic states. For large $d$, the entanglement of formation
of each clone tends to one half the entanglement of the input state, which
corresponds to a classical behavior. Finally, we investigate a local
entanglement cloner, which yields entangled clones with one fourth the input
entanglement in the large-$d$ limit.


title:
Non-locality and gauge freedom in Deutsch and Hayden's formulation of
  quantum mechanics

abstract:
  Deutsch and Hayden have proposed an alternative formulation of quantum
mechanics which is completely local. We argue that their proposal must be
understood as having a form of `gauge freedom' according to which
mathematically distinct states are physically equivalent. Once this gauge
freedom is taken into account, their formulation is no longer local.


title:
Controllability of multi-partite quantum systems and selective
  excitation of quantum dots

abstract:
  We consider the degrees of controllability of multi-partite quantum systems
as well as necessary and sufficient criteria for each case. The results are
applied to the problem of simultaneous control of an ensemble of quantum dots
with a single laser pulse. Finally, we apply optimal control techniques to
demonstrate selective excitation of individual dots for a simultaneously
controllable ensemble.


title:
A relational quantum computer using only two-qubit total spin
  measurement and an initial supply of highly mixed single qubit states

abstract:
  We prove that universal quantum computation is possible using only (i) the
physically natural measurement on two qubits which distinguishes the singlet
from the triplet subspace, and (ii) qubits prepared in almost any three
different (potentially highly mixed) states. In some sense this measurement is
a `more universal' dynamical element than a universal 2-qubit unitary gate,
since the latter must be supplemented by measurement. Because of the rotational
invariance of the measurement used, our scheme is robust to collective
decoherence in a manner very different to previous proposals - in effect it is
only ever sensitive to the relational properties of the qubits.


title: Quantifying Entanglement with Witness Operators

abstract:
  We present an unifying approach to the quantification of entanglement based
on entanglement witnesses, which includes several already established
entanglement measures such as the negativity, the concurrence and the
robustness of entanglement. We then introduce an infinite family of new
entanglement quantifiers, having as its limits the best separable approximation
measure and the generalized robustness. Gaussian states, states with symmetry,
states constrained to super-selection rules and states composed of
indistinguishable particles are studied under the view of the witnessed
entanglement. We derive new bounds to the fidelity of teleportation d_{min},
for the distillable entanglement E_{D} and for the entanglement of formation. A
particular measure, the PPT-generalized robustness, stands out due to its easy
calculability and provides sharper bounds to d_{min} and E_{D} than the
negativity in most of states. We illustrate our approach studying
thermodynamical properties of entanglement in the Heisenberg XXX and dimerized
models.


title: Quantum process tomography of a single solid state qubit

abstract:
  We present an example of quantum process tomography performed on a single
solid state qubit. The qubit used is two energy levels of the triplet state in
the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied
to a qubit which has been allowed to decohere for three different time periods.
In each case the process is found in terms of the $\chi$ matrix representation
and the affine map representation. The discrepancy between experimentally
estimated process and the closest physically valid process is noted.


abstract:
  A representation of complex rational numbers in quantum mechanics is
described that is not based on logical or physical qubits. It stems from noting
that the zeros in a product qubit state do not contribute to the number. They
serve only as place holders. The representation is based on the distribution of
four types of systems on an integer lattice. The four types, labelled as
positive real, negative real, positive imaginary, and negative imaginary, are
represented by creation and annihilation operators acting on the system vacuum
state. Complex rational string number states correspond to strings of creation
operators acting on the vacuum. Various operators, including those for the
basic arithmetic operations, are described. The representation used here is
based on occupation number states and is given for bosons and fermions.


title:
Short-time decoherence of Josephson charge qubits in Ohmic and 1/f noise
  environment

abstract:
  In this paper we investigate the short-time decoherence from Ohmic and 1/f
noise of single Josephson charge qubit (JCQ). At first, we use the short-time
approximation to obtain the dynamics of the open JCQ. Then we calculate the
decoherence the measure of which is chosen as the maximum norm of the deviation
density operator. It is shown that the decoherence from 1/f noise plays the
central role. The total decoherence from Ohmic and 1/f noise is serious at
present experiential conditions according to the DiVincenzo criterion.


title: Probing the light induced dipole-dipole interaction in momentum space

abstract:
  We theoretically investigate the mechanical effect of the light-induced
dipole-dipole interaction potential on the atoms in a Bose-Einstein condensate.
We present numerical calculations on the magnitude and shape of the induced
potentials for different experimentally accessible geometries. It is shown that
the mechanical effect can be distinguished from the effect of incoherent
scattering for an experimentally feasible setting.


title: Secure Communication Using Qubits

abstract:
  A two-layer quantum protocol for secure transmission of data using qubits is
presented. The protocol is an improvement over the BB84 QKD protocol. BB84, in
conjunction with the one-time pad algorithm, has been shown to be
unconditionally secure. However it suffers from two drawbacks: (1) Its security
relies on the assumption that Alice's qubit source is perfect in the sense that
it does not inadvertently emit multiple copies of the same qubit. A multi-qubit
emission attack can be launched if this assumption is violated. (2) BB84 cannot
transfer predetermined keys; the keys it can distribute are generated in the
process. Our protocol does not have these drawbacks.
  As in BB84, our protocol requires an authenticated public channel so as to
detect an intruder's interaction with the quantum channel, but unlike in
symmetric-key cryptography, the confidentiality of transmitted data does not
rely on a shared secret key.


title:
Kochen-Specker theorem as a precondition for secure quantum key
  distribution

abstract:
  We show that (1) the violation of the Ekert 91 inequality is a sufficient
condition for certification of the Kochen-Specker (KS) theorem, and (2) the
violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a
sufficient condition for certification of the KS theorem. Therefore the success
in each QKD protocol reveals the nonclassical feature of quantum theory, in the
sense that the KS realism is violated. Further, it turned out that the Ekert
inequality and the BBM inequality are depictured by distillable entanglement
witness inequalities. Here, we connect the success in these two key
distribution processes into the no-hidden-variables theorem and into witness on
distillable entanglement. We also discuss the explicit difference between the
KS realism and Bell's local realism in the Hilbert space formalism of quantum
theory.


title:
Abstract algebra, projective geometry and time encoding of quantum
  information

abstract:
  Algebraic geometrical concepts are playing an increasing role in quantum
applications such as coding, cryptography, tomography and computing. We point
out here the prominent role played by Galois fields viewed as cyclotomic
extensions of the integers modulo a prime characteristic $p$. They can be used
to generate efficient cyclic encoding, for transmitting secrete quantum keys,
for quantum state recovery and for error correction in quantum computing.
Finite projective planes and their generalization are the geometric counterpart
to cyclotomic concepts, their coordinatization involves Galois fields, and they
have been used repetitively for enciphering and coding. Finally the characters
over Galois fields are fundamental for generating complete sets of mutually
unbiased bases, a generic concept of quantum information processing and quantum
entanglement. Gauss sums over Galois fields ensure minimum uncertainty under
such protocols. Some Galois rings which are cyclotomic extensions of the
integers modulo 4 are also becoming fashionable for their role in time encoding
and mutual unbiasedness.


title: Entanglement in quantum catastrophes

abstract:
  We classify entanglement singularities for various two-mode bosonic systems
in terms of catastrophe theory. Employing an abstract phase-space
representation, we obtain exact results in limiting cases for the entropy in
cusp, butterfly, and two-dimensional catastrophes. We furthermore use numerical
results to extract the scaling of the entropy with the non-linearity parameter,
and discuss the role of mixing entropies in more complex systems.


title:
Globally controlled artificial semiconducting molecules as quantum
  computers

abstract:
  Quantum computers are expected to be considerably more efficient than
classical computers for the execution of some specific tasks. The difficulty in
the practical implementation of thoose computers is to build a microscopic
quantum system that can be controlled at a larger mesoscopic scale. Here I show
that vertical lines of donor atoms embedded in an appropriate Zinc Oxide
semiconductor structure can constitute artificial molecules that are as many
copy of the same quantum computer. In this scalable architecture, each unit of
information is encoded onto the electronic spin of a donor. Contrary to most
existing practical proposals, here the logical operations only require a global
control of the spins by electromagnetic pulses. Ensemble measurements simplify
the readout. With appropriate improvement of its growth and doping methods,
Zinc Oxide could be a good semiconductor for the next generation of computers.


title:
Transition From Quantum To Classical Mechanics As Information
  Localization

abstract:
  Quantum parallelism implies a spread of information over the space in
contradistinction to the classical mechanical situation where the information
is "centered" on a fixed trajectory of a classical particle. This means that a
quantum state becomes specified by more indefinite data. The above spread
resembles, without being an exact analogy, a transfer of energy to smaller and
smaller scales observed in the hydrodynamical turbulence. There, in spite of
the presence of dissipation (in a form of kinematic viscosity), energy is still
conserved. The analogy with the information spread in classical to quantum
transition means that in this process the information is also conserved. To
illustrate that, we show (using as an example a specific case of a coherent
quantum oscillator) how the Shannon information density continuously changes in
the above transition . In a more general scheme of things, such an analogy
allows us to introduce a "dissipative" term (connected with the information
spread) in the Hamilton-Jacobi equation and arrive in an elementary fashion at
the equations of classical quantum mechanics (ranging from the Schr\"{o}dinger
to Klein-Gordon equations). We also show that the principle of least action in
quantum mechanics is actually the requirement for the energy to be bounded from
below.


title: On decoherence in noncommutative plane with perpendicular magnetic field

abstract:
  In the last years noncommutative quantum mechanics has been investigated
intensively. We consider the influence of magnetic field on decoherence of a
system in the noncommutative quantum plane. Particularly, we point out a model
in which the magnetic field allows {\it in situ} dynamical control of
decoherence as well as, in principle, observation of noncommutativity.


title: Generic Bell inequalities for multipartite arbitrary dimensional systems

abstract:
  We present generic Bell inequalities for multipartite multi-dimensional
systems. The inequalities that any local realistic theories must obey are
violated by quantum mechanics for even-dimensional multipartite systems. A
large set of variants are shown to naturally emerge from the generic Bell
inequalities. We discuss particular variants of Bell inequalities, that are
violated for all the systems including odd-dimensional systems.


title: Attosecond double-slit experiment

abstract:
  A new scheme for a double-slit experiment in the time domain is presented.
Phase-stabilized few-cycle laser pulses open one to two windows (``slits'') of
attosecond duration for photoionization. Fringes in the angle-resolved energy
spectrum of varying visibility depending on the degree of which-way information
are observed. A situation in which one and the same electron encounters a
single and a double slit at the same time is discussed. The investigation of
the fringes makes possible interferometry on the attosecond time scale. The
number of visible fringes, for example, indicates that the slits are extended
over about 500as.


title:
On Dirac theory in the space with deformed Heisenberg algebra. Exact
  solutions

abstract:
  The Dirac equation has been studied in which the Dirac matrices
$\hat{\boldmath$\alpha$}, \hat\beta$ have space factors, respectively $f$ and
$f_1$, dependent on the particle's space coordinates. The $f$ function deforms
Heisenberg algebra for the coordinates and momenta operators, the function
$f_1$ being treated as a dependence of the particle mass on its position. The
properties of these functions in the transition to the Schr\"odinger equation
are discussed. The exact solution of the Dirac equation for the particle motion
in the Coulomnb field with a linear dependence of the $f$ function on the
distance $r$ to the force centre and the inverse dependence on $r$ for the
$f_1$ function has been found.


title: Phase-space reconstruction of an atomic chaotic system

abstract:
  We consider the dynamics of a single atom submitted to periodic pulses of a
far-detuned standing wave generated by a high-finesse optical cavity, which is
an atomic version of the well-known ``kicked rotor''. We show that the
classical phase-space map can be ``reconstructed'' by monitoring the
transmission of the cavity. We also studied the effect of spontaneous emission
on the reconstruction, and put limits to the maximum acceptable spontaneous
emission rate.


title: Quantum information cannot be split into complementary parts

abstract:
  We prove a new impossibility for quantum information (the no-splitting
theorem): an unknown quantum bit (qubit) cannot be split into two complementary
qubits. This impossibility, together with the no-cloning theorem, demonstrates
that an unknown qubit state is a single entity, which cannot be cloned or
split. This sheds new light on quantum computation and quantum information.


title: Purifying Quantum States: Quantum and Classical Algorithms

abstract:
  I give analytical estimates and numerical simulation results for the
performance of Kitaev's 2d topological error-correcting codes. By providing
methods for the execution of an encoded three-qubit Toffoli gate, I complete a
universal gate set for these codes. I also examine the utility of Bohm's and
Bohm-inspired interpretations of quantum mechanics for numerical solution of
many-body dynamics and ``mechanism identification'' heuristics in discrete
systems. Further, I show an unexpected quantitative correspondence between the
previously known continuum of stochastic-Bohm trajectory theories on the one
hand and extant path integral Monte Carlo methods on the other hand.


title: The Quantum Mechanics of Hyperion

abstract:
  This paper is motivated by the suggestion [W. Zurek, Physica Scripta, T76,
186 (1998)] that the chaotic tumbling of the satellite Hyperion would become
non-classical within 20 years, but for the effects of environmental
decoherence. The dynamics of quantum and classical probability distributions
are compared for a satellite rotating perpendicular to its orbital plane,
driven by the gravitational gradient. The model is studied with and without
environmental decoherence. Without decoherence, the maximum quantum-classical
(QC) differences in its average angular momentum scale as hbar^{2/3} for
chaotic states, and as hbar^2 for non-chaotic states, leading to negligible QC
differences for a macroscopic object like Hyperion. The quantum probability
distributions do not approach their classical limit smoothly, having an
extremely fine oscillatory structure superimposed on the smooth classical
background. For a macroscopic object, this oscillatory structure is too fine to
be resolved by any realistic measurement. Either a small amount of smoothing
(due to the finite resolution of the apparatus) or a very small amount of
environmental decoherence is sufficient ensure the classical limit. Under
decoherence, the QC differences in the probability distributions scale as
(hbar^2/D)^{1/6}, where D is the momentum diffusion parameter. We conclude that
decoherence is not essential to explain the classical behavior of macroscopic
bodies.


title: Can the Salecker-Wigner clock be microscopic?

abstract:
  Half a century ago H. Salecker and E. P. Wigner examined the functioning of a
quantum clock of very simple construction [1]. They raised the question whether
such a clock can be microscopic or not, but no clear-cut answer has been
reached in [1] (see also [2]). In this note it is shown that their clock can
have a microscopic mass and size only if its accuracy is poor, but if the size
is macroscopic, a decent accuracy can be achieved even if the mass is
microscopic.


title: The Aharonov-Bohm Effect in the Momentum Space

abstract:
  The Schrodinger formalism of quantum mechanics is used to demonstrate the
existence of the Aharonov-Bohm effect in momentum space and set-ups for
experimentally demonstrating it are proposed for either free or ballistic
electrons.


title:
Continuous optimal ensembles I: A geometrical characterization of
  robustly separable quantum states

abstract:
  A geometrical characterization of robustly separable (that is, remaining
separable under sufficiently small variiations) mixed states of a bipartite
quantum system is given. It is shown that the density matrix of any such state
can be represented as a normal vector to a hypersurface in the Euclidean space
of all self-adjoint operators in the state space of the whole system. The
expression for this hypersurface is provided.


title: Simulation of many-qubit quantum computation with matrix product states

abstract:
  Matrix product states provide a natural entanglement basis to represent a
quantum register and operate quantum gates on it. This scheme can be
materialized to simulate a quantum adiabatic algorithm solving hard instances
of a NP-Complete problem. Errors inherent to truncations of the exact action of
interacting gates are controlled by the size of the matrices in the
representation. The property of finding the right solution for an instance and
the expected value of the energy are found to be remarkably robust against
these errors. As a symbolic example, we simulate the algorithm solving a
100-qubit hard instance, that is, finding the correct product state out of ~
10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow
growth of the average minimum time to solve hard instances with
highly-truncated simulations of adiabatic quantum evolution.


title:
Gravitational field measurement with an equilibrium ensemble of cold
  atoms

abstract:
  A new approach to the measurement of gravitational fields with an equilibrium
ensemble of ultra-cold alkali atoms confined in a cell of volume $V$ is
investigated. The proposed model of the gravitational sensor is based on a
variation of the density profile of the ensemble due to changing of the
gravitational field. For measurement the atomic density variations of the
ensemble the electromagnetically induced transparency method is used.


title: Studies in the Theory of Quantum Games

abstract:
  Theory of quantum games is a new area of investigation that has gone through
rapid development during the last few years. Initial motivation for playing
games, in the quantum world, comes from the possibility of re-formulating
quantum communication protocols, and algorithms, in terms of games between
quantum and classical players. The possibility led to the view that quantum
games have a potential to provide helpful insight into working of quantum
algorithms, and even in finding new ones. This thesis analyzes and compares
some interesting games when played classically and quantum mechanically. A
large part of the thesis concerns investigations into a refinement notion of
the Nash equilibrium concept. The refinement, called an evolutionarily stable
strategy (ESS), was originally introduced in 1970s by mathematical biologists
to model an evolving population using techniques borrowed from game theory.
Analysis is developed around a situation when quantization changes ESSs without
affecting corresponding Nash equilibria. Effects of quantization on
solution-concepts other than Nash equilibrium are presented and discussed. For
this purpose the notions of value of coalition, backwards-induction outcome,
and subgame-perfect outcome are selected. Repeated games are known to have
different information structure than one-shot games. Investigation is presented
into a possible way where quantization changes the outcome of a repeated game.
Lastly, two new suggestions are put forward to play quantum versions of
classical matrix games. The first one uses the association of De Broglie's
waves, with travelling material objects, as a resource for playing a quantum
game. The second suggestion concerns an EPR type setting exploiting directly
the correlations in Bell's inequalities to play a bi-matrix game.


title: Evolution of pairwise entanglement in a coupled n-body system

abstract:
  We study the exact evolution of two non-interacting qubits, initially in a
Bell state, in the presence of an environment, modeled by a kicked Ising spin
chain. Dynamics of this model range from integrable to chaotic and we can
handle numerics for a large number of qubits. We find that the entanglement (as
measured by concurrence) of the two qubits has a close relation to the purity
of the pair, and follows an analytic relation derived for Werner states. As a
collateral result we find that an integrable environment causes quadratic decay
of concurrence, while a chaotic environment causes linear decay.


title: Withdrawn

abstract: This paper has been withdrawn.


title: Lifting Bell inequalities

abstract:
  A Bell inequality defined for a specific experimental configuration can
always be extended to a situation involving more observers, measurement
settings or measurement outcomes. In this article, such "liftings" of Bell
inequalities are studied. It is shown that if the original inequality defines a
facet of the polytope of local joint outcome probabilities then the lifted one
also defines a facet of the more complex polytope.


title: Quantum logic via optimal control in holographic dipole traps

abstract:
  We propose a scheme for quantum logic with neutral atoms stored in an array
of holographic dipole traps where the positions of the atoms can be rearranged
by using holographic optical tweezers. In particular, this allows for the
transport of two atoms to the same well where an external control field is used
to perform gate operations via the molecular interaction between the atoms. We
show that optimal control techniques allow for the fast implementation of the
gates with high fidelity.


title:
Atom Nano-lithography with Multi-layer Light Masks: Particle Optics
  Analysis

abstract:
  We study the focusing of atoms by multiple layers of standing light waves in
the context of atom lithography. In particular, atomic localization by a
double-layer light mask is examined using the optimal squeezing approach.
Operation of the focusing setup is analyzed both in the paraxial approximation
and in the regime of nonlinear spatial squeezing for the thin-thin as well as
thin-thick atom lens combinations. It is shown that the optimized double light
mask may considerably reduce the imaging problems, improve the quality of
focusing and enhance the contrast ratio of the deposited structures.


title: Representations of Spacetime Alternatives and Their Classical Limits

abstract:
  Different quantum mechanical operators can correspond to the same classical
quantity. Hermitian operators differing only by operator ordering of the
canonical coordinates and momenta at one moment of time are the most familiar
example. Classical spacetime alternatives that extend over time can also be
represented by different quantum operators. For example, operators representing
a particular value of the time average of a dynamical variable can be
constructed in two ways: First, as the projection onto the value of the time
averaged Heisenberg picture operator for the dynamical variable. Second, as the
class operator defined by a sum over those histories of the dynamical variable
that have the specified time-averaged value. We show both by explicit example
and general argument that the predictions of these different representations
agree in the classical limit and that sets of histories represented by them
decohere in that limit.


title: Entanglement of Two Impurities through Electron Scattering

abstract:
  We study how two magnetic impurities embedded in a solid can be entangled by
an injected electron scattering between them and by subsequent measurement of
the electron's state. We start by investigating an ideal case where only the
electronic spin interacts successively through the same unitary operation with
the spins of the two impurities. In this case, high (but not maximal)
entanglement can be generated with a significant success probability. We then
consider a more realistic description which includes both the forward and back
scattering amplitudes. In this scenario, we obtain the entanglement between the
impurities as a function of the interaction strength of the electron-impurity
coupling. We find that our scheme allows us to entangle the impurities
maximally with a significant probability.


title:
Continuous-Variable Quantum State Transfer with Partially Disembodied
  Transport

abstract:
  We propose a new protocol of implementing continuous-variable quantum state
transfer using partially disembodied transport. This protocol may improve the
fidelity at the expense of the introduction of a semi-quantum channel between
the parties, in comparison with quantum teleportation using the same strength
of entanglement. Depending on the amount of information destroyed in the
measurement, this protocol may be regarded as a teleportation protocol
(complete destruction of input state), or as a $1\to M$ cloning protocol
(partial destruction), or as a direct transmission (no destruction). This
scheme can be straightforwardly implemented with the experimentally accessible
setup at present.


title:
Signatures of chaotic and non-chaotic-like behaviour in a non-linear
  quantum oscillator through photon detection

abstract:
  The driven non-linear duffing osillator is a very good, and standard, example
of a quantum mechanical system from which classical-like orbits can be
recovered from unravellings of the master equation. In order to generated such
trajectories in the phase space of this oscillator in this paper we use a the
quantum jumps unravelling together with a suitable application of the
correspondence principle. We analyse the measured readout by considering the
power spectra of photon counts produced by the quantum jumps. Here we show that
localisation of the wave packet from the measurement of the oscillator by the
photon detector produces a concomitant structure in the power spectra of the
measured output. Furthermore, we demonstrate that this spectral analysis can be
used to distinguish between different modes of the underlying dynamics of the
oscillator.


title:
Quantum Theory for Generation of Nonclassical Photon Pairs by a Medium
  with Coherent Atomic Memory

abstract:
  We present a fully quantum mechanical treatment of recent experiments on
creation of collective quantum memory and generation of non-classically
correlated photon pairs from an atomic ensemble via the protocol of Duan et al.
[Nature {\bf 414,} 413(2001)]. The temporal evolution of photon numbers, photon
statistics and cross-correlation between the Stokes and anti-Stokes fields is
found by solving the equation of motion for atomic spin-wave excitations. We
consider a low-finesse cavity model with collectively enhanced signal-to-noise
ratio, which remains still considerably large in the free-space limit. Our
results describe analytically the dependence of quantum correlations on spin
decoherence time and time-delay between the write and read lasers and reproduce
the observed data very well including the generated pulse shapes, strong
violation of Cauchy-Schwarz inequality and conditional generation of
anti-Stokes single-photon pulse. The theory we developed may serve as a basic
approach for quantum description of storage and retrieval of quantum
information, especially when the statistical properties of non-classical pulses
are studied.


title: Existence of Time Operator for a Singular Harmonic Oscillator

abstract:
  The time operator for a quantum singular oscillator of the
Calogero-Sutherland type is constructed in terms of the generators of the
SU(1,1) group. In the space spanned by the eigenstates of the Hamiltonian, the
time operator is not self-adjoint. We show, that the time-energy uncertainty
relation can be given the meaning within the Barut-Girardello coherent states
defined for the singular oscillator.We have also shown the relationship with
the time-of-arrival operator of Aharonov and Bohm.


title: Quantum computing of delocalization in small-world networks

abstract:
  We study a quantum small-world network with disorder and show that the system
exhibits a delocalization transition. A quantum algorithm is built up which
simulates the evolution operator of the model in a polynomial number of gates
for exponential number of vertices in the network. The total computational gain
is shown to depend on the parameters of the network and a larger than quadratic
speed-up can be reached.
  We also investigate the robustness of the algorithm in presence of
imperfections.

categories: quant-ph cond-mat.dis-nn cond-mat.stat-mech nlin.AO


title: Generalizing Elitzur-Vaidman interaction free measurements

abstract:
  In the early 1990's A. Elitzur and L. Vaidman proposed an interaction free
measurement (IFM) that allows researchers to find infinitely fragile objects
without destroying them. But Elitzur-Vaidman IFM has been used only to
determine the position of opaque objects. In this paper, we propose an
extension of such a technique that allows measurement of classical electric and
magnetic fields. Our main goal is to offer a framework for future
investigations about the role of the measurement processes, expanding the
physical properties that are measurable by means of IFM.


title: Decoherence in non integrable systems

abstract:
  Self-induced decoherence formalism and the corresponding classical limit are
extended from quantum integrable systems to non-integrable ones.


abstract:
  The classical-statistical limit of quantum mechanics is studied. It is proved
that the limit $\hbar \to 0$ is the good limit for the operators algebra but it
si not so for the state compact set. In the last case decoherence must be
invoked to obtain the classical-statistical limit.


title: Experimental Quantum Key Distribution with Decoy States

abstract:
  To increase dramatically the distance and the secure key generation rate of
quantum key distribution (QKD), the idea of quantum decoys--signals of
different intensities--has recently been proposed. Here, we present the first
experimental implementation of decoy state QKD. By making simple modifications
to a commercial quantum key distribution system, we show that a secure key
generation rate of 165bit/s, which is 1/4 of the theoretical limit, can be
obtained over 15km of a Telecom fiber. We also show that with the same
experimental parameters, not even a single bit of secure key can be extracted
with a non-decoy-state protocol. Compared to building single photon sources,
decoy state QKD is a much simpler method for increasing the distance and key
generation rate of unconditionally secure QKD.


title: A simple formula for pooling knowledge about a quantum system

abstract:
  When various observers obtain information in an independent fashion about a
classical system, there is a simple rule which allows them to pool their
knowledge, and this requires only the states-of-knowledge of the respective
observers. Here we derive an equivalent quantum formula. While its realm of
applicability is necessarily more limited, it does apply to a large class of
measurements, and we show explicitly for a single qubit that it satisfies the
intuitive notions of what it means to pool knowledge about a quantum system.
This analysis also provides a physical interpretation for the trace of the
product of two density matrices.


title: Cones of ball-ball separable elements

abstract:
  Let B_1,B_2 be balls in finite-dimensional real vector spaces E_1,E_2,
centered around unit length vectors v_1,v_2 and not containing zero. An element
in the tensor product space E_1 \otimes E_2 is called B_1 \otimes B_2-separable
if it is contained in the convex conic hull of elements of the form w_1 \otimes
w_2, where w_1 \in B_1, w_2 \in B_2. We study the cone formed by the separable
elements in E_1 \otimes E_2. We determine the largest faces of this cone via a
description of the extreme rays of the dual cone, i.e. the cone of the
corresponding positive linear maps. We compute the radius of the largest ball
centered around v_1 \otimes v_2 that consists of separable elements. As an
application we obtain lower bounds on the radius of the largest ball of
separable unnormalized states around the identity matrix for a multi-qubit
system. These bounds are approximately 12% better than the best previously
known. Our results are extendible to the case where B_1,B_2 are solid
ellipsoids.


title: Instability and entanglement of the ground state of the Dicke model

abstract:
  Using tools of quantum information theory we show that the ground state of
the Dicke model exhibits an infinite sequence of instabilities
(quantum-phase-like transitions). These transitions are characterized by abrupt
changes of the bi-partite entanglement between atoms at critical values
$\kappa_j$ of the atom-field coupling parameter $\kappa$ and are accompanied by
discontinuities of the first derivative of the energy of the ground state. We
show that in a weak-coupling limit ($\kappa_1\leq \kappa \leq \kappa_2$) the
Coffman-Kundu-Wootters (CKW) inequalities are saturated which proves that for
these values of the coupling no intrinsic multipartite entanglement (neither
among the atoms nor between the atoms and the field) is generated by the
atom-field interaction. We analyze also the atom-field entanglement and we show
that in the strong-coupling limit the field is entangled with the atoms so that
the von Neumann entropy of the atomic sample (that serves as a measure of the
atom-field entanglement) takes the value $S_A={1/2}\ln (N+1)$. The entangling
interaction with atoms leads to a highly sub-Poissonian photon statistics of
the field mode.


title: Quantum Scattering in Strong Cylindrical Confinement

abstract:
  A Green's function formalism to analyze the scattering properties in confined
geometries is developed. This includes scattering from a central field inside
the guide created e.g. by impurities. For atomic collisions our approach
applies to the case of parabolic confinement and, with certain restrictions,
also to an anharmonic one. The coupling between the angular momentum phase
shifts $\delta_l$ of a spherically symmetric scattering potential $V(r)$ due to
the cylindrical confinement is analysed. Under these general conditions, a
broad range of scattering energies covering many transversal excitations is
considered and changes to the bound states of $V(r)$ are derived. For
collisions between identical atoms, the boson-fermion and fermion-boson
mappings are demonstrated.


title:
Analytic pulse design for selective population transfer in many-level
  quantum systems: optimizing the pulse duration

abstract:
  In the previous paper on this topic it was shown how, for a pulse of
arbitrary shape and duration, the drive frequency can be analytically optimized
to maximize the amplitude of the population oscillations between the selected
two levels in a general many level quantum system. It was shown how the
standard Rabi theory can be extended beyond the simple two-level systems. Now,
in order to achieve the quickest and as complete as possible population
transfer between two pre-selected levels, driving pulse should be tailored so
that it produces only a single half-oscillation of the population. In this
paper, this second (and final) step towards the controlled population transfer
using modified (i.e. many level system) Rabi oscillations is discussed. The
results presented herein can be regarded as an extension of the standard
$\pi$-pulse theory - also strictly valid only in the two level systems - to the
coherently driven population oscillations in general many level systems.


title: Non-Commutative Worlds -- A Summary

abstract:
  This paper summarizes the contents of the paper "Non-Commutative Worlds" by
the author (published in New Journal of Physics Vol. 6, November 2004, pp. 2 -
46; quant-ph/0403012) and gives a new derivation of our generalization of
electromagnetism in a non-commutative context. This generalization extends the
Feynman-Dyson derivation and it admits discrete models. The methods of the
present paper are diagrammatic. In this form, the theory is entirely a
consequence of the choice of definition of space and time derivatives as
commutators.


title:
Simulation of a Heisenberg XY- chain and realization of a perfect state
  transfer algorithm using liquid nuclear magnetic resonance

abstract:
  The three- spin chain with Heisenberg XY- interaction is simulated in a
three- qubit nuclear magnetic resonance (NMR) quantum computer. The evolution
caused by the XY- interaction is decomposed into a series of single- spin
rotations and the $J$- coupling evolutions between the neighboring spins. The
perfect state transfer (PST) algorithm proposed by M. Christandl et al [Phys.
Rev. Lett, 92, 187902(2004)] is realized in the XY- chain.


title: Decoherence in regular systems

abstract:
  We consider unitary evolution of finite bipartite quantum systems and study
time dependence of purity for initial cat states -- coherent superpositions of
Gaussian wave-packets. We derive explicit formula for purity in systems with
nonzero time averaged coupling, a typical situation for systems where an
uncoupled part of the Hamiltonian is Liouville integrable. Previous analytical
studies have been limited to harmonic oscillator systems but with our theory we
are able to derive analytical results for general integrable systems. Two
regimes are clearly identified, at short times purity decays due to decoherence
whereas at longer times it decays because of relaxation.


title: The GRA Beam-Splitter Experiments and Particle-Wave Duality of Light

abstract:
  Grangier, Roger and Aspect (GRA) performed a beam-splitter experiment to
demonstrate the particle behaviour of light and a Mach-Zehnder interferometer
experiment to demonstrate the wave behaviour of light. The distinguishing
feature of these experiments is the use of a gating system to produce near
ideal single photon states. With the demonstration of both wave and particle
behaviour (in two mutually exclusive experiments) they claim to have
demonstrated the dual particle-wave behaviour of light and hence to have
confirmed Bohr's principle of complementarity. The demonstration of the wave
behaviour of light is not in dispute. But we want to demonstrate, contrary to
the claims of GRA, that their beam-splitter experiment does not conclusively
confirm the particle behaviour of light, and hence does not confirm
particle-wave duality, nor, more generally, does it confirm complementarity.
Our demonstration consists of providing a detailed model based on the Causal
Interpretation of Quantum Fields (CIEM), which does not involve the particle
concept, of GRA's which-path experiment. We will also give a brief outline of a
CIEM model for the second, interference, GRA experiment.


title: Theoretical Analyses of Quantum Counting against Decoherence Errors

abstract:
  In this paper, we analyze the quantum counting under the decoherence, which
can find the number of solutions satisfying a given oracle. We investigate
probability distributions related to the first order term of the error rate on
the quantum counting with the depolarizing channel. We also implement two
circuits for the quantum counting -- the ascending-order circuit and the
descending-order circuit -- by reversing ordering of application of
controlled-Grover operations. By theoretical and numerical calculations for
probability distributions, we reveal the difference of probability
distributions on two circuits in the presence of decoherence and show that the
ascending-order circuit is more robust against the decoherence than the
descending-order circuit. This property of the robustness is applicable to the
phase estimation such as the factoring.


title: An algebraic SU(1,1) solution for the relativistic hydrogen atom

abstract:
  The bound eigenfunctions and spectrum of a Dirac hydrogen atom are found
taking advantage of the $SU(1, 1)$ Lie algebra in which the radial part of the
problem can be expressed. For defining the algebra we need to add to the
description an additional angular variable playing essentially the role of a
phase. The operators spanning the algebra are used for defining ladder
operators for the radial eigenfunctions of the relativistic hydrogen atom and
for evaluating its energy spectrum. The status of the Johnson-Lippman operator
in this algebra is also investigated.


title:
Entangling ability of a beam splitter in the presence of temporal
  which-path information

abstract:
  We calculate the amount of polarization-entanglement induced by two-photon
interference at a lossless beam splitter. Entanglement and its witness are
quantified respectively by concurrence and the Bell-CHSH parameter. In the
presence of a Mandel dip, the interplay of two kinds of which-path information
-- temporal and polarization -- gives rise to the existence of entangled
polarization-states that cannot violate the Bell-CHSH inequality.


title: A different kind of quantum search

abstract:
  The quantum search algorithm consists of an alternating sequence of selective
inversions and diffusion type operations, as a result of which it can find a
target state in an unsorted database of size N in only sqrt(N) queries. This
paper shows that by replacing the selective inversions by selective phase
shifts of Pi/3, the algorithm gets transformed into something similar to a
classical search algorithm. Just like classical search algorithms this
algorithm has a fixed point in state-space toward which it preferentially
converges. In contrast, the original quantum search algorithm moves uniformly
in a two-dimensional state space. This feature leads to robust search
algorithms and also to conceptually new schemes for error correction.


title: Markovian feedback to control continuous variable entanglement

abstract:
  We present a model to realize quantum feedback control of continuous variable
entanglement. It consists of two interacting bosonic modes subject to amplitude
damping and achieving entangled Gaussian steady state. The possibility to
greatly improve the degree of entanglement by means of Markovian (direct)
feedback is then shown.


title: Decoherence of multi-dimensional entangled coherent states

abstract:
  For entangled states of light both the amount of entanglement and the
sensitivity to noise generally increase with the number of photons in the
state. The entanglement-sensitivity tradeoff is investigated for a particular
set of states, multi-dimensional entangled coherent states. Those states
possess an arbitrarily large amount of entanglement $E$ provided the number of
photons is at least of order $2^{2E}$. We calculate how fast that entanglement
decays due to photon absorption losses and how much entanglement is left. We
find that for very small losses the amount of entanglement lost is equal to
$2/\log(2)\approx 2.89$ ebits per absorbed photon, irrespective of the amount
of pure-state entanglement $E$ one started with. In contrast, for larger losses
it tends to be the remaining amount of entanglement that is independent of $E$.
This may provide a useful strategy for creating states with a fixed amount of
entanglement.


title: Elliptical orbits in the Bloch sphere

abstract:
  As is well known, when an SU(2) operation acts on a two-level system, its
Bloch vector rotates without change of magnitude. Considering a system composed
of two two-level systems, it is proven that for a class of nonlocal
interactions of the two subsystems including \sigma_i\otimes\sigma_j (with i,j
\in {x,y,z}) and the Heisenberg interaction, the geometric description of the
motion is particularly simple: each of the two Bloch vectors follows an
elliptical orbit within the Bloch sphere. The utility of this result is
demonstrated in two applications, the first of which bears on quantum control
via quantum interfaces. By employing nonunitary control operations, we extend
the idea of controllability to a set of points which are not necessarily
connected by unitary transformations. The second application shows how the
orbit of the coherence vector can be used to assess the entangling power of
Heisenberg exchange interaction.


title:
Influence of relaxation on propagation, storage and retrieving of light
  pulses in electromagnetically induced transparency medium

abstract:
  By solving the self-consistent system of Maxwell and density matrix equations
to the first order with respect to nonadiabaticity, we obtain an analytical
solution for the probe pulse propagation. The conditions for efficient storage
of light are analyzed. The necessary conditions for optical propagation
distance has been obtained.


title: Convergence Conditions for Random Quantum Circuits

abstract:
  Efficient methods for generating pseudo-randomly distributed unitary
operators are needed for the practical application of Haar distributed random
operators in quantum communication and noise estimation protocols. We develop a
theoretical framework for analyzing pseudo-random ensembles generated through a
random circuit composition. We prove that the measure over random circuits
converges exponentially (with increasing circuit length) to the uniform (Haar)
measure on the unitary group and describe how the rate of convergence may be
calculated for specific applications.


title: Relativistic motion with linear dissipation

abstract:
  A general formalism for obtaining the Lagrangian and Hamiltonian for a one
dimensional dissipative system is developed. The formalism is illustrated by
applying it to the case of a relativistic particle with linear dissipation. The
relativistic wave equation is solved for a free particle with linear
dissipation.


title:
On the Electric Charge Quantization from the Dirac-Aharonov-Bohm
  Potential

abstract:
  The purpose of this paper is to show that, under certain restrictions, we can
take a Dirac-Aharonov-Bohm potential as a pure gauge field. We argue that a
modified quantization condition comes out for the electric charge that may open
up the way for the understanding of fractional charges. One does not need any
longer to rely on the existence of a magnetic monopole to justify electric
charge quantization.


title: On the Coherent State Path Integral for Linear Systems

abstract:
  We present a computation of the coherent state path integral for a generic
linear system using ``functional methods'' (as opposed to discrete time
approaches). The Gaussian phase space path integral is formally given by a
determinant built from a first-order differential operator with coherent state
boundary conditions. We show how this determinant can be expressed in terms of
the symplectic transformation generated by the (in general, time-dependent)
quadratic Hamiltonian for the system. We briefly discuss the conditions under
which the coherent state path integral for a linear system actually exists. A
necessary -- but not sufficient -- condition for existence of the path integral
is that the symplectic transformation generated by the Hamiltonian is
(unitarily) implementable on the Fock space for the system.


title:
Extended statistical modeling under symmetry; the link toward quantum
  mechanics

abstract:
  We derive essential elements of quantum mechanics from a parametric structure
extending that of traditional mathematical statistics. The basic setting is a
set $\mathcal{A}$ of incompatible experiments, and a transformation group $G$
on the cartesian product $\Pi$ of the parameter spaces of these experiments.
The set of possible parameters is constrained to lie in a subspace of $\Pi$, an
orbit or a set of orbits of $G$. Each possible model is then connected to a
parametric Hilbert space. The spaces of different experiments are linked
unitarily, thus defining a common Hilbert space $\mathbf{H}$. A state is
equivalent to a question together with an answer: the choice of an experiment
$a\in\mathcal{A}$ plus a value for the corresponding parameter. Finally,
probabilities are introduced through Born's formula, which is derived from a
recent version of Gleason's theorem. This then leads to the usual formalism of
elementary quantum mechanics in important special cases. The theory is
illustrated by the example of a quantum particle with spin.


title: Neutron wave packet tomography

abstract:
  A tomographic technique is introduced in order to determine the quantum state
of the center of mass motion of neutrons. An experiment is proposed and
numerically analyzed.


title:
Calculating the hydrogen molecule ion using the two particle
  Schr"odinger equation

abstract:
  We calculate the hydrogen molecule ion from the two particle Schr"odinger
equation. Therefore a very simple two particle basis set is chosen. We suggest
this ansatz to be used to solve the "two electron one phonon" three particle
wave-function of a BCS superconductor. Possibly it can give hints for high
temperature superconductors.


title: Hong-Ou-Mandel interferometer with cavities: theory

abstract:
  We study the number of coincidences in a Hong-Ou-Mandel interferometer exit
whose arms have been supplemented with the addition of one or two optical
cavities. The fourth-order correlation function at the beam-splitter exit is
calculated. In the regime where the cavity length are larger than the
one-photon coherence length, photon coalescence and anti-coalescence
interference is observed. Feynman's path diagrams for the indistinguishable
processes that lead to quantum interference are presented. As application for
the Hong-Ou-Mandel interferometer with two cavities, it is discussed the
construction of an optical XOR gate.


title: Continuity bounds on the quantum relative entropy

abstract:
  The quantum relative entropy is frequently used as a distance, or
distinguishability measure between two quantum states. In this paper we study
the relation between this measure and a number of other measures used for that
purpose, including the trace norm distance. More precisely, we derive lower and
upper bounds on the relative entropy in terms of various distance measures for
the difference of the states based on unitarily invariant norms. The upper
bounds can be considered as statements of continuity of the relative entropy
distance in the sense of Fannes. We employ methods from optimisation theory to
obtain bounds that are as sharp as possible.


title: Violation of the entropic area law for Fermions

abstract:
  We investigate the scaling of the entanglement entropy in an infinite
translational invariant Fermionic system of any spatial dimension. The states
under consideration are ground states and excitations of tight-binding
Hamiltonians with arbitrary interactions. We show that the entropy of a finite
region typically scales with the area of the surface times a logarithmic
correction. Thus, in contrast to analogous Bosonic systems, the entropic area
law is violated for Fermions. The relation between the entanglement entropy and
the structure of the Fermi surface is discussed, and it is proven, that the
presented scaling law holds whenever the Fermi surface is finite. This is in
particular true for all ground states of Hamiltonians with finite range
interactions.


title: Statistical Properties of Quantum Graph Spectra

abstract:
  A general analytical approach to the statistical description of quantum graph
spectra based on the exact periodic orbit expansions of quantum levels is
discussed. The exact and approximate expressions obtained in \cite{Anima} for
the probability distribution functions using the spectral hierarchy method are
analyzed. In addition, the mechanism of appearance of the universal statistical
properties of spectral fluctuations of quantum-chaotic systems is considered in
terms of the semiclassical theory of periodic orbits.


title:
Tensor products of convex sets and the volume of separable states on N
  qudits

abstract:
  This note deals with estimating the volume of the set of separable mixed
quantum states when the dimension of the state space grows to infinity. This
has been studied recently for qubits; here we consider larger particles and
conclude that, in all cases, the proportion of the states that are separable is
super-exponentially small in the dimension of the set. We also show that the
partial transpose criterion becomes imprecise when the dimension increases, and
that the lower bound $6^{-N/2}$ on the (Hilbert-Schmidt) inradius of the set of
separable states on N qubits obtained recently by Gurvits and Barnum is
essentially optimal. We employ standard tools of classical convexity,
high-dimensional probability and geometry of Banach spaces. One relatively
non-standard point is a formal introduction of the concept of projective tensor
products of convex bodies, and an initial study of this concept.
  PACS numbers: 03.65.Ud, 03.67.Mn, 03.65.Db, 02.40.Ft, 02.50.Cw
  MSC-class: 46B28, 47B10, 47L05, 52A38, 81P68


title: Quantum projection filter for a highly nonlinear model in cavity QED

abstract:
  Both in classical and quantum stochastic control theory a major role is
played by the filtering equation, which recursively updates the information
state of the system under observation. Unfortunately, the theory is plagued by
infinite-dimensionality of the information state which severely limits its
practical applicability, except in a few select cases (e.g. the linear Gaussian
case.) One solution proposed in classical filtering theory is that of the
projection filter. In this scheme, the filter is constrained to evolve in a
finite-dimensional family of densities through orthogonal projection on the
tangent space with respect to the Fisher metric. Here we apply this approach to
the simple but highly nonlinear quantum model of optical phase bistability of a
stongly coupled two-level atom in an optical cavity. We observe near-optimal
performance of the quantum projection filter, demonstrating the utility of such
an approach.


title: Inversion of Gamow's Formula and Inverse Scattering

abstract:
  We present a pedagogical description of the inversion of Gamow's tunnelling
formula and we compare it with the corresponding classical problem. We also
discuss the issue of uniqueness in the solution and the result is compared with
that obtained by the method of Gel'fand and Levitan. We hope that the article
will be a valuable source to students who have studied classical mechanics and
have some familiarity with quantum mechanics.


title: Resolution in rotation measurements

abstract:
  The limiting resolution in optical interferometry is set by the number of
photons used, with the functional dependence determined by the state of light
that is prepared. We consider the problem of measuring the rotation of a beam
of light about an optical axis and show how the limiting resolution depends on
the total number of quanta of orbital angular momentum carried by the light
beam.


title: Quantum Averages of Weak Values

abstract:
  We re-examine the status of the weak value of a quantum mechanical observable
as an objective physical concept, addressing its physical interpretation and
general domain of applicability. We show that the weak value can be regarded as
a \emph{definite} mechanical effect on a measuring probe specifically designed
to minimize the back-reaction on the measured system. We then present a new
framework for general measurement conditions (where the back-reaction on the
system may not be negligible) in which the measurement outcomes can still be
interpreted as \emph{quantum averages of weak values}. We show that in the
classical limit, there is a direct correspondence between quantum averages of
weak values and posterior expectation values of classical dynamical properties
according to the classical inference framework.


title:
Robust Hadamard gate for optical and ion trap holonomic quantum
  computers

abstract:
  We consider one possible implementation of Hadamard gate for optical and ion
trap holonomic quantum computers. The expression for its fidelity determining
the gate stability with respect to the errors in the single-mode squeezing
parameter control is analytically derived. We demonstrate by means of this
expression the cancellation of the squeezing control errors up to the fourth
order on their magnitude.


title: Generating qudits with d=3,4 encoded on two-photon states

abstract:
  We present an experimental method to engineer arbitrary pure states of qudits
with d=3,4 using linear optics and a single nonlinear crystal.


title: Physics of Factorization

abstract:
  The N distinct prime numbers that make up a composite number M allow
$2^{N-1}$ bi partioning into two relatively prime factors. Each such pair
defines a pair of conjugate representations. These pairs of conjugate
representations, each of which spans the M dimensional space are the familiar
complete sets of Zak transforms (J. Zak, Phys. Rev. Let.{\bf 19}, 1385 (1967))
which are the most natural representations for periodic systems. Here we show
their relevance to factorizations. An example is provided for the manifestation
of the factorization.


title: On the plasticity of nonlocal quantum correlations

abstract:
  The quantum correlations of two or more entangled particles present the
possibility of stronger-than-classical outcome coincidences. We investigate
two-partite correlations of spin one, three-half and higher quanta in a state
satisfying a uniqueness property in the sense that knowledge of an outcome of
one particle observable entails the certainty that, if this observable were
measured on the other particle(s) as well, the outcome of the measurement would
be a unique function of the outcome of the measurement performed. We also
investigate correlations of four spin one-half particles.


title: Programmable Quantum Networks with Pure States

abstract:
  Modern classical computing devices, except of simplest calculators, have von
Neumann architecture, i.e., a part of the memory is used for the program and a
part for the data. It is likely, that analogues of such architecture are also
desirable for the future applications in quantum computing, communications and
control. It is also interesting for the modern theoretical research in the
quantum information science and raises challenging questions about an
experimental assessment of such a programmable models. Together with some
progress in the given direction, such ideas encounter specific problems arising
from the very essence of quantum laws. Currently are known two different ways
to overcome such problems, sometime denoted as a stochastic and deterministic
approach. The presented paper is devoted to the second one, that is also may be
called the programmable quantum networks with pure states.
  In the paper are discussed basic principles and theoretical models that can
be used for the design of such nano-devices, e.g., the conditional quantum
dynamics, the Nielsen-Chuang "no-programming theorem, the idea of deterministic
and stochastic quantum gates arrays. Both programmable quantum networks with
finite registers and hybrid models with continuous quantum variables are
considered. As a basic model for the universal programmable quantum network
with pure states and finite program register is chosen a "Control-Shift"
quantum processor architecture with three buses introduced in earlier works. It
is shown also, that quantum cellular automata approach to the construction of
an universal programmable quantum computer often may be considered as the
particular case of such design.


title: Finite-time stochastic reduction models

abstract:
  A new energy-based stochastic extension of the Schrodinger equation for which
the wave function collapses after the passage of a finite amount of time is
proposed. An exact closed-form solution to the dynamical equation, valid for
all finite-dimensional quantum systems, is presented and used to verify
explicitly that reduction of the state vector to an energy eigenstate occurs. A
time-change technique is introduced to construct a `clock' variable that
relates the asymptotic and the finite-time collapse models by means of a
nonlinear transformation.


title: Nonlocality of single fermions - branches that borrow particles

abstract:
  An experiment performed in 2002 by Sciarrino et al. provided a simple proof
of the nonlocality of a single photon whose wave function is multi-branched.
The difference between this experiment and others similar, is that the
tester-particle used by Sciarrino to "feel" this nonlocality is another photon
identical to the tested one. Such an experiment be can in principle performed
with fermions too, and this is the case ivestigated in this article. The novel
phenomenon revealed by Sciarrino's experiment, is the particle "borrowing". If
a single particle is described by a two-branched wave function, then only one
of these branches produces a detection at a time, the other ranch remains
"silent". What happens in this experiment is that the silent branch "borrows" a
particle from another source, if available in the neighborhood, and also
produces a detection. To illustrate this feature more obviously, a modificaton
of Sciarrino's experiment is proposed. Two sources of particles are made
available in the neighborhood of the two branches. What then happens is that
each branch takes and populates itself with a particle from whichever source is
at hand.


title: Classical and Quantum Contents of Solvable Game Theory on Hilbert Space

abstract:
  A simple and general formulation of the quantum game theory is presented,
accommodating all possible strategies in the Hilbert space for the first time.
The theory is solvable for the two strategy quantum game, which is shown to be
equivalent to a family of classical games supplemented by quantum interference.
Our formulation gives a clear perspective to understand why and how quantum
strategies outmaneuver classical strategies. It also reveals novel aspects of
quantum games such as the stone-scissor-paper phase sub-game and the
fluctuation-induced moderation.

categories: quant-ph cond-mat.other math-ph math.MP nlin.CD nlin.SI physics.bio-ph


title: Entanglement Decay Versus Energy Change: A Model

abstract:
  We present a simple quantum open system to show quantitatively how
entanglement decoherence is related to the energy transfer between the system
of interest and its environment. Particularly, in the case of the exact
entanglement decoherence of two qubits, we find an upper bound for the energy
transfer between the two-qubit system and its environments.


title:
Solvability and PT-symmetry in a double-well model with point
  interactions

abstract:
  We show that and how point interactions offer one of the most suitable guides
towards a quantitative analysis of properties of certain specific non-Hermitian
(usually called PT-symmetric) quantum-mechanical systems. A double-well model
is chosen, an easy solvability of which clarifies the mechanisms of the
unavoided level crossing and of the spontaneous PT-symmetry breaking. The
latter phenomenon takes place at a certain natural boundary of the domain of
the "acceptable" parameters of the model. Within this domain the model mediates
a nice and compact explicit illustration of the not entirely standard
probabilistic interpretation of the physical bound states in the very recently
developed (so called PT symmetric or, in an alternative terminology,
pseudo-Hermitian) new, fairly exciting and very quickly developing branch of
Quantum Mechanics.


title: On Self-Dual Quantum Codes, Graphs, and Boolean Functions

abstract:
  A short introduction to quantum error correction is given, and it is shown
that zero-dimensional quantum codes can be represented as self-dual additive
codes over GF(4) and also as graphs. We show that graphs representing several
such codes with high minimum distance can be described as nested regular graphs
having minimum regular vertex degree and containing long cycles. Two graphs
correspond to equivalent quantum codes if they are related by a sequence of
local complementations. We use this operation to generate orbits of graphs, and
thus classify all inequivalent self-dual additive codes over GF(4) of length up
to 12, where previously only all codes of length up to 9 were known. We show
that these codes can be interpreted as quadratic Boolean functions, and we
define non-quadratic quantum codes, corresponding to Boolean functions of
higher degree. We look at various cryptographic properties of Boolean
functions, in particular the propagation criteria. The new aperiodic
propagation criterion (APC) and the APC distance are then defined. We show that
the distance of a zero-dimensional quantum code is equal to the APC distance of
the corresponding Boolean function. Orbits of Boolean functions with respect to
the {I,H,N}^n transform set are generated. We also study the peak-to-average
power ratio with respect to the {I,H,N}^n transform set (PAR_IHN), and prove
that PAR_IHN of a quadratic Boolean function is related to the size of the
maximum independent set over the corresponding orbit of graphs. A construction
technique for non-quadratic Boolean functions with low PAR_IHN is proposed. It
is finally shown that both PAR_IHN and APC distance can be interpreted as
partial entanglement measures.


abstract:
  These notes originated out of a set of lectures in Quantum Optics and Quantum
Information given by one of us (MGAP) at the University of Napoli and the
University of Milano. A quite broad set of issues are covered, ranging from
elementary concepts to current research topics, and from fundamental concepts
to applications. A special emphasis has been given to the phase space analysis
of quantum dynamics and to the role of Gaussian states in continuous variable
quantum information.


title: Optimization of Partial Search

abstract:
  Quantum Grover search algorithm can find a target item in a database faster
than any classical algorithm. One can trade accuracy for speed and find a part
of the database (a block) containing the target item even faster, this is
partial search. A partial search algorithm was recently suggested by Grover and
Radhakrishnan. Here we optimize it. Efficiency of the search algorithm is
measured by number of queries to the oracle. The author suggests new version of
Grover-Radhakrishnan algorithm which uses minimal number of queries to the
oracle. The algorithm can run on the same hardware which is used for the usual
Grover algorithm.


title:
On Approximately Symmetric Informationally Complete Positive
  Operator-Valued Measures and Related Systems of Quantum States

abstract:
  We address the problem of constructing positive operator-valued measures
(POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which
have an inner product close to uniform. This is motivated by the related
question of constructing symmetric informationally complete POVMs (SIC-POVMs)
for which the inner products are perfectly uniform. However, SIC-POVMs are
notoriously hard to construct and despite some success of constructing them
numerically, there is no analytic construction known. We present two
constructions of approximate versions of SIC-POVMs, where a small deviation
from uniformity of the inner products is allowed. The first construction is
based on selecting vectors from a maximal collection of mutually unbiased bases
and works whenever the dimension of the system is a prime power. The second
construction is based on perturbing the matrix elements of a subset of mutually
unbiased bases.
  Moreover, we construct vector systems in $\C^n$ which are almost orthogonal
and which might turn out to be useful for quantum computation. Our
constructions are based on results of analytic number theory.


title:
A Scheme of Generating and Spatially Separating Two-Component Entangled
  Atom Lasers

abstract:
  Entanglement of remote atom lasers is obtained via quantum state transfer
technique from lights to matter waves in a five-level $M$-type system. The
considered atom-atom collisions can yield an effective Kerr susceptibility for
this system and lead to the self- and cross- phase modulation between the two
output atom lasers. This effect results in generation of entangled states of
output fields. Particularly, under different conditions of space-dependent
control fields, the entanglement of atom lasers and of atom-light fields can be
obtained, respectively. Furthermore, based on the Bell-state measurement, an
useful scheme is proposed to spatially separate the generated entangled atom
lasers.


title:
Stochastic simulations of conditional states of partially observed
  systems, quantum and classical

abstract:
  In a partially observed quantum or classical system the information that we
cannot access results in our description of the system becoming mixed even if
we have perfect initial knowledge. That is, if the system is quantum the
conditional state will be given by a state matrix $\rho_r(t)$ and if classical
the conditional state will be given by a probability distribution $P_r(x,t)$
where $r$ is the result of the measurement. Thus to determine the evolution of
this conditional state under continuous-in-time monitoring requires an
expensive numerical calculation. In this paper we demonstrating a numerical
technique based on linear measurement theory that allows us to determine the
conditional state using only pure states. That is, our technique reduces the
problem size by a factor of $N$, the number of basis states for the system.
Furthermore we show that our method can be applied to joint classical and
quantum systems as arises in modeling realistic measurement.


title: The Episodic Time Interpretation of Reality

abstract:
  A notably enhanced comprehension of the underlying meaning of quantum
observations is achieved via a novel premise. Assessments, from first
principles, are made of unexamined presumptions that lie at the heart of both
conventional conceptions of the nature of physical existence and most
interpretations of Quantum Mechanics. An alternative hypothesis, termed
Episodic Time Inhabitation, is proposed to resolve major Quantum quandaries,
including the EPR paradox. A logical argument gedanken experiment demonstrates
that the conventional presumptions appear to create causal loops, and that
Episodic Time Inhabitation avoids them. A physically realizable version of the
gedanken experiment is outlined, and currently testable predictions for its
outcome are made. Consequences of the experiment are summarized and
ramifications of the hypothesis are discussed.


title: Scalable Noise Estimation with Random Unitary Operators

abstract:
  We describe a scalable stochastic method for the experimental measurement of
generalized fidelities characterizing the accuracy of the implementation of a
coherent quantum transformation. The method is based on the motion reversal of
random unitary operators. In the simplest case our method enables direct
estimation of the average gate fidelity. The more general fidelities are
characterized by a universal exponential rate of fidelity loss. In all cases
the measurable fidelity decrease is directly related to the strength of the
noise affecting the implementation -- quantified by the trace of the
superoperator describing the non--unitary dynamics. While the scalability of
our stochastic protocol makes it most relevant in large Hilbert spaces (when
quantum process tomography is infeasible), our method should be immediately
useful for evaluating the degree of control that is achievable in any prototype
quantum processing device. By varying over different experimental arrangements
and error-correction strategies additional information about the noise can be
determined.


title: Calculation of Hydrogenic Bethe Logarithms for Rydberg States

abstract:
  We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all
states with principal quantum numbers n <= 200. While, in principle, the
calculation of the Bethe logarithm is a rather easy computational problem
involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom,
certain calculational difficulties affect highly excited states, and in
particular states for which the principal quantum number is much larger than
the orbital angular momentum quantum number. Two evaluation methods are
contrasted. One of these is based on the calculation of the principal value of
a specific integral over a virtual photon energy. The other method relies
directly on the spectral representation of the Schroedinger-Coulomb propagator.
Selected numerical results are presented. The full set of values is available
at quant-ph/0504002.


title: Bethe Logarithms for Rydberg States: Numerical Values for n <= 200

abstract:
  This document provides reference data for all Bethe logarithms of hydrogenic
bound states with principal quantum numbers n <= 200.


title: Eavesdropping without quantum memory

abstract:
  In quantum cryptography the optimal eavesdropping strategy requires that the
eavesdropper uses quantum memories in order to optimize her information. What
happens if the eavesdropper has no quantum memory? It is shown that the best
strategy is actually to adopt the simple intercept/resend strategy.


title:
No-Switching Quantum Key Distribution using Broadband Modulated Coherent
  Light

abstract:
  We realize an end-to-end no-switching quantum key distribution protocol using
continuous-wave coherent light. We encode weak broadband Gaussian modulations
onto the amplitude and phase quadratures of light beams at the Shannon's
information limit. Our no-switching protocol achieves high secret key rate via
a post-selection protocol that utilizes both quadrature information
simultaneously. We establish a secret key rate of 25 Mbits/s for a lossless
channel and 1 kbit/s, per 17 MHz of detected bandwidth, for 90% channel loss.
Since our scheme is truly broadband, it can potentially deliver orders of
magnitude higher key rates by extending the encoding bandwidth with higher-end
telecommunication technology.


title: Spin squeezing inequalities and entanglement of $N$ qubit states

abstract:
  We derive spin squeezing inequalities that generalize the concept of the spin
squeezing parameter and provide necessary and sufficient conditions for genuine
2-, or 3- qubit entanglement for symmetric states, and sufficient condition for
general states of $N$ qubits. Our inequalities have a clear physical
interpretation as entanglement witnesses, can be relatively easy measured, and
are given by complex, but {\it elementary} expressions.


title: On the KK system as two-kaons system

abstract:
  The time evolution of the KK system as a two-qubit system is given. The
effect which is interpreted as CP violation in neutral kaon decays is explained
via violation of quantum correlations during time evolution of the KK system as
two-kaons system and description is via Yang-Baxterization and unitary time
dependent R-matrices to con- struct Hamiltonian, determining the time evolution
of two-kaons sys- tem. The nonseparability ideas and criterion can be extended
on all mixing state-antistate system and all CP violation cases in particle
physics.


title: Probabilistic Model--Checking of Quantum Protocols

abstract:
  We establish fundamental and general techniques for formal verification of
quantum protocols. Quantum protocols are novel communication schemes involving
the use of quantum-mechanical phenomena for representation, storage and
transmission of data. As opposed to quantum computers, quantum communication
systems can and have been implemented using present-day technology; therefore,
the ability to model and analyse such systems rigorously is of primary
importance.
  While current analyses of quantum protocols use a traditional mathematical
approach and require considerable understanding of the underlying physics, we
argue that automated verification techniques provide an elegant alternative. We
demonstrate these techniques through the use of PRISM, a probabilistic
model-checking tool. Our approach is conceptually simpler than existing proofs,
and allows us to disambiguate protocol definitions and assess their properties.
It also facilitates detailed analyses of actual implemented systems. We
illustrate our techniques by modelling a selection of quantum protocols (namely
superdense coding, quantum teleportation, and quantum error correction) and
verifying their basic correctness properties. Our results provide a foundation
for further work on modelling and analysing larger systems such as those used
for quantum cryptography, in which basic protocols are used as components.


title: Communication complexity of remote state preparation with entanglement

abstract:
  We consider the problem of remote state preparation recently studied in
several papers. We study the communication complexity of this problem, in the
presence of entanglement and in the scenario of single use of the channel.


title:
Representations of Monomiality Principle with Sheffer-type Polynomials
  and Boson Normal Ordering

abstract:
  We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1
in terms of ladder operators acting in the space of Sheffer-type polynomials.
Thus we establish a link between the monomiality principle and the umbral
calculus. We use certain operator identities which allow one to evaluate
explicitly special boson matrix elements between the coherent states. This
yields a general demonstration of boson normal ordering of operator functions
linear in either creation or annihilation operators. We indicate possible
applications of these methods in other fields.


title: Quantum Games and Programmable Quantum Systems

abstract:
  Attention to the very physical aspects of information characterizes the
current research in quantum computation, quantum cryptography and quantum
communication. In most of the cases quantum description of the system provides
advantages over the classical approach. Game theory, the study of decision
making in conflict situation has already been extended to the quantum domain.
We would like to review the latest development in quantum game theory that is
relevant to information processing. We will begin by illustrating the general
idea of a quantum game and methods of gaining an advantage over
  "classical opponent". Then we review the most important game theoretical
aspects of quantum information processing. On grounds of the discussed
material, we reason about possible future development of quantum game theory
and its impact on information processing and the emerging information society.
The idea of quantum artificial intelligence is explained.


title: Hidden Variables and the Large-Scale Structure of Spacetime

abstract:
  We discuss how to embed quantum nonlocality in an approximately classical
spacetime background, a question which must be answered irrespective of any
underlying microscopic theory of spacetime. We argue that, in deterministic
hidden-variables theories, the choice of spacetime kinematics should be
dictated by the properties of generic non-equilibrium states, which allow
nonlocal signalling. Such signalling provides an operational definition of
absolute simultaneity, which may naturally be associated with a preferred
foliation of classical spacetime. The argument applies to any deterministic
hidden-variables theory, and to both flat and curved spacetime backgrounds. We
include some critical discussion of Einstein's 1905 'operational' approach to
relativity, and compare it with that of Poincare.


title: Quantum search algorithms

abstract:
  We review some of quantum algorithms for search problems: Grover's search
algorithm, its generalization to amplitude amplification, the applications of
amplitude amplification to various problems and the recent quantum algorithms
based on quantum walks.


title: Quantum entanglement and wedge product

abstract:
  In this paper, I will derive a measure of entanglement that coincides with
the generalized concurrence for a general pure bi-and three-partite state based
on wedge product. I will show that a further generalization of this idea to a
general pure multipartite state with more than three subsystems will fail to
quantify entanglement, but it defines the set of separable state for such
composite state.