title: From Fermat's last theorem to the quantum computer

abstract:
  Despite of an active work of many researchers in the theory of quantum
computations, this area still saves some mysterious charm. It is already an
almost common idea, that maybe many fashionable current projects will fade in
future, but some absolutely unpredictable applications appear instead. Why such
optimistic predictions are legal here, despite of an extreme difficulty to
suggest each one new promising quantum algorithm or realistic "industrial"
application? One reason -- is very deep contents of this area. It maybe only an
extremely unlucky occasion, if such a fundamental thing won't supply us with
some bright insights and serious new applications. A sign of such nontrivial
contents of a theory -- are unexpected links between different branches of our
knowledge. In the present paper is mentioned one such link -- between
application of Weyl quantization in the theory of quantum computations and
abstract mathematical constructions born in mid of XIX century due to
unsuccessful tries to prove Fermat's last theorem.


title: Quantum wave packet revivals in circular billiards

abstract:
  We examine the long-term time-dependence of Gaussian wave packets in a
circular infinite well (billiard) system and find that there are approximate
revivals. For the special case of purely $m=0$ states (central wave packets
with no momentum) the revival time is $T_{rev}^{(m=0)} = 8\mu R^2/\hbar \pi$,
where $\mu$ is the mass of the particle, and the revivals are almost exact. For
all other wave packets, we find that $T_{rev}^{(m \neq 0)} = (\pi^2/2)
T_{rev}^{(m=0)} \approx 5T_{rev}^{(m=0)}$ and the nature of the revivals
becomes increasingly approximate as the average angular momentum or number of
$m \neq 0$ states is/are increased. The dependence of the revival structure on
the initial position, energy, and angular momentum of the wave packet and the
connection to the energy spectrum is discussed in detail. The results are also
compared to two other highly symmetrical 2D infinite well geometries with exact
revivals, namely the square and equilateral triangle billiards. We also show
explicitly how the classical periodicity for closed orbits in a circular
billiard arises from the energy eigenvalue spectrum, using a WKB analysis.


title: Optical Schemes for Quantum Computation in Quantum Dot Molecules

abstract:
  We give three methods for entangling quantum states in quantum dots. We do
this by showing how to tailor the resonant energy (Foerster-Dexter) transfer
mechanisms and the biexciton binding energy in a quantum dot molecule. We
calculate the magnitude of these two electrostatic interactions as a function
of dot size, interdot separation, material composition, confinement potential
and applied electric field by using an envelope function approximation in a
two-cuboid dot molecule. In the first implementation, we show that it is
desirable to suppress the Foerster coupling and to create entanglement by using
the biexciton energy alone. We show how to perform universal quantum logic in a
second implementation which uses the biexciton energy together with
appropriately tuned laser pulses: by selecting appropriate materials parameters
high fidelity logic can be achieved. The third implementation proposes
generating quantum entanglement by switching the Foerster interaction itself.
We show that the energy transfer can be fast enough in certain dot structures
that switching can occur on a timescale which is much less than the typical
decoherence times.


title: Geometric Phase in a Bose-Einstein Josephson Junction

abstract:
  We calculate the geometric phase associated with the time evolution of the
wave function of a Bose-Einstein condensate system in a double-well trap by
using a model for tunneling between the wells. For a cyclic evolution, this
phase is shown to be half the solid angle subtended by the evolution of a unit
vector whose z component and azimuthal angle are given by the population
difference and phase difference between the two condensates. For a non-cyclic
evolution an additional phase term arises. We show that the geometric phase can
also be obtained by mapping the tunneling equations onto the equations os a
space curve. The importance of a geometric phase in the context of some recent
experiments is pointed out.


title:
Lower bounds on the entanglement of formation for general Gaussian
  states

abstract:
  We derive two lower bounds on entanglement of formation for arbitrary mixed
Gaussian states by two distinct methods. To achieve the first one we use a
local measurement procedure derived by Giedke et al [Quantum Inf. and Comp.
vol.1, 79 (2001)] that symmetrizes a general Gaussian state and the fact that
entanglement cannot increase under local operations and classical
communications. The second one is obtained via a generalization to mixed states
of an interesting result derived by Giedke et al [quant-ph/0304042], who show
that squeezed states are those that, for a fixed amount of entanglement,
maximize Einstein-Podolsky-Rosen-like correlations.


title: On Quantum Operations as Quantum States

abstract:
  We formalize the correspondence between quantum states and quantum operations
isometrically, and harness its consequences. This correspondence was already
implicit in the various proofs of the operator sum representation of Completely
Positive-preserving linear maps; we go further and show that all of the
important theorems concerning quantum operations can be derived directly from
those concerning quantum states. As we do so the discussion first provides an
elegant and original review of the main features of quantum operations. Next
(in the second half of the paper) we find more results stemming from our
formulation of the correspondence. Thus we provide a factorizability condition
for quantum operations, and give two novel Schmidt-type decompositions of
bipartite pure states. By translating the composition law of quantum
operations, we define a group structure upon the set of totally entangled
states. The question whether the correspondence is merely mathematical or can
be given a physical interpretation is addressed throughout the text: we provide
formulae which suggest quantum states inherently define a quantum operation
between two of their subsystems, and which turn out to have applications in
quantum cryptography. Keywords: Kraus, CP-maps, superoperators, extremality,
trace-preserving, factorizable, triangular.


title:
Enhanced single-photon emission from a quantum dot in a micropost
  microcavity

abstract:
  We demonstrate a single-photon source based on a quantum dot in a micropost
microcavity that exhibits a large Purcell factor together with a small
multi-photon probability. For a quantum dot on resonance with the cavity, the
spontaneous emission rate is increased by a factor of five, while the
probability to emit two or more photons in the same pulse is reduced to 2%
compared to a Poisson-distributed source of the same intensity. In addition to
the small multi-photon probability, such a strong Purcell effect is important
in a single-photon source for improving the photon outcoupling efficiency and
the single-photon generation rate, and for bringing the emitted photon pulses
closer to the Fourier transform limit.


title: Measurement, Trace, Information Erasure and Entropy

abstract:
  We show that both information erasure process and trace process can be
realized by projective measurement. And a partial trace operation consists to a
projective measurement on a subsystem. We show that a nonunitary operation will
destroy the wave-behavior of a particle. We give a quantum manifestation of
Maxwell's demon and give a quantum manifestation of the second law of
therodynamics. We show that, considering the law of memontum-energy
conversation, the evolution of a closed system should be unitary and the von
Neumann entropy of the closed quantum system should be least.


title:
Faithful remote state preparation using finite classical bits and a
  non-maximally entangled state

abstract:
  We present many ensembles of states that can be remotely prepared by using
minimum classical bits from Alice to Bob and their previously shared entangled
state and prove that we have found all the ensembles in two-dimensional case.
Furthermore we show that any pure quantum state can be remotely and faithfully
prepared by using finite classical bits from Alice to Bob and their previously
shared nonmaximally entangled state though no faithful quantum teleportation
protocols can be achieved by using a nonmaximally entangled state.


title:
Characterizing the spin state of an atomic ensemble using the
  magneto-optical resonance method

abstract:
  Quantum information protocols utilizing atomic ensembles require preparation
of a coherent spin state (CSS) of the ensemble as an important starting point.
We investigate the magneto-optical resonance method for characterizing a spin
state of cesium atoms in a paraffin coated vapor cell. Atoms in a constant
magnetic field are subject to an off-resonant laser beam and an RF magnetic
field. The spectrum of the Zeeman sub-levels, in particular the weak quadratic
Zeeman effect, enables us to measure the spin orientation, the number of atoms,
and the transverse spin coherence time. Notably the use of 894nm pumping light
on the D1-line, ensuring the state F=4, m_F=4 to be a dark state, helps us to
achieve spin orientation of better than 98%. Hence we can establish a CSS with
high accuracy which is critical for the analysis of the entangled states of
atoms.


title: Quantization of the stag hunt game and the Nash equilibrilum

abstract:
  In this paper I quantize the stag hunt game in the framework proposed by
Marinatto and Weber which, is introduced to quantize the Battle of the Sexes
game and gives a general quntization scheme of various game theories. Then I
discuss the Nash equibilium solution in the cases of which starting strategies
are taken in both non entangled state and entangled state and uncover the
structure of Nash Equilibrium solutions and compare the case of the Battle of
the Sexes game. Since the game has 4 parameters in the payoff matrix has rather
rich structure than the Battle of the Sexes game with 3-parameters in the
payoff matrix, the relations of the magnitude of these payoff values in Nash
Equilibriums are much involuved. This structure is uncovered completly and it
is found that the best strategy which give the maximal sum of the payoffs of
both players strongly depends on the initial quntum state. As the bonus of the
formulation the stag hunt game with four parameters we can discuss various
types of symmetric games played by two players by using the latter formulation,
i.e. Chicken game. As result some common properties are found between them and
the stag hunt game. Lastly a little remark is made on Prisoner's Dillemma.


title:
Loss of the sensitivity of a gravitational wave detector due to
  temperature

abstract:
  Using an explicit solution for the Schr\"odinger equation describing the
model of the gravitational wave detector (LIGO-project), we prove that the SQL
(standard quantum limit) for dimensionless amplitude for gravitational
perturbations of metric exceeds $10^{-19}$ at temperature 100K.


title: Multipole interaction between atoms and their photonic environment

abstract:
  Macroscopic field quantization is presented for a nondispersive photonic
dielectric environment, both in the absence and presence of guest atoms.
Starting with a minimal-coupling Lagrangian, a careful look at functional
derivatives shows how to obtain Maxwell's equations before and after choosing a
suitable gauge. A Hamiltonian is derived with a multipolar interaction between
the guest atoms and the electromagnetic field. Canonical variables and fields
are determined and in particular the field canonically conjugate to the vector
potential is identified by functional differentiation as minus the full
displacement field. An important result is that inside the dielectric a dipole
couples to a field that is neither the (transverse) electric nor the
macroscopic displacement field. The dielectric function is different from the
bulk dielectric function at the position of the dipole, so that local-field
effects must be taken into account.


title: Tests of quantum-vacuum geometric phases via Casimir's effect

abstract:
  An experimentally feasible realization of testing quantum-vacuum geometric
phases of photons by using a gyrotropic-medium optical fibre via Casimir's
effect is proposed.


title:
Spatial correlations of vacuum fluctuations and the Casimir-Polder
  potential

abstract:
  We calculate the Casimir-Polder intermolecular potential using an effective
Hamiltonian recently introduced. We show that the potential can be expressed in
terms of the dynamical polarizabilities of the two atoms and the equal-time
spatial correlation of the electric field in the vacuum state. This gives
support to an interesting physical model recently proposed in the literature,
where the potential is obtained from the classical interaction between the
instantaneous atomic dipoles induced and correlated by the vacuum fluctuations.
Also, the results obtained suggest a more general validity of this intuitive
model, for example when external boundaries or thermal fields are present.


title: Decoherence as a Probe of Coherent Quantum Dynamics

abstract:
  The effect of decoherence, induced by spontaneous emission, on the dynamics
of cold atoms periodically kicked by an optical lattice is experimentally and
theoretically studied. Ideally, the mean energy growth is essentially
unaffected by weak decoherence, but the resonant momentum distributions are
fundamentally altered. It is shown that experiments are inevitably sensitive to
certain nontrivial features of these distributions, in a way that explains the
puzzle of the observed enhancement of resonances by decoherence [Phys. Rev.
Lett. 87, 074102 (2001)]. This clarifies both the nature of the coherent
evolution, and the way in which decoherence disrupts it.


title:
Quantum mechanics of the two-dimensional circular billiard plus baffle
  system and half-integral angular momentum

abstract:
  We examine the quantum mechanical eigensolutions of the two-dimensional
infinite well or quantum billiard system consisting of a circular boundary with
an infinite barrier or baffle along a radius. Because of the change in boundary
conditions, this system includes quantized angular momentum values
corresponding to half-integral multiples of $\hbar/2$. We discuss the resulting
energy eigenvalue spectrum and visualize some of the novel energy eigenstates
found in this system. We also discuss the density of energy eigenvalues,
$N(E)$, comparing this system to the standard circular well. These two billiard
geometries have the same area (A=$\pi R^2$), but different perimeters ($P=2\pi
R$ versus $(2\pi + 2) R$), and we compare both cases to fits of $N(E)$ which
make use of purely geometric arguments involving only $A$ and $P$. We also
point out connections between the angular solutions of this system and the
familiar pedagogical example of the one-dimensional infinite well plus
$\delta$-function potential.


title: Dynamics of entanglement in quantum computers with imperfections

abstract:
  The dynamics of the pairwise entanglement in a qubit lattice in the presence
of static imperfections exhibits different regimes. We show that there is a
transition from a perturbative region, where the entanglement is stable against
imperfections, to the ergodic regime, in which a pair of qubits becomes
entangled with the rest of the lattice and the pairwise entanglement drops to
zero. The transition is almost independent of the size of the quantum computer.
We consider both the case of an initial maximally entangled and separable
state. In this last case there is a broad crossover region in which the
computer imperfections can be used to create a significant amount of pairwise
entanglement.


title: Quantum Process

abstract:
  The exact scattering solutions of the Klein-Gordon equation in cylindrically
symmetric field are constructed as eigenfunctions of a complete set of
commuting operators. The matrix elements and the corresponding differential
scattering cross-section are calculated. Properties of the pair production at
various limits are discussed.


title: Minimum-error discrimination between a pure and a mixed two-qubit state

abstract:
  The problem of discriminating with minimum error between two mixed quantum
states is reviewed, with emphasize on the detection operators necessary for
performing the measurement. An analytical result is derived for the minimum
probability of errors in deciding whether the state of a quantum system is
either a given pure state or a uniform statistical mixture of any number of
mutually orthogonal states. The result is applied to two-qubit states, and the
minimum error probabilities achievable by collective and local measurements on
the qubits are compared.


title: Decoherence in a driven three-level system

abstract:
  Dissipation and decoherence, and the evolution from pure to mixed states in
quantum physics are handled through master equations for the density matrix.
Master equations such as the Lindblad equation preserve the trace of this
matrix. Viewing them as first-order time-dependent operator equations for the
elements of the density matrix, a unitary integration procedure can be adapted
to solve for these matrix elements. A simple model for decoherence preserves
the hermiticity of the density matrix. A single, classical Riccati equation is
the only one requiring numerical handling to obtain a full solution of the
quantum evolution. The procedure is general, valid for any number of levels,
but is illustrated here for a three-level system with two driving fields. For
various choices of the initial state, we study the evolution of the system as a
function of the amplitudes, relative frequencies and phases of the driven
fields, and of the strength of the decoherence. The monotonic growth of the
entropy is followed as the system evolves from a pure to a mixed state. An
example is provided by the $n=3$ states of the hydrogen atom in a
time-dependent electric field, such degenerate manifolds affording an
analytical solution.


title: Decoherence free algebra

abstract:
  We consider the decoherence free subalgebra which satisfies the minimal
condition introduced by Alicki. We show the manifest form of it and relate the
subalgebra with the Kraus representation. The arguments also provides a new
proof for generalized L\"{u}ders theorem.


title:
Visualizing the collapse and revival of wavepackets in the infinite
  square well using expectation values

abstract:
  We investigate the short-, medium-, and long-term time dependence of wave
packets in the infinite square well. In addition to emphasizing the appearance
of wave packet revivals, i.e., situations where a spreading wave packet reforms
with close to its initial shape and width, we also examine in detail the
approach to the collapsed phase where the position-space probability density is
almost uniformly spread over the well. We focus on visualizing these phenomena
in both position- and momentum-space as well as by following the time-dependent
expectation values of and uncertainties in position and momentum. We discuss
the time scales for wave packet collapse, using both an autocorrelation
function analysis, as well as focusing on expectation values and find two
relevant time scales which describe different aspects of the decay phase. In an
Appendix, we briefly discuss wave packet revival and collapse in a more
general, one-dimensional power-law potential given by $V_{(k)}(x) = V_0|x/a|^k$
which interpolates between the case of the harmonic oscillator ($k=2$) and the
infinite well ($k=\infty$).


title:
Baseband Detection of Bistatic Electron Spin Signals in Magnetic
  Resonance Force Microscopy (MRFM)

abstract:
  In single spin Magnetic Resonance Force Microscopy (MRFM), the objective is
to detect the presence of an electron (or nuclear) spin in a sample volume by
measuring spin-induced attonewton forces using a micromachined cantilever. In
the OSCAR method of single spin MRFM, the spins are manipulated by an external
rf field to produce small periodic deviations in the resonant frequency of the
cantilever. These deviations can be detected by frequency demodulation followed
by conventional amplitude or energy detection. In this paper, we present an
alternative to these detection methods, based on optimal detection theory and
Gibbs sampling. On the basis of simulations, we show that our detector
outperforms the conventional amplitude and energy detectors for realistic MRFM
operating conditions. For example, to achieve a 10% false alarm rate and an 80%
correct detection rate our detector has an 8 dB SNR advantage as compared with
the conventional amplitude or energy detectors. Furthermore, at these detection
rates it comes within 4 dB of the omniscient matched-filter lower bound.


title: Two-way teleportation

abstract:
  A protocol for teleporting two qudits simultaneously in opposite directions
using a single pair of maximally entangled qudits is presented. This procedure
works provided that the product of dimensions of the two qudits to be
teleported does not exceed the dimension of the individual qudits in the
maximally entangled pair.


title: Appearance of Schrodinger Cat States in the Measurement Process

abstract:
  Although quantum mechanics is a mature theory, fundamental problems discussed
during its time of foundation have remained with us to this day. These problems
are centered on the problematic relation between the quantum and classical
worlds. The most famous element is the measurement problem, i.e., the
measurement of a quantum system by a classical apparatus, and the concomitant
phenomena of wave packet reduction, the appearance of probability, and the
problems related to Schr\"odinger cat states. A fundamental question in this
context is whether quantum mechanics can bootstrap itself to the classical
world: is quantum mechanics self-consistent, such that the measurement process
can be understood within quantum mechanics itself, or does this process require
additional elements from the realm outside of traditional quantum mechanics?
Here, we point to a problematic aspect in the traditional Schr\"odinger cat
argument which can be overcome through its extension with a proper macroscopic
preparation device; the deliberate creation of a cat state and its
identification then turns into a non-trivial problem requiring the
determination of the evolution of a quantum system entangled with a macroscopic
reservoir. We describe a new type of wave-function correlator testing for the
appearance of Schr\"odinger cat states and discuss its implications for
theories deriving the wave function collapse from a unitary evolution.


title: Entangling two atoms via spontaneous emission

abstract:
  We discuss the creation of entanglement between two two-level atoms in the
dissipative process of spontaneous emission. It is shown that spontaneous
emission can lead to a transient entanglement between the atoms even if the
atoms were prepared initially in an unentangled state. The amount of
entanglement created in the system is quantified by using two different
measures: concurrence and negativity. We find analytical formulas for the
evolution of concurrence and negativity in the system. We also find the
analytical relation between the two measures of entanglement. The system
consists of two two-level atoms which are separated by an arbitrary distance
$r_{12}$ and interact with each other via the dipole-dipole interaction, and
the antisymmetric state of the system is included throughout, even for small
inter-atomic separations, in contrast to the small sample model. It is shown
that for sufficiently large values of the dipole-dipole interaction initially
the entanglement exhibits oscillatory behaviour with considerable entanglement
in the peaks. For longer times the amount of entanglement is directly related
to the population of the slowly decaying antisymmetric state.


title:
Expectation value analysis of wave packet solutions for the quantum
  bouncer: short-term classical and long-term revival behavior

abstract:
  We discuss the time development of Gaussian wave packet solutions of the
quantum bouncer' (a quantum mechanical particle subject to a uniform downward
force, above an impermeable flat surface). We focus on the evaluation and
visualization of the expectation values and uncertainties of position and
momentum variables during a single quasi-classical period as well as during the
long term collapsed phase and several revivals. This approach complements
existing analytic and numerical analyses of this system, as well as being
useful for comparison with similar results for the harmonic oscillator and
infinite well cases.


title: Lamb Shift of Laser-Dressed Atomic States

abstract:
  We discuss radiative corrections to an atomic two-level system subject to an
intense driving laser field. It is shown that the Lamb shift of the
laser-dressed states, which are the natural state basis of the combined
atom-laser system, cannot be explained in terms of the Lamb shift received by
the atomic bare states which is usually observed in spectroscopic experiments.
In the final part, we propose an experimental scheme to measure these
corrections based on the incoherent resonance fluorescence spectrum of the
driven atom.


title: Dynamics of Entanglement in One-Dimensional Spin Systems

abstract:
  We study the dynamics of quantum correlations in a class of exactly solvable
Ising-type models. We analyze in particular the time evolution of initial Bell
states created in a fully polarized background and on the ground state. We find
that the pairwise entanglement propagates with a velocity proportional to the
reduced interaction for all the four Bell states. Singlet-like states are
favored during the propagation, in the sense that triplet-like states change
their character during the propagation under certain circumstances.
Characteristic for the anisotropic models is the instantaneous creation of
pairwise entanglement from a fully polarized state; furthermore, the
propagation of pairwise entanglement is suppressed in favor of a creation of
different types of entanglement. The ``entanglement wave'' evolving from a Bell
state on the ground state turns out to be very localized in space-time. Further
support to a recently formulated conjecture on entanglement sharing is given.


title: Quantum Cryptography in Practice

abstract:
  BBN, Harvard, and Boston University are building the DARPA Quantum Network,
the world's first network that delivers end-to-end network security via
high-speed Quantum Key Distribution, and testing that Network against
sophisticated eavesdropping attacks. The first network link has been up and
steadily operational in our laboratory since December 2002. It provides a
Virtual Private Network between private enclaves, with user traffic protected
by a weak-coherent implementation of quantum cryptography. This prototype is
suitable for deployment in metro-size areas via standard telecom (dark) fiber.
In this paper, we introduce quantum cryptography, discuss its relation to
modern secure networks, and describe its unusual physical layer, its
specialized quantum cryptographic protocol suite (quite interesting in its own
right), and our extensions to IPsec to integrate it with quantum cryptography.


title: Suppressing Weak Ising Couplings: Tailored Gates for Quantum Computation

abstract:
  I describe the use of techniques based on composite rotations to develop
controlled phase gates in which the effects of weak Ising couplings are
suppressed. A tailored composite phase gate is described which both suppresses
weak couplings and is relatively insensitive to systematic errors in the size
of strong couplings.


title: On Discrete Quasiprobability Distributions

abstract:
  We analyze quasi probability distributions in discrete phase space related to
the discrete Heisenberg-Weyl group. In particular, we discuss the relation
between the Discrete Wigner and Q- functions.


title: Environment Induced Entanglement in Markovian Dissipative Dynamics

abstract:
  We show that two, non interacting 2-level systems, immersed in a common bath,
can become mutually entangled when evolving according to a Markovian,
completely positive reduced dynamics.


title: Relating quantum privacy and quantum coherence: an operational approach

abstract:
  We describe how to achieve optimal entanglement generation and one-way
entanglement distillation rates by coherent implementation of a class of secret
key generation and secret key distillation protocols, respectively.
  This short paper is a high-level descrioption of our detailed papers [8] and
[10].


title: An Electron-Nucleon Double Spin Solid-State Quantum Computer

abstract:
  An electron-nucleon double spin(ENDOS) solid-state quantum computer scheme is
proposed. In this scheme, the qubits are the nuclear spins of phosphorus ion
implanted on the (111) surface of $^{28}$Si substrate. An $^{13}$C atom on a
scanning tunnelling probe tip is used both to complete single qubit and
two-qubit control-not operation, and single qubit measurement. The scheme does
not require interactions between qubits, and can accomplish two qubits without
the use of SWAP gate.
  This scheme is scalable, and can be implemented with present-day or
near-future technologies.


title: Parallel Quantum Computing in a Single Ensemble Quantum Computer

abstract:
  We propose a parallel quantum computing mode for ensemble quantum computer.
In this mode, some qubits can be in pure states while other qubits in mixed
states. It enables a single ensemble quantum computer to perform
$"$single-instruction-multi-data" type of parallel computation. In Grover's
algorithm and Shor's algorithm, parallel quantum computing can provide
additional speedup. In addition, it also makes a fuller use of qubit resources
in an ensemble quantum computer. As a result, some qubits discarded in the
preparation of an effective pure state in the Schulman-Varizani, and the
Cleve-DiVincenzo algorithms can be re-utilized.


title:
Visualizing classical and quantum probability densities for momentum
  using variations on familiar one-dimensional potentials

abstract:
  After briefly reviewing the definitions of classical probability densities
for position, $P_{CL}(x)$, and for momentum, $P_{CL}(p)$, we present several
examples of classical mechanical potential systems, mostly variations on such
familiar cases as the infinite well and the uniformly accelerated particle for
which the classical distributions can be easily derived and visualized. We
focus especially on a simple potential which interpolates between the symmetric
linear potential, $V(x) = F|x|$, and the infinite well, which can illustrate,
in a mathematically straightforward way, how the divergent, $\delta$-function
classical probability density for momentum for the infinite well can be easily
seen to arise. Such examples can help students understand the quantum
mechanical momentum-space wavefunction (and its corresponding probability
density) in much the same way that other semi-classical techniques, such as the
WKB approximation, can be used to visualize position-space wavefunctions.


title:
Uncertainty Relations for Noise and Disturbance in Generalized Quantum
  Measurements

abstract:
  Heisenberg's uncertainty relation for measurement noise and disturbance
states that any position measurement with noise epsilon brings the momentum
disturbance not less than hbar/2epsilon. This relation holds only for
restricted class of measuring apparatuses. Here, Heisenberg's uncertainty
relation is generalized to a relation that holds for all the possible quantum
measurements, from which conditions are obtained for measuring apparatuses to
satisfy Heisenberg's relation. In particular, every apparatus with the noise
and the disturbance statistically independent from the measured object is
proven to satisfy Heisenberg's relation. For this purpose, all the possible
quantum measurements are characterized by naturally acceptable axioms. Then, a
mathematical notion of the distance between probability operator valued
measures and observables is introduced and the basic properties are explored.
Based on this notion, the measurement noise and disturbance are naturally
defined for any quantum measurements in a model independent formulation. Under
this formulation, various uncertainty relations are also derived for
apparatuses with independent noise, independent disturbance, unbiased noise,
and unbiased disturbance as well as noiseless apparatuses and nondisturbing
apparatuses. Two models of position measurements are discussed to show that
Heisenberg's relation can be violated even by approximately repeatable position
measurements.


title: Numerical Analysis of the Capacities for Two-Qubit Unitary Operations

abstract:
  We present numerical results on the capacities of two-qubit unitary
operations for creating entanglement and increasing the Holevo information of
an ensemble. In all cases tested, the maximum values calculated for the
capacities based on the Holevo information are close to the capacities based on
the entanglement. This indicates that the capacities based on the Holevo
information, which are very difficult to calculate, may be estimated from the
capacities based upon the entanglement, which are relatively straightforward to
calculate.


title:
A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries
  and the Position Operator for Klein-Gordon Fields

abstract:
  Generalized parity (P), time-reversal (T), and charge-conjugation
(C)operators were initially definedin the study of the pseudo-Hermitian
Hamiltonians. We construct a concrete realization of these operators for
Klein-Gordon fields and show that in this realization PT and C operators
respectively correspond to the ordinary time-reversal and charge-grading
operations. Furthermore, we present a complete description of the quantum
mechanics of Klein-Gordon fields that is based on the construction of a Hilbert
space with a relativistically invariant, positive-definite, and conserved inner
product. In particular we offer a natural construction of a position operator
and the corresponding localized and coherent states. The restriction of this
position operator to the positive-frequency fields coincides with the
Newton-Wigner operator. Our approach does not rely on the conventional
restriction to positive-frequency fields. Yet it provides a consistent quantum
mechanical description of Klein-Gordon fields with a genuine probabilistic
interpretation.


title: Entanglement frustration for Gaussian states on symmetric graphs

abstract:
  We investigate the entanglement properties of multi-mode Gaussian states,
which have some symmetry with respect to the ordering of the modes. We show how
the symmetry constraints the entanglement between two modes of the system. In
particular, we determine the maximal entanglement of formation that can be
achieved in symmetric graphs like chains, 2d and 3d lattices, mean field models
and the platonic solids. The maximal entanglement is always attained for the
ground state of a particular quadratic Hamiltonian. The latter thus yields the
maximal entanglement among all quadratic Hamiltonians having the considered
symmetry.


title: Cloning of spin-coherent states

abstract:
  We consider optimal cloning of the spin coherent states in Hilbert spaces of
different dimensionality d. We give explicit form of optimal cloning
transformation for spin coherent states in the three-dimensional space,
analytical results for the fidelity of the optimal cloning in d=3 and d=4 as
well as numerical results for higher dimensions. In the low-dimensional case we
construct the corresponding completely positive maps and exhibit their
structure with the help of Jamiolkowski isomorphism. This allows us to
formulate some conjectures about the form of optimal coherent cloning CP maps
in arbitrary dimension.


title: Robust Control of Quantum Information

abstract:
  Errors in the control of quantum systems may be classified as unitary,
decoherent and incoherent. Unitary errors are systematic, and result in a
density matrix that differs from the desired one by a unitary operation.
Decoherent errors correspond to general completely positive superoperators, and
can only be corrected using methods such as quantum error correction.
Incoherent errors can also be described, on average, by completely positive
superoperators, but can nevertheless be corrected by the application of a
locally unitary operation that ``refocuses'' them. They are due to reproducible
spatial or temporal variations in the system's Hamiltonian, so that information
on the variations is encoded in the system's spatiotemporal state and can be
used to correct them. In this paper liquid-state nuclear magnetic resonance
(NMR) is used to demonstrate that such refocusing effects can be built directly
into the control fields, where the incoherence arises from spatial
inhomogeneities in the quantizing static magnetic field as well as the
radio-frequency control fields themselves. Using perturbation theory, it is
further shown that the eigenvalue spectrum of the completely positive
superoperator exhibits a characteristic spread that contains information on the
Hamiltonians' underlying distribution.


title:
Quantum mechanical analysis of the equilateral triangle billiard:
  periodic orbit theory and wave packet revivals

abstract:
  Using the fact that the energy eigenstates of the equilateral triangle
infinite well (or billiard) are available in closed form, we examine the
connections between the energy eigenvalue spectrum and the classical closed
paths in this geometry, using both periodic orbit theory and the short-term
semi-classical behavior of wave packets. We also discuss wave packet revivals
and show that there are exact revivals, for all wave packets, at times given by
$T_{rev} = 9 \mu a^2/4\hbar \pi$ where $a$ and $\mu$ are the length of one side
and the mass of the point particle respectively. We find additional cases of
exact revivals with shorter revival times for zero-momentum wave packets
initially located at special symmetry points inside the billiard. Finally, we
discuss simple variations on the equilateral
($60^{\circ}-60^{\circ}-60^{\circ}$) triangle, such as the half equilateral
($30^{\circ}-60^{\circ}-90^{\circ}$) triangle and other `foldings', which have
related energy spectra and revival structures.


title:
Unconditional preparation of entanglement between atoms in cascaded
  optical cavities

abstract:
  We propose a scheme to unconditionally entangle the internal states of atoms
trapped in separate high finesse optical cavities. The scheme uses the
technique of quantum reservoir engineering in a cascaded cavity QED setting,
and for ideal (lossless) coupling between the cavities generates an entangled
pure state. Highly entangled states are also shown to be possible for
realizable cavity QED parameters and with nonideal coupling.


title: Teleportation in a noisy environment: a quantum trajectories approach

abstract:
  We study the fidelity of quantum teleportation for the situation in which
quantum logic gates are used to provide the long distance entanglement required
in the protocol, and where the effect of a noisy environment is modeled by
means of a generalized amplitude damping channel. Our results demonstrate the
effectiveness of the quantum trajectories approach, which allows the simulation
of open systems with a large number of qubits (up to 24). This shows that the
method is suitable for modeling quantum information protocols in realistic
environments.


title: N Level System with RWA and Analytical Solutions Revisited

abstract:
  In this paper we consider a model of an atom with n energy levels interacting
with n(n-1)/2 external (laser) fields which is a natural extension of two level
system, and assume the rotating wave approximation (RWA) from the beginning. We
revisit some construction of analytical solutions (which correspond to Rabi
oscillations) of the model in the general case and examine it in detail in the
case of three level system.


title: Multipartite entanglement in 2 x 2 x n quantum systems

abstract:
  We classify multipartite entangled states in the 2 x 2 x n (n >= 4) quantum
system, for example the 4-qubit system distributed over 3 parties, under local
filtering operations. We show that there exist nine essentially different
classes of states, and they give rise to a five-graded partially ordered
structure, including the celebrated Greenberger-Horne-Zeilinger (GHZ) and W
classes of 3 qubits. In particular, all 2 x 2 x n-states can be
deterministically prepared from one maximally entangled state, and some
applications like entanglement swapping are discussed.


title: More on Exact $\CP$-Symmetric Quantum Mechanics

abstract:
  In this article, we discussed certain properties of non-Hermitian
$\CP$-symmetry Hamiltonian, and it is shown that a consistent physical theory
of quantum mechanics can be built on a ${\cal C} \CP$-symmetry Hamiltonian. In
particular, we show that these theories have unitary time evolution, and
conservation probability. Furthermore, transition from quantum mechanics to
classical mechanics is investigate and it is found that the Ehrenfest theorem
is satisfied.


title:
Quantization of the Optical Phase Space S^2 = {phi mod 2pi, I > 0} in
  Terms of the Group SO(1,2)

abstract:
  The problem of quantizing the canonical pair angle and action variables phi
and I is almost as old as quantum mechanics itself and since decades a strongly
debated but still unresolved issue in quantum optics. The present paper
proposes a new approach to the problem, namely quantization in terms of the
group SO(1,2): The crucial point is that the phase space S^2 = {phi mod 2pi,
I>0} has the global structure S^1 x R^+ (a simple cone) and cannot be quantized
in the conventional manner. As the group SO(1,2) acts appropriately on that
space its unitary representations of the positive discrete series provide the
correct quantum theoretical framework. The space S^2 has the conic structure of
an orbifold R^2/Z_2. That structure is closely related to the center Z_2 of the
symplectic group Sp(2,R). The basic variables on S^2 are the functions h_0 = I,
h_1 = I cosphi and h_2 = -I sinphi, the Poisson brackets of which obey the Lie
algebra so(1,2). In the quantum theory they are represented by self-adjoint
generators K_0, K_1 and K_2 of a unitary representation. A crucial prediction
is that the classical Pythagorean relation h_1^2+h_2^2 = h_0^2 may be violated
in the quantum theory. For each representation one can define 3 different types
of coherent states the complex phases of which can be "measured" by means of
K_1 and K_2 alone without introducing any new phase operators! The SO(1,2)
structure of optical squeezing and interference properties as well as that of
the harmonic oscillator are analyzed in detail. The new coherent states can be
used for the introduction of (Husimi type) Q and (Sudarshan-Glauber type) P
representations of the density operator. The 3 operators K_0, K_1 and K_2 are
fundamental in the sense that one can construct (composite) position and
momentum operators out of them!

categories: quant-ph hep-th math-ph math.MP physics.optics


title:
Wave packet construction in two-dimensional quantum billiards:
  Blueprints for the square, equilateral triangle, and circular cases

abstract:
  We present quasi-analytical and numerical calculations of Gaussian wave
packet solutions of the Schr\"odinger equation for two-dimensional infinite
well and quantum billiard problems with equilateral triangle, square, and
circular footprints. These cases correspond to N=3, N=4, and $N \to \infty$
regular polygonal billiards and infinite wells, respectively. In each case the
energy eigenvalues and wavefunctions are given in terms of familiar special
functions. For the first two systems, we obtain closed form expressions for the
expansion coefficients for localized Gaussian wavepackets in terms of the
eigenstates of the particular geometry. For the circular case, we discuss
numerical approaches. We use these results to discuss the short-time,
quasi-classical evolution in these geometries and the structure of wave packet
revivals. We also show how related half-well problems can be easily solved in
each of the three cases.


title: On Statistical Query Sampling and NMR Quantum Computing

abstract:
  We introduce a ``Statistical Query Sampling'' model, in which the goal of an
algorithm is to produce an element in a hidden set $Ssubseteqbit^n$ with
reasonable probability. The algorithm gains information about $S$ through
oracle calls (statistical queries), where the algorithm submits a query
function $g(cdot)$ and receives an approximation to $Pr_{x in S}[g(x)=1]$. We
show how this model is related to NMR quantum computing, in which only
statistical properties of an ensemble of quantum systems can be measured, and
in particular to the question of whether one can translate standard quantum
algorithms to the NMR setting without putting all of their classical
post-processing into the quantum system. Using Fourier analysis techniques
developed in the related context of {em statistical query learning}, we prove a
number of lower bounds (both information-theoretic and cryptographic) on the
ability of algorithms to produces an $xin S$, even when the set $S$ is fairly
simple. These lower bounds point out a difficulty in efficiently applying NMR
quantum computing to algorithms such as Shor's and Simon's algorithm that
involve significant classical post-processing. We also explicitly relate the
notion of statistical query sampling to that of statistical query learning.
  An extended abstract appeared in the 18th Aunnual IEEE Conference of
Computational Complexity (CCC 2003), 2003.
  Keywords: statistical query, NMR quantum computing, lower bound


title: Non-Transitive Quantum Games

abstract:
  Non-transitivity can arise in games with three or more strategies $A,B,C$,
when $A$ beats $B$, $B$ beats $C$, and $C$ beats $A$, ($A>B>C>A$). An example
is the children's game \textquotedblleft rock, scissors, paper" ($R,S,P$) where
$R>S>P>R$. We discuss the conditions under which quantum versions of $R,S,P$
retain the non-transitive characteristics of the corresponding classical game.
Some physical implications of non-transitivity in quantum game theory are also
considered.


title:
Symplectic invariants, entropic measures and correlations of Gaussian
  states

abstract:
  We present a derivation of the Von Neumann entropy and mutual information of
arbitrary two--mode Gaussian states, based on the explicit determination of the
symplectic eigenvalues of a generic covariance matrix. The key role of the
symplectic invariants in such a determination is pointed out. We show that the
Von Neumann entropy depends on two symplectic invariants, while the purity (or
the linear entropy) is determined by only one invariant, so that the two
quantities provide two different hierarchies of mixed Gaussian states. A
comparison between mutual information and entanglement of formation for
symmetric states is considered, remarking the crucial role of the symplectic
eigenvalues in qualifying and quantifying the correlations present in a generic
state.

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


title: Planar lightwave circuits for quantum cryptographic systems

abstract:
  We propose a quantum cryptographic system based on a planar lightwave circuit
(PLC) and report on optical interference experiments using PLC-based unbalanced
Mach-Zehnder interferometers (MZIs). The interferometers exhibited
high-visibility (>0.98) interference even when the polarisation in the optical
fibre connecting the two MZIs was randomly modulated. The results demonstrate
that a PLC-based setup is suitable for achieving a polarisation-insensitive
phase-coding cryptographic system.


title: Quantum Zeno Effect for Exponentially Decaying Systems

abstract:
  The quantum Zeno effect -- suppression of decay by frequent measurements --
was believed to occur only when the response of the detector is so quick that
the initial tiny deviation from the exponential decay law is detectable.
However, we show that it can occur even for exactly exponentially decaying
systems, for which this condition is never satisfied, by considering a
realistic case where the detector has a finite energy band of detection. The
conventional theories correspond to the limit of an infinite bandwidth. This
implies that the Zeno effect occurs more widely than expected so far.


title: Quantum Symmetrically-Private Information Retrieval

abstract:
  Private information retrieval systems (PIRs) allow a user to extract an item
from a database that is replicated over k>=1 servers, while satisfying various
privacy constraints. We exhibit quantum k-server symmetrically-private
information retrieval systems (QSPIRs) that use sublinear communication, do not
use shared randomness among the servers, and preserve privacy against honest
users and dishonest servers. Classically, SPIRs without shared randomness do
not exist at all.


title: A New Interpretation for Orthofermions

abstract:
  In this article we introduce a simple physical model which realizes the
algebra of orthofermions. The model is constructed from a cylinder which can be
filled with some balls. The creation and annihilation operators of
orthofermions are related to the creation and annihilation operators of balls
in certain positions in the cylinder. Relationship between this model and
topological symmetries in quantum mechanics is investigated.


title:
The interpretation of non-Markovian stochastic Schr\"odinger equations
  as a hidden-variable theory

abstract:
  Do diffusive non-Markovian stochastic Schr\"odinger equations (SSEs) for open
quantum systems have a physical interpretation? In a recent paper [Phys. Rev. A
66, 012108 (2002)] we investigated this question using the orthodox
interpretation of quantum mechanics. We found that the solution of a
non-Markovian SSE represents the state the system would be in at that time if a
measurement was performed on the environment at that time, and yielded a
particular result. However, the linking of solutions at different times to make
a trajectory is, we concluded, a fiction. In this paper we investigate this
question using the modal (hidden variable) interpretation of quantum mechanics.
We find that the noise function $z(t)$ appearing in the non-Markovian SSE can
be interpreted as a hidden variable for the environment. That is, some chosen
property (beable) of the environment has a definite value $z(t)$ even in the
absence of measurement on the environment. The non-Markovian SSE gives the
evolution of the state of the system ``conditioned'' on this environment hidden
variable. We present the theory for diffusive non-Markovian SSEs that have as
their Markovian limit SSEs corresponding to homodyne and heterodyne detection,
as well as one which has no Markovian limit.


title:
Wave packet revivals and the energy eigenvalue spectrum of the quantum
  pendulum

abstract:
  The rigid pendulum, both as a classical and as a quantum problem, is an
interesting system as it has the exactly soluble harmonic oscillator and the
rigid rotor systems as limiting cases in the low- and high-energy limits
respectively. The energy variation of the classical periodicity ($\tau$) is
also dramatic, having the special limiting case of $\tau \to \infty$ at the
'top' of the classical motion (i.e. the separatrix.) We study the
time-dependence of the quantum pendulum problem, focusing on the behavior of
both the (approximate) classical periodicity and especially the quantum revival
and superrevival times, as encoded in the energy eigenvalue spectrum of the
system. We provide approximate expressions for the energy eigenvalues in both
the small and large quantum number limits, up to 4th order in perturbation
theory, comparing these to existing handbook expansions for the characteristic
values of the related Mathieu equation, obtained by other methods. We then use
these approximations to probe the classical periodicity, as well as to extract
information on the quantum revival and superrevival times. We find that while
both the classical and quantum periodicities increase monotonically as one
approaches the 'top' in energy, from either above or below, the revival times
decrease from their low- and high-energy values until very near the separatrix
where they increase to a large, but finite value.


title: Kraus representation of destruction of states for one qudit

abstract:
  Quantum operations arise naturally in many fields of quantum information
theory and quantum computing. One of the simplest example of quantum operation
is the von Neumann-Lueders measurement. Destruction of states in quantum
mechanics can be treated as a supplement to the von Neumann-Lueders measurement
[P. Caban, J. Rembielinski, K. A. Smolinski and Z. Walczak, J. Phys. A 35, 3265
(2002)]. We show that destruction of states in one-qudit system is a quantum
operation by finding its Kraus representation.


title:
Numerical analysis of a spontaneous collapse model for a two-level
  system

abstract:
  We study a spontaneous collapse model for a two-level (spin) system, in which
the Hamiltonian and the stochastic terms do not commute. The numerical solution
of the equations of motions allows to give precise estimates on the regime at
which the collapse of the state vector occurs, the reduction and delocalization
times, and the reduction probabilities; it also allows to quantify the effect
that an Hamiltonian which does not commute with the reducing terms has on the
collapse mechanism. We also give a clear picture of the transition from the
"microscopic" regime (when the noise terms are weak and the Hamiltonian
prevents the state vector to collapse) to the "macroscopic" regime (when the
noise terms are dominant and the collapse becomes effective for very long
times). Finally, we clarify the distinction between decoherence and collapse.


title: The Counterfactual Meaning of the ABL Rule

abstract:
  The Aharonov-Bergmann-Lebowitz rule assigns probabilities to quantum
measurement results at time t on the condition that the system is prepared in a
given way at t_1 < t and found in a given state at t_2 > t. The question
whether the rule can also be applied counterfactually to the case where no
measurement is performed at the intermediate time t has recently been the
subject of controversy. I argue that the counterfactual meaning may be
understood in terms of the true value of an observable at t. Such a value
cannot be empirically determined for, by stipulation, the measurement that
would yield it is not performed. Nevertheless, it may or may not be
well-defined depending on one's proposed interpretation of quantum mechanics.
Various examples are discussed illustrating what can be asserted at the
intermediate time without running into contradictions.


title: Spontaneous-emission suppression via multiphoton quantum interference

abstract:
  The spontaneous emission is investigated for an effective atomic two-level
system in an intense coherent field with frequency lower than the
vacuum-induced decay width. As this additional low-frequency field is assumed
to be intense, multiphoton processes may be induced, which can be seen as
alternative transition pathways in addition to the simple spontaneous decay.
The interplay of the various interfering transition pathways influences the
decay dynamics of the two-level system and may be used to slow down the
spontaneous decay considerably. We derive from first principles an expression
for the Hamiltonian including up to three-photon processes. This Hamiltonian is
then applied to a quantum mechanical simulation of the decay dynamics of the
two-level system. Finally, we discuss numerical results of this simulation
based on a rubidium atom and show that the spontaneous emission in this system
may be suppressed substantially.


title:
Quantum states of a generalized time-dependent inverted harmonic
  oscillator

abstract:
  We discuss the extension of the Lewis and Riesenfeld method of solving the
time-dependent Schr\"odinger equation to cases where the invariant has
continuous eigenvalues and apply it to the case of a generalized time-dependent
inverted harmonic oscillator. As a special case, we consider a generalized
inverted oscillator with constant frequency and exponentially increasing mass.


title:
Perfect initialization of a quantum computer of neutral atoms in an
  optical lattice of large lattice constant

abstract:
  We propose a scheme for the initialization of a quantum computer based on
neutral atoms trapped in an optical lattice with large lattice constant. Our
focus is the development of a compacting scheme to prepare a perfect optical
lattice of simple orthorhombic structure with unit occupancy. Compacting is
accomplished by sequential application of two types of operations: a flip
operator that changes the internal state of the atoms, and a shift operator
that moves them along the lattice principal axis. We propose physical
mechanisms for realization of these operations and we study the effects of
motional heating of the atoms. We carry out an analysis of the complexity of
the compacting scheme and show that it scales linearly with the number of
lattice sites per row of the lattice, thus showing good scaling behavior with
the size of the quantum computer.


title: How well can you know the edge of a quantum pyramid?

abstract:
  The methods of quantum cryptography enable one to have perfectly secure
communication lines, whereby the laws of quantum physics protect the privacy of
the data exchanged. Each quantum-cryptography scheme has its own security
criteria that need to be met in a practical implementation. We find, however,
that the generally accepted criteria are flawed for a whole class of such
schemes.


title: Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models

abstract:
  It is shown that spontaneous symmetry breaking does not modify the
ground-state entanglement of two spins, as defined by the concurrence, in the
XXZ- and the transverse field Ising-chain. Correlation function inequalities,
valid in any dimensions for these models, are presented outlining the regimes
where entanglement is unaffected by spontaneous symmetry breaking.


title: Sympathetic cooling of $^9Be^+$ and $^{24}Mg^+$ for quantum logic

abstract:
  We demonstrate the cooling of a two species ion crystal consisting of one
$^9Be^+$ and one $^{24}Mg^+$ ion. Since the respective cooling transitions of
these two species are separated by more than 30 nm, laser manipulation of one
ion has negligible effect on the other even when the ions are not individually
addressed. As such this is a useful system for re-initializing the motional
state in an ion trap quantum computer without affecting the qubit information.
Additionally, we have found that the mass difference between ions enables a
novel method for detecting and subsequently eliminating the effects of radio
frequency (RF) micro-motion.


title: A consistent quantum model for continuous photodetection processes

abstract:
  We are modifying some aspects of the continuous photodetection theory,
proposed by Srinivas and Davies [Optica Acta 28, 981 (1981)], which describes
the non-unitary evolution of a quantum field state subjected to a continuous
photocount measurement. In order to remedy inconsistencies that appear in their
approach, we redefine the `annihilation' and `creation' operators that enter in
the photocount superoperators. We show that this new approach not only still
satisfies all the requirements for a consistent photocount theory according to
Srinivas and Davies precepts, but also avoids some weird result appearing when
previous definitions are used.


title:
Differences between the trajectory representation and Copenhagen
  regarding the past and present in quantum theory

abstract:
  We examine certain pasts and presents in the classically forbidden region. We
show that for a given past the trajectory representation does not permit some
presents while the Copenhagen predicts a finite probability for these presents
to exist. This suggests another gedanken experiment to invalidate either
Copenhagen or the trajectory representation.


title: Coherent Communication of Classical Messages

abstract:
  We define "coherent communication" in terms of a simple primitive, show it is
equivalent to the ability to send a classical message with a unitary or
isometric operation, and use it to relate other resources in quantum
information theory. Using coherent communication, we are able to generalize
super-dense coding to prepare arbitrary quantum states instead of only
classical messages. We also derive single-letter formulae for the classical and
quantum capacities of a bipartite unitary gate assisted by an arbitrary fixed
amount of entanglement per use.


title: Comment on Papers by Gill and Gill, Weihs, Zeilinger and Zukowski

abstract:
  We show that the proofs of Gill as well as of Gill, Weihs, Zeilinger and
Zukowski contain serious mathematical and physical deficiencies which render
them invalid.


title: Two-Level Atom in the Resonant Field - Critical Remarks

abstract:
  We review the validity of the several representations of the two-level
approximation


title: Experimental limit on Spontaneous Parametric Up Conversion

abstract:
  We present a first experimental test of the existence of Spontaneus
Parametric Up Conversion, predicted by a specific local realistic model based
on Wigner function formalism. The measurement has been made using a ccd camera
on the emission of a LiIO3 crystal pumped by a 351 nm and/or a 789 (1064) nm
lasers.
  We obtain an upper limit of 160 times on the ratio between intensity of
Spontaneus Parametric Up Conversion and Spontaneous Parametric Down conversion.


title: Quantum authentication scheme based on algebraic coding

abstract:
  This paper presents a simple, but efficient class of non-interactive
protocols for quantum authentication of $m$-length clas sical messages. The
message is encoded using a classical linear algebraic code $C[n,m,t]$. We
assume that Alice and Bob share a classical secret key, $x_{AB}$, of $n$ bits.
Alice creates $n$ qubits based on the code word and the key, that indicates the
bases used to create each qubit. The quantum states are sent to Bob through a
noiseless quantum channel. We calculate the failure probability of the protocol
considering several types of attacks.


title:
Preparation and control of a cavity-field state through atom-driven
  field interaction: towards long-lived mesoscopic states

abstract:
  The preparation of mesoscopic states of the radiation and matter fields
through atom-field interactions has been achieved in recent years and employed
for a range of striking applications in quantum optics. Here we present a
technique for the preparation and control of a cavity mode which, besides
interacting with a two-level atom, is simultaneously submitted to linear and
parametric amplification processes. The role of the amplification-controlling
fields in the achievement of real mesoscopic states, is to produce
highly-squeezed field states and, consequently, to increase both: i) the
distance in phase space between the components of the prepared superpositions
and ii) the mean photon number of such superpositions. When submitting the
squeezed superposition states to the action of similarly squeezed reservoirs,
we demonstrate that under specific conditions the decoherence time of the
states becomes independent of both the distance in phase space between their
components and their mean photon number. An explanation is presented to support
this remarkable result, together with a discussion on the experimental
implementation of our proposal. We also show how to produce number states with
fidelities higher than those derived as circular states.


title: New scheme for generating GHZ like state of $n$ photons

abstract:
  In this paper we propose a new scheme for creating a three photons GHZ state
using only linear optics elements and single photon detectors. We furthermore
generalize the scheme for producing any GHZ-like state of $n$ photons. The
input state of the scheme consists of a non-entangled state of $n$ photons.
Experimental aspects regarding the implementation of the scheme are presented.
Finally, the role of such schemes in quantum information processing with
photons is discussed.


title: Broadband channel capacities

abstract:
  We study the communication capacities of bosonic broadband channels in the
presence of different sources of noise. In particular we analyze lossy channels
in presence of white noise and thermal bath. In this context, we provide a
numerical solution for the entanglement assisted capacity and upper and lower
bounds for the classical and quantum capacities.


title:
Time evolution, cyclic solutions and geometric phases for general spin
  in an arbitrarily varying magnetic field

abstract:
  A neutral particle with general spin and magnetic moment moving in an
arbitrarily varying magnetic field is studied. The time evolution operator for
the Schr\"odinger equation can be obtained if one can find a unit vector that
satisfies the equation obeyed by the mean of the spin operator. There exist at
least $2s+1$ cyclic solutions in any time interval. Some particular time
interval may exist in which all solutions are cyclic. The nonadiabatic
geometric phase for cyclic solutions generally contains extra terms in addition
to the familiar one that is proportional to the solid angle subtended by the
closed trace of the spin vector.


title: Remote preparation of quantum states

abstract:
  Remote state preparation is the variant of quantum state teleportation in
which the sender knows the quantum state to be communicated. The original paper
introducing teleportation established minimal requirements for classical
communication and entanglement but the corresponding limits for remote state
preparation have remained unknown until now: previous work has shown, however,
that it not only requires less classical communication but also gives rise to a
trade-off between these two resources in the appropriate setting. We discuss
this problem from first principles, including the various choices one may
follow in the definitions of the actual resources. Our main result is a general
method of remote state preparation for arbitrary states of many qubits, at a
cost of 1 bit of classical communication and 1 bit of entanglement per qubit
sent. In this "universal" formulation, these ebit and cbit requirements are
shown to be simultaneously optimal by exhibiting a dichotomy. Our protocol then
yields the exact trade-off curve for arbitrary ensembles of pure states and
pure entangled states (including the case of incomplete knowledge of the
ensemble probabilities), based on the recently established quantum-classical
trade-off for quantum data compression. The paper includes an extensive
discussion of our results, including the impact of the choice of model on the
resources, the topic of obliviousness, and an application to private quantum
channels and quantum data hiding.


title: Quantum State Engineering with the rf-SQUID: A Brief Introduction

abstract:
  Quantum computers take advantage of the superpositional logic of quantum
mechanics to allow for dramatic increases in computational efficiency.
rf-SQUIDs show potential for quantum computing applications by forming the
qubit component of a quantum computer, through simply treating the direction of
current - clockwise or counterclockwise - as the value of the bit. rf-SQUIDs
present a major advantage over atomic-scale qubit systems - they are sensitive
to parameters that can be engineered. Flux qubits are linked through controlled
inductive coupling: the magnetic field of each junction affects the others. The
strength of this coupling can be 'tuned,' allowing for refined control over the
behaviour of the system. rf-SQUIDs can also be mass produced on-chip, making
large-scale production feasible.


title:
Quantum integrability and Bethe ansatz solution for interacting
  matter-radiation systems

abstract:
  A unified integrable system, generating a new series of interacting
matter-radiation models with interatomic coupling and different atomic
frequencies, is constructed and exactly solved through algebraic Bethe ansatz.
  Novel features in Rabi oscillation and vacuum Rabi splitting are shown on the
example of an integrable two-atom Buck-Sukumar model with resolution of some
important controversies in the Bethe ansatz solution including its possible
degeneracy for such models.


title: Les ordinateurs quantiques affrontent le chaos

abstract:
  Quantum computers facing chaos. Quantum parallelism allows to perform
computation in a radically new manner. A quantum computer based on these new
principles may resolve certain problems exponentially faster than a classical
computer. We discuss how quantum computers can simulate complex dynamics, in
particularly the dynamics of chaotic systems, where the errors of classical
computation grow exponentially fast.
  -----
  Le parallelisme autorise par la mecanique quantique permet d'effectuer des
calculs d'une maniere radicalement nouvelle. Un ordinateur quantique fonde sur
ces principes pourrait resoudre certains problemes exponentiellement plus vite
qu'un ordinateur classique. Nous discutons comment un ordinateur quantique
realiste peut simuler une dynamique complexe, en particulier les systemes
chaotiques ou les fautes de l'ordinateur classique croissent exponentiellement
vite.


title: Randomizing quantum states: Constructions and applications

abstract:
  The construction of a perfectly secure private quantum channel in dimension d
is known to require 2 log d shared random key bits between the sender and
receiver. We show that if only near-perfect security is required, the size of
the key can be reduced by a factor of two. More specifically, we show that
there exists a set of roughly d log d unitary operators whose average effect on
every input pure state is almost perfectly randomizing, as compared to the d^2
operators required to randomize perfectly. Aside from the private quantum
channel, variations of this construction can be applied to many other tasks in
quantum information processing. We show, for instance, that it can be used to
construct LOCC data hiding schemes for bits and qubits that are much more
efficient than any others known, allowing roughly log d qubits to be hidden in
2 log d qubits. The method can also be used to exhibit the existence of quantum
states with locked classical correlations, an arbitrarily large amplification
of the correlation being accomplished by sending a negligibly small classical
key. Our construction also provides the basic building block for a method of
remotely preparing arbitrary d-dimensional pure quantum states using
approximately log d bits of communication and log d ebits of entanglement.


title: Quantum teleportation with a quantum dot single photon source

abstract:
  We report the experimental demonstration of a quantum teleportation protocol
with a semiconductor single photon source. Two qubits, a target and an ancilla,
each defined by a single photon occupying two optical modes (dual-rail qubit),
were generated independently by the single photon source. Upon measurement of
two modes from different qubits and postselection, the state of the two
remaining modes was found to reproduce the state of the target qubit. In
particular, the coherence between the target qubit modes was transferred to the
output modes to a large extent. The observed fidelity is 80 %, a figure which
can be explained quantitatively by the residual distinguishability between
consecutive photons from the source. An improved version of this teleportation
scheme using more ancillas is the building block of the recent KLM proposal for
efficient linear-optics quantum computation \cite{ref:klm}.


title: Distillation of continuous-variable entanglement with optical means

abstract:
  We present an event-ready procedure that is capable of distilling Gaussian
two-mode entangled states from a supply of weakly entangled states that have
become mixed in a decoherence process. This procedure relies on passive optical
elements and photon detectors distinguishing the presence and the absence of
photons, but does not make use of photon counters. We identify fixed points of
the iteration map, and discuss in detail its convergence properties. Necessary
and sufficient criteria for the convergence to two-mode Gaussian states are
presented. On the basis of various examples we discuss the performance of the
procedure as far as the increase of the degree of entanglement and two-mode
squeezing is concerned. Finally, we consider imperfect operations and outline
the robustness of the scheme under non-unit detection efficiencies of the
detectors. This analysis implies that the proposed protocol can be implemented
with currently available technology and detector efficiencies.


title:
Wigner rotations, Bell states, and Lorentz invariance of entanglement
  and von Neumann entropy

abstract:
  We compute, for massive particles, the explicit Wigner rotations of
one-particle states for arbitrary Lorentz transformations; and the explicit
Hermitian generators of the infinite-dimensional unitary representation. For a
pair of spin 1/2 particles, Einstein-Podolsky-Rosen-Bell entangled states and
their behaviour under the Lorentz group are analysed in the context of quantum
field theory. Group theoretical considerations suggest a convenient definition
of the Bell states which is slightly different from the conventional
assignment. The behaviour of Bell states under arbitrary Lorentz
transformations can then be described succinctly. Reduced density matrices
applicable to identical particles are defined through Yang's prescription. The
von Neumann entropy of each of the reduced density matrix is Lorentz invariant;
and its relevance as a measure of entanglement is discussed, and illustrated
with an explicit example. A regularization of the entropy in terms of
generalized zeta functions is also suggested.


title: Renormalisation and fixed points in Hilbert Space

abstract:
  The energies of low-lying bound states of a microscopic quantum many-body
system of particles can be worked out in a reduced Hilbert space. We present
here and test a specific non-perturbative truncation procedure. We also show
that real exceptional points which may be present in the spectrum can be
identified as fixed points of coupling constants in the truncation procedure.


title:
Amplitude and phase of time dependent Hamiltonian systems under the
  minimum uncertainty condition

abstract:
  We investigate dynamical systems with time-dependent mass and frequency, with
particular attention on models attaining the minimum value of uncertainty
formula. A criterium of minimum uncertainty is presented and illustrated by
means of explicit and exactly solved examples. The role of the Bogolubov
coefficients, in general and in the context of minimum uncertainty case, is
discussed.


title: Entanglement and quantum fluctuations

abstract:
  We discuss maximum entangled states of quantum systems in terms of quantum
fluctuations of all essential measurements responsible for manifestation of
entanglement. Namely, we consider maximum entanglement as a property of states,
for which quantum fluctuations come to their extreme.


title: Quantum Circuit Identities

abstract:
  There are quantum circuit identities that simplify quantum circuits, reducing
the effort needed physically to implement them. This paper constructs all
identities made from 3 or fewer operations taken from a common set of one qubit
operations, and explains how they may be used to simplify the cost of
constructing quantum circuit identities.


title: Information rate of waveguide

abstract:
  We calculate the communication capacity of a broadband electromagnetic
waveguide as a function of its spatial dimensions and input power. We analyze
the two cases in which either all the available modes or only a single
directional mode are employed. The results are compared with those for the free
space bosonic channel.


title: Do quantum states evolve? Apropos of Marchildon's remarks

abstract:
  Marchildon's (favorable) assessment (quant-ph/0303170, to appear in Found.
Phys.) of the Pondicherry interpretation of quantum mechanics raises several
issues, which are addressed. Proceeding from the assumption that quantum
mechanics is fundamentally a probability algorithm, this interpretation
determines the nature of a world that is irreducibly described by this
probability algorithm. Such a world features an objective fuzziness, which
implies that its spatiotemporal differentiation does not "go all the way down".
This result is inconsistent with the existence of an evolving instantaneous
state, quantum or otherwise.


title: Einstein-Podolsky-Rosen correlation in gravitational field

abstract:
  For quantum communication in a gravitational field, the properties of the
Einstein-Podolsky-Rosen (EPR) correlation are studied within the framework of
general relativity. Acceleration and gravity are shown to deteriorate the
perfect anti-correlation of an EPR pair of spins in the same direction, and
apparently decrease the degree of the violation of Bell's inequality. To
maintain the perfect EPR correlation and the maximal violation of Bell's
inequality, observers must measure the spins in appropriately chosen different
directions. Which directions are appropriate depends on the velocity of the
particles, the curvature of the spacetime, and the positions of the observers.
Near the event horizon of a black hole, the appropriate directions depend so
sensitively on the positions of the observers that even a very small
uncertainty in the identification of the observers' positions leads to a fatal
error in quantum communication, unless the observers fall into the black hole
together with the particles.


title: Entanglement distillation for W class states

abstract:
  In this paper, we first propose a general entanglement distillation protocol
for three-particle W class state, which can concentrate the state
(non-maximally entangled W state). The general protocol is mainly based on the
unitary transformations on the auxiliary particles and the entangled particles,
and a feasible physical scheme is suggested based on the cavity QED techniques.
The protocol and scheme can be extended to the entanglement concentration of
N-particle case.


title: Nonlinear Schrodinger Equation for Quantum Computation

abstract:
  Utilization of a quantum system whose time-development is described by the
nonlinear Schrodinger equation in the transformation of qubits would make it
possible to construct quantum algorithms which would be useful in a large class
of problems. An example of such a system for implementing the logical NOR
operation is demonstrated.


title: An Extra Dimensional Approach of Entanglement

abstract:
  Motivated by the apparent lack of a workable hypothesis we developed a model
to describe phenomena such as entanglement and the EPR-paradox. In the model we
propose the existence of extra hidden dimensions. Through these dimensions it
will be possible for particles, which originate from one source, to remain
connected. This connection results in an instantaneous reaction of one particle
when the other particle is manipulated. We imagine entanglement in such a
model. The results of the experiments which have been performed on this item do
not contradict with the existence of the extra dimension(s). In addition, the
model opens the possibility to unify the theory of quantum mechanics,
gravitation and the general theory of relativity.


title: Atomic motion in tilted optical lattices

abstract:
  This paper presents a formalism describing the dynamics of a quantum particle
in a one-dimensional, time-dependent, tilted lattice. The formalism uses the
Wannier-Stark states, which are localized in each site of the lattice, and
provides a simple framework allowing fully-analytical developments. Analytic
solutions describing the particle motion are explicit derived, and the
resulting dynamics is studied.


title: Ray chaos in optical cavities based upon standard laser mirrors

abstract:
  We present a composite optical cavity made of standard laser mirrors; the
cavity consists of a suitable combination of stable and unstable cavities. In
spite of its very open nature the composite cavity shows ray chaos, which may
be either soft or hard, depending on the cavity configuration. This opens a
new, convenient route for experimental studies of the quantum aspects of a
chaotic wave field.


title: Is Entanglement Monogamous?

abstract:
  In this article I discuss Charlie's Bennett's influence in quantum
information theory and our answers to the question whether quantum entanglement
is `monogamous'.


title: Discovering Quantum Mechanics Once Again

abstract:
  We expand on a recent development by Hardy, in which quantum mechanics is
derived from classical probability theory supplemented by a single new axiom,
Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend'
Heisenberg who seeks to construct a dynamical theory of probabilities and is
lead -- seemingly inevitably -- to the Principles of Quantum Mechanics.


title: Experimental realization of entangled qutrits for quantum communication

abstract:
  We have experimentally realized a technique to generate, control and measure
entangled qutrits, 3-dimensional quantum systems. This scheme uses spontaneous
parametric down converted photons and unbalanced 3-arm fiber optic
interferometers in a scheme analogous to the Franson interferometric
arrangement for qubits. The results reveal a source capable of generating
maximally entangled states with a net state fidelity, F = 0.985 $\pm$ 0.018.
Further the control over the system reveals a high, net, 2-photon interference
fringe visibility, V = 0.919 $\pm$ 0.026. This has all been done at telecom
wavelengths thus facilitating the advancement towards long distance higher
dimensional quantum communication.


title: Bell inequalities and incompatible measurements

abstract:
  Bell inequalities are a consequence of measurement incompatibility (not, as
generally thought, of nonlocality). In classical terms, this is equivalent to
contextuality -- measurement devices do have a significant effect. Contextual
models are reasonable in classical physics, which always took the view that we
ignore measurement devices whenever possible, but if that isn't good enough
then we do have to model measurement devices. It is also argued that quantum
theory should only be taken with counterfactual seriousness, because
measurement incompatibility is a counterfactual concept.


title:
Entanglement, Mixedness, and Spin-Flip Symmetry in Multiple-Qubit
  Systems

abstract:
  A relationship between a recently introduced multipartite entanglement
measure, state mixedness, and spin-flip symmetry is established for any finite
number of qubits. It is also shown that, within those classes of states
invariant under the spin-flip transformation, there is a complementarity
relation between multipartite entanglement and mixedness. A number of example
classes of multiple-qubit systems are studied in light of this relationship.


title: The statistical strength of nonlocality proofs

abstract:
  There exist numerous proofs of Bell's theorem, stating that quantum mechanics
is incompatible with local realistic theories of nature. Here we define the
strength of such nonlocality proofs in terms of the amount of evidence against
local realism provided by the corresponding experiments. This measure tells us
how many trials of the experiment we should perform in order to observe a
substantial violation of local realism. Statistical considerations show that
the amount of evidence should be measured by the Kullback-Leibler or relative
entropy divergence between the probability distributions over the measurement
outcomes that the respective theories predict. The statistical strength of a
nonlocality proof is thus determined by the experimental implementation of it
that maximizes the Kullback-Leibler divergence from experimental (quantum
mechanical) truth to the set of all possible local theories. An implementation
includes a specification with which probabilities the different measurement
settings are sampled, and hence the maximization is done over all such setting
distributions.
  We analyze two versions of Bell's nonlocality proof (his original proof and
an optimized version by Peres), and proofs by Clauser-Horne-Shimony-Holt,
Hardy, Mermin, and Greenberger-Horne-Zeilinger. We find that the GHZ proof is
at least four and a half times stronger than all other proofs, while of the
two-party proofs, the one of CHSH is the strongest.


title: Comment on "Quantum identification schemes with entanglements"

abstract:
  In a recent paper, [Phys. Rev. A 65, 052326 (2002)], Mihara presented several
cryptographic protocols that were claimed to be quantum mechanical in nature.
In this comment it is pointed out that these protocols can be described in
purely classical terms. Hence, the security of these schemes does not rely on
the usage of entanglement or any other quantum mechanical property.


title: On Quantum State Observability and Measurement

abstract:
  We consider the problem of determining the state of a quantum system given
one or more readings of the expectation value of an observable. The system is
assumed to be a finite dimensional quantum control system for which we can
influence the dynamics by generating all the unitary evolutions in a Lie group.
We investigate to what extent, by an appropriate sequence of evolutions and
measurements, we can obtain information on the initial state of the system. We
present a system theoretic viewpoint of this problem in that we study the {\it
observability} of the system. In this context, we characterize the equivalence
classes of indistinguishable states and propose algorithms for state
identification.


title: Model identification for spin networks

abstract:
  We consider the problem of determining the unknown parameters of the
Hamiltonian of a network of spin 1/2 particles. In particular, we study
experiments in which the system is driven by an externally applied
electro-magnetic field and the expectation value of the total magnetization is
measured. Under appropriate assumptions, we prove that, if it is possible to
prepare the system in a known initial state, the above experiment allows to
identify the parameters of the Hamiltonian. In the case where the initial state
is itself an unknown parameter, we characterize all the pairs
Hamiltonian-Initial State which give the same value of the magnetization for
every form of the driving electro-magnetic field. The analysis is motivated by
recent results on the isospectrality of Hamiltonians describing Magnetic
Molecules.


title:
Controllability, Observability and Parameter Identification of two
  coupled spin 1's

abstract:
  In this paper, we study the control theoretic properties of a couple of
interacting spin 1's driven by an electro-magnetic field. In particular, we
assume that it is possible to observe the expectation value of the total
magnetization and we study controllability, observability and parameter
identification of these systems. We give conditions for controllability and
observability and characterize the classes of equivalent models which have the
same input-output behavior. The analysis is motivated by the recent interest in
three level systems in quantum information theory and quantum cryptography as
well as by the problem of modeling molecular magnets as spin networks.


title: Multi-party entanglement in graph states

abstract:
  Graph states are multi-particle entangled states that correspond to
mathematical graphs, where the vertices of the graph take the role of quantum
spin systems and edges represent Ising interactions. They are many-body spin
states of distributed quantum systems that play a significant role in quantum
error correction, multi-party quantum communication, and quantum computation
within the framework of the one-way quantum computer. We characterize and
quantify the genuine multi-particle entanglement of such graph states in terms
of the Schmidt measure, to which we provide upper and lower bounds in graph
theoretical terms. Several examples and classes of graphs will be discussed,
where these bounds coincide. These examples include trees, cluster states of
different dimension, graphs that occur in quantum error correction, such as the
concatenated [7,1,3]-CSS code, and a graph associated with the quantum Fourier
transform in the one-way computer. We also present general transformation rules
for graphs when local Pauli measurements are applied, and give criteria for the
equivalence of two graphs up to local unitary transformations, employing the
stabilizer formalism. For graphs of up to seven vertices we provide complete
characterization modulo local unitary transformations and graph isomorphies.


title: Entanglement, quantum phase transition and scaling in XXZ chain

abstract:
  Motivated by recent development in quantum entanglement, we study relations
among concurrence $C$, SU$_q$(2) algebra, quantum phase transition and
correlation length at the zero temperature for the XXZ chain. We find that at
the SU(2) point, the ground state possess the maximum concurrence. When the
anisotropic parameter $\Delta$ is deformed, however, its value decreases. Its
dependence on $\Delta$ scales as $C=C_0-C_1(\Delta-1)^2$ in the XY metallic
phase and near the critical point (i.e. $1<\Delta<1.3$) of the Ising-like
insulating phase. We also study the dependence of $C$ on the correlation length
$\xi$, and show that it satisfies $C=C_0-1/2\xi$ near the critical point. For
different size of the system, we show that there exists a universal scaling
function of $C$ with respect to the correlation length $\xi$.


title: A Class of Linear Positive Maps in Matrix Algebras

abstract:
  A class of linear positive, trace preserving maps in $M_n$ is given in terms
of affine maps in $\bBR^{n^2-1}$ which map the closed unit ball into itself.


title: Coherent states and Chebyshev polynomials

abstract:
  We define the coherent states for the oscillator-like systems, connected with
the Chebyshev polynomials $T_n(x)$ and $U_n(x)$ of the 1-st and 2-nd kind.


title:
Entanglement production in coupled chaotic systems : Case of the Kicked
  Tops

abstract:
  Entanglement production in coupled chaotic systems is studied with the help
of kicked tops. Deriving the correct classical map, we have used the reduced
Husimi function, the Husimi function of the reduced density matrix, to
visualize the possible behaviors of a wavepacket. We have studied a phase space
based measure of the complexity of a state and used random matrix theory (RMT)
to model the strongly chaotic cases. Extensive numerical studies have been done
for the entanglement production in coupled kicked tops corresponding to
different underlying classical dynamics and different coupling strengths. An
approximate formula, based on RMT, is derived for the entanglement production
in coupled strongly chaotic systems. This formula, applicable for arbitrary
coupling strengths and also valid for long time, complements and extends
significantly recent perturbation theories for strongly chaotic weakly coupled
systems.


title: Entanglement dynamics and quantum state transport in spin chains

abstract:
  We study the dynamics of a Heisenberg-XY spin chain with an unknown state
coded into one qubit or a pair of entangled qubits, with the rest of the spins
being in a polarized state. The time evolution involves magnon excitations, and
through them the entanglement is transported across the channel. For a large
number of qubits, explicit formulae for the concurrences, measures for
two-qubit entanglements, and the fidelity for recovering the state some
distance away are calculated as functions of time. Initial states with an
entangled pair of qubits show better fidelity, which takes its first maximum
value at earlier times, compared to initial states with no entangled pair. In
particular initial states with a pair of qubits in an unknown state (alpha
up-up + beta down-down) are best suited for quantum state transport.


title:
Neutral Radical Molecules Ordered in Self-Assembled Monolayer Systems
  for Quantum Information Processing

abstract:
  Implementation of quantum information processing based on spatially localized
electronic spins in stable molecular radicals is discussed. The necessary
operating conditions for such molecules are formulated in self-assembled
monolayer (SAM) systems. As a model system we start with 1, 3 -diketone types
of neutral radicals. Using first principles quantum chemical calculations we
prove that these molecules have the stable localized electron spin, which may
represent a qubit in quantum information processing.


title: On the position uncertainty measure on the circle

abstract:
  New position uncertainty (delocalization) measures for a particle on the
circle are proposed and illustrated on several examples, where the previous
measures (based on 2pi-periodic position operators) appear to be
unsatisfactory. The new measures are suitably constructed using the standard
multiplication angle operator variances. They are shown to depend solely on the
state of the particle and to obey uncertainty relations of the
Schroedinger-Robertson type.


title: Iterative Optimization of Quantum Error Correcting Codes

abstract:
  We introduce a convergent iterative algorithm for finding the optimal coding
and decoding operations for an arbitrary noisy quantum channel. This algorithm
does not require any error syndrome to be corrected completely, and hence also
finds codes outside the usual Knill-Laflamme definition of error correcting
codes. The iteration is shown to improve the figure of merit "channel fidelity"
in every step.


title:
Generalizations of Kochen and Specker's Theorem and the Effectiveness of
  Gleason's Theorem

abstract:
  Kochen and Specker's theorem can be seen as a consequence of Gleason's
theorem and logical compactness. Similar compactness arguments lead to stronger
results about finite sets of rays in Hilbert space, which we also prove by a
direct construction. Finally, we demonstrate that Gleason's theorem itself has
a constructive proof, based on a generic, finite, effectively generated set of
rays, on which every quantum state can be approximated.


title:
Relation between discrete and continuous teleportation using linear
  elements

abstract:
  We discuss the relation between discrete and continuous linear teleportation,
i.e. teleportation schemes that use only linear optical elements and
photodetectors. For this the existing qubit protocols are generalized to qudits
with a discrete and finite spectrum but with an arbitrary number of states or
alternatively to continuous variables. Correspondingly a generalization of
linear optical operations and detection is made. It is shown that linear
teleportation is only possible in a probabilistic sense. A general expression
for the success probability is derived which is shown to depend only on the
dimensions of the input and ancilla Hilbert spaces. From this the known results
$p=1/2$ and $p=1$ for the discrete and continuous cases can be recovered. We
also discuss the probabilistic teleportation scheme of Knill, Laflamme and
Milburn and argue that it does not make optimum use of resources.


title: Analysis of Grover's quantum search algorithm as a dynamical system

abstract:
  Grover's quantum search algorithm is analyzed for the case in which the
initial state is an arbitrary pure quantum state $|\phi>$ of $n$ qubits. It is
shown that the optimal time to perform the measurement is independent of $|
\phi>$, namely, it is identical to the optimal time in the original algorithm
in which $| \phi > = | 0>$, with the same number of marked states, $r$. The
probability of success $P_{\rm s}$ is obtained, in terms of the amplitudes of
the state $| \phi>$, and is shown to be independent of $r$. A class of states,
which includes fixed points and cycles of the Grover iteration operator is
identified. The relevance of these results in the context of using the success
probability as an entanglement measure is discussed. In particular, the
Groverian entanglement measure, previously limited to a single marked state, is
generalized to the case of several marked states.


title: The effect of unitary noise on Grover's quantum search algorithm

abstract:
  The effect of unitary noise on the performance of Grover's quantum search
algorithm is studied. This type of noise may result from tiny fluctuations and
drift in the parameters of the (quantum) components performing the computation.
The resulting operations are still unitary, but not precisely those assumed in
the design of the algorithm. Here we focus on the effect of such noise in the
Hadamard gate $W$, which is an essential component in each iteration of the
quantum search process. To this end $W$ is replaced by a noisy Hadamard gate
$U$. The parameters of $U$ at each iteration are taken from an arbitrary
probability distribution (e.g. Gaussian distribution) and are characterized by
their statistical moments around the parameters of $W$. For simplicity we
assume that the noise is unbiased and isotropic, namely all noise variables in
the parametrization we use have zero average and the same standard deviation
$\epsilon$. The noise terms at different calls to $U$ are assumed to be
uncorrelated. For a search space of size $N=2^n$ (where $n$ is the number of
qubits used to span this space) it is found that as long as $\epsilon <
O(n^{-{1/2}} N^{-{1/4}})$, the algorithm maintains significant efficiency,
while above this noise level its operation is hampered completely. It is also
found that below this noise threshold, when the search fails, it is likely to
provide a state that differs from the marked state by only a few bits. This
feature can be used to search for the marked state by a classical
post-processing, even if the quantum search has failed, thus improving the
success rate of the search process.


title: Violations of Locality Beyond Bell's Theorem

abstract:
  Locality and realism are two main assumptions in deriving Bell's
inequalities. Though the experimentally demonstrated violations of Bell's
inequalities rule out local realism, it is, however, not clear what role each
of the two assumptions solely plays in the observed violations. Here we show
that two testable inequalities for the statistical predictions of two-qubit
systems can be derived by assuming either locality or realism. It turns out
that quantum mechanics respects a nonlocal classical realism, and it is
locality that is incompatible with experimental observations and quantum
mechanics.