title:
Mimicking Time Evolution within a Quantum Ground State: Ground-State
  Quantum Computation, Cloning, and Teleportation

abstract:
  Ground-state quantum computers mimic quantum mechanical time evolution within
the amplitudes of a time-independent quantum state. We explore the principles
that constrain this mimicking. A no-cloning argument is found to impose strong
restrictions. It is shown, however, that there is flexibility that can be
exploited using quantum teleportation methods to improve ground-state quantum
computer design.


title: Photon statistics characterization of a single photon source

abstract:
  n a recent experiment, we reported the time-domain intensity noise
measurement of a single photon source relying on single molecule fluorescence
control. In this article we present data processing, starting from photocount
timestamps. The theoretical analytical expression of the time-dependent Mandel
parameter Q(T) of an intermittent single photon source is derived from ON<->OFF
dynamics . Finally, source intensity noise analysis using the Mandel parameter
is quantitatively compared to the usual approach relying on the time
autocorrelation function, both methods yielding the same molecular dynamical
parameters.


title: New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

abstract:
  We examine in detail the possibilty of applying Darboux transformation to non
Hermitian hamiltonians. In particular we propose a simple method of
constructing exactly solvable PT symmetric potentials by applying Darboux
transformation to higher states of an exactly solvable PT symmetric potential.
It is shown that the resulting hamiltonian and the original one are pseudo
supersymmetric partners. We also discuss application of Darboux transformation
to hamiltonians with spontaneously broken PT symmetry.


title:
Wigner quasi-probability distribution for the infinite square well:
  energy eigenstates and time-dependent wave packets

abstract:
  We calculate the Wigner quasi-probability distribution for position and
momentum, P_W^(n)(x,p), for the energy eigenstates of the standard infinite
well potential, using both x- and p-space stationary-state solutions, as well
as visualizing the results. We then evaluate the time-dependent Wigner
distribution, P_W(x,p;t), for Gaussian wave packet solutions of this system,
illustrating both the short-term semi-classical time dependence, as well as
longer-term revival and fractional revival behavior and the structure during
the collapsed state. This tool provides an excellent way of demonstrating the
patterns of highly correlated Schrodinger-cat-like `mini-packets' which appear
at fractional multiples of the exact revival time.


title:
Entanglement purification for arbitrary unknown ionic states via linear
  optics

abstract:
  An entanglement purification scheme for arbitrary unknown(mixed and pure
non-maximally) entangled ionic states is proposed by using linear optical
elements. The main advantage of the scheme is that not only two-ion maximally
entangled pairs but also four-ion maximally entangled pairs can be extracted
from the less entangled pairs. The scheme is within current technology.


title:
Analysis and interpretation of high transverse entanglement in optical
  parametric down conversion

abstract:
  Quantum entanglement associated with transverse wave vectors of down
conversion photons is investigated based on the Schmidt decomposition method.
We show that transverse entanglement involves two variables: orbital angular
momentum and transverse frequency. We show that in the monochromatic limit high
values of entanglement are closely controlled by a single parameter resulting
from the competition between (transverse) momentum conservation and
longitudinal phase matching. We examine the features of the Schmidt eigenmodes,
and indicate how entanglement can be enhanced by suitable mode selection
methods.


title:
Generation of exactly solvable non-Hermitian potentials with real
  energies

abstract:
  A series of exactly solvable non-trivial complex potentials (possessing real
spectra) are generated by applying the Darboux transformation to the excited
eigenstates of a non-Hermitian potential V(x). This method yields an infinite
number of non-trivial partner potentials, defined over the whole real line,
whose spectra are nearly exactly identical to the original potential.


title:
Casimir force between a sphere and a plane: spectral representation
  formalism

abstract:
  We develop a spectral representation formalism to calculate the Casimir force
in the non-retarded limit, between a spherical particle and a substrate, both
with arbitrary local dielectric properties. This spectral formalism allows one
to do a systematic study of the force as a function of the geometrical
variables separately from the dielectric properties. We found that the force
does not follow a simple power-law as a function of the separation between the
sphere and substrate. As a consequence, the non-retarded Casimir force is
enhanced by several orders of magnitude as the sphere approaches the substrate,
while at large separations the dipolar term dominates the force.


title:
Existence of incomparable pure bipartite states in infinite dimensional
  systems

abstract:
  Based on set theoretic ordering properties, a general formulation for
constructing a pair of convertibility monotones, which are generalizations of
distillable entanglement and entanglement cost, is presented. The new pair of
monotones do not always coincide for pure bipartite infinite dimensional states
under SLOCC (stochastic local operations and classical communications),
demonstrating the existence of SLOCC incomparable pure bipartite states, a new
property of entanglement in infinite dimensional systems, with no counterpart
in the corresponding finite dimensional systems.


title:
Mesoscopic Superposition of States with Sub-Planck Structures in Phase
  Space

abstract:
  We propose a method using the dispersive interaction between atoms and a high
quality cavity to realize the mesoscopic superposition of coherent states which
would exhibit sub-Planck structures in phase space. In particular we focus on a
superposition involving four coherent states. We show interesting interferences
in the conditional measurements involving two atoms.


title:
Group Velocity of a Probe Light in an Ensemble of Lambda Atoms under
  Two-Photon Resonance

abstract:
  We study the propagation of a probe light in an ensemble of $\Lambda$-type
atoms, utilizing the dynamic symmetry as recently discovered when the atoms are
coupled to a classical control field and a quantum probe field {[Sun {\it et
al.,} Phys. Rev. Lett. {\bf 91}, 147903 (2003)]}. Under two-photon resonance,
we calculate the group velocity of the probe light with collective atomic
excitations. Our result gives the dependence of the group velocity on the
common one-photon detuning, and can be compared with the recent experiment (E.
E. Mikhailov, Y. V. Rostovtsev, and G. R. Welch, quant-ph/0309173).


title: Geometry of decomposition dependent evolutions of mixed states

abstract:
  We examine evolutions where each component of a given decomposition of a
mixed quantal state evolves independently in a unitary fashion. The geometric
phase and parallel transport conditions for this type of decomposition
dependent evolution are delineated. We compare this geometric phase with those
previously defined for unitarily evolving mixed states, and mixed state
evolutions governed by completely positive maps.


title:
Quantum information entropies of the eigenstates and the coherent state
  of the P\"oschl-Teller potential

abstract:
  The position and momentum space information entropies, of the ground state of
the P\"oschl-Teller potential, are exactly evaluated and are found to satisfy
the bound, obtained by Beckner, Bialynicki-Birula and Mycielski. These
entropies for the first excited state, for different strengths of the potential
well, are then numerically obtained. Interesting features of the entropy
densities, owing their origin to the excited nature of the wave functions, are
graphically demonstrated. We then compute the position space entropies of the
coherent state of the P\"oschl-Teller potential, which is known to show revival
and fractional revival. Time evolution of the coherent state reveals many
interesting patterns in the space-time flow of information entropy.


title:
Geometrical and physical properties of maths-type q-deformed coherent
  states for $0<q<1$ or $q > 1$

abstract:
  We compare the geometrical and physical properties of the maths-type coherent
states for $q>1$ with those of the same for $0 < q < 1$.


title: Probabilistic Quantum Encoder for Single-Photon Qubits

abstract:
  We describe an experiment in which a physical qubit represented by the
polarization state of a single-photon was probabilistically encoded in the
logical state of two photons. The experiment relied on linear optics,
post-selection, and three-photon interference effects produced by a parametric
down-conversion photon pair and a weak coherent state. An interesting
consequence of the encoding operation was the ability to observe entangled
three-photon Greenberger-Horne-Zeilinger states.


title: Parity Measurements, Decoherence and Spiky Wigner Functions

abstract:
  Notwithstanding radical conceptual differences between classical and quantum
mechanics, it is usually assumed that physical measurements concern observables
common to both theories . Not so with the eigenvalues ($\pm 1$) of the parity
operator. The effect of such a measurement on a mixture of even and odd states
of the harmonic oscillator is akin to separating at a single stroke a pair of
shuffled card decks: the result is a set of definite parity, though otherwise
mixed. The Wigner function should be a sensitive probe for this phenomenon, for
it can be interpreted as the expectation value of the parity operator. We here
derive the general form of Wigner functions $W_{\pm}$, resulting from an ideal
parity measurement on $W(\x)$. Even if $W(\x)$ resembles a classical
distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$
and negative for $W_-$. However we conjecture that $W_+$ always has negative
values.


title: Disentanglement by Dissipative Open System Dynamics

abstract:
  This paper investigates disentanglement as a result of evolution according to
a class of master equations which include dissipation and interparticle
interactions. Generalizing an earlier result of Di\'{o}si, the time taken for
complete disentanglement is calculated (i.e. for disentanglement from any other
system). The dynamics of two harmonically coupled oscillators is solved in
order to study the competing effects of environmental noise and interparticle
coupling on disentanglement. An argument based on separability conditions for
gaussian states is used to arrive at a set of conditions on the couplings
sufficient for all initial states to disentangle for good after a finite time.


title: Quantum probabilistic teleportation via entangled coherent states

abstract:
  We study the entanglement of entangled coherent states in vacuum environment
by employing the entanglement of formation and propose a scheme to
probabilistically teleport a coherent superposition state via entangled
coherent states, in which the amount of classical information sent by Alice is
restricted to one bit. The influence of decoherence due to photon absorpation
is considered. It is shown that decoherence can improve the mean fidelity of
probabilistic teleportation in some situations.


title:
Concurrence in the two dimensional XXZ- and transverse field
  Ising-models

abstract:
  Numerical results for the concurrence and bounds on the localizable
entanglement are obtained for the square lattice spin-1/2 XXZ-model and the
transverse field Ising-model at low temperatures using quantum Monte Carlo.


title:
Generalized Partitioned Quantum Cellular Automata and Quantization of
  Classical CA

abstract:
  In this paper, in order to investigate natural transformations from discrete
CA to QCA, we introduce a new formulation of finite cyclic QCA and generalized
notion of partitioned QCA. According to the formulations, we demonstrate the
condition of local transition functions, which induce a global transition of
well-formed QCA. Following the results, extending a natural correspondence of
classical cells and quantum cells to the correspondence of classical CA and
QCA, we have the condition of classical CA such that CA generated by
quantumization of its cells is well-formed QCA. Finally we report some results
of computer simulations of quantumization of classical CA.


title:
Convolutionless Non-Markovian master equations and quantum trajectories:
  Brownian motion revisited

abstract:
  Stochastic Schr{\"o}dinger equations for quantum trajectories offer an
alternative and sometimes superior approach to the study of open quantum system
dynamics. Here we show that recently established convolutionless non-Markovian
stochastic Schr{\"o}dinger equations may serve as a powerful tool for the
derivation of convolutionless master equations for non-Markovian open quantum
systems. The most interesting example is quantum Brownian motion (QBM) of a
harmonic oscillator coupled to a heat bath of oscillators, one of the
most-employed exactly soluble models of open system dynamics. We show
explicitly how to establish the direct connection between the exact
convolutionless master equation of QBM and the corresponding convolutionless
exact stochastic Schr\"odinger equation.


title: Mean Field Approximations and Multipartite Thermal Correlations

abstract:
  The relationship between the mean-field approximations in various interacting
models of statistical physics and measures of classical and quantum
correlations is explored. We present a method that allows us to bound the total
amount of correlations (and hence entanglement) in a physical system in thermal
equilibrium at some temperature in terms of its free energy and internal
energy. This method is first illustrated using two qubits interacting through
the Heisenberg coupling, where entanglement and correlations can be computed
exactly. It is then applied to the one dimensional Ising model in a transverse
magnetic field, for which entanglement and correlations cannot be obtained by
exact methods. We analyze the behavior of correlations in various regimes and
identify critical regions, comparing them with already known results. Finally,
we present a general discussion of the effects of entanglement on the
macroscopic, thermodynamical features of solid-state systems. In particular, we
exploit the fact that a $d$ dimensional quantum system in thermal equilibrium
can be made to corresponds to a d+1 classical system in equilibrium to
substitute all entanglement for classical correlations.


title: An exact effective two-qubit gate in a chain of three spins

abstract:
  We show that an effective two-qubit gate can be obtained from the free
evolution of three spins in a chain with nearest neighbor XY coupling, without
local manipulations. This gate acts on the two remote spins and leaves the
mediating spin unchanged. It can be used to perfectly transfer an arbitrary
quantum state from the first spin to the last spin or to simultaneously
communicate one classical bit in each direction. One ebit can be generated in
half of the time for state transfer.
  For longer spin chains, we present methods to create or transfer entanglement
between the two end spins in half of the time required for quantum state
transfer, given tunable coupling strength and local magnetic field. We also
examine imperfect state transfer through a homogeneous XY chain.


title:
Dirac's hole theory versus field theory for a time dependent
  perturbation

abstract:
  Dirac's hole theory (HT) and quantum field theory (QFT) are generally
considered to be equivalent to each other. However, it has been recently shown
that for a time independent perturbation different results are obtained when
the change in the vacuum energy is calculated. Here we shall extend this
discussion to include a time dependent perturbation. It will be shown that HT
and QFT yield different results for the change in the vacuum energy due to a
time dependent perturbation.


title: Comparative Computational Strength of Quantum Oracles

abstract:
  It is an established fact that for many of the interesting problems quantum
algorithms based on queries of the standard oracle bring no significant
improvement in comparison to known classical algorithms. It is conceivable that
there are other oracles of algorithmic importance acting in a less intuitive
fashion to which such limitations do not apply. Thus motivated this article
suggests a broader understanding towards what a general quantum oracle is.
  We propose a general definition of a quantum oracle and give a classification
of quantum oracles based on the behavior of the eigenvalues and eigenvectors of
their queries. Our aim is to determine the computational characteristics of a
quantum oracle in terms of these eigenvalues and eigenvectors. Within this
framework we attempt to describe the class of quantum oracles that are
efficiently simulated by the standard oracle and compare the computational
strength of different kinds of quantum oracles by an adversary argument using
trigonometric polynomials.


title: Quantum coherence: myth or fact?

abstract:
  It has recently been argued that the inability to measure the absolute phase
of an electromagnetic field prohibits the representation of a laser's output as
a quantum optical coherent state. This argument has generally been considered
technically correct but conceptually disturbing. Indeed, it would seem to place
in question the very concept of the coherent state. Here we show that this
argument fails to take into account a fundamental principle that not only
re-admits the coherent state as legitimate, but formalizes a fundamental
concept about model building in general, and in quantum mechanics in
particular.


title:
Robustness of non-abelian holonomic quantum gates against parametric
  noise

abstract:
  We present a numerical study of the robustness of a specific class of
non-abelian holonomic quantum gates . We take into account the parametric noise
due to stochastic fluctuations of the control fields which drive the
time-dependent Hamiltonian along an adiabatic loop. The performance estimator
used is the state fidelity between noiseless and noisy holonomic gates.
  We carry over our analysis with different correlation times and we find out
that noisy holonomic gates seem to be close to the noiseless ones for 'short'
and 'long' noise correlation times. This result can be interpreted as a
consequence of to the geometric nature of the holonomic operator. Our
simulation have been performed by using parameters relevant to the excitonic
proposal for implementation of holonomic quantum computation
  [P. Solinas et al. Phys. Rev. B 67, 121307 (2003)]


title:
Relation Between Catalyst-assisted Entanglement Transformation and
  Multiple-copy Transformation

abstract:
  We show that in some cases, catalyst-assisted entanglement transformation
cannot be implemented by multiple-copy transformation for pure states. This
fact, together with the result we obtained in [R. Y. Duan, Y. Feng, X. Li, and
M. S. Ying, Phys. Rev. A 71, 042319 (2005)] that the latter can be completely
implemented by the former, indicates that catalyst-assisted transformation is
strictly more powerful than multiple-copy transformation. For purely
probabilistic setting we find, however, these two kinds of transformations are
geometrically equivalent in the sense that the sets of pure states which can be
converted into a given pure state with maximal probabilities not less than a
given value have the same closure, no matter catalyst-assisted transformation
or multiple-copy transformation is used.


title: Introduction to Quantum Computation

abstract:
  This is an introductory review on the basic principles of quantum
computation. Various important quantum logic gates and algorithms based on them
are introduced. Quantum teleportation and decoherence are discussed briefly.
Some problems, without solutions, are included.


title: Teleportation on a quantum dot array

abstract:
  We present a model of quantum teleportation protocol based on a double
quantum dot array. The unknown qubit is encoded using a pair of quantum dots,
coupled by tunneling, with one excess electron. It is shown how to create
maximally entangled states with this kind of qubits using an adiabatically
increasing Coulomb repulsion between different pairs. This entangled states are
exploited to perform teleportation again using an adiabatic coupling between
them and the incoming unknown state. Finally, a sudden separation of Bob's
qubit enables a time evolution of Alice's state providing a modified version of
standard Bell measurement. Substituting the four quantum dots entangled state
with a chain of coupled DQD's, a quantum channel with high fidelity arises from
this scheme allowing the transmission over long distances.


title: A Qubit on the Faraday Mirror

abstract:
  In the context of Quantum Information (QI) the ''Faraday Mirror'' acts as a
non-universal NOT Gate. As such its behaviour complies with the principles of
quantum mechanics. This non trivial result, at the core of some recent
misinterpretations in the QI community, has been reached by a thorough
experimental investigation of the properties of the device including the
adoption of modern Quantum Process Tomography. In addition, the ''universal
optical compensation'' method devised by Mario Martinelli, of common use in
long distance quantum-cryptography, has been fully investigated theoretically
and experimentally.


title:
Particle-number scaling of the phase sensitivity in realistic Bayesian
  twin-mode Heisenberg-limited interferometry

abstract:
  We investigate the scaling of the phase sensitivity of a nonideal
Heisenberg-limited interferometer with the particle number N, in the case of
the Bayesian detection procedure proposed by Holland and Burnett [p.r.l. 71, p.
1355 (1993)] for twin boson input modes. Using Monte Carlo simulations for up
to 10,000 bosons, we show that the phase error of a nonideal interferometer
scales with the Heisenberg limit if the losses are of the order of N^-1.
Greater losses degrade the scaling which is then in N^-1/2, like the shot-noise
limit, yet the sensitivity stays sub-shot-noise as long as photon correlations
are present. These results give the actual limits of Bayesian detection for
twin-mode interferometry and prove that it is an experimentally feasible
scheme, contrary to what is implied by the coincidence-detection analysis of
Kim et al. [p.r.a. 60, p. 708 (1999)].


title: A Simple Set of Separable States in a Commutative Simplex

abstract:
  In this note a very crude but simple approximation to the set of separable
states in an arbitrary simplex of commutative states is given using the fact
that on the lines connecting the maximally mixed state and an arbitrary pure
state the positivity of the partial transpose is both necessary and sufficient
condition for separability of states. The lower limit to the volume of
separable states in a simplex is slightly improved.


title: Incoherent Noise and Quantum Information Processing

abstract:
  Incoherence in the controlled Hamiltonian is an important limitation on the
precision of coherent control in quantum information processing. Incoherence
can typically be modelled as a distribution of unitary processes arising from
slowly varying experimental parameters. We show how it introduces artifacts in
quantum process tomography and we explain how the resulting estimate of the
superoperator may not be completely positive. We then go on to attack the
inverse problem of extracting an effective distribution of unitaries that
characterizes the incoherence via a perturbation theory analysis of the
superoperator eigenvalue spectra.


title: The structure of Bell inequalities

abstract:
  We present an analysis of the structure of Bell inequalities, mainly for the
case of N qubits with two observables each. We show that these inequalities are
related to Hadamard matrices and define Bell polynomials (in one variable) as
an additional tool. With these aids we raise several conditions the
coefficients of Bell inequalities must satisfy, and recursively generate the
whole set of inequalities starting from N=1. Moreover, we prove some
characteristic features of this set, such as that most of the inequalities
contain all expectation values under consideration. Finally, we show how the
presented results can be used to construct Bell inequalities with certain
properties. An outlook on further research topics concludes the paper.


title:
Conditional preparation of single photons for scalable quantum-optical
  networking

abstract:
  A fundamental prerequisite for the implementation of linear optical quantum
computation is a source of single-photon wavepackets capable of high-visibility
interference in scalable networks. These conditions can be met with
micro-structured waveguides in conjunction with ultra-short classical timing
pulses. By exploiting a novel type-II phasematching configuration we
demonstrate a waveguided single photon source exhibiting a conditional
detection efficiency exceeding 51% (which corresponds to a preparation
efficiency of 85%) and extraordinarily high detection rates of up to 8.5x10^5
coincidences/[s.mW].


title:
Packet narrowing and quantum entanglement in photoionization and
  photodissociation

abstract:
  The narrowing of electron and ion wave packets in the process of
photoionization is investigated, with the electron-ion recoil fully taken into
account. Packet localization of this type is directly related to entanglement
in the joint quantum state of electron and ion, and to Einstein-Podolsky-Rosen
localization. Experimental observation of such packet-narrowing effects is
suggested via coincidence registration by two detectors, with a fixed position
of one and varying position of the other. A similar effect, typically with an
enhanced degree of entanglement, is shown to occur in the case of
photodissociation of molecules.


title:
Quantum chaos and random matrix theoryfor fidelity decay in quantum
  computationswith static imperfections

abstract:
  We determine the universal law for fidelity decayin quantum computations of
complex dynamics in presenceof internal static imperfections in a quantum
computer. Our approach is based on random matrix theory applied toquantum
computations in presence of imperfections.The theoretical predictions are
tested and confirmed in extensive numerical simulations of a quantum algorithm
for quantum chaos in the dynamical tent map with up to 18 qubits. The theory
developed determines the time scales forreliable quantum computations in
absence of the quantum error correction codes. These time scales are related to
the Heisenberg time, the Thouless time, and the decay time given by Fermi's
golden rule which are well known in the context of mesoscopic systems. The
comparison is presented for static imperfection effects and random errors in
quantum gates. A new convenientmethod for the quantum computation of the
coarse-grained Wigner function is also proposed.


title: Generalized Intelligent States for Nonlinear Oscillators

abstract:
  The construction of Generalized Intelligent States (GIS) for the $x^4$%
-anharmonic oscillator is presented. These GIS families are required to
minimize the Robertson-Schr\"odinger uncertainty relation. As a particular
case, we will get the so-called Gazeau-Klauder coherent states. The properties
of the latters are discussed in detail. Analytical representation is also
considered and its advantage is shown in obtaining the GIS in an analytical
way. Further extensions are finally proposed.


title:
Coherent and generalized intelligent states for infinite square well
  potential and nonlinear oscillators

abstract:
  This article is an illustration of the construction of coherent and
generalized intelligent states which has been recently proposed by us for an
arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the
infinite square well potential and the nonlinear oscillators. By means of the
analytical representation of the coherent states \`{a} la Gazeau-Klauder and
those \`{a} la Klauder-Perelomov, we derive the generalized intelligent states
in analytical ways.


title: Many copies may be required for entanglement distillation

abstract:
  A mixed quantum state shared between two parties is said to be distillable
if, by means of a protocol involving only local quantum operations and
classical communication, the two parties can transform some number of copies of
that state into a single shared pair of qubits having high fidelity with a
maximally entangled state state. In this paper it is proved that there exist
states that are distillable, but for which an arbitrarily large number of
copies is required before any distillation procedure can produce a shared pair
of qubits with even a small amount of entanglement. Specifically, for every
positive integer n there exists a state that is distillable, but given n or
fewer copies of that state every distillation procedure outputting a single
shared pair of qubits will output those qubits in a separable state.
Essentially all previous examples of states proved to be distillable were such
that some distillation procedure could output an entangled pair of qubits given
a single copy of the state in question.


title:
Contextual, Optimal and Universal Realization of the Quantum Cloning
  Machine and of the NOT gate

abstract:
  A simultaneous realization of the Universal Optimal Quantum Cloning Machine
(UOQCM) and of the Universal-NOT gate by a quantum injected optical parametric
amplification (QIOPA), is reported. The two processes, forbidden in their exact
form for fundamental quantum limitations, are found universal and optimal, and
the measured fidelity F<1 is found close to the limit values evaluated by
quantum theory. This work may enlighten the yet little explored
interconnections of fundamental axiomatic properties within the deep structure
of quantum mechanics.


title:
Magnetic field effects on the optimal fidelity of standard teleportation
  via the two qubits Heisenberg XX chain in thermal equilibrium

abstract:
  We study the two qubits Heisenberg XX chain with magnetic impurity in the
presence of the external magnetic field and calculate the optimal fidelity of
standard teleportation via the thermal equilibrium state. It is found that the
combined influence of magnetic impurity and external magnetic field can
increase the critical temperatures of entanglement and quantum teleportation
without limit. The relation between two kinds of critical temperatures is
revealed.


title: Statics and Dynamics of Quantum XY and Heisenberg Systems on Graphs

abstract:
  We consider the statics and dynamics of distinguishable spin-1/2 systems on
an arbitrary graph G with N vertices. In particular, we consider systems of
quantum spins evolving according to one of two hamiltonians: (i) the XY
hamiltonian H_XY, which contains an XY interaction for every pair of spins
connected by an edge in G; and (ii) the Heisenberg hamiltonian H_Heis, which
contains a Heisenberg interaction term for every pair of spins connected by an
edge in G. We find that the action of the XY (respectively, Heisenberg)
hamiltonian on state space is equivalent to the action of the adjacency matrix
(respectively, combinatorial laplacian) of a sequence G_k, k=0,..., N of graphs
derived from G (with G_1=G). This equivalence of actions demonstrates that the
dynamics of these two models is the same as the evolution of a free particle
hopping on the graphs G_k. Thus we show how to replace the complicated dynamics
of the original spin model with simpler dynamics on a more complicated
geometry. A simple corollary of our approach allows us to write an explicit
spectral decomposition of the XY model in a magnetic field on the path
consisting of N vertices. We also use our approach to utilise results from
spectral graph theory to solve new spin models: the XY model and heisenberg
model in a magnetic field on the complete graph.


title: Quantum phases of a qutrit

abstract:
  We consider various approaches to treat the phases of a qutrit. Although it
is possible to represent qutrits in a convenient geometrical manner by
resorting to a generalization of the Poincare sphere, we argue that the
appropriate way of dealing with this problem is through phase operators
associated with the algebra su(3). The rather unusual properties of these
phases are caused by the small dimension of the system and are explored in
detail. We also examine the positive operator-valued measures that can describe
the qutrit phase properties.


title: Quantum dense key distribution

abstract:
  This paper proposes a new protocol for quantum dense key distribution. This
protocol embeds the benefits of a quantum dense coding and a quantum key
distribution and is able to generate shared secret keys four times more
efficiently than BB84 one. We hereinafter prove the security of this scheme
against individual eavesdropping attacks, and we present preliminary
experimental results, showing its feasibility.


title: Correlated motion of two atoms trapped in a single mode cavity field

abstract:
  We study the motion of two atoms trapped at distant positions in the field of
a driven standing wave high-Q optical resonator. Even without any direct
atom-atom interaction the atoms are coupled through their position dependent
influence on the intracavity field. For sufficiently good trapping and low
cavity losses the atomic motion becomes significantly correlated and the two
particles oscillate in their wells preferentially with a 90 degrees relative
phase shift. The onset of correlations seriously limits cavity cooling
efficiency, raising the achievable temperature to the Doppler limit. The
physical origin of the correlation can be traced back to a cavity mediated
cross-friction, i.e. a friction force on one particle depending on the velocity
of the second particle. Choosing appropriate operating conditions allows for
engineering these long range correlations. In addition this cross-friction
effect can provide a basis for sympathetic cooling of distant trapped clouds.


title: Storing quantum information using dark state polaritons

abstract:
  The possibility of using a solid medium to store few-photon laser pulses as
coupled excitations between light and matter is investigated. The role of
inhomogeneous broadening and nonadiabaticity are considered, and conditions
governing the feasibility of the scheme are derived. The merits of a number of
classes of solid are examined.


title: Quantum Computer with Mixed States and Four-Valued Logic

abstract:
  In this paper we discuss a model of quantum computer in which a state is an
operator of density matrix and gates are general quantum operations, not
necessarily unitary. A mixed state (operator of density matrix) of n two-level
quantum systems is considered as an element of 4^n-dimensional operator Hilbert
space (Liouville space). It allows to use a quantum computer model with
four-valued logic. The gates of this model are general superoperators which act
on n-ququat state. Ququat is a quantum state in a four-dimensional (operator)
Hilbert space. Unitary two-valued logic gates and quantum operations for an
n-qubit open system are considered as four-valued logic gates acting on
n-ququat. We discuss properties of quantum four-valued logic gates. In the
paper we study universality for quantum four-valued logic gates.


title: Operations and single particle interferometry

abstract:
  Interferometry of single particles with internal degrees of freedom is
investigated. We discuss the interference patterns obtained when an internal
state evolution device is inserted into one or both the paths of the
interferometer. The interference pattern obtained is not uniquely determined by
the completely positive maps (CPMs) that describe how the devices evolve the
internal state of a particle. By using the concept of gluing of CPMs, we
investigate the structure of all possible interference patterns obtainable for
given trace preserving internal state CPMs. We discuss what can be inferred
about the gluing, given a sufficiently rich set of interference experiments. It
is shown that the standard interferometric setup is limited in its abilities to
distinguish different gluings. A generalized interferometric setup is
introduced with the capacity to distinguish all gluings. We also connect to
another approach using the well known fact that channels can be realized using
a joint unitary evolution of the system and an ancillary system. We deduce the
set of all such unitary `representations' and relate the structure of this set
to gluings and interference phenomena.


title: Propagating Quantum Walks: the origin of interference structures

abstract:
  We analyze the solution of the coined quantum walk on a line. First, we
derive the full solution, for arbitrary unitary transformations, by using a new
approach based on the four "walk fields" which we show determine the dynamics.
The particular way of deriving the solution allows a rigorous derivation of a
long wavelength approximation. This long wavelength approximation is useful as
it provides an approximate analytical expression that captures the basics of
the quantum walk and allows us to gain insight into the physics of the process.


title: Transmission of Quantum Images Through Long Distances

abstract:
  We report on an experiment demonstrating the principle for transmitting
quantum images through long distances. Signal and idler beams carrying
correlated images have natural divergences that can be compensated by the use
of collimating lenses and at the same time preserving the information contained
in their correlated angular spectra.


title:
Homodyne tomography characterization and nonlocality of a dual-mode
  optical qubit

abstract:
  A single photon, delocalized over two optical modes, is characterized by
means of quantum homodyne tomography. The reconstructed four-dimensional
density matrix extends over the entire Hilbert space and thus reveals, for the
first time, complete information about the dual-rail optical quantum bit as a
state of the electromagnetic field. The experimental data violate the Bell
inequality albeit with a loophole similar to the detection loophole in photon
counting experiments.


title: Understanding Deutsch's probability in a deterministic multiverse

abstract:
  Difficulties over probability have often been considered fatal to the Everett
interpretation of quantum mechanics. Here I argue that the Everettian can have
everything she needs from `probability' without recourse to indeterminism,
ignorance, primitive identity over time or subjective uncertainty: all she
needs is a particular *rationality principle*.
  The decision-theoretic approach recently developed by Deutsch and Wallace
claims to provide just such a principle. But, according to Wallace, decision
theory is itself applicable only if the correct attitude to a future Everettian
measurement outcome is subjective uncertainty. I argue that subjective
uncertainty is not to be had, but I offer an alternative interpretation that
enables the Everettian to live without uncertainty: we can justify Everettian
decision theory on the basis that an Everettian should *care about* all her
future branches. The probabilities appearing in the decision-theoretic
representation theorem can then be interpreted as the degrees to which the
rational agent cares about each future branch. This reinterpretation, however,
reduces the intuitive plausibility of one of the Deutsch-Wallace axioms
(Measurement Neutrality).


title:
Entanglement characteristics of subharmonic modes reflected from cavity
  for type II second harmonic generation

abstract:
  Quantum fluctuation and quantum entanglement of the pump field reflected from
an optical cavity for type II second harmonic generation are theoretically
analyzed. The correlation spectra between the quadratures of the reflected
subharmonic fields are interpreted in terms of pump parameter, intracavity
losses and normalized frequency. Large correlation degrees of both amplitude
and phase quadratures can be accessed in a triple resonant cavity before the
pitchfork bifurcation occurs. The two reflected subharmonic fields are in an
entangled state with the quantum correlation of phase quadratures and
anticorrelation of amplitude quadratures. The proposed system can be exploited
to be a new source generating entangled states of continuous variables.


title:
Reply to Cereceda's comment on "Quantum nonlocality for a three-particle
  nonmaximally entangled state without inequaltiy"

abstract:
  This is to reply to Cereceda's comment on "Quantum nonlocality for a
three-particle nonmaximally entangled state without inequaltiy"


title:
Electron spin detection in the frequency domain under the interrupted
  Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR) Protocol

abstract:
  Magnetic Resonance Force Microscopy (MRFM) is an emergent technology for
measuring spin-induced attonewton forces using a micromachined cantilever. In
the interrupted Oscillating Cantilever-driven Adiabatic Reversal (iOSCAR)
method, small ensembles of electron spins are manipulated by an external radio
frequency (RF) magnetic 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 develop optimal detectors for several signal models that have
been hypothesized for measurements induced by iOSCAR spin manipulation. We show
that two simple variants of the energy detector--the filtered energy detector
and a hybrid filtered energy/amplitude/energy detector--are approximately
asymptotically optimal for the Discrete-Time (D-T) random telegraph signal
model assuming White Gaussian Noise (WGN). For the D-T random walk signal
model, the filtered energy detector performs close to the optimal Likelihood
Ratio Test (LRT) when the transition probabilities are symmetric.


title: Dynamics of a large spin with weak dissipation

abstract:
  We investigate the generalization of the spin-boson model to arbitrary spin
size. The Born-Markov approximation is employed to derive a master equation in
the regime of small coupling strengths to the environment. For spin one half,
the master equation transforms into a set of Bloch equations, the solution of
which is in good agreement with results of the spin-boson model for weak ohmic
dissipation. For larger spins, we find a superradiance-like behavior known from
the Dicke model. The influence of the nonresonant bosons of the dissipative
environment can lead to the formation of a beat pattern in the dynamics of the
$z$-component of the spin. The beat frequency is approximately proportional to
the cutoff $\omega_c$ of the spectral function.


title: The Propagation of Quantum Information Through a Spin System

abstract:
  It has been recently suggested that the dynamics of a quantum spin system may
provide a natural mechanism for transporting quantum information. We show that
one dimensional rings of qubits with fixed (time-independent) interactions,
constant around the ring, allow high fidelity communication of quantum states.
We show that the problem of maximising the fidelity of the quantum
communication is related to a classical problem in fourier wave analysis. By
making use of this observation we find that if both communicating parties have
access to limited numbers of qubits in the ring (a fraction that vanishes in
the limit of large rings) it is possible to make the communication arbitrarily
good.


title: Covariant fuzzy observables and coarse-graining

abstract:
  A fuzzy observable is regarded as a smearing of a sharp observable, and the
structure of covariant fuzzy observables is studied. It is shown that the
covariant coarse-grainings of sharp observables are exactly the covariant fuzzy
observables. A necessary and sufficient condition for a covariant fuzzy
observable to be informationally equivalent to the corresponding sharp
observable is given.


title: Quantum signatures of breather-breather interactions

abstract:
  The spectrum of the Quantum Discrete Nonlinear Schr\"odinger equation on a
periodic 1D lattice shows some interesting detailed band structure which may be
interpreted as the quantum signature of a two-breather interaction in the
classical case. We show that this fine structure can be interpreted using
degenerate perturbation theory.


title:
Dynamical tunneling of bound systems through a potential barrier:
  complex way to the top

abstract:
  A semiclassical method of complex trajectories for the calculation of the
tunneling exponent in systems with many degrees of freedom is further
developed. It is supplemented with an easily implementable technique, which
enables one to single out the physically relevant trajectory from the whole set
of complex classical trajectories. The method is applied to semiclassical
transitions of a bound system through a potential barrier. We find that the
properties of physically relevant complex trajectories are qualitatively
different in the cases of potential tunneling at low energy and dynamical
tunneling at energies exceeding the barrier height. Namely, in the case of high
energies, the physically relevant complex trajectories describe tunneling via
creation of a state close to the top of the barrier. The method is checked
against exact solutions of the Schrodinger equation in a quantum mechanical
system of two degrees of freedom.


title:
Quantum and classical features in the explanation of collisional
  decoherence

abstract:
  A most simple theoretical argument is given in order to explain the
quantitative estimate of the effect of collisional decoherence in matter-wave
interferometry. The argument highlights the relevance of quantum and classical
features in the description of the phenomenon, showing in particular the
connection between the formula used for the experimental fit and the loss term
in the classical linear Boltzmann equation.


title: Geometric phase for mixed states: a differential geometric approach

abstract:
  A new definition and interpretation of geometric phase for mixed state cyclic
unitary evolution in quantum mechanics are presented. The pure state case is
formulated in a framework involving three selected Principal Fibre Bundles, and
the well known Kostant-Kirillov-Souriau symplectic structure on (co) adjoint
orbits associated with Lie groups. It is shown that this framework generalises
in a natural and simple manner to the mixed state case. For simplicity, only
the case of rank two mixed state density matrices is considered in detail. The
extensions of the ideas of Null Phase Curves and Pancharatnam lifts from pure
to mixed states are also presented.


title: Quantum dynamics in single spin measurement

abstract:
  We study the quantum dynamics of a model for the single-spin measurement in
magnetic-resonance force microscopy. We consider an oscillating driven
cantilever coupled with the magnetic moment of the sample. Then, the cantilever
is damped through an external bath and its readout is provided by a radiation
field. Conditions for reliable measurements will be discussed.


title: Energy-dependent Hamiltonians and their pseudo-Hermitian interpretation

abstract:
  The concept of energy-dependent forces in quantum mechanics is re-analysed.
We suggest a simplification of their study via the representation of each
self-adjoint and energy-dependent Hamiltonian H=H(E) with real spectrum by an
auxiliary non-Hermitian operator K which remains energy-independent. Practical
merits of such an approach to the Schroedinger equations with energy-dependent
potentials are illustrated using their quasi-exactly solvable example.


title:
A probabilistic and information theoretic interpretation of quantum
  evolutions

abstract:
  In quantum mechanics, outcomes of measurements on a state have a
probabilistic interpretation while the evolution of the state is treated
deterministically. Here we show that one can also treat the evolution as being
probabilistic in nature and one can measure `which unitary' happened. Likewise,
one can give an information-theoretic interpretation to evolutions by defining
the entropy of a completely positive map. This entropy gives the rate at which
the informational content of the evolution can be compressed. One cannot
compress this information and still have the evolution act on an unknown state,
but we demonstrate a general scheme to do so probabilistically. This allows one
to generalize super-dense coding to the sending of quantum information. One can
also define the ``interaction-entanglement'' of a unitary, and concentrate this
entanglement.


title:
No-signalling-based version of Zurek's derivation of quantum
  probabilities: A note on "Environment-assisted invariance, entanglement, and
  probabilities in quantum physics"

abstract:
  Zurek has derived the quantum probabilities for Schmidt basis states of
bipartite quantum systems in pure joint states, from the assumption that they
should be not be affected by one party's action if the action can be undone by
the other party (``envariance of probability'') and an auxiliary assumption. We
argue that a natural generalization of the auxiliary assumption is actually
strong enough to yield the Born rule itself, but that Zurek's argument and
protocol can be adapted to do without this assumption, at the cost of using
envariance of probability in both directions. We consider alternative
motivations for envariance, one based on the no-signalling constraint that
actions on one subsystem of a quantum system not allow signalling to another
subsystem entirely distinct from the first, and another which is perhaps
strongest in the context of a relative-state interpretation of quantum
mechanics. In part because of this, we argue that the relative appeal of our
version and the original version of Zurek's argument depends in part upon
whether one interprets the quantum formalism in terms of relative states or
definite measurement outcomes.


title: Handedness of complex PT-symmetric potential barriers

abstract:
  Generally, when imaginary part of an optical potential is non-symmetric the
reflectivity, $R(E)$, shows left/right handedness, further if it is not
negative-definite the reflection and transmission, $T(E)$, coefficients become
anomalous in some energy intervals and absorption is indefinite ($\pm$). We
find that the complex PT-symmetric potentials could be exceptional in this
regard. They may act effectively like an absorptive potential for any incident
energy provided the particle enters from the preferred (absorptive) side.


title: Time-dependent Displaced and Squeezed Number States

abstract:
  We generalize the wave functions of the displaced and squeezed number states,
found by Nieto, to a time-dependent harmonic oscillator with variable mass and
frequency. These time-dependent displaced and squeezed number states are
obtained by first squeezing and then displacing the exact number states and are
exact solutions of the Schr\"{o}dinger equation. Further, these wave functions
are the time-dependent squeezed harmonic-oscillator wave functions centered at
classical trajectories.


title:
Polarization enhancement in $\vec{d}(\vec{p}$,$^2$He)n reaction: Nuclear
  teleportation

abstract:
  I show that an experimental technique used in nuclear physics may be
successfully applied to quantum teleportation (QT) of spin states of massive
matter. A new non-local physical effect the `quantum-teleportation-effect' is
discovered for the nuclear polarization measurement. Enhancement of the neutron
polarization is expected in the proposed experiment for QT that discriminates
{\it only} one of the Bell states.


title: Quantum Information approach to the Ising model

abstract:
  We present detailed analytical calculations for an 1D Ising ring of arbitrary
number of spin-1/2 particles, in order to reveal entanglement properties of the
stationary states. We show that the ground state and specific eigenstates of
the Ising Hamiltonian posses remarkable entanglement properties that can reveal
new insight into quantum correlations present in the Ising model. This
correlations might be exploited in quantum information processing. We propose
an intuitive picture of the behaviour of multipartite entanglement and discuss
a relation of our results to some aspects of phase transitions in the Ising
model.


title: Nonlocality and information flow: The approach of Deutsch and Hayden

abstract:
  Deutsch and Hayden claim to have provided an account of quantum mechanics
which is particularly local, and which clarifies the nature of information
transmission in entangled quantum systems. In this paper, a perspicuous
description of their formalism is offered and their claim assessed. It proves
essential to distinguish, as Deutsch and Hayden do not, between two ways of
interpreting the formalism. On the first, conservative, interpretation, no
benefits with respect to locality accrue that are not already available on
either an Everettian or a statistical interpretation; and the conclusions
regarding information flow are equivocal. The second, ontological,
interpretation, offers a framework with the novel feature that global
properties of quantum systems are reduced to local ones; but no conclusions
follow concerning information flow in more standard quantum mechanics.


title: Light-Matter Quantum Interface

abstract:
  We propose a quantum interface which applies multiple passes of a pulse of
light through an atomic sample with phase/polarization rotations in between the
passes. Our proposal does not require nonclassical light input or measurements
on the system, and it predicts rapidly growing unconditional entanglement of
light and atoms from just coherent inputs. The proposed interface makes it
possible to achieve a number of tasks within quantum information processing
including teleportation between light and atoms, quantum memory for light and
squeezing of atomic and light variables.


title:
Quantum Probability from Subjective Likelihood: improving on Deutsch's
  proof of the probability rule

abstract:
  I present a proof of the quantum probability rule from decision-theoretic
assumptions, in the context of the Everett interpretation. The basic ideas
behind the proof are those presented in Deutsch's recent proof of the
probability rule, but the proof is simpler and proceeds from weaker
decision-theoretic assumptions. This makes it easier to discuss the conceptual
ideas involved in the proof, and to show that they are defensible.


title:
Scaling behavior of interactions in a modular quantum system and the
  existence of local temperature

abstract:
  We consider a quantum system of fixed size consisting of a regular chain of
$n$-level subsystems, where $n$ is finite. Forming groups of $N$ subsystems
each, we show that the strength of interaction between the groups scales with
$N^{- 1/2}$. As a consequence, if the total system is in a thermal state with
inverse temperature $\beta$, a sufficient condition for subgroups of size $N$
to be approximately in a thermal state with the same temperature is $\sqrt{N}
\gg \beta \bar{\delta E}$, where $\bar{\delta E}$ is the width of the occupied
level spectrum of the total system. These scaling properties indicate on what
scale local temperatures may be meaningfully defined as intensive variables.
This question is particularly relevant for non-equilibrium scenarios such as
heat conduction etc.


title: Dynamical suppression of 1/f noise processes in qubit systems

abstract:
  We investigate the capability of dynamical decoupling techniques to reduce
decoherence from a realistic environment generating 1/f noise. The predominance
of low frequency modes in the noise profile allows for decoherence scenarios
where relatively slow control rates suffice for a drastic improvement. However,
the actual figure of merit is very sensitive to the details of the dynamics,
with decoupling performance which may deteriorate for non-Gaussian noise and/or
high frequency working points. Our results are promising for robust solid-state
qubits and beyond.


title: Causality, Entanglement, and Quantum Evolution Beyond Cauchy Horizons

abstract:
  We consider a bipartite entangled system half of which falls through the
event horizon of an evaporating black hole, while the other half remains
coherently accessible to experiments in the exterior region. Beyond complete
evaporation, the evolution of the quantum state past the Cauchy horizon cannot
remain unitary, raising the questions: How can this evolution be described as a
quantum map, and how is causality preserved? The answers are subtle, and are
linked in unexpected ways to the fundamental laws of quantum mechanics. We show
that terrestrial experiments can be designed to constrain exactly how these
laws might be altered by evaporation.


title: Oblivious transfer using quantum entanglement

abstract:
  Based on quantum entanglement, an all-or-nothing oblivious transfer protocol
is proposed and is proven to be secure. The distinct merit of the present
protocol lies in that it is not based on quantum bit commitment. More
intriguingly, this OT protocol does not belong to a class of protocols denied
by the Lo's no-go theorem of one-sided two-party secure computation, and thus
its security can be achieved.


title: How to realize a universal quantum gate with trapped ions

abstract:
  We report the realization of an elementary quantum processor based on a
linear crystal of trapped ions. Each ion serves as a quantum bit (qubit) to
store the quantum information in long lived electronic states. We present the
realization of single-qubit and of universal two-qubit logic gates. The
qwo-qubit operation relies on the coupling of the ions through their collective
quantized motion. A detailed description of the setup and the methods is
included.


title: The band spectrum of periodic potentials with PT-symmetry

abstract:
  A real band condition is shown to exist for one dimensional periodic complex
non-hermitian potentials exhibiting PT-symmetry. We use an exactly solvable
ultralocal periodic potential to obtain the band structure and discuss some
spectral features of the model, specially those concerning the role of the
imaginary parameters of the couplings. Analytical results as well as some
numerical examples are provided.


title: On optimal quantum codes

abstract:
  We present families of quantum error-correcting codes which are optimal in
the sense that the minimum distance is maximal. These maximum distance
separable (MDS) codes are defined over q-dimensional quantum systems, where q
is an arbitrary prime power. It is shown that codes with parameters
[[n,n-2d+2,d]]_q exist for all 3 <= n <= q and 1 <= d <= n/2+1. We also present
quantum MDS codes with parameters [[q^2,q^2-2d+2,d]]_q for 1 <= d <= q which
additionally give rise to shortened codes [[q^2-s,q^2-2d+2-s,d]]_q for some s.


title:
Quantum noise limited interferometric measurement of atomic noise:
  towards spin squeezing on the Cs clock transition

abstract:
  We investigate theoretically and experimentally a nondestructive
interferometric measurement of the state population of an ensemble of laser
cooled and trapped atoms. This study is a step towards generation of (pseudo-)
spin squeezing of cold atoms targeted at the improvement of the Caesium clock
performance beyond the limit set by the quantum projection noise of atoms. We
calculate the phase shift and the quantum noise of a near resonant optical
probe pulse propagating through a cloud of cold 133Cs atoms. We analyze the
figure of merit for a quantum non-demolition (QND) measurement of the
collective pseudo-spin and show that it can be expressed simply as a product of
the ensemble optical density and the pulse integrated rate of the spontaneous
emission caused by the off-resonant probe light. Based on this, we propose a
protocol for the sequence of operations required to generate and utilize spin
squeezing for the improved atomic clock performance via a QND measurement on
the probe light. In the experimental part we demonstrate that the
interferometric measurement of the atomic population can reach the sensitivity
of the order of N_at^1/2 in a cloud of N_at cold atoms, which is an important
benchmark towards the experimental realisation of the theoretically analyzed
protocol.


title: Sensitivity of a cavityless optomechanical system

abstract:
  We study the possibility of revealing a weak coherent force by using a
pendular mirror as a probe, and coupling this to a radiation field, which acts
as the meter, in a cavityless configuration. We determine the sensitivity of
such a scheme and show that the use of an entangled meter state greatly
improves the ultimate detection limit. We also compare this scheme with that
involving an optical cavity.


title: Optimal reconstruction of a pure qubit state with local measurements

abstract:
  We analyse the reconstruction of an unknown pure qubit state. We derive the
optimal guess that can be inferred from any set of measurements on N identical
copies of the system with the fidelity as a figure of merit. We study in detail
the estimation process with individual von Neumann measurements and demonstrate
that they are very competitive as compared to (complicated) collective
measurements. We compute the expressions of the fidelity for large $N$ and show
that individual measurement schemes can perform optimally in the asymptotic
regime.


title:
Self Focussing as a Coherence Propagation Phenomena. An Application to
  Calculate the Coherence Length for an Atom Laser

abstract:
  A theoretical description in terms of the coherence propagation is given for
self-focussing. The concept of coherence length is defined in terms of free,
self-focussing propagation giving results in accordance with well known
experimental criteria for the laser. Extension of the method is given for an
Atom Laser showing good results in agreement with recents numerical results of
Trippenbach et. al.: J. Phys. B:At. Mol. Opt. Phys. 33, 47-54 (2000).


title:
From Linear Optical Quantum Computing to Heisenberg-Limited
  Interferometry

abstract:
  The working principles of linear optical quantum computing are based on
photodetection, namely, projective measurements. The use of photodetection can
provide efficient nonlinear interactions between photons at the single-photon
level, which is technically problematic otherwise. We report an application of
such a technique to prepare quantum correlations as an important resource for
Heisenberg-limited optical interferometry, where the sensitivity of phase
measurements can be improved beyond the usual shot-noise limit. Furthermore,
using such nonlinearities, optical quantum nondemolition measurements can now
be carried out at the single-photon level.


title:
Physically-motivated dynamical algorithms for the graph isomorphism
  problem

abstract:
  We investigate classical and quantum physics-based algorithms for solving the
graph isomorphism problem. Our work integrates and extends previous work by
Gudkov et al. (cond-mat/0209112) and by Rudolph (quant-ph/0206068). Gudkov et
al. propose an algorithm intended to solve the graph isomorphism problem in
polynomial time by mimicking a classical dynamical many-particle process. We
show that this algorithm fails to distinguish pairs of non-isomorphic strongly
regular graphs, thus providing an infinite class of counterexamples. We also
show that the simplest quantum generalization of the algorithm also fails.
However, by combining Gudkov et al.'s algorithm with a construction proposed by
Rudoph in which one examines a graph describing the dynamics of two particles
on the original graph, we find an algorithm that successfully distinguishes all
pairs of non-isomorphic strongly regular graphs that we tested (with up to 29
vertices).


title:
Analysis for practical realization of number-state manipulation by
  number-sum Bell measurement with linear optics

abstract:
  We analyze the linear optical realization of number-sum Bell measurement and
number-state manipulation by taking into account the realistic experimental
situation, specifically imperfectness of single-photon detector. The present
scheme for number-state manipulation is based on the number-sum Bell
measurement, which is implemented with linear optical elements, i.e., beam
splitters, phase shifters and zero-one-photon detectors. Squeezed vacuum states
and coherent states are used as optical sources. The linear optical Bell state
detector is formulated quantum theoretically with a probability operator
measure. Then, the fidelity of manipulation and preparation of number-states,
particularly for qubits and qutrits, is evaluated in terms of the quantum
efficiency and dark count of single-photon detector. It is found that a high
fidelity is achievable with small enough squeezing parameters and coherent
state amplitudes.


title:
Coherent Eavesdropping Attacks in Quantum Cryptography: Nonequivalence
  of Quantum and Classical Key Distillation

abstract:
  The security of a cryptographic key that is generated by communication
through a noisy quantum channel relies on the ability to distill a shorter
secure key sequence from a longer insecure one. We show that -- for protocols
that use quantum channels of any dimension and completely characterize them by
state tomography -- the noise threshold for classical advantage distillation is
substantially lower than the threshold for quantum entanglement distillation
because the eavesdropper can perform powerful coherent attacks. The earlier
claims that the two noise thresholds are identical, which were based on
analyzing incoherent attacks only, are therefore invalid.


title:
Effect of the unpolarized spin state in spin-correlation measurement of
  two protons produced in the 12C(d,2He) reaction

abstract:
  In this note we discuss the effect of the unpolarized state in the
spin-correlation measurement of the $^1S_0$ two-proton state produced in
12C(d,2He) reaction at the KVI, Groningen. We show that in the presence of the
unpolarized state the maximal violation of the CHSH-Bell inequality is lower
than the classical limit if the purity of the state is less than $ \sim
\verb+70%+$. In particular, for the KVI experiment the violation of the
CHSH-Bell inequality should be corrected by a factor $\sim\verb+10%+$ from the
pure $^1S_0$ state.


title: Quantum Computation, Categorical Semantics and Linear Logic

abstract: This preprint has been withdrawn.


title: Control of Raman Lasing in the Nonimpulsive Regime

abstract:
  We explore coherent control of stimulated Raman scattering in the
nonimpulsive regime. Optical pulse shaping of the coherent pump field leads to
control over the stimulated Raman output. A model of the control mechanism is
investigated.


title: Minimal assumption derivation of a Bell-type inequality

abstract:
  John Bell showed that a big class of local hidden-variable models stands in
conflict with quantum mechanics and experiment. Recently, there were
suggestions that empirical adequate hidden-variable models might exist, which
presuppose a weaker notion of local causality. We will show that a Bell-type
inequality can be derived also from these weaker assumptions.


title: Electronic coherence theory

abstract:
  We withdraw our paper as the factorizability of the correlation functions is
unproven.


title: Physical Principles and Properties of Unstable States

abstract:
  The main subject of the paper is the description of unstable states in
quantum mechanics and quantum field theory. Unstable states in quantum field
theory can only be introduced as the intermediate states and not as asymptotic
states. The absence of the intermediate unstable states from the asymptotic
states is compatible with unitarity. Thus the concept of an unstable state is
not introduced in quantum field theory despite the fact that an unstable state
has well defined linear momentum, angular momentum and other intrinsic quantum
numbers. In the rigged Hilbert space quantum mechanics one can define vectors
that correspond to the unstable states. These vectors are the generalized
eigenvectors (kets in the rigged Hilbert space) with complex eigenvalues of the
self-adjoint Hamiltonian. The real part of the eigenvalue corresponds to the
mass of an unstable state and the imaginary part is one half of the total
width. Such vectors form the minimally complex semigroup representation of the
Poincar\'e transformations into the forward light cone.


title:
Quantum time ordering and degeneracy. I: Time ordering in quantum
  mechanics

abstract:
  We examine how time ordering works in quantum mechanics and in classical
mechanics.


title: Two-qubit Quantum Logic Gate in Molecular Magnets

abstract:
  We proposed a scheme to realize a controlled-NOT quantum logic gate in a
dimer of exchange coupled single-molecule magnets, $[\textrm{Mn}_4]_2$. We
chosen the ground state and the three low-lying excited states of a dimer in a
finite longitudinal magnetic field as the quantum computing bases and
introduced a pulsed transverse magnetic field with a special frequency. The
pulsed transverse magnetic field induces the transitions between the quantum
computing bases so as to realize a controlled-NOT quantum logic gate. The
transition rates between the quantum computing bases and between the quantum
computing bases and other excited states are evaluated and analyzed.


title: Single-atom lasing induced atomic self trapping

abstract:
  We study motion and field dynamics of a single-atom laser consisting of a
single incoherently pumped free atom moving in an optical high-{\it Q}
resonator. For sufficient pumping, the system starts lasing whenever the atom
is close to a field antinode. If the field mode eigenfrequency is larger than
the atomic transition frequency, the generated laser light attracts the atom to
the field antinode and cools its motion. Using quantum Monte Carlo wave
function simulations, we investigate this coupled atom-field dynamics including
photon recoil and cavity decay. In the regime of strong coupling, the generated
field shows strong nonclassical features like photon antibunching, and the atom
is spatially confined and cooled to sub-Doppler temperatures.


title: Observation of Exceptional Points in Electronic Circuits

abstract:
  Two damped coupled oscillators have been used to demonstrate the occurrence
of exceptional points in a purely classical system. The implementation was
achieved with electronic circuits in the kHz-range. The experimental results
perfectly match the mathematical predictions at the exceptional point. A
discussion about the universal occurrence of exceptional points -- connecting
dissipation with spatial orientation -- concludes the paper.


title: Marginality in non-compatible random events

abstract:
  We present a way of introducing joint distibution function and its marginal
distribution functions for non-compatible observables. Each such marginal
distribution function has the property of commutativity. Models based on this
approach can be used to better explain some classical phenomena in stochastic
processes.


title: Decoherence of electron beams by electromagnetic field fluctuations

abstract:
  Electromagnetic field fluctuations are responsible for the destruction of
electron coherence (dephasing) in solids and in vacuum electron beam
interference. The vacuum fluctuations are modified by conductors and
dielectrics, as in the Casimir effect, and hence, bodies in the vicinity of the
beams can influence the beam coherence. We calculate the quenching of
interference of two beams moving in vacuum parallel to a thick plate with
permittivity $\epsilon(\omega)=\epsilon_{0}+i 4\pi\sigma/\omega$. In case of an
ideal conductor or dielectric $(|\epsilon|=\infty)$ the dephasing is suppressed
when the beams are close to the surface of the plate, because the random
tangential electric field $E_{t}$, responsible for dephasing, is zero at the
surface. The situation is changed dramatically when
  $\epsilon_{0}$ or $\sigma$ are finite. In this case there exists a layer near
the surface, where the fluctuations of $E_{t}$ are strong due to evanescent
near fields. The thickness of this near - field layer is of the order of the
wavelength in the dielectric or the skin depth in the conductor, corresponding
to a frequency which is the inverse electron time of flight from the emitter to
the detector. When the beams are within this layer their dephasing is enhanced
and for slow enough electrons can be even stronger than far from the surface.


title: Generalized reduction criterion for separability of quantum states

abstract:
  A new necessary separability criterion that relates the structures of the
total density matrix and its reductions is given. The method used is based on
the realignment method [K. Chen and L.A. Wu, Quant. Inf. Comput. 3, 193
(2003)]. The new separability criterion naturally generalizes the reduction
separability criterion introduced independently in previous work of [M.
Horodecki and P. Horodecki, Phys. Rev. A 59, 4206 (1999)] and [N.J. Cerf, C.
Adami and R.M. Gingrich, Phys. Rev. A 60, 898 (1999)]. In special cases, it
recovers the previous reduction criterion and the recent generalized partial
transposition criterion [K. Chen and L.A. Wu, Phys. Lett. A 306, 14 (2002)].
The criterion involves only simple matrix manipulations and can therefore be
easily applied.


title: Super-resolving phase measurements with a multi-photon entangled state

abstract:
  Using a linear optical elements and post-selection, we construct an entangled
polarization state of three photons in the same spatial mode. This state is
analogous to a ``photon-number path entangled state'' and can be used for
super-resolving interferometry. Measuring a birefringent phase shift, we
demonstrate two- and three-fold improvements in phase resolution.


title:
Sagnac interferometry based on ultra-slow polaritons in cold atomic
  vapors

abstract:
  The advantages of light and matter-wave Sagnac interferometers -- large area
on one hand and high rotational sensitivity per unit area on the other -- can
be combined utilizing ultra-slow light in cold atomic gases. While a
group-velocity reduction alone does not affect the Sagnac phase shift, the
associated momentum transfer from light to atoms generates a coherent
matter-wave component which gives rise to a substantially enhanced rotational
signal. It is shown that matter-wave sensitivity in a large-area interferometer
can be achieved if an optically dense vapor at sub-recoil temperatures is used.
Already a noticeable enhancement of the Sagnac phase shift is possible however
with much less cooling requirements.


title:
A discrete approach to the vacuum Maxwell equations and the fine
  structure constant

abstract:
  We recommended consequent discrete combinatorial research in mathematical
physics. Here we show an example how discretization of partial differential
equations can be done and that quickly unexpected new findings can result from
research in this up to now unexplored area. We transformed the vacuum Maxwell
equations into finite-difference equations, provided simple initial conditions
and studied the development of the electromagnetic fields using special
software (see http://www.orthuber.com). The development is wave-like as
expected. But it is not trivial, the wave maxima have different heights. If all
(by definition minimal) finite differences of the location coordinates are
multiplied by numbers (coupling factors) whose squares are equal to the fine
structure constant, we noticed:
  1. The first two wave maxima have nearly the same height. Of course this can
be also coincidental.
  2. The following maxima are at first slightly decreasing and then, beginning
with the 6th maximum, exponentially increasing.


title:
Quantum state transfer between field and atoms in Electromagnetically
  Induced Transparency

abstract:
  We show that a quasi-perfect quantum state transfer between an atomic
ensemble and fields in an optical cavity can be achieved in Electromagnetically
Induced Transparency (EIT). A squeezed vacuum field state can be mapped onto
the long-lived atomic spin associated to the ground state sublevels of the
Lambda-type atoms considered. The EIT on-resonance situation show interesting
similarities with the Raman off-resonant configuration. We then show how to
transfer the atomic squeezing back to the field exiting the cavity, thus
realizing a quantum memory-type operation.


title:
Scalable Quantum Computation in the Presence of Large Detected-Error
  Rates

abstract:
  The tolerable erasure error rate for scalable quantum computation is shown to
be at least 0.292, given standard scalability assumptions. This bound is
obtained by implementing computations with generic stabilizer code
teleportation steps that combine the necessary operations with error
correction. An interesting consequence of the technique is that the only errors
that affect the maximum tolerable error rate are storage and Bell measurement
errors. If storage errors are negligible, then any detected Bell measurement
error below 1/2 is permissible. Another consequence of the technique is that
the maximum tolerable depolarizing error rate is dominated by how well one can
prepare the required encoded states. For example, if storage and Bell
measurement errors are relatively small, then independent depolarizing errors
with error rate close to 0.1 per qubit are tolerable in the prepared states.
The implementation overhead is dominated by the efficiency with which the
required encoded states can be prepared. At present, this efficiency is very
low, particularly for error rates close to the maximum tolerable ones.


title:
Bayesian Approach to Inverse Quantum Statistics: Reconstruction of
  Potentials in the Feynman Path Integral Representation of Quantum Theory

abstract:
  The Feynman path integral representation of quantum theory is used in a
non--parametric Bayesian approach to determine quantum potentials from
measurements on a canonical ensemble. This representation allows to study
explicitly the classical and semiclassical limits and provides a unified
description in terms of functional integrals: the Feynman path integral for the
statistical operator, and the integration over the space of potentials for
calculating the predictive density. The latter is treated in maximum a
posteriori approximation, and various approximation schemes for the former are
developed and discussed. A simple numerical example shows the applicability of
the method.


title: Ultrafast Pulse Shaping Approaches to Quantum Computing

abstract:
  Quantum computing exploits the quantum-mechanical nature of matter to exist
in multiple possible states simultaneously. This new approach promises to
revolutionize the present form of computing. As an approach to quantum
computing, we discuss ultrafast laser pulse shaping, in particular, the
acousto-optic modulator based Fourier-Transform pulse-shaper, which has the
ability to modulate tunable high power ultrafast laser pulses. We show that
optical pulse shaping is an attractive route to quantum computing since shaped
pulses can be transmitted over optical hardware and the same infrastructure can
be used for computation and optical information transfer. We also address the
problem of extending coherence-times for optically induced processes.


title: Minimum construction of two-qubit quantum operations

abstract:
  Optimal construction of quantum operations is a fundamental problem in the
realization of quantum computation. We here introduce a newly discovered
quantum gate, B, that can implement any arbitrary two-qubit quantum operation
with minimal number of both two- and single-qubit gates. We show this by giving
an analytic circuit that implements a generic nonlocal two-qubit operation from
just two applications of the B gate. We also demonstrate that for the highly
scalable Josephson junction charge qubits, the B gate is also more easily and
quickly generated than the CNOT gate for physically feasible parameters.


title: Schrodinger cats and their power for quantum information processing

abstract:
  We outline a toolbox comprised of passive optical elements, single photon
detection and superpositions of coherent states (Schrodinger cat states). Such
a toolbox is a powerful collection of primitives for quantum information
processing tasks. We illustrate its use by outlining a proposal for universal
quantum computation. We utilize this toolbox for quantum metrology
applications, for instance weak force measurements and precise phase
estimation. We show in both these cases that a sensitivity at the Heisenberg
limit is achievable.


title:
Bichromatic electromagnetically induced transparency in cold rubidium
  atoms

abstract:
  In a three-level atomic system coupled by two equal-amplitude laser fields
with a frequency separation 2$\delta$, a weak probe field exhibits a
multiple-peaked absorption spectrum with a constant peak separation $\delta$.
The corresponding probe dispersion exhibits steep normal dispersion near the
minimum absorption between the multiple absorption peaks, which leads to
simultaneous slow group velocities for probe photons at multiple frequencies
separated by $\delta$. We report an experimental study in such a
bichromatically coupled three-level $\Lambda$ system in cold $^{87}$Rb atoms.
The multiple-peaked probe absorption spectra under various experimental
conditions have been observed and compared with the theoretical calculations.


title: Geometric Approach to Digital Quantum Information

abstract:
  We present geometric methods for uniformly discretizing the continuous
N-qubit Hilbert space. When considered as the vertices of a geometrical figure,
the resulting states form the equivalent of a Platonic solid. The
discretization technique inherently describes a class of pi/2 rotations that
connect neighboring states in the set, i.e. that leave the geometrical figures
invariant. These rotations are shown to generate the Clifford group, a general
group of discrete transformations on N qubits. Discretizing the N-qubit Hilbert
space allows us to define its digital quantum information content, and we show
that this information content grows as N^2. While we believe the discrete sets
are interesting because they allow extra-classical behavior--such as quantum
entanglement and quantum parallelism--to be explored while circumventing the
continuity of Hilbert space, we also show how they may be a useful tool for
problems in traditional quantum computation. We describe in detail the discrete
sets for one and two qubits.


title: De Broglie Wavelength of a Nonlocal Four-Photon

abstract:
  Superposition is one of the most distinct features of quantum theory and has
been demonstrated in numerous realizations of Young's classical double-slit
interference experiment and its analogues. However, quantum entanglement - a
significant coherent superposition in multiparticle systems - yields phenomena
that are much richer and more interesting than anything that can be seen in a
one-particle system. Among them, one important type of multi-particle
experiments uses path-entangled number-states, which exhibit pure higher-order
interference and allow novel applications in metrology and imaging such as
quantum interferometry and spectroscopy with phase sensitivity at the
Heisenberg limit or quantum lithography beyond the classical diffraction limit.
Up to now, in optical implementations of such schemes lower-order interference
effects would always decrease the overall performance at higher particle
numbers. They have thus been limited to two photons. We overcome this
limitation and demonstrate a linear-optics-based four-photon interferometer.
Observation of a four-particle mode-entangled state is confirmed by
interference fringes with a periodicity of one quarter of the single-photon
wavelength. This scheme can readily be extended to arbitrary photon numbers and
thus represents an important step towards realizable applications with
entanglement-enhanced performance.


title: Quantum Mechanics and Reality are Really Local

abstract:
  We attempt to pull together various lines of research whose ultimate
conclusion points to the actual ``locality'' of Quantum Mechanics (QM). We note
that just as John Bell discovered various errors in previous ``proofs'' of the
completeness of QM, he made an error of his own in deriving the
``non-locality'' of QM. We show that QM satisfies the correct locality bound
for non-commuting variables -- and is therefore local for 2 or more particles.
We further show that the entangled wavefunctions that produce non-local
de-Broglie-Bohm guidance equations are an artifact of First Quantization, and
that the wavefunctions describing such experiments do factorize in Second
Quantization (QED).


title: General framework for the probabilistic description of experiments

abstract:
  We introduce a new mathematical framework for the probabilistic description
of an experiment on a system of any type in terms of information representing
this system initially. Based on the notions of an information state and a
generalized observable, this framework allows us to subsume different types of
randomness and experiment effects within a single mathematical structure.
Adjusting this framework to the quantum case, we clarify what is really
"quantum" in quantum measurement theory.


title:
Partial Wave Analysis of Scattering with Nonlocal Aharonov-Bohm Effect
  and Anomalous Cross Section induced by Quantum Interference

abstract:
  Partial wave theory of a three dmensional scattering problem for an arbitray
short range potential and a nonlocal Aharonov-Bohm magnetic flux is
established. The scattering process of a ``hard shere'' like potential and the
magnetic flux is examined. An anomalous total cross section is revealed at the
specific quantized magnetic flux at low energy which helps explain the
composite fermion and boson model in the fractional quantum Hall effect. Since
the nonlocal quantum interference of magnetic flux on the charged particles is
universal, the nonlocal effect is expected to appear in quite general potential
system and will be useful in understanding some other phenomena in mesoscopic
phyiscs.


title: Motion of a charged particle in the magnetic dipole field

abstract:
  This note discusses the motion of a charged particle in the magnetic dipole
field and a modified Barut's lepton mass formula. It is shown that a charged
particle in the magnetic dipole filed has no bound states, which means that
Barut's lepton mass formula may have no physical basis.


title:
Hierarchical Dobinski-type relations via substitution and the moment
  problem

abstract:
  We consider the transformation properties of integer sequences arising from
the normal ordering of exponentiated boson ([a,a*]=1) monomials of the form
exp(x (a*)^r a), r=1,2,..., under the composition of their exponential
generating functions (egf). They turn out to be of Sheffer-type. We demonstrate
that two key properties of these sequences remain preserved under
substitutional composition: (a)the property of being the solution of the
Stieltjes moment problem; and (b) the representation of these sequences through
infinite series (Dobinski-type relations). We present a number of examples of
such composition satisfying properties (a) and (b). We obtain new Dobinski-type
formulas and solve the associated moment problem for several hierarchically
defined combinatorial families of sequences.


title: 1/N-expansion for the Dicke model and the decoherence program

abstract:
  An analysis of the Dicke model, N two-level atoms interacting with a single
radiation mode, is done using the Holstein-Primakoff transformation. The main
aim of the paper is to show that, changing the quantization axis with respect
to the common usage, it is possible to prove a general result either for N or
the coupling constant going to infinity for the exact solution of the model.
This completes the analysis, known in the current literature, with respect to
the same model in the limit of N and volume going to infinity, keeping the
density constant. For the latter the proper axis of quantization is given by
the Hamiltonian of the two-level atoms and for the former the proper axis of
quantization is defined by the interaction. The relevance of this result relies
on the observation that a general measurement apparatus acts using
electromagnetic interaction and so, one can states that the thermodynamic limit
is enough to grant the appearance of classical effects. Indeed, recent
experimental results give first evidence that superposition states disappear
interacting with an electromagnetic field having a large number of photons.

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


title: There is no generalization of known formulas for mutually unbiased bases

abstract:
  In a quantum system having a finite number $N$ of orthogonal states, two
orthonormal bases $\{a_i\}$ and $\{b_j\}$ are called mutually unbiased if all
inner products $<a_i|b_j>$ have the same modulus $1/\sqrt{N}$. This concept
appears in several quantum information problems. The number of pairwise
mutually unbiased bases is at most $N+1$ and various constructions of $N+1$
such bases have been found when $N$ is a power of a prime number. We study
families of formulas that generalize these constructions to arbitrary
dimensions using finite rings.We then prove that there exists a set of $N+1$
mutually unbiased bases described by such formulas, if and only if $N$ is a
power of a prime number.


title:
DC field induced enhancement and inhibition of spontaneous emission in a
  cavity

abstract:
  We demonstrate how spontaneous emission in a cavity can be controlled by the
application of a dc field. The method is specially suitable for Rydberg atoms.
We present a simple argument for the control of emission.


title: Difficulties with the Klein-Gordon Equation

abstract:
  Relying on the variational principle, it is proved that new contradictions
emerge from an analysis of the Lagrangian density of the Klein-Gordon field:
normalization problems arise and interaction with external electromagnetic
fields cannot take place. By contrast, the Dirac equation is free of these
problems. Other inconsistencies arise if the Klein-Gordon field is regarded as
a classical field.


title: Gaussian Decoherence from Random Spin Environments

abstract:
  We examine an exactly solvable model of decoherence - a spin-system
interacting with a collection of environment spins. We show that in this model
(introduced some time ago to illustrate environment-induced superselection)
generic assumptions about the coupling strengths lead to a universal (Gaussian)
suppression of coherence between pointer states. We explore the regimes of
validity of these results and discuss their relation to the spectral features
of the environment and to the Loschmidt echo (or fidelity). Finally, we comment
on the observation of such time dependence in spin echo experiments.


title: Quantum Lower Bounds for Fanout

abstract:
  We prove several new lower bounds for constant depth quantum circuits. The
main result is that parity (and hence fanout) requires log depth circuits, when
the circuits are composed of single qubit and arbitrary size Toffoli gates, and
when they use only constantly many ancill\ae. Under this constraint, this bound
is close to optimal. In the case of a non-constant number $a$ of ancillae, we
give a tradeoff between $a$ and the required depth, that results in a
non-trivial lower bound for fanout when $a = n^{1-o(1)}$.


title: Bounds on the Power of Constant-Depth Quantum Circuits

abstract:
  We show that if a language is recognized within certain error bounds by
constant-depth quantum circuits over a finite family of gates, then it is
computable in (classical) polynomial time. In particular, our results imply
EQNC^0 is contained in P, where EQNC^0 is the constant-depth analog of the
class EQP. On the other hand, we adapt and extend ideas of Terhal and
DiVincenzo (quant-ph/0205133) to show that, for any family F of quantum gates
including Hadamard and CNOT gates, computing the acceptance probabilities of
depth-five circuits over F is just as hard as computing these probabilities for
circuits over F. In particular, this implies that NQNC^0 = NQACC = NQP = coC=P
where NQNC^0 is the constant-depth analog of the class NQP. This essentially
refutes a conjecture of Green et al. that NQACC is contained in TC^0
(quant-ph/0106017).


title:
Quantum Process Tomography on Vibrational States of Atoms in an Optical
  Lattice

abstract:
  Quantum process tomography is used to fully characterize the evolution of the
quantum vibrational state of atoms. Rubidium atoms are trapped in a shallow
optical lattice supporting only two vibrational states, which we charcterize by
reconstructing the 2x2 density matrix. Repeating this process for a complete
set of inputs allows us to completely characterize both the system's intrinsic
decoherence and resonant coupling.


title: Conditioned Unitary Transformation on biphotons

abstract:
  A conditioned unitary transformation ($90^o$ polarization rotation) is
performed at single-photon level. The transformation is realized by rotating
polarization for one of the photons of a polarization-entangled biphoton state
(signal photon) by means of a Pockel's cell triggered by the detection of the
other (idler) photon after polarization selection. As a result, polarization
degree for the signal beam changes from zero to the value given by the idler
detector quantum efficiency. This result is relevant to practical realization
of various quantum information schemes and can be used for developing a new
method of absolute quantum efficiency calibration.


title:
Efficient extraction of quantum Hamiltonians from optimal laboratory
  data

abstract:
  Optimal Identification (OI) is a recently developed procedure for extracting
optimal information about quantum Hamiltonians from experimental data using
shaped control fields to drive the system in such a manner that dynamical
measurements provide maximal information about its Hamiltonian. However, while
optimal, OI is computationally expensive as initially presented. Here, we
describe the unification of OI with highly efficient global, nonlinear
map-facilitated data inversion procedures. This combination is expected to make
OI techniques more suitable for laboratory implementation. A simulation of
map-facilitated OI is performed demonstrating that the input-output maps can
greatly accelerate the inversion process.


title: Quantum and Classical Tradeoffs

abstract:
  We propose an approach for quantifying a quantum circuit's quantumness as a
means to understand the nature of quantum algorithmic speedups. Since quantum
gates that do not preserve the computational basis are necessary for achieving
quantum speedups, it appears natural to define the quantumness of a quantum
circuit using the number of such gates. Intuitively, a reduction in the
quantumness requires an increase in the amount of classical computation, hence
giving a ``quantum and classical tradeoff''.
  In this paper we present two results on this direction. The first gives an
asymptotic answer to the question: ``what is the minimum number of
non-basis-preserving gates required to generate a good approximation to a given
state''. This question is the quantum analogy of the following classical
question, ``how many fair coins are needed to generate a given probability
distribution'', which was studied and resolved by Knuth and Yao in 1976. Our
second result shows that any quantum algorithm that solves Grover's Problem of
size n using k queries and l levels of non-basis-preserving gates must have
k*l=\Omega(n).


title: Existence of temperature on the nanoscale

abstract:
  We consider a regular chain of quantum particles with nearest neighbour
interactions in a canonical state with temperature $T$. We analyse the
conditions under which the state factors into a product of canonical density
matrices with respect to groups of $n$ particles each and under which these
groups have the same temperature $T$. In quantum mechanics the minimum group
size $n_{min}$ depends on the temperature $T$, contrary to the classical case.
We apply our analysis to a harmonic chain and find that $n_{min} = const.$ for
temperatures above the Debye temperature and $n_{min} \propto T^{-3}$ below.


title: Generation of pure, ionic entangled states via linear optics

abstract:
  In this paper, we propose a novel scheme to generate two-ion maximally
entangled states from either pure product states or mixed states using linear
optics. Our new scheme is mainly based on the ionic interference. Because the
proposed scheme can generate pure maximally entangled states from mixed states,
we denote it as purification-like generation scheme. The scheme does not need a
Bell state analyzer as the existing entanglement generation schemes do, it also
avoids the difficulty of synchronizing the arrival time of the two scattered
photons faced by the existing schemes, thus the proposed new entanglement
generation scheme can be implemented more easily in practice.


title:
Bounds on classical information capacities for a class of quantum memory
  channels

abstract:
  The maximum rates for information transmission through noisy quantum channels
has primarily been developed for memoryless channels, where the noise on each
transmitted state is treated as independent. Many real world communication
channels experience noise which is modelled better by errors that are
correlated between separate channel uses. In this paper, upper bounds on the
classical information capacities of a class of quantum memory channels are
derived. The class of channels consists of indecomposable quantum memory
channels, a generalization of classical indecomposable finite-state channels.


title: Evolution speed in some coupled-spin models

abstract:
  We investigate the time evolution of some models with N spins and pairwise
couplings, for the case of large N, in order to compare evolution times with
"speed limit" minima derived in the literature. Both in a (symmetric) case with
couplings of the same strength between each pair and in a case of broken
symmetry, the times necessary for evolution to a state in which the simplest
initial state has evolved into a nearly orthogonal state are proportional to
1/N, as is the speed limit time. However the coefficient in the broken symmetry
case comes much closer to the speed limit value. Introducing a different
criterion for evolution speed, based on macroscopic changes in occupation, we
find a corresponding enhancement in rates in the asymmetric case as compared to
the symmetric case.