title: On the Power of Quantum Algorithms for Vector Valued Mean Computation

abstract:
  We study computation of the mean of sequences with values in finite
dimensional normed spaces and compare the computational power of classical
randomized with that of quantum algorithms for this problem. It turns out that
in contrast to the known superiority of quantum algorithms in the scalar case,
in high dimensional $L_p^M$ spaces classical randomized algorithms are
essentially as powerful as quantum algorithms.


title:
Measurable nonlocal effect of bipartite system during a local cyclic
  evolution of its subsystem

abstract:
  In this letter, a nonlocal effect for a bipartite system which is induced by
a local cyclic evolution of one of its subsystem is suggested. This effect
vanishes when the system is at a disentangled pure state but can be observed
for some disentangled mixed states. As a paradigm, we study the effect for the
system of two qubits in detail. It is interesting that the effect is directly
related to the degree of entanglement for pure state of qubit pairs.
Furthermore, we suggest a Bell-type experiment to measure this nonlocal effect
for qubit pairs.


title: A Quantum Many-Body Instability in the Thermodynamic Limit

abstract:
  Intrinsic decoherence in the thermodynamic limit is shown for a large class
of many-body quantum systems in the unitary evolution in NMR and cavity QED.
The effect largely depends on the inability of the system to recover the
phases. Gaussian decaying in time of the fidelity is proved for spin systems
and radiation-matter interaction.


title: Quantum cryptography with correlated twin laser beams

abstract:
  The data transmission protocol, based on the use of a strongly correlated
pair of laser beams, is proposed. The properties of the corresponding states
are described in detail. The protocol is based on the strong correlation of
photon numbers in both beams in each measurement. The protocol stability
against the interception attempts is analyzed.


title:
Counterintuitive transitions in the multistate Landau-Zener problem with
  linear level crossings

abstract:
  We generalize the Brundobler-Elser hypothesis in the multistate Landau-Zener
problem to the case when instead of a state with the highest slope of the
diabatic energy level there is a band of states with an arbitrary number of
parallel levels having the same slope. We argue that the probabilities of
counterintuitive transitions among such states are exactly zero.


title:
Graph-based simulation of quantum computation in the density matrix
  representation

abstract:
  Quantum-mechanical phenomena are playing an increasing role in information
processing, as transistor sizes approach the nanometer level, and quantum
circuits and data encoding methods appear in the securest forms of
communication. Simulating such phenomena efficiently is exceedingly difficult
because of the vast size of the quantum state space involved. A major
complication is caused by errors (noise) due to unwanted interactions between
the quantum states and the environment. Consequently, simulating quantum
circuits and their associated errors using the density matrix representation is
potentially significant in many applications, but is well beyond the
computational abilities of most classical simulation techniques in both time
and memory resources. The size of a density matrix grows exponentially with the
number of qubits simulated, rendering array-based simulation techniques that
explicitly store the density matrix intractable. In this work, we propose a new
technique aimed at efficiently simulating quantum circuits that are subject to
errors. In particular, we describe new graph-based algorithms implemented in
the simulator QuIDDPro/D. While previously reported graph-based simulators
operate in terms of the state-vector representation, these new algorithms use
the density matrix representation. To gauge the improvements offered by
QuIDDPro/D, we compare its simulation performance with an optimized array-based
simulator called QCSim. Empirical results, generated by both simulators on a
set of quantum circuit benchmarks involving error correction, reversible logic,
communication, and quantum search, show that the graph-based approach far
outperforms the array-based approach.


title:
A practical limitation for continuous-variable quantum cryptography
  using coherent states

abstract:
  In this letter, first, we investigate the security of a continuous-variable
quantum cryptographic scheme with a postselection process against individual
beam splitting attack. It is shown that the scheme can be secure in the
presence of the transmission loss owing to the postselection. Second, we
provide a loss limit for continuous-variable quantum cryptography using
coherent states taking into account excess Gaussian noise on quadrature
distribution. Since the excess noise is reduced by the loss mechanism, a
realistic intercept-resend attack which makes a Gaussian mixture of coherent
states gives a loss limit in the presence of any excess Gaussian noise.


title: Two-photon nonlinearity in general cavity QED systems

abstract:
  We have investigated the two-photon nonlinearity at general cavity QED
systems, which covers both weak and strong coupling regimes and includes
radiative loss from the atom. The one- and two-photon propagators are obtained
in analytic forms. By surveying both coupling regimes, we have revealed the
conditions on the photonic wavepacket for yielding large nonlinearity depending
on the cavity Q-value. We have also discussed the effect of radiative loss on
the nonlinearity.


title: Genuine quantum trajectories for non-Markovian processes

abstract:
  A large class of non-Markovian quantum processes in open systems can be
formulated through time-local master equations which are not in Lindblad form.
It is shown that such processes can be embedded in a Markovian dynamics which
involves a time dependent Lindblad generator on an extended state space. If the
state space of the open system is given by some Hilbert space ${\mathcal{H}}$,
the extended state space is the triple Hilbert space
${\mathcal{H}}\otimes{\mathbb C}^3$ which is obtained by combining the open
system with a three state system. This embedding is used to derive an
unraveling for non-Markovian time evolution by means of a stochastic process in
the extended state space. The process is defined through a stochastic
Schr\"odinger equation which generates genuine quantum trajectories for the
state vector conditioned on a continuous monitoring of an environment. The
construction leads to a continuous measurement interpretation for non-Markovian
dynamics within the framework of the theory of quantum measurement.


title: Experimental Purification of Single Qubits

abstract:
  We report the experimental realization of the purification protocol for
single qubits sent through a depolarization channel. The qubits are associated
with polarization encoded photon particles and the protocol is achieved by
means of passive linear optical elements. The present approach may represent a
convenient alternative to the distillation and error correction protocols of
quantum information.


title: Entangled states of light

abstract:
  These notes are more or less a faithful representation of my talk at the
Workshop on ``Quantum Coding and Quantum Computing'' held at the University of
Virginia. As such it is an introduction for non-physicists to the topics of the
quantum theory of light and entangled states of light. In particular, I discuss
the photon concept and what is really entangled in an entangled state of light
(it is not the photons). Moreover, I discuss an example that highlights the
peculiar behavior of entanglement in an infinite-dimensional Hilbert space.


title: Quantum walks and their algorithmic applications

abstract:
  Quantum walks are quantum counterparts of Markov chains. In this article, we
give a brief overview of quantum walks, with emphasis on their algorithmic
applications.


title: Cavity QED "By The Numbers"

abstract:
  The number of atoms trapped within the mode of an optical cavity is
determined in real time by monitoring the transmission of a weak probe beam.
Continuous observation of atom number is accomplished in the strong coupling
regime of cavity quantum electrodynamics and functions in concert with a
cooling scheme for radial atomic motion. The probe transmission exhibits sudden
steps from one plateau to the next in response to the time evolution of the
intracavity atom number, from N >= 3 to N = 2 to 1 to 0, with some trapping
events lasting over 1 second.


title:
Effect of electron-nuclear spin interactions on electron-spin qubits
  localized in self-assembled quantum dots

abstract:
  The effect of electron-nuclear spin interactions on qubit operations is
investigated for a qubit represented by the spin of an electron localized in a
self-assembled quantum dot. The localized electron wave function is evaluated
within the atomistic tight-binding model. The magnetic field generated by the
nuclear spins is estimated in the presence of an inhomogeneous environment
characterized by a random nuclear spin configuration, by the dot-size
distribution, by alloy disorder, and by interface disorder. Due to these
inhomogeneities, the magnitude of the nuclear magnetic field varies from one
qubit to another by the order of 100 G, 100 G, 10 G, and 0.1 G, respectively.
The fluctuation of the magnetic field causes errors in exchange operations due
to the inequality of the Zeeman splitting between two qubits. We show that the
errors can be made lower than the quantum error threshold if an exchange energy
larger than 0.1 meV is used for the operation.


title: General expression for the quantum Zeno and anti-Zeno effects

abstract:
  In this paper we investigate the quantum Zeno and anti-Zeno effects without
using any particular model of the measurement. Making a few assumptions about
the measurement process we derive an expression for the jump probability during
the measurement. From this expression the equation, obtained by Kofman and
Kurizki [Nature (London) 405, 546 (2000)] can be derived as a special case.


title:
Distinguishing mixed quantum states: Minimum-error discrimination versus
  optimum unambiguous discrimination

abstract:
  We consider two different optimized measurement strategies for the
discrimination of nonorthogonal quantum states. The first is conclusive
discrimination with a minimum probability of inferring an erroneous result, and
the second is unambiguous, i. e. error-free, discrimination with a minimum
probability of getting an inconclusive outcome, where the measurement fails to
give a definite answer. For distinguishing between two mixed quantum states, we
investigate the relation between the minimum error probability achievable in
conclusive discrimination, and the minimum failure probability that can be
reached in unambiguous discrimination of the same two states. The latter turns
out to be at least twice as large as the former for any two given states. As an
example, we treat the case that the state of the quantum system is known to be,
with arbitrary prior probability, either a given pure state, or a uniform
statistical mixture of any number of mutually orthogonal states. For this case
we derive an analytical result for the minimum probability of error and perform
a quantitative comparison to the minimum failure probability.


title: Push button generation of multiphoton entanglement

abstract:
  Photon entanglement is an essential ingredient for linear optics quantum
computing schemes, quantum cryptographic protocols and fundamental tests of
quantum mechanics. Here we describe a setup that allows for the generation of
polarisation-entangled N-photon states on demand. The photons are obtained by
mapping the entangled state of N atoms, each of them trapped inside an optical
cavity, onto the free radiation field. The required initial state can be
prepared by performing postselective measurements on the collective emission
from the cavities through a multiport beamsplitter.


title: Dynamical entanglement-transfer for quantum information networks

abstract:
  A key element in the architecture of a quantum information processing network
is a reliable physical interface between fields and qubits. We study a process
of entanglement transfer engineering, where two remote qubits respectively
interact with entangled two-mode continuous variable (CV) field. We quantify
the entanglement induced in the qubit state at the expenses of the loss of
entanglement in the CV system. We discuss the range of mixed entangled states
which can be obtained with this set-up. Furthermore, we suggest a protocol to
determine the residual entangling power of the light fields, inferring, thus,
the entanglement left in the field modes which, after the interaction, are no
longer in a Gaussian state. Two different set-ups are proposed: a cavity-QED
system and an interface between superconducting qubits and field modes. We
address in details the practical difficulties inherent in these two proposals,
showing that the latter is promising under many aspects.


title: Quantum Algorithms and Covering Spaces

abstract:
  In this paper we isolate the combinatorial property responsible (at least in
part) for the computational speedups recently observed in some quantum walk
algorithms. We find that continuous-time quantum walks can exploit the covering
space property of certain graphs. We demonstrate that a quantum walk on a graph
Y which covers a smaller graph X can be equivalent to a quantum walk on the
smaller graph X. This equivalence occurs only when the walk begins on certain
initial states, fibre-constant states, which respect the graph covering space
structure. We illustrate these observations with walks on Cayley graphs; we
show that walks on fibre-constant initial states for Cayley graphs are
equivalent to walks on the induced Schreier graph. We also consider the problem
of constructing efficient gate sequences simulating the time evolution of a
continuous-time quantum walk. For the case of the walk on the m-torus graph T^m
on 2^n vertices we construct a gate sequence which uses O(\poly(n)) gates which
is independent of the time t the walk is simulated for (and so the sequence can
simulate the walk for exponential times). We argue that there exists a wide
class of nontrivial operators based on quantum walks on graphs which can be
measured efficiently. We introduce a new general class of computational
problems, HiddenCover, which includes a variant of the general hidden subgroup
problem as a subclass. We argue that quantum computers ought to be able to
utilise covering space structures to efficiently solve HiddenCover problems.


title: Casimir-Polder forces: A non-perturbative approach

abstract:
  Within the frame of macroscopic QED in linear, causal media, we study the
radiation force of Casimir-Polder type acting on an atom which is positioned
near dispersing and absorbing magnetodielectric bodies and initially prepared
in an arbitrary electronic state. It is shown that minimal and multipolar
coupling lead to essentially the same lowest-order perturbative result for the
force acting on an atom in an energy eigenstate. To go beyond perturbation
theory, the calculations are based on the exact center-of-mass equation of
motion. For a nondriven atom in the weak-coupling regime, the force as a
function of time is a superposition of force components that are related to the
electronic density-matrix elements at a chosen time. Even the force component
associated with the ground state is not derivable from a potential in the
ususal way, because of the position dependence of the atomic polarizability.
Further, when the atom is initially prepared in a coherent superposition of
energy eigenstates, then temporally oscillating force components are observed,
which are due to the interaction of the atom with both electric and magnetic
fields.


title: Two exactly-solvable problems in one-dimensional hyperbolic Space

abstract:
  In this paper we establish a relation between two exactly-solvable problems
on one-dimensional hyperbolics space, namely singular Coulomb and singular
oscillator systems.


title: Towards a time-reversal mirror for quantum systems

abstract:
  The reversion of the time evolution of a quantum state can be achieved by
changing the sign of the Hamiltonian as in the polarization echo experiment in
NMR. In this work we describe an alternative mechanism inspired by the acoustic
time reversal mirror. By solving the inverse time problem in a discrete space
we develop a new procedure, the perfect inverse filter. It achieves the exact
time reversion in a given region by reinjecting a prescribed wave function at
its periphery.


title:
Unconditional security of coherent-state quantum key distribution with
  strong phase-reference pulse

abstract:
  We prove the unconditional security of a quantum key distribution protocol in
which bit values are encoded in the phase of a weak coherent-state pulse
relative to a strong reference pulse. In contrast to implementations in which a
weak pulse is used as a substitute for a single-photon source, the achievable
key rate is found to decrease only linearly with the transmission of the
channel.


title: The evolution of atomic matter waves inside an atom fiber

abstract:
  A phenomenological description of time evolution of atomic matter waves
inside a spiral shaped atomic-wave guide is presented in this report. We study
three related topics: (i) the effective Hamiltonian and the time-development
equation governing the matter waves; (ii) wavefunctions describing the matter
waves in the noncoplanar atom guide; (iii) showing that such wavefunctions
obtained is just the eigenstates of the atomic momentum operator. It is
believed that both the idea and the results presented here may have relevance
to some fundamental problems of atom optics.


title: Universally composable privacy amplification against quantum adversaries

abstract:
  Privacy amplification is the art of shrinking a partially secret string Z to
a highly secret key S. We show that, even if an adversary holds quantum
information about the initial string Z, the key S obtained by two-universal
hashing is secure, according to a universally composable security definition.
Additionally, we give an asymptotically optimal lower bound on the length of
the extractable key S in terms of the adversary's (quantum) knowledge about Z.
Our result has applications in quantum cryptography. In particular, it implies
that many of the known quantum key distribution protocols are universally
composable.


title: Locally Accessible Information and Distillation of Entanglement

abstract:
  A new type of complementary relation is found between locally accessible
information and final average entanglement for given ensemble. It is also shown
that in some well known distillation protocol, this complementary relation is
optimally satisfied. We discuss the interesting trade-off between locally
accessible information and distillable entanglement for some states.


title:
Entanglement at the boundary of spin chains near a quantum critical
  point and in systems with boundary critical points

abstract:
  We analyze the entanglement properties of spins (qubits) attached to the
boundary of spin chains near quantum critical points, or to dissipative
environments, near a boundary critical point, such as Kondo-like systems or the
dissipative two level system. In the first case, we show that the properties of
the entanglement are significantly different from those for bulk spins. The
influence of the proximity to a transition is less marked at the boundary. In
the second case, our results indicate that the entanglement changes abruptly at
the point where coherent quantum oscillations cease to exist. The phase
transition modifies significantly less the entanglement.


title:
A Bloch-Sphere-Type Model for Two Qubits in the Geometric Algebra of a
  6-D Euclidean Vector Space

abstract:
  Geometric algebra is a mathematical structure that is inherent in any metric
vector space, and defined by the requirement that the metric tensor is given by
the scalar part of the product of vectors. It provides a natural framework in
which to represent the classical groups as subgroups of rotation groups, and
similarly their Lie algebras. In this article we show how the geometric algebra
of a six-dimensional real Euclidean vector space naturally allows one to
construct the special unitary group on a two-qubit (quantum bit) Hilbert space,
in a fashion similar to that used in the well-established Bloch sphere model
for a single qubit. This is then used to illustrate the Cartan decompositions
and subalgebras of the four-dimensional special unitary group, which have
recently been used by J. Zhang, J. Vala, S. Sastry and K. B. Whaley [Phys. Rev.
A 67, 042313, 2003] to study the entangling capabilities of two-qubit
unitaries.


title:
Defending Continuous Variable Teleportation: Why a laser is a clock, not
  a quantum channel

abstract:
  It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87},
077903 (2001)] that continuous-variable quantum teleportation at optical
frequencies has not been achieved because the source used (a laser) was not
`truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, {\bf 88}, 027902
(2002)], while arguing against Rudolph and Sanders, also accept that an
`absolute phase' is achievable, even if it has not been achieved yet. I will
argue to the contrary that `true coherence' or `absolute phase' is always
illusory, as the concept of absolute time (at least for frequencies beyond
direct human experience) is meaningless. All we can ever do is to use an agreed
time standard. In this context, a laser beam is fundamentally as good a `clock'
as any other. I explain in detail why this claim is true, and defend my
argument against various objections. In the process I discuss super-selection
rules, quantum channels, and the ultimate limits to the performance of a laser
as a clock. For this last topic I use some earlier work by myself [Phys. Rev. A
{\bf 60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803
(2002)] to show that a Heisenberg-limited laser with a mean photon number $\mu$
can synchronize $M$ independent clocks each with a mean-square error of
$\sqrt{M}/4\mu$ radians$^2$.


title: Phase diagram for the Grover algorithm with static imperfections

abstract:
  We study effects of static inter-qubit interactions on the stability of the
Grover quantum search algorithm. Our numerical and analytical results show
existence of regular and chaotic phases depending on the imperfection strength
$\epsilon$. The critical border $\epsilon_c$ between two phases drops
polynomially with the number of qubits $n_q$ as $\epsilon_c \sim n_q^{-3/2}$.
In the regular phase $(\epsilon < \epsilon_c)$ the algorithm remains robust
against imperfections showing the efficiency gain $\epsilon_c / \epsilon$ for
$\epsilon \gtrsim 2^{-n_q/2}$. In the chaotic phase $(\epsilon > \epsilon_c)$
the algorithm is completely destroyed.


title:
The effect of parallel static and microwave electric fields on excited
  hydrogen atoms

abstract:
  Motivated by recent experiments we analyse the classical dynamics of a
hydrogen atom in parallel static and microwave electric fields. Using an
appropriate representation and averaging approximations we show that resonant
ionisation is controlled by a separatrix, and provide necessary conditions for
a dynamical resonance to affect the ionisation probability.
  The position of the dynamical resonance is computed using a high-order
perturbation series, and estimate its radius of convergence. We show that the
position of the dynamical resonance does not coincide precisely with the
ionisation maxima, and that the field switch-on time can dramatically affect
the ionisation signal which, for long switch times, reflects the shape of an
incipient homoclinic. Similarly, the resonance ionisation time can reflect the
time-scale of the separatrix motion, which is therefore longer than
conventional static field Stark ionisation. We explain why these effects should
be observed in the quantum dynamics.
  PACs: 32.80.Rm, 33.40.+f, 34.10.+x, 05.45.Ac, 05.45.Mt


title:
Improved Lower Bounds for Locally Decodable Codes and Private
  Information Retrieval

abstract:
  We prove new lower bounds for locally decodable codes and private information
retrieval. We show that a 2-query LDC encoding n-bit strings over an l-bit
alphabet, where the decoder only uses b bits of each queried position of the
codeword, needs code length m = exp(Omega(n/(2^b Sum_{i=0}^b {l choose i})))
Similarly, a 2-server PIR scheme with an n-bit database and t-bit queries,
where the user only needs b bits from each of the two l-bit answers, unknown to
the servers, satisfies t = Omega(n/(2^b Sum_{i=0}^b {l choose i})). This
implies that several known PIR schemes are close to optimal. Our results
generalize those of Goldreich et al. who proved roughly the same bounds for
linear LDCs and PIRs. Like earlier work by Kerenidis and de Wolf, our classical
lower bounds are proved using quantum computational techniques. In particular,
we give a tight analysis of how well a 2-input function can be computed from a
quantum superposition of both inputs.


title: Note on the Khaneja Glaser Decomposition

abstract:
  Recently, Vatan and Williams utilize a matrix decomposition of SU(2^n)
introduced by Khaneja and Glaser to produce CNOT-efficient circuits for
arbitrary three-qubit unitary evolutions. In this note, we place the Khaneja
Glaser Decomposition (KGD) in context as a SU(2^n)=KAK decomposition by proving
that its Cartan involution is type AIII, given n is greater than 2. The
standard type AIII involution produces the Cosine-Sine Decomposition (CSD), a
well-known decomposition in numerical linear algebra which may be computed
using mature, stable algorithms. In the course of our proof that the KGD is
type AIII, we further establish the following. Khaneja and Glaser allow for a
particular degree of freedom, namely the choice of a commutative algebra a, in
their construction. Let SWAP denote a swap between qubits 1 and n. Then for
appropriate choice of a, the KGD by (SWAP v SWAP)=k1 a k2 may be recovered from
a CSD by v = (SWAP k1 SWAP) (SWAP a SWAP) (SWAP k2 SWAP).


title: Effect of hydrogen-switchable mirrors on the Casimir force

abstract:
  We present systematic measurements of the Casimir force between a gold-coated
plate and a sphere coated with a Hydrogen Switchable Mirror (HSM). HSMs are
shiny metals that can become transparent by hydrogenation. In spite of such a
dramatic change of the optical properties of the sphere, we did not observe any
significant decrease of the Casimir force after filling the experimental
apparatus with hydrogen. This counterintuitive result can be explained by the
Lifshitz theory that describes the Casimir attraction between metallic and
dielectric materials.


title:
Refocusing schemes for holonomic quantum computation in presence of
  dissipation

abstract:
  The effects of dissipation on a holonomic quantum computation scheme are
analyzed within the quantum-jump approach. We extend to the non-Abelian case
the refocusing strategies formerly introduced for (Abelian) geometric
computation. We show how double loop symmetrization schemes allow one to get
rid of the unwanted influence of dissipation in the no-jump trajectory.


title:
Quantum key distribution over 30km of standard fiber using energy-time
  entangled photon pairs: a comparison of two chromatic dispersion reduction
  methods

abstract:
  We present a full implementation of a quantum key distribution system using
energy-time entangled photon pairs and functioning with a 30km standard telecom
fiber quantum channel. Two bases of two orthogonal states are implemented and
the setup is quite robust to environmental constraints such as temperature
variation. Two different ways to manage chromatic dispersion in the quantum
channel are discussed.


title: Derivation of the wave equation

abstract:
  We shall formulate the postulates, from which the wave equation can be
obtained. In the end it will be understandable, that it is the most natural law
describing the motion of a system. The postulates themselves are simple and
apparent: the first and the fifth postulate set the definition of the
coordinate and the definition of its evolution. The second and the fourth
postulate define the momentum and define its evolution. The third postulate
sets the superposition principle. On the basis of these statements it is
possible to obtain the wave equation.


title: Distributed quantum computing: A distributed Shor algorithm

abstract:
  We present a distributed implementation of Shor's quantum factoring algorithm
on a distributed quantum network model. This model provides a means for small
capacity quantum computers to work together in such a way as to simulate a
large capacity quantum computer. In this paper, entanglement is used as a
resource for implementing non-local operations between two or more quantum
computers. These non-local operations are used to implement a distributed
factoring circuit with polynomially many gates. This distributed version of
Shor's algorithm requires an additional overhead of O((log N)^2) communication
complexity, where N denotes the integer to be factored.


title: Unambiguous discrimination between quantum mixed states

abstract:
  We prove that the states secretly chosen from a mixed state set can be
perfectly discriminated if and only if these states are orthogonal. The
sufficient and necessary condition when nonorthogonal quantum mixed states can
be unambiguously discriminated is also presented. Furthermore, we derive a
series of lower bounds on the inconclusive probability of unambiguous
discrimination of states from a mixed state set with \textit{a prior}
probabilities.


title:
Robustness of the BB84 quantum key distribution protocol against general
  coherent attacks

abstract:
  It is demonstrated that for the entanglement-based version of the
Bennett-Brassard (BB84) quantum key distribution protocol, Alice and Bob share
provable entanglement if and only if the estimated qubit error rate is below
25% or above 75%. In view of the intimate relation between entanglement and
security, this result sheds also new light on the unconditional security of the
BB84 protocol in its original prepare-and-measure form. In particular, it
indicates that for small qubit error rates 25% is the ultimate upper security
bound for any prepare-and-measure BB84-type QKD protocol. On the contrary, for
qubit error rates between 25% and 75% we demonstrate that the correlations
shared between Alice and Bob can always be explained by separable states and
thus, no secret key can be distilled in this regime.


title: Quantum statistics and locality

abstract:
  It is shown that two observers have mutually commuting observables if they
are able to prepare in each subsector of their common state space some state
exhibiting no mutual correlations. This result establishes a heretofore missing
link between statistical and locality (commensurability) properties of the
observables of spacelike separated observers in relativistic quantum physics,
envisaged four decades ago by Haag and Kastler. It is based on a discussion of
coincidence experiments and suggests a physically meaningful quantitative
measure of possible violations of Einstein causality.


title:
Quantum State Detector Design: Optimal Worst-Case a posteriori
  Performance

abstract:
  The problem addressed is to design a detector which is maximally sensitive to
specific quantum states. Here we concentrate on quantum state detection using
the worst-case a posteriori probability of detection as the design criterion.
This objective is equivalent to asking the question: if the detector declares
that a specific state is present, what is the probability of that state
actually being present? We show that maximizing this worst-case probability
(maximizing the smallest possible value of this probability) is a quasiconvex
optimization over the matrices of the POVM (positive operator valued measure)
which characterize the measurement apparatus. We also show that with a given
POVM, the optimization is quasiconvex in the matrix which characterizes the
Kraus operator sum representation (OSR) in a fixed basis. We use Lagrange
Duality Theory to establish the optimality conditions for both deterministic
and randomized detection. We also examine the special case of detecting a
single pure state. Numerical aspects of using convex optimization for quantum
state detection are also discussed.


title: Compatibility Relations between the Reduced and Global Density Matrixes

abstract:
  It is a hard and important problem to find the criterion of the set of
positive-definite matrixes which can be written as reduced density operators of
a multi-partite quantum state. This problem is closely related to the study of
many-body quantum entanglement which is one of the focuses of current quantum
information theory. We give several results on the necessary compatibility
relations between a set of reduced density matrixes, including: (i)
compatibility conditions for the one-party reduced density matrixes of any
$N_A\times N_B$ dimensional bi-partite mixed quantum state, (ii) compatibility
conditions for the one-party and two-party reduced density matrixes of any
$N_A\times N_B\times N_C$ dimensional tri-partite mixed quantum state, and
(iii) compatibility conditions for the one-party reduced matrixes of any
$M$-partite pure quantum state with the dimension $N^{\otimes M}$.


title: Quantum gates and decoherence

abstract:
  In the lectures we will be concerned with some aspects of physical
implementations of quantum gate operations which are necessary for quantum
information processing. We will discuss two possible realizations. One of them
is based on qubits being encoded in atomic degrees of freedom where the atoms
are manipulated in optical lattices above atom chips. The other realization is
based on photonic qubits and measurement-induced nonlinearities in linear
optics. Both implementations have in common that their main decoherence
mechanism is absorption in dielectric materials. The quantum theory of light in
absorbing media and its implications to decoherence will form the last part of
the lectures.


title: Localization of Multi-State Quantum Walk in One Dimension

abstract:
  We show analytically that particle trapping appears in a quantum process
called "quantum walk", in which the particle moves macroscopically correlating
to the inner states. It has been well known that a particle in the ``Hadamard
walk" with two inner states spreads away quickly on a line. In contrast, we
find one-dimensional quantum walk with multi-state in which a particle stays at
the starting point entirely with high positive probability. This striking
difference is explained from difference between degeneration of eigenvalues of
the time-evolution matrices.


title:
Examples of nonuniform limiting distributions for the quantum walk on
  even cycles

abstract:
  In the note we show how the choice of the initial states can influence the
evolution of time-averaged probability distribution of the quantum walk on even
cycles.


title: Controlled quantum teleportation and secure direct communication

abstract:
  We present a controlled quantum teleportation protocol. In the protocol,
quantum information of an unknown state of a 2-level particle is faithfully
transmitted from a sender (Alice) to a remote receiver (Bob) via an initially
shared triplet of entangled particles under the control of the supervisor
Charlie. The distributed entangled particles shared by Alice, Bob and Charlie
function as a quantum information channel for faithful transmission. We also
propose a controlled and secure direct communication scheme by means of this
teleportation. After insuring the security of the quantum channel, Alice
encodes the secret message directly on a sequence of particle states and
transmits them to Bob supervised by Charlie using this controlled quantum
teleportation. Bob can read out the encoded message directly by the measurement
on his qubit. In this scheme, the controlled quantum teleportation transmits
Alice's message without revealing any information to a potential eavesdropper.
Because there is not a transmission of the qubit carrying the secret message
between Alice and Bob in the public channel, it is completely secure for
controlled and direct secret communication if perfect quantum channel is used.
The feature of this scheme is that the communication between two sides depends
on the agreement of the third side.


title: On the quantum potential

abstract:
  We survey various origins and expressions for the quantum potential with some
new observations.


title: Entanglement generation in the Unruh effect

abstract:
  The master equation describing the completely positive time evolution of a
uniformly accelerated two-level system in weak interaction with a scalar field
in the Minkowski vacuum is derived and explicitly solved. It encodes the well
known Unruh effect, leading to a purely thermal equilibrium state. This
asymptotic state turns out to be entangled when the uniformly accelerating
system is composed by two, independent two-level atoms.


title:
Dynamical Casimir-Polder energy between an excited and a ground-state
  atom

abstract:
  We consider the Casimir-Polder interaction between two atoms, one in the
ground state and the other in its excited state. The interaction is
time-dependent for this system, because of the dynamical self-dressing and the
spontaneous decay of the excited atom. We calculate the dynamical
Casimir-Polder potential between the two atoms using an effective Hamiltonian
approach. The results obtained and their physical meaning are discussed and
compared with previous results based on a time-independent approach which uses
a non-normalizable dressed state for the excited atom.


title: Interaction-free quantum computation

abstract:
  In this paper, we study the quantum computation realized by an
interaction-free measurement (IFM). Using Kwiat et al.'s interferometer, we
construct a two-qubit quantum gate that changes one particle's trajectory
according to whether or not the other particle exists in the interferometer. We
propose a method for distinguishing Bell-basis vectors, each of which consists
of a pair of an electron and a positron, by this gate. (This is called the
Bell-basis measurement.) This method succeeds with probability 1 in the limit
of $N \to \infty$, where N is the number of beam splitters in the
interferometer. Moreover, we can carry out a controlled-NOT gate operation by
the above Bell-basis measurement and the method proposed by Gottesman and
Chuang. Therefore, we can prepare a universal set of quantum gates by the IFM.
This means that we can execute any quantum algorithm by the IFM.


title: Universal Quantum Gates For Tensors

abstract:
  A universal quantum gate is introduced for tensors of vector spaces. By using
integer powers of such a gate and by using classical reversible gates one can
approximate any element of the unitary group to any accuracy needed. The proof
uses a version of Kronecker's theory and the structure of the Bloch sphere for
tensors.


title:
Decoherence-full subsystems and the cryptographic power of a private
  shared reference frame

abstract:
  We show that private shared reference frames can be used to perform private
quantum and private classical communication over a public quantum channel. Such
frames constitute a novel type of private shared correlation (distinct from
private classical keys or shared entanglement) useful for cryptography. We
present optimally efficient schemes for private quantum and classical
communication given a finite number of qubits transmitted over an insecure
channel and given a private shared Cartesian frame and/or a private shared
reference ordering of the qubits. We show that in this context, it is useful to
introduce the concept of a decoherence-full subsystem, wherein every state is
mapped to the completely mixed state under the action of the decoherence.


title: Entropic localization in non-unitary Newtonian gravity

abstract:
  The localizing properties and the entropy production of the Newtonian limit
of a nonunitary version of fourth order gravity are analyzed. It is argued that
pure highly unlocalized states of the center of mass motion of macroscopic
bodies rapidly evolve into unlocalized ensembles of highly localized states.
The localization time and the final entropy are estimated.


title: Entanglement changing power of two-qubit unitary operations

abstract:
  We consider a two-qubit unitary operation along with arbitrary local unitary
operations acts on a two-qubit pure state, whose entanglement is C_0. We give
the conditions that the final state can be maximally entangled and be
non-entangled. When the final state can not be maximally entangled, we give the
maximal entanglement C_max it can reach. When the final state can not be
non-entangled, we give the minimal entanglement C_min it can reach. We think
C_max and C_min represent the entanglement changing power of two-qubit unitary
operations. According to this power we define an order of gates.


title:
Quantum Branching Programs and Space-Bounded Nonuniform Quantum
  Complexity

abstract:
  In this paper, the space complexity of nonuniform quantum computations is
investigated. The model chosen for this are quantum branching programs, which
provide a graphic description of sequential quantum algorithms. In the first
part of the paper, simulations between quantum branching programs and
nonuniform quantum Turing machines are presented which allow to transfer lower
and upper bound results between the two models. In the second part of the
paper, different variants of quantum OBDDs are compared with their
deterministic and randomized counterparts. In the third part, quantum branching
programs are considered where the performed unitary operation may depend on the
result of a previous measurement. For this model a simulation of randomized
OBDDs and exponential lower bounds are presented.


title: Optimal probabilistic cloning and purification of quantum states

abstract:
  We investigate the probabilistic cloning and purification of quantum states.
The performance of these probabilistic operations is quantified by the average
fidelity between the ideal and actual output states. We provide a simple
formula for the maximal achievable average fidelity and we explictly show how
to construct a probabilistic operation that achieves this fidelity. We
illustrate our method on several examples such as the phase covariant cloning
of qubits, cloning of coherent states, and purification of qubits transmitted
via depolarizing channel and amplitude damping channel. Our examples reveal
that the probabilistic cloner may yield higher fidelity than the best
deterministic cloner even when the states that should be cloned are linearly
dependent and are drawn from a continuous set.


title: Thermal spin flips in atom chips

abstract:
  We derive the spontaneous and thermal spin-flip rates for a neutral two-level
ultra-cold atom that is coupled to a magnetic field. We apply this theory to an
atom in the vicinity of a 2-layer cylindrical absorbing dielectric body
surrounded by an unbounded homogeneous medium. An analytical expression is
obtained for the spontaneous and thermal spin-flip rate in this particular
geometry. The corresponding lifetime is then computed numerically. We compare
these theoretical lifetimes to those measured by Jones et al. [M.P.A. Jones,
C.J. Vale, D. Sahagun, B.V. Hall, and E.A. Hinds, Phys. Rev. Lett. {\bf 91},
080401 (2003)]. We investigate how the lifetime depends on the materials (skin
depths) of the cylindrical body. We also show how scaling of the dimensions of
the cylindrical body affects the lifetime when (i) the distance from the wire
to the atom is fixed and (ii) when the distance from the wire to the atom is
scaled.


title: Classical information deficit and monotonicity on local operations

abstract:
  We investigate classical information deficit: a candidate for measure of
classical correlations emerging from thermodynamical approach initiated in
[Phys. Rev. Lett 89, 180402]. It is defined as a difference between amount of
information that can be concentrated by use of LOCC and the information
contained in subsystems. We show nonintuitive fact, that one way version of
this quantity can increase under local operation, hence it does not possess
property required for a good measure of classical correlations. Recently it was
shown by Igor Devetak, that regularised version of this quantity is monotonic
under LO. In this context, our result implies that regularization plays a role
of "monotoniser".


title: Exact quantum query complexity for total Boolean functions

abstract:
  We will show that if there exists a quantum query algorithm that exactly
computes some total Boolean function f by making T queries, then there is a
classical deterministic algorithm A that exactly computes f making O(T^3)
queries. The best know bound previously was O(T^4) due to Beals et al.


title:
Dual entanglement measures based on no local cloning and no local
  deleting

abstract:
  Impossibility of cloning and deleting of unknown states are important
restrictions on processing of information in the quantum world. On the other
hand, a known quantum state can always be cloned or deleted. However if we
restrict the class of allowed operations, there will arise restrictions on the
ability of cloning and deleting machines. We have shown that cloning and
deleting of known states is in general not possible by local operations. This
impossibility hints at quantum correlation in the state. We propose dual
measures of quantum correlation based on the dual restrictions of no local
cloning and no local deleting. The measures are relative entropy distances of
the desired states in a (generally impossible) perfect local cloning or local
deleting process from the best approximate state that is actually obtained by
imperfect local cloning or deleting machines. Just like the dual measures of
entanglement cost and distillable entanglement, the proposed measures are based
on important processes in quantum information. We discuss their properties. For
the case of pure states, estimations of these two measures are also provided.
Interestingly, the entanglement of cloning for a maximally entangled state of
two two-level systems is not unity.


title: When Catalysis is Useful for Probabilistic Entanglement Transformation

abstract:
  We determine all $2\times 2$ quantum states that can serve as useful
catalysts for a given probabilistic entanglement transformation, in the sense
that they can increase the maximal transformation probability. When
higher-dimensional catalysts are considered, a sufficient and necessary
condition is derived under which a certain probabilistic transformation has
useful catalysts.


title: Quantum Memory Process with a Four-Level Atomic Ensemble

abstract:
  We examine in detail the quantum memory technique for photons in a double
$\Lambda$ atomic ensemble in this work. The novel application of the present
technique to create two different quantum probe fields as well as entangled
states of them is proposed. A larger zero-degeneracy class besides dark-state
subspace is investigated and the adiabatic condition is confirmed in the
present model. We extend the single-mode quantum memory technique to the case
with multi-mode probe fields, and reveal the exact pulse matching phenomenon
between two quantized pulses in the present system.


title: Secure quantum cryptographic network based on quantum key distribution

abstract:
  We present a protocol for quantum cryptographic network consisting of a
quantum network center and many users, in which any pair of parties with
members chosen from the whole users on request can secure a quantum key
distribution by help of the center. The protocol is based on the quantum
authentication scheme given by Barnum et al. [Proc. 43rd IEEE Symp. FOCS'02, p.
449 (2002)]. We show that exploiting the quantum authentication scheme the
center can safely make two parties share nearly perfect entangled states used
in the quantum key distribution. This implies that the quantum cryptographic
network protocol is secure against all kinds of eavesdropping.


title:
Reduction of multipartite qubit density matrixes to bipartite qubit
  density matrixes and criteria of partial separability of multipartite qubit
  density matrixes

abstract:
  The partial separability of multipartite qubit density matrixes is strictly
defined. We give a reduction way from N-partite qubit density matrixes to
bipartite qubit density matrixes, and prove a necessary condition that a
N-partite qubit density matrix to be partially separable is its reduced density
matrix to satisfy PPT condition.


title: Quantum entanglement as information theoretic resource

abstract:
  We address the following criterion for quantifying the quantum information
resources: classically simulable {\it vs.} classically non-simulable
information processing. This approach gives rise to existence of a deeper level
of quantum information processing--which we refer to as "quantum communication
channel". We particularly show, that following the recipes of the standard
theory of entanglement measures does not necessarily give rise to un-locking
the quantum communication channel, which is naturally quantified by Bell
inequalities.


title:
Generalizing Tsirelson's bound on Bell inequalities using a min-max
  principle

abstract:
  Bounds on the norm of quantum operators associated with classical Bell-type
inequalities can be derived from their maximal eigenvalues. This quantitative
method enables detailed predictions of the maximal violations of Bell-type
inequalities.


title:
Qubit Channels Which Require Four Inputs to Achieve Capacity:
  Implications for Additivity Conjectures

abstract:
  An example is given of a qubit quantum channel which requires four inputs to
maximize the Holevo capacity. The example is one of a family of channels which
are related to 3-state channels. The capacity of the product channel is studied
and numerical evidence presented which strongly suggests additivity. The
numerical evidence also supports a conjecture about the concavity of output
entropy as a function of entanglement parameters. However, an example is
presented which shows that for some channels this conjecture does not hold for
all input states. A numerical algorithm for finding the capacity and optimal
inputs is presented and its relation to a relative entropy optimization
discussed.


title:
An Exact Solution to the Time-dependent Schrodinger Equation for a Model
  One-dimensional Potential

abstract:
  Analytical solutions to the time-dependent Shr\"{o}dinger equation in one
dimension are developed for time-independent potentials, one consisting of an
infinite wall and a repulsive delta function. An exact solution is obtained by
means of a convolution of time-independent solutions spanning the given Hilbert
space with appropriately chosen spectral functions. Square-integrability and
the boundary conditions are satisfied. The probability for the particle to be
found inside the potential well is calculated and shown to exhibit
non-exponential decay decreasing at large times as $t^{-3}$. The result is
generalized for all square-integrable solutions to this problem.


title: Localized Entanglement in one-dimensional Anderson model

abstract:
  The entanglement in one-dimensional Anderson model is studied. We show that
the pairwise entanglement measured by the average concurrence has a direct
relation to the localization length. The numerical study indicates that the
disorder significantly reduces the average entanglement, and entanglement
distribution clearly displays the entanglement localization. The maximal
pairwise entanglement exhibits a maximum as the disorder strength
increases,experiencing a transition from increase to decrease. The entanglement
between the center of localization and other site decreases exponentially along
the spatial direction. Finally,we study effects of disorder on dynamical
properties of entanglement.


title:
Noncommutative Bayesian Statistical Inference from a wedge of a
  Bifurcate Killing Horizon

abstract:
  Expanding a remark of my PHD-thesis the noncommutative bayesian statistical
inference from one wedge of a bifurcate Killing horizon is analyzed looking at
its inter-relation with the Unruh effect


title: Complete conditions for entanglement transfer

abstract:
  We investigate the conditions to entangle two qubits interacting with local
environments driven by a continuous-variable correlated field. We find the
conditions to transfer the entanglement from the driving field to the qubits
both in dynamical and steady-state cases. We see how the quantum correlations
initially present in the driving field play a critical role in the
entanglement-transfer process. The system we treat is general enough to be
adapted to different physical setups.


title: Axiomatic Foundations of Galilean Quantum Field Theories

abstract:
  A realistic axiomatic formulation of Galilean Quantum Field Theories is
presented, from which the most important theorems of the theory can be deduced.
In comparison with others formulations, the formal aspect has been improved by
the use of certain mathematical theories, such as group theory and the theory
of rigged Hilbert spaces. Our approach regards the fields as real things with
symmetry properties. The general structure is analyzed and contrasted with
relativistic theories.


title: Efficiency of tunable band-gap structures for single-photon emission

abstract:
  The efficiency of recently proposed single-photon emitting sources based on
tunable planar band-gap structures is examined. The analysis is based on the
study of the total and ``radiative'' decay rates, the expectation value of
emitted radiation energy and its collimating cone. It is shown that the scheme
operating in the frequency range near the defect resonance of a defect band-gap
structure is more efficient than the one operating near the band edge of a
perfect band-gap structure.


title:
Steps towards the axiomatic foundations of the relativistic quantum
  field theory: Spin-statistics, commutation relations and CPT theorems

abstract:
  A realistic physical axiomatic approach of the relativistic quantum field
theory is presented. Following the action principle of Schwinger, a covariant
and general formulation is obtained. The correspondence principle is not
invoked and the commutation relations are not postulated but deduced. The most
important theorems such as spin-statistics, and CPT are proved. The theory is
constructed form the notion of basic field and system of basic fields. In
comparison with others formulations, in our realistic approach fields are
regarded as real things with symmetry properties. Finally, the general
structure is contrasted with other formulations.


title: Coupled Classical and Quantum Oscillators

abstract:
  Some of the most enduring questions in physics--including the quantum
measurement problem and the quantization of gravity--involve the interaction of
a quantum system with a classical environment. Two linearly coupled harmonic
oscillators provide a simple, exactly soluble model for exploring such
interaction. Even the ground state of a pair of identical oscillators exhibits
effects on the quantum nature of one oscillator, e.g., a diminution of position
uncertainty, and an increase in momentum uncertainty and uncertainty product,
from their unperturbed values. Interaction between quantum and classical
oscillators is simulated by constructing a quantum state with one oscillator
initially in its ground state, the other in a coherent or Glauber state. The
subsequent wave function for this state is calculated exactly, both for
identical and distinct oscillators. The reduced probability distribution for
the quantum oscillator, and its position and momentum expectation values and
uncertainties, are obtained from this wave function. The oscillator acquires an
oscillation amplitude corresponding to a beating between the normal modes of
the system; the behavior of the position and momentum uncertainties can become
quite complicated. For oscillators with equal unperturbed frequencies, i.e., at
resonance, the uncertainties exhibit a time-dependent quantum squeezing which
can be extreme.


title:
First-order super-radiant phase transitions in a multi-qubit--cavity
  system

abstract:
  We predict the existence of novel first-order phase transitions in a general
class of multi-qubit-cavity systems. Apart from atomic systems, the associated
super-radiant phase transition should be observable in a variety of solid-state
experimental systems, including the technologically important case of
interacting quantum dots coupled to an optical cavity mode.


title: Deterministic Secure Direct Bidirectional Communication Protocol

abstract:
  In this letter a deterministic secure direct bidirectional communication
protocol is proposed by using the quantum entanglement and local unitary
operations on one photon of the Einstein-Podolsky-Rosen (EPR) photon pair.


title:
On trace inequalities and their applications to noncommutative
  communication theory

abstract:
  Certain trace inequalities related to matrix logarithm are shown.
  These results enable us to give a partial answer of the open problem
conjectured by A.S.Holevo.
  That is, concavity of the auxiliary function which appears in the random
coding exponent as the lower bound of the quantum reliability function for
general quantum states is proven in the case of $0\leq s\leq 1$.


title: Zero-error capacity of a quantum channel

abstract:
  We define the quantum zero-error capacity, a new kind of classical capacity
of a noisy quantum channel. Moreover, the necessary requirement for which a
quantum channel has zero-error capacity greater than zero is also given.


title:
Not So SuperDense Coding - Deterministic Dense Coding with Partially
  Entangled States

abstract:
  The utilization of a $d$-level partially entangled state, shared by two
parties wishing to communicate classical information without errors over a
noiseless quantum channel, is discussed. We analytically construct
deterministic dense coding schemes for certain classes of non-maximally
entangled states, and numerically obtain schemes in the general case. We study
the dependency of the information capacity of such schemes on the partially
entangled state shared by the two parties. Surprisingly, for $d>2$ it is
possible to have deterministic dense coding with less than one ebit. In this
case the number of alphabet letters that can be communicated by a single
particle, is between $d$ and 2d. In general we show that the alphabet size
grows in "steps" with the possible values $ d, d+1, ..., d^2-2 $. We also find
that states with less entanglement can have greater communication capacity than
other more entangled states.


title: Entanglement is not very useful for estimating multiple phases

abstract:
  The problem of the estimation of multiple phases (or of commuting unitaries)
is considered. This is a sub-model of the estimation of a completely unknown
unitary operation where it has been shown in recent works that there are
considerable improvements by using entangled input states and entangled
measurements. Here it is shown that when estimating commuting unitaries, there
is practically no advantage in using entangled input states or entangled
measurements.


title: Proposal for a loophole-free Bell test using homodyne detection

abstract:
  We propose a feasible optical setup allowing for a loophole-free Bell test
with efficient homodyne detection. A non-gaussian entangled state is generated
from a two-mode squeezed vacuum by subtracting a single photon from each mode,
using beamsplitters and standard low-efficiency single-photon detectors. A Bell
violation exceeding 1% is achievable with 6-dB squeezed light and an homodyne
efficiency around 95%. A detailed feasibility analysis, based upon the recent
generation of single-mode non-gaussian states, confirms that this method opens
a promising avenue towards a complete experimental Bell test.


title: Decoherence in the quantum walk on the line

abstract:
  We investigate the quantum walk on the line when decoherences are introduced
either through simultaneous measurements of the chirality and particle
position, or as a result of broken links. Both mechanisms drive the system to a
classical diffusive behavior. In the case of measurements, we show that the
diffusion coefficient is proportional to the variance of the initially
localized quantum random walker just before the first measurement. When links
between neighboring sites are randomly broken with probability $p$ per unit
time, the evolution becomes decoherent after a characteristic time that scales
as $1/p$. The fact that the quadratic increase of the variance is eventually
lost even for very small frequencies of disrupting events, suggests that the
implementation of a quantum walk on a real physical system may be severely
limited by thermal noise and lattice imperfections.


title: Quantum weak coin-flipping with bias of 0.192

abstract:
  A family of protocols for quantum weak coin-flipping which asymptotically
achieve a bias of 0.192 is described in this paper. The family contains
protocols with n+2 messages for all n>1. The case n=2 is equivalent to the
protocol of Spekkens and Rudolph with bias of 0.207. The case n=3 achieves a
bias of 0.199, and n=8 achieves a bias of 0.193. The analysis of the protocols
uses Kitaev's description of coin-flipping as a semidefinite program. The paper
constructs an analytical solution to the dual problem which provides an upper
bound on the amount that a party can cheat.


title: Recoil Effects in Microwave Ramsey Spectroscopy

abstract:
  We present a theory of recoil effects in two zone Ramsey spectroscopy,
particularly adapted to microwave frequency standards using laser cooled atoms.
We describe the atoms by a statistical distribution of Gaussian wave packets
which enables us to derive and quantify effects that are related to the
coherence properties of the atomic source and that have not been considered
previously. We show that, depending on the experimental conditions, the
expected recoil frequency shift can be partially cancelled by these effects
which can be significant at microwave wavelengths whilst negligible at optical
ones. We derive analytical expressions for the observed interference signal in
the weak field approximation, and numerical results for realistic caesium
fountain parameters. In the near future Cs and Rb fountain clocks are expected
to reach uncertainties which are of the same order of magnitude (10^{-16}) as
first estimates of the recoil shift at microwave frequencies. We show, however,
that the partial cancellation predicted by the complete theory presented here
leads to frequency shifts which are up to an order of magnitude smaller.
Nonetheless observation of the microwave recoil shift should be possible under
particular experimental conditions (increased microwave power, variation of
atomic temperature and launching height etc.). We hope that the present paper
can provide some guidance for such experiments that would test the underlying
theory and its assumptions, which in turn is essential for the next generation
of microwave frequency standards.


title:
On the momentum-space approach to calculation of one-electron energy
  spectra and wave functions of atomic clusters

abstract:
  Momentum-space approach to calculation of one-electron energies and wave
functions proposed initially by Fock for a hydrogen atom and considered later
by Shibuya, Wulfman, and Koga for diatomic molecules is applied to clusters
composed of three and more atoms. The corresponding basis set in the coordinate
space is of the Sturmian type since all the hydrogenlike orbitals in this set
have a common exponent, i.e., correspond to the same energy (as opposed to
one-electron atomic orbitals). By the examples of He$_4^{+7}$ and He$_6^{+11}$
cluster ions it is shown that increase in the number of orbitals in the set
results in rapid convergence of eigenenergies and eigenfunctions of highly
excited states. The momentum-space approach to the one-electron many-center
problem may be used for various solid-state and quantum-chemical applications.


title: Periodic Quasi - Exactly Solvable Models

abstract:
  Various quasi-exact solvability conditions, involving the parameters of the
periodic associated Lam{\'e} potential, are shown to emerge naturally in the
quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity
of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible
for the surprisingly large number of allowed solvability conditions in the
associated Lam{\'e} case. We also study the singularity structure of the
quantum momentum function, which yields the band edge eigenvalues and
eigenfunctions.


title:
Quantum computations with atoms in optical lattices: marker qubits and
  molecular interactions

abstract:
  We develop a scheme for quantum computation with neutral atoms, based on the
concept of "marker" atoms, i.e., auxiliary atoms that can be efficiently
transported in state-independent periodic external traps to operate quantum
gates between physically distant qubits. This allows for relaxing a number of
experimental constraints for quantum computation with neutral atoms in
microscopic potential, including single-atom laser addressability. We discuss
the advantages of this approach in a concrete physical scenario involving
molecular interactions.


title:
Automatical generation of nonadiabatic conditional geometric phase shift
  via a noncoplanar fiber system

abstract:
  A new scheme of realizing the nonadiabatic conditional geometric phase shift
via a noncoplanar (and coiled) fiber system is presented in this Letter. It is
shown that the effective Hamiltonian that describes the interaction of
polarized photons with the fiber medium is just the Wang-Keiji type of
Hamiltonian. This, therefore, means that the coiled fiber system may be an
ideal implementation of realizing the nonadiabatic geometric phase gates for
the topological quantum computation. The remarkable feature of the present
method is that it can automatically meet the conditions and requirements
proposed in the Wang-Keiji scheme: (i) in the coiled fiber system, the
dynamical phase of photon wavefunction caused by the interaction Hamiltonian
automatically vanishes; (ii) the Wang-Keiji requirement for the parameters in
the Wang-Keiji Hamiltonian can be exactly satisfied automatically in the fiber
system; (iii) the conditional initial state can be easily achieved by
manipulating the initial wave vector of polarized photons. Due to these three
advantages, the coiled fiber system may be a potentially practical way of
achieving the nonadiabatic conditional geometric phase shift (and hence the
nonadiabatic geometric quantum gates).


title:
The Role of the Exclusion Principle for Atoms to Stars: A Historical
  Account

abstract:
  In a first historical part I shall give a detailed description of how Pauli
discovered --before the advent of the new quantum mechanics -- his exclusion
principle. The second part is devoted to the insight and results that have been
obtained in more recent times in our understanding of the stability of matter
in bulk, both for ordinary matter (like stones) and self-gravitating bodies.


title:
Three-party pure quantum states are determined by two two-party reduced
  states

abstract:
  We can uniquely calculate almost all entangled state vectors of tripartite
systems ABC if we know the reduced states of any two bipartite subsystems,
e.g., of AB and of BC. We construct the explicit solution.


title: Hillery-type squeezing in fan-states

abstract:
  We study the Hillery-type, i.e. $N$-th power, amplitude squeezing in the
fan-state $| \xi ;2k,f>_{F}$ characterized by $\xi \in \mathcal{C}$,
$k=1,2,3,...$ and $f$ a nonlinear operator-valued function. We show that for a
given $k$ there exists a critical $\xi_c$ such that for $0<|\xi|\leq|\xi_c|$
squeezing occurs simultaneously in $2k$ directions for the powers $N$ which are
a multiple of $2k$. This result does not depend on the concrete form of $f$,
i.e. it holds true for both $f\equiv 1$ and $f\neq 1$. However, for $f\neq 1$,
which is realized here in the ion trap context, the squeezing directions as
well as the magnitude of $\xi$ can be controlled by adjusting the system
driving parameters.


title: Relativistic and Radiative Corrections to the Mollow Spectrum

abstract:
  The incoherent, inelastic part of the resonance fluorescence spectrum of a
laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev.
188, 1969 (1969)]. Starting from this level of description, we discuss
theoretical foundations of high-precision spectroscopy using the resonance
fluorescence light of strongly laser-driven atoms. Specifically, we evaluate
the leading relativistic and radiative corrections to the Mollow spectrum, up
to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and
Bloch-Siegert shifts as well as stimulated radiative corrections involving
off-resonant virtual states. Complete results are provided for the hydrogen
1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction
terms up to the specified order of approximation and could directly be compared
to experimental data. As an application, the outcome of such experiments would
allow for a sensitive test of the validity of the dressed-state basis as the
natural description of the combined atom-laser system.


title:
Identification via Quantum Channels in the Presence of Prior Correlation
  and Feedback

abstract:
  Continuing our earlier work (quant-ph/0401060), we give two alternative
proofs of the result that a noiseless qubit channel has identification capacity
2: the first is direct by a "maximal code with random extension" argument, the
second is by showing that 1 bit of entanglement (which can be generated by
transmitting 1 qubit) and negligible (quantum) communication has identification
capacity 2.
  This generalises a random hashing construction of Ahlswede and Dueck: that 1
shared random bit together with negligible communication has identification
capacity 1.
  We then apply these results to prove capacity formulas for various quantum
feedback channels: passive classical feedback for quantum-classical channels, a
feedback model for classical-quantum channels, and "coherent feedback" for
general channels.


title: Off-diagonal quantum holonomy along density operators

abstract:
  Uhlmann's concept of quantum holonomy for paths of density operators is
generalised to the off-diagonal case providing insight into the geometry of
state space when the Uhlmann holonomy is undefined. Comparison with previous
off-diagonal geometric phase definitions is carried out and an example
comprising the transport of a Bell-state mixture is given.


title:
Control of decoherence: analysis and comparison of three different
  strategies

abstract:
  We analyze and compare three different strategies, all aimed at controlling
and eventually halting decoherence. The first strategy hinges upon the quantum
Zeno effect, the second makes use of frequent unitary interruptions
("bang-bang" pulses and their generalization, quantum dynamical decoupling),
and the third of a strong, continuous coupling. Decoherence is shown to be
suppressed only if the frequency N of the measurements/pulses is large enough
or if the coupling K is sufficiently strong. Otherwise, if N or K are large,
but not extremely large, all these control procedures accelerate decoherence.
We investigate the problem in a general setting and then consider some
practical examples, relevant for quantum computation.


title: Quantum correlations from Brownian diffusion of chaotic level-spacings

abstract:
  Quantum chaos is linked to Brownian diffusion of the underlying quantum
energy level-spacing sequences. The level-spacings viewed as functions of their
order execute random walks which imply uncorrelated random increments of the
level-spacings while the integrability to chaos transition becomes a change
from Poisson to Gauss statistics for the level-spacing increments. This
universal nature of quantum chaotic spectral correlations is numerically
demonstrated for eigenvalues from random tight binding lattices and for zeros
of the Riemann zeta function.


title:
On the relation between quantum mechanical probabilities and event
  frequencies

abstract:
  The probability `measure' for measurements at two consecutive moments of time
is non-additive. These probabilities, on the other hand, may be determined by
the limit of relative frequency of measured events, which are by nature
additive. We demonstrate that there are only two ways to resolve this problem.
The first solution places emphasis on the precise use of the concept of
conditional probability for successive measurements. The physically correct
conditional probabilities define additive probabilities for two-time
measurements. These probabilities depend explicitly on the resolution of the
physical device and do not, therefore, correspond to a function of the
associated projection operators. It follows that quantum theory distinguishes
between physical events and propositions about events, the latter are not
represented by projection operators and that the outcomes of two-time
experiments cannot be described by quantum logic.
  The alternative explanation is rather radical: it is conceivable that the
relative frequencies for two-time measurements do not converge, unless a
particular consistency condition is satisfied. If this is true, a strong
revision of the quantum mechanical formalism may prove necessary. We stress
that it is possible to perform experiments that will distinguish the two
alternatives.


title: Enscription of Quantum Texts

abstract:
  We investigate an entangled deformation of the deterministic quantum cloning
process, called enscription, that can be applied to (certain) sets of distinct
quantum states which are not necessarily orthogonal, called texts. Some basic
theorems on enscribable texts are given, and a relationship to probabilistic
quantum cloning is demonstrated.


title:
Towards a Coherent Theory of Physics and Mathematics: The
  Theory-Experiment Connection

abstract:
  The problem of how mathematics and physics are related at a foundational
level is of much interest. One approach is to work towards a coherent theory of
physics and mathematics together. Here steps are taken in this direction by
first examining the theory experiment connection. The role of an implied theory
hierarchy and use of computers in comparing theory and experiment is described.
The main idea of the paper is to tighten the theory experiment connection by
bringing physical theories, as mathematical structures over C, the complex
numbers, closer to what is actually done in experimental measurements and
computations. The method replaces C by C_{n} which is the set of pairs,
R_{n},I_{n}, of n figure rational numbers in some basis. The properties of
these numbers are based on the type of numbers that represent measurement
outcomes for continuous variables. A model of space and time based on R_{n} is
discussed. The model is scale invariant with regions of constant step size
interrupted by exponential jumps. A method of taking the limit n to infinity to
obtain locally flat continuum based space and time is outlined. Possibly the
most interesting result is that R_{n} based space is invariant under scale
transformations which correspond to expansion and contraction of space relative
to a flat background. Also the location of the origin, which is a space and
time singularity, does not change under these transformations. Some properties
of quantum mechanics based on C_{n} and on R_{n} space are briefly
investigated.


title: Translation of Quantum Texts

abstract:
  In the companion to this paper, we described a generalization of the
deterministic quantum cloning process, called enscription, which utilizes
entanglement in order to achieve the "copying" of (certain) sets of distinct
quantum states which are not orthogonal, called texts. Here we provide a
further generalization, called translation, which allows us to completely
determine all translatable texts, and which displays an intimate relationship
to the mathematical theory of graphs.


title:
Some Effects of Classical Feedback on the Classical Capacity of a
  Memoryless Quantum Channel

abstract:
  Classical feedback is defined here as the knowledge by the transmitter of the
quantum state of the qubit received by the receiver. Such classical feedback
doubles capacities of certain memoryless quantum channels without preexisting
entanglement between transmitter and receiver. The increase in capacity, which
is absent on classical memoryless channels, occurs because we can transform an
entangled qubit pair into any other entangled state by applying a unitary
operator to only one of the qubits.


title: Macroscopic Observables

abstract:
  We study macroscopic observables defined as the total value of a physical
quantity over a collection of quantum systems. We show that previous results
obtained for infinite ensemble of identically prepared systems lead to
incorrect conclusions for finite ensembles. In particular, exact measurement of
a macroscopic observable significantly disturbs the state of any finite
ensemble. However, we show how this disturbance can be made arbitrarily small
when the measurement are of finite accuracy. We demonstrate a tradeoff between
state disturbance and measurement coarseness as a function of the size of the
ensemble. Using this tradeoff, we show that the histories generated by any
sequence of finite accuracy macroscopic measurements always generate a
consistent family in the absence of large scale entanglement, for sufficiently
large ensembles. Hence, macroscopic observables behave "classically" provided
that their accuracy is coarser than the quantum correlation length-scale of the
system. The role of these observable is also discussed in the context of NMR
quantum information processing and bulk ensemble quantum state tomography.


title: Adiabatic Geometric Phase for a General Quantum States

abstract:
  A geometric phase is found for a general quantum state that undergoes
adiabatic evolution. For the case of eigenstates, it reduces to the original
Berry's phase. Such a phase is applicable in both linear and nonlinear quantum
systems. Furthermore, this new phase is related to Hannay's angles as we find
that these angles, a classical concept, can arise naturally in quantum systems.
The results are demonstrated with a two-level model.


title: Entanglement of electron spins of non-interacting electron gases

abstract:
  We study entanglement of electron spins in many-body systems based on the
Green's function approach. As an application we obtain the two-particle density
matrix of a non-interacting electron gas and identify its two-spin density
matrix as a Werner state. We calculate entanglement measures, a classical
correlation, mutual information, and a pair distribution function of two
electrons at zero and finite temperatures. We find that changes of entanglement
measures are proportional to $T^2$ at low temperatures.


title:
Secure direct bidirectional communication protocol using the
  Einstein-Podolsky-Rosen pair block

abstract:
  In light of Deng-Long-Liu's two-step secret direct communication protocol
using the Einstein-Podolsky-Rosen pair block [Phys. Rev. A {\bf 68}, 042317
(2003)], by introducing additional local operations for encoding, we propose a
brand-new secure direct communication protocol, in which two legitimate users
can simultaneously transmit their different secret messages to each other in a
set of quantum communication device.


title: q-Fermionic Numbers and Their Roles in Some Physical Problems

abstract:
  The q-fermion numbers emerging from the q-fermion oscillator algebra are used
to reproduce the q-fermionic Stirling and Bell numbers. New recurrence
relations for the expansion coefficients in the 'anti-normal ordering' of the
q-fermion operators are derived. The roles of the q-fermion numbers in
q-stochastic point processes and the Bargmann space representation for
q-fermion operators are explored.


title: Secure Bidirectional Communication Protocol without Quantum Channel

abstract:
  In this letter we propose a theoretical deterministic secure direct
bidirectional quantum communication protocol by using swapping quantum
entanglement and local unitary operations, in which the quantum channel for
photon transmission can be discarded, hence any attack with or without
eavesdropping or even the destructive attack without scruple is impossible.


title:
Deterministic secure direct communication by using swapping quantum
  entanglement and local unitary operations

abstract:
  A deterministic direct quantum communication protocol by using swapping
quantum entanglement and local unitary operations is proposed in this paper. A
set of ordered EPR pairs in one of the four Bell states is used. For each pair,
each of the two legitimate users owns a photon of the entangled pair via
quantum channel. The pairs are divided into two types of group, i.e., the
checking groups and the encoding-decoding groups. In the checking groups,
taking advantage of the swapping quantum entanglement and Alice's (the message
sender's) public announcement, the eavesdropping can be detected provided that
the number of the checking groups is big enough. After insuring the security of
the quantum channel, Alice encodes her bits via the local unitary operations on
the encoding-decoding groups. Then she performs her Bell measurements on her
photons and publicly announces her measurement results. After her announcement,
the message receiver Bob performs his Bell measurements on his photons and
directly extracts the encoding bits by using the property of the quantum
entanglement swapping. The security of the present scheme is also discussed:
under the attack scenarios to our best knowledge, the scheme is secure.


title: Entropic uncertainty relations and entanglement

abstract:
  We discuss the relationship between entropic uncertainty relations and
entanglement. We present two methods for deriving separability criteria in
terms of entropic uncertainty relations. Especially we show how any entropic
uncertainty relation on one part of the system results in a separability
condition on the composite system. We investigate the resulting criteria using
the Tsallis entropy for two and three qubits.


title: Improving quantum dense key distribution

abstract:
  The capacity of the quantum dense key distribution (QDKD) [Phys. Rev. A69,
032310 (2004)] is doubled by introducing the dense coding. The security of the
improved QDKD against eavesdropping is pointed out to be easily proven. In both
the original QDKD and the present improved QDKD, a strategy to double the
efficiency of generating the secret key with given length is proposed. In
addition, we point out a leak of security of the original QDKD and fix it.


title: Multiparty quantum secret sharing of secure direct communication

abstract:
  Based on the two-step protocol [Phys. Rev. A68(03)042317], we propose a
$(n,n)$-threshold multiparty quantum secret sharing protocol of secure direct
communication. In our protocol only all the sharers collaborate can the
sender's secure direct communication message be extracted. We show a variant
version of this protocol based on the variant two-step protocol. This variant
version can considerably reduce the realization difficulty in experiment. In
contrast to the use of multi-particle GHZ states in the case that the sharer
number is larger than 3, the use and identification of Bell states are enough
in our two protocols disregarding completely the sharer number, hence, our
protocols are more feasible in technique.


title: Anyons and transmutation of statistics via vacuum induced Berry phase

abstract:
  We show that bosonic fields may present anyonic behavior when interacting
with a fermion in a Jaynes-Cummings-like model. The proposal is accomplished
via the interaction of a two-level system with two quantized modes of a
harmonic oscillator; under suitable conditions, the system acquires a
fractional geometric phase. A crucial role is played by the entanglement of the
system eigenstates, which provides a two-dimensional confinement in the
effective evolution of the system, leading to the anyonic behavior. For a
particular choice of parameters, we show that it is possible to transmute the
statistics of the system continually from fermions to bosons. We also present
an experimental proposal, in an ion-trap setup, in which fractional statistical
features can be generated, controlled, and measured.


title: Linear representation of energy-dependent Hamiltonians

abstract:
  Effective (i.e., subspace-constrained) Hamiltonians become, by construction,
energy-dependent while all the energy-dependent forces prove non-linear because
the energy itself is merely an eigenvalue of the Hamiltonian H. One of the most
natural resolutions of such a puzzle is proposed via an introduction of teh two
separate linear representatives of the respective right and left action of
H=H(E). Both the new energy-independent operators are non-Hermitian so that the
formalism admits a natural extension to non-Hermitian initial H(E)s.


title:
Compact Source of EPR Entanglement and Squeezing at Very Low Noise
  Frequencies

abstract:
  We report on the experimental demonstration of strong quadrature EPR
entanglement and squeezing at very low noise sideband frequencies produced by a
single type-II, self-phase-locked, frequency degenerate optical parametric
oscillator below threshold. The generated two-mode squeezed vacuum state is
preserved for noise frequencies as low as 50 kHz. Designing simple setups able
to generate non-classical states of light in the kHz regime is a key challenge
for high sensitivity detection of ultra-weak physical effects such as
gravitational wave or small beam displacement.


title: Selective spin coupling through a single exciton

abstract:
  We present a novel scheme for performing a conditional phase gate between two
spin qubits in adjacent semiconductor quantum dots through delocalized single
exciton states, formed through the inter-dot Foerster interaction. We consider
two resonant quantum dots, each containing a single excess conduction band
electron whose spin embodies the qubit. We demonstrate that both the two-qubit
gate, and arbitrary single-qubit rotations, may be realized to a high fidelity
with current semiconductor and laser technology.


title:
Measuring errors in single qubit rotations by pulsed electron
  paramagnetic resonance

abstract:
  The ability to measure and reduce systematic errors in single-qubit logic
gates is crucial when evaluating quantum computing implementations. We describe
pulsed electron paramagnetic resonance (EPR) sequences that can be used to
measure precisely even small systematic errors in rotations of
electron-spin-based qubits. Using these sequences we obtain values for errors
in rotation angle and axis for single-qubit rotations using a commercial EPR
spectrometer. We conclude that errors in qubit operations by pulsed EPR are not
limiting factors in the implementation of electron-spin based quantum
computers.


title:
Coherence protection by the quantum Zeno effect and non-holonomic
  control in a Rydberg Rubidium isotope

abstract:
  The protection of the coherence of open quantum systems against the influence
of their environment is a very topical issue. A scheme is proposed here which
protects a general quantum system from the action of a set of arbitrary
uncontrolled unitary evolutions. This method draws its inspiration from ideas
of standard error-correction (ancilla adding, coding and decoding) and the
Quantum Zeno Effect. A pedagogical demonstration of our method on a simple
atomic system, namely a Rubidium isotope, is proposed.


title: Quantum Knots

abstract:
  This paper proposes the definition of a quantum knot as a linear
superposition of classical knots in three dimensional space. The definition is
constructed and examples are discussed. Then the paper details extensions and
also limitations of the Aravind Hypothesis for comparing quantum measurement
with classical topological measurement. We propose a separate, network model
for quantum evolution and measurement, where the background space is replaced
by an evolving network. In this model there is an analog of the Aravind
Hypothesis that promises to directly illuminate relationships between physics,
topology and quantum knots.


title: Quantum Hidden Subgroup Algorithms: The Devil Is in the Details

abstract:
  We conjecture that one of the main obstacles to creating new non-abelian
quantum hidden subgroup algorithms is the correct choice of a transversal.


title:
Generalizing Several Theoretical Deterministic Secure Direct
  Bidirectional Communications to Improve Their Capacities

abstract:
  Several theoretical Deterministic Secure Direct Bidirectional Communication
protocols are generalized to improve their capacities by introducing the
superdense-coding in the case of high-dimension quantum states.


title:
Effect of intersubsystem coupling on the geometric phase in a bipartite
  system

abstract:
  The influence of intersubsystem coupling on the cyclic adiabatic geometric
phase in bipartite systems is investigated. We examine the geometric phase
effects for two uniaxially coupled spin$-{1/2}$ particles, both driven by a
slowly rotating magnetic field. It is demonstrated that the relation between
the geometric phase and the solid angle enclosed by the magnetic field is
broken by the spin-spin coupling, in particular leading to a quenching effect
on the geometric phase in the strong coupling limit.


title: Global entangling properties of the coupled kicked tops

abstract:
  We study global entangling properties of the system of coupled kicked tops
testing various hypotheses and predictions concerning entanglement in quantum
chaotic systems. In order to analyze the averaged initial entanglement
production rate and the averaged asymptotic entanglement different ensembles of
initial product states are evolved. Two different ensembles with natural
probability distribution are considered: product states of independent
spin-coherent states and product states of arbitrary states. It appears that
the choice of either of these ensembles results in significantly different
averaged entanglement behavior. We investigate also a relation between the
averaged asymptotic entanglement and the mean entanglement of the eigenvectors
of an evolution operator. Lower bound on the averaged asymptotic entanglement
is derived, expressed in terms of the eigenvector entanglement.


title:
Spatial structures and localization of vacuum entanglement in the linear
  harmonic chain

abstract:
  We study the structure of vacuum entanglement for two complimentary segments
of a linear harmonic chain, applying the modewise decomposition of entangled
gaussian states discussed in \cite {modewise}. We find that the resulting
entangled mode shape hierarchy shows a distinctive layered structure with well
defined relations between the depth of the modes, their characteristic
wavelength, and their entanglement contribution. We re-derive in the strong
coupling (diverging correlation length) regime, the logarithmic dependence of
entanglement on the segment size predicted by conformal field theory for the
boson universality class, and discuss its relation with the mode structure. We
conjecture that the persistence of vacuum entanglement between arbitrarily
separated finite size regions is connected with the localization of the highest
frequency innermost modes.


title: Pulsed squeezed vacuum characterization without homodyning

abstract:
  Direct photon detection is experimentally implemented to measure the
squeezing and purity of a single-mode squeezed vacuum state without an
interferometric homodyne detection. Following a recent theoretical proposal
[arXiv quant-ph/0311119], the setup only requires a tunable beamsplitter and a
single-photon detector to fully characterize the generated Gaussian states. The
experimental implementation of this procedure is discussed and compared with
other reference methods.


title:
Quantum and Thermal Corrections to a Classically Chaotic Dissipative
  System

abstract:
  The effects of quantum and thermal corrections on the dynamics of a damped
nonlinearly kicked harmonic oscillator are studied. This is done via the
Quantum Langevin Equation formalism working on a truncated moment expansion of
the density matrix of the system. We find that the type of bifurcations present
in the system change upon quantization and that chaotic behavior appears for
values of the nonlinear parameter that are far below the chaotic threshold for
the classical model. Upon increase of temperature or Planck's constant,
bifurcation points and chaotic thresholds are shifted towards lower values of
the nonlinear parameter. There is also an anomalous reverse behavior for low
values of the cutoff frequency.


title: Fractal atom-photon dynamics in a cavity

abstract:
  Nonlinear dynamics in the fundamental interaction between a two-level atom
with recoil and a quantized radiation field in a high-quality cavity is
studied. We consider the strongly coupled atom-field system as a
quantum-classical hybrid with dynamically coupled quantum and classical degrees
of freedom. We show that, even in the absence of any other interaction with
environment, the interaction of the purely quantum atom-field system with the
external atomic degree of freedom provides the emergence of classical dynamical
chaos from quantum electrodynamics. Atomic fractals with self-similar
intermittency of smooth and unresolved structures are found in the exit-time
scattering function. Tiny interplay between all the degrees of freedom is
responsible for dynamical trapping of atoms even in a very short microcavity.
Gedanken experiments are proposed to detect manifestations of atomic fractals
in cavity quantum electrodynamics.


title: Fault Testing for Reversible Circuits

abstract:
  Applications of reversible circuits can be found in the fields of low-power
computation, cryptography, communications, digital signal processing, and the
emerging field of quantum computation. Furthermore, prototype circuits for
low-power applications are already being fabricated in CMOS. Regardless of the
eventual technology adopted, testing is sure to be an important component in
any robust implementation.
  We consider the test set generation problem. Reversibility affects the
testing problem in fundamental ways, making it significantly simpler than for
the irreversible case. For example, we show that any test set that detects all
single stuck-at faults in a reversible circuit also detects all multiple
stuck-at faults. We present efficient test set constructions for the standard
stuck-at fault model as well as the usually intractable cell-fault model. We
also give a practical test set generation algorithm, based on an integer linear
programming formulation, that yields test sets approximately half the size of
those produced by conventional ATPG.


title: Resources required for exact remote state preparation

abstract:
  It has been shown [M.-Y. Ye, Y.-S. Zhang, and G.-C. Guo, Phys. Rev. A 69,
022310 (2004)] that it is possible to perform exactly faithful remote state
preparation using finite classical communication and any entangled state with
maximal Schmidt number. Here we give an explicit procedure for performing this
remote state preparation. We show that the classical communication required for
this scheme is close to optimal for remote state preparation schemes of this
type. In addition we prove that it is necessary that the resource state have
maximal Schmidt number.


title: Minimum output entropy of bosonic channels: a conjecture

abstract:
  The von Neumann entropy at the output of a bosonic channel with thermal noise
is analyzed. Coherent-state inputs are conjectured to minimize this output
entropy. Physical and mathematical evidence in support of the conjecture is
provided. A stronger conjecture--that output states resulting from
coherent-state inputs majorize the output states from other inputs--is also
discussed.


title:
Representing multiqubit unitary evolutions: spin coherences and
  infinitesimal coherences

abstract:
  For the tensor of coherences parametrization of a multiqubit density
operator, we provide an explicit formulation of the corresponding unitary
dynamics at infinitesimal level. The main advantage of this formalism (clearly
reminiscent of the idea of ``coherences'' and ``coupling Hamiltonians'' of spin
systems) is that the pattern of correlation between qubits and the pattern of
infinitesimal correlation are highlighted simultaneously and can be used
constructively for qubit manipulation. For example, it allows to compute
explicitly a Rodrigues' formula for the one-parameter orbits of nonlocal
Hamiltonians. The result is easily generalizable to orbits of Cartan
subalgebras and allows to write the Cartan decomposition of unitary propagators
as a linear action.


title: Two analytic continuations of the Lippmann-Schwinger eigenfunctions

abstract:
  We first present two possible analytic continuations of the
Lippmann-Schwinger eigenfunctions to the second sheet of the Riemann surface,
and then we compare the different Gamow vectors that are obtained through each
analytic continuation.


title:
Qualitative aspects of entanglement in the Jaynes-Cummings model with an
  external quantum field

abstract:
  We present a mathematical procedure which leads us to obtain analytical
solutions for the atomic inversion and Wigner function in the framework of the
Jaynes-Cummings model with an external quantum field, for any kinds of cavity
and driving fields. Such solutions are expressed in the integral form, with
their integrands having a commom term that describes the product of the
Glauber-Sudarshan quasiprobability distribution functions for each field, and a
kernel responsible for the entanglement. Considering two specific initial
states of the tripartite system, the formalism is then applied to calculate the
atomic inversion and Wigner function where, in particular, we show how the
detuning and amplitude of the driving field modify the entanglement. In
addition, we also obtain the correct