title: Self-Protected Quantum Algorithms Based on Quantum State Tomography

abstract:
  Only a few classes of quantum algorithms are known which provide a speed-up
over classical algorithms. However, these and any new quantum algorithms
provide important motivation for the development of quantum computers. In this
article new quantum algorithms are given which are based on quantum state
tomography. These include an algorithm for the calculation of several quantum
mechanical expectation values and an algorithm for the determination of
polynomial factors. These quantum algorithms are important in their own right.
However, it is remarkable that these quantum algorithms are immune to a large
class of errors. We describe these algorithms and provide conditions for
immunity.


title: Quantum Annealing for Heisenberg Spin Chains

abstract:
  We suggest using the method of quantum annealing for computing the ground
state of the Heisenberg spin chains. Our initial Hamiltonian describes a spin
system in a highly non-uniform magnetic field. The initial Hamiltonian
gradually transforms into the Heisenberg Hamiltonian, which describes the
exchange interaction and the Zeeman interaction with the uniform magnetic
field. We demonstrate quantum annealing for 2-, 3-, and 9-spin systems. In
particular, we consider the alternate (ferro- and antiferromagnetic) exchange
integral. By changing the sign of the exchange integrals we switch from the
frustrated to the corresponding non-frustrated spin system. We discuss the
similarity and difference between the frustrated and non-frustrated spin
systems.


title:
Demonstration of deterministic and high fidelity squeezing of quantum
  information

abstract:
  By employing at recent proposal (R. Filip, P. Marek and U.L. Andersen, Phys.
Rev. A {\bf 71}, 042308 (2005) \cite{Filip05.pra}), we experimentally
demonstrate a universal, deterministic and high-fidelity squeezing
transformation of an optical field. It relies only on linear optics, homodyne
detection, feedforward and an ancillary squeezed vacuum state, thus direct
interaction between a strong pump and the quantum state is circumvented. We
demonstrate three different squeezing levels for a coherent state input. This
scheme is highly suitable for the fault-tolerant squeezing transformation in a
continuous variable quantum computer.


title:
Comment on "Resilient Quantum Computation in Correlated Environments: A
  Quantum Phase Transition Perspective" and "Fault-tolerant Quantum Computation
  with Longe-range Correlated Noise"

abstract:
  Critical comments on the recent papers supporting the idea of resilient
quantum computations are presented.


title:
Spin tunneling in magnetic molecules: Quantitative estimates for Fe8
  clusters

abstract:
  Spin tunneling in the particular case of the magnetic molecular cluster
octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows
for an angle-based description of the process. The presence of an external
magnetic field along the easy axis is also taken into account in this
description. Analytic expressions for the energy levels and barriers are
obtained from a harmonic approximation of the potential function which give
results in good agreement with the experimental results. The energy splittings
due to spin tunneling is treated in an adapted WKB approach and it is shown
that the present description can give results to a reliable degree of accuracy.


title:
On the solutions of the Schrodinger equation with some molecular
  potentials: wave function ansatz

abstract:
  Making an ansatz to the wave function, the exact solutions of the $D$%
-dimensional radial Schrodinger equation with some molecular potentials like
pseudoharmonic and modified Kratzer potentials are obtained. The restriction on
the parameters of the given potential, $\delta $ and $\eta $ are also given,
where $\eta $ depends on a linear combination of the angular momentum quantum
number $\ell $ and the spatial dimensions $D$ and $\delta $ is a parameter in
the ansatz to the wave function. On inserting D=3, we find that the bound state
eigensolutions recover their standard analytical forms in literature.


title: Resonance fluorescence of a cold atom in a high-finesse resonator

abstract:
  We study the spectra of emission of a system composed by an atom, tightly
confined inside a high-finesse resonator, when the atom is driven by a laser
and is at steady state of the cooling dynamics induced by laser and cavity
field. In general, the spectrum of resonance fluorescence and the spectrum at
the cavity output contain complementary information about the dynamics
undergone by the system. In certain parameter regimes, quantum interference
effects between the scattering processes induced by cavity and laser field lead
to the selective suppression of features of the resonance fluorescence
spectrum, which are otherwise visible in the spectrum of laser-cooled atoms in
free space.


title: Strongly-Driven One-Atom Laser and Decoherence Monitoring

abstract:
  We propose the implementation of a strongly-driven one-atom laser, based on
the off-resonant interaction of a three-level atom in $\Lambda$-configuration
with a single cavity mode and three laser fields. We show that the system can
be described equivalently by a two-level atom resonantly coupled to the cavity
and driven by a strong effective coherent field. The effective dynamics can be
solved exactly, including a thermal field bath, allowing an analytical
description of field statistics and entanglement properties. We also show the
possible generation of Schr\"odinger cat states for the whole atom-field system
and for the field alone after atomic measurement. We propose a way to monitor
the system decoherence by measuring atomic population. Finally, we confirm the
validity of our model through numerical solutions.


title: Entanglement oscillations in non-Markovian quantum channels

abstract:
  We study the non-Markovian dynamics of a two-mode bosonic system interacting
with two uncorrelated thermal bosonic reservoirs. We present the solution to
the exact microscopic Master equation in terms of the quantum characteristic
function and study in details the dynamics of entanglement for bipartite
Gaussian states. In particular, we analyze the effects of short-time
system-reservoir correlations on the separability thresholds and show that the
relevant parameter is the reservoir spectral density. If the frequencies of the
involved modes are within the reservoir spectral density entanglement persists
for a longer time than in a Markovian channel. On the other hand, when the
reservoir spectrum is out of resonance short-time correlations lead to a faster
decoherence and to the appearance of entanglement oscillations.


title:
Stimulated emission of two photons in parametric amplification and its
  interpretation as multi-photon interference

abstract:
  Stimulated emission of two photons is observed experimentally in the
parametric amplification process and is compared to a three-photon interference
scheme. We find that the underlying physics of stimulated emission is simply
the constructive interference due to photon indistinguishability. So the
observed signal enhancement upon the input of photons is a result of
multi-photon interference of the input photons and the otherwise spontaneously
emitted photon from the amplifier.


title:
Functional Quantum Nodes for Entanglement Distribution over Scalable
  Quantum Networks

abstract:
  We demonstrate entanglement distribution between two remote quantum nodes
located 3 meters apart. This distribution involves the asynchronous preparation
of two pairs of atomic memories and the coherent mapping of stored atomic
states into light fields in an effective state of near maximum polarization
entanglement. Entanglement is verified by way of the measured violation of a
Bell inequality, and can be used for communication protocols such as quantum
cryptography. The demonstrated quantum nodes and channels can be used as
segments of a quantum repeater, providing an essential tool for robust
long-distance quantum communication.


title:
Mathematical Modeling of Physical and Engineering Systems in Quantum
  Information

abstract:
  Several concrete examples in quantum information are discussed to demonstrate
the importance of proper modeling that relates the mathematical description to
real-world applications. In particular, it is shown that some commonly accepted
conclusions are not adequately supported by their purported justifications in
the logical manner required.


title: Spin chains and channels with memory

abstract:
  In most studies of the channel capacity of quantum channels, it is assumed
that the errors in each use of the channel are independent. However, recent
work has begun to investigate the effects of memory or correlations in the
error. This work has led to speculation that interesting non-analytic behaviour
may occur in the capacity. Motivated by these observations, we connect the
study of channel capacities under correlated error to the study of critical
behaviour in many-body physics. This connection enables us the techniques of
many-body physics to either completely solve or understand qualitatively a
number of interesting models of correlated error. The models can display
analogous behaviour to associated many-body systems, including `phase
transitions'.


title:
Comment on ``Lateral Casimir force beyond the proximity-force
  approximation''

abstract:
  We demonstrate that the approach by Rodrigues et al. (PRL, v.96, 100402,
2006) to the description of the lateral Casimir force between corrugated
surfaces is in disagreement with a path-integral theory by Emig et al. (PRA,
v.67, 022114, 2003), and the approximations used are not appropriate for
comparison to experiment.


title: The Casimir Effect in Relativistic Quantum Field Theories

abstract:
  We review recent developments in the Casimir effect which arises in
quantization volumes restricted by material boundaries and in spaces with
non-Euclidean topology. The starting point of our discussion is the novel exact
solution for the electromagnetic Casimir force in the configuration of a
cylinder above a plate. The related work for the scalar Casimir effect in
sphere-plate configuration is also considered, and the application region of
the proximity force theorem is discussed. Next we consider new experiments on
the measurement of the Casimir force between metals and between metal and
semiconductor. The complicated problem connected with the theory of the thermal
Casimir force between real metals is analyzed in detail. The present situation
regarding different theoretical approaches to the resolution of this problem is
summarized. We conclude with new constraints on non-Newtonian gravity obtained
using the results of latest Casimir force measurements and compare them with
constraints following from the most recent gravitational experiments.


title:
Practical scheme for quantum dense coding between three parties using
  microwave radiation in trapped ions

abstract:
  We propose a practical scheme for implementing two-dimension quantum dense
coding (QDC) between three parties through manipulating three ions confined in
microtraps addressed by microwaves and assisted by a magnetic field gradient.
The ions in our scheme are not required to be strictly cooled to the
vibrational ground state because single-qubit and multi-qubit operations are
made via Ising terms, in which the vibrational modes of the ions remain
unchanged throughout the scheme, rendering our scheme robust to the heating of
the ions. We also present the detailed steps and parameters for implementing
the three-party QDC experimentally and show that the proposed scheme is within
the current techniques of ion-trap experiments.


title:
On an additional realization of supersymmetry in orthopositronium
  lifetime anomalies

abstract:
  Expansion of Standard Model for the quantitative description of the
orthopositronium lifetime anomalies (from QED to supersymmetric QED) allows to
formulate experimental tests of supervision of additional realization of the
supersymmetry in final state of the positron beta-decay of the nuclei such as
Na-22, Ga-68. The expermentum crucis program is based on supervision of the
orthopositronium "isotope anomaly", on the quantitative description of the
"lifetime anomaly", and will allow to resolve the alternative as results of the
last Michigan work (2003).


title: Practical effects in cat state breeding

abstract:
  A cat state is a superposition of macroscopically distinct states. In quantum
optics one such type of state is a superposition of distinct coherent states.
Recently, a protocol has been proposed for preparing large optical cat states
from a resource of smaller ones. We consider the effects of mode-mismatch and
loss in the preparation of large cat states using this protocol with a view to
understand experimental limitations. (This paper is written in an experimental
rapid communication format).


title: Noise thresholds for entanglement purification

abstract:
  We consider the effects of gate noise on the operation of an entanglement
purification protocol. We characterize the performance of the protocol by two
measures, the minimum purifiable input state fidelity, and the maximum output
state fidelity. Both these measures are a function of gate error rate. For
sufficiently large gate error rate these two measures converge, defining a
threshold on gate error rates. Numerically, we estimate this threshold to be
$9.2\times 10^{-2}$, which is achievable with many present day experimental
architectures. (This paper is written in an experimental rapid communication
format).


title:
Rectification of the lateral Casimir force in a vibrating non-contact
  rack and pinion

abstract:
  The nonlinear dynamics of a cylindrical pinion that is kept at a distance
from a vibrating rack is studied, and it is shown that the lateral Casimir
force between the two corrugated surfaces can be rectified. The effects of
friction and external load are taken into account and it is shown that the
pinion can do work against loads of up to a critical value, which is set by the
amplitude of the lateral Casimir force. We present a phase diagram for the
rectified motion that could help its experimental investigations, as the system
exhibits a chaotic behavior in a large part of the parameter space.


title: Spatial Entanglement From Off-Diagonal Long Range Order in a BEC

abstract:
  We investigate spatial entanglement - particle-number entanglement between
regions of space - in an ideal Bosonic gas. We quantify the amount spatial
entanglement around the transition temperature for condensation by probing the
gas with two localised two-level systems. We show that spatial entanglement in
the gas is directly related to filling of the ground state energy level and
therefore to the off-diagonal long-range order of the system and the onset of
condensation.


title:
How continuous quantum measurements in finite dimension are actually
  discrete

abstract:
  We show that in finite dimension a quantum measurement with continuous set of
outcomes is always equivalent to a continuous random choice of measurements
with only finite outcomes.


title: Entanglement of Gaussian states

abstract:
  This Dissertation collects my results on the interpretation,
characterization, quantification and application of bipartite and multipartite
entanglement in Gaussian states of continuous variable systems.

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


title:
Theory of quantum fluctuations of optical dissipative structures and its
  application to the squeezing properties of bright cavity solitons

abstract:
  We present a method for the study of quantum fluctuations of dissipative
structures forming in nonlinear optical cavities, which we illustrate in the
case of a degenerate, type I optical parametric oscillator. The method consists
in (i) taking into account explicitly, through a collective variable
description, the drift of the dissipative structure caused by the quantum
noise, and (ii) expanding the remaining -internal- fluctuations in the
biorthonormal basis associated to the linear operator governing the evolution
of fluctuations in the linearized Langevin equations. We obtain general
expressions for the squeezing and intensity fluctuations spectra. Then we
theoretically study the squeezing properties of a special dissipative
structure, namely, the bright cavity soliton. After reviewing our previous
result that in the linear approximation there is a perfectly squeezed mode
irrespectively of the values of the system parameters, we consider squeezing at
the bifurcation points, and the squeezing detection with a plane--wave local
oscillator field, taking also into account the effect of the detector size on
the level of detectable squeezing.


title: A Cyclic Cooling Algorithm

abstract:
  We introduce a scheme to perform the cooling algorithm, first presented by
Oscar Boykin et al. in 2002, for an arbitrary number of times on the same set
of qbits. We achieve this goal by adding an additional SWAP-gate and a bath
contact to the algorithm. This way one qbit may repeatedly be cooled without
adding additional qbits to the system. By using a product Liouville space to
model the bath contact we calculate the density matrix of the system after a
given number of applications of the algorithm.


title: Markovian Entanglement Networks

abstract:
  Graphical models of probabilistic dependencies have been extensively
investigated in the context of classical uncertainty. However, in some domains
(most notably, in computational physics and quantum computing) the nature of
the relevant uncertainty is non-classical, and the laws of classical
probability theory are superseded by those of quantum mechanics. In this paper
we introduce Markovian Entanglement Networks (MEN), a novel class of graphical
representations of quantum-mechanical dependencies in the context of such
non-classical systems. MEN are the quantum-mechanical analogue of Markovian
Networks, a family of undirected graphical representations which, in the
classical domain, exploit a notion of conditional independence among
subsystems.
  After defining a notion of conditional independence appropriate to our domain
(conditional separability), we prove that the conditional separabilities
induced by a quantum-mechanical wave function are effectively reflected in the
graphical structure of MEN. Specifically, we show that for any wave function
there exists a MEN which is a perfect map of its conditional separabilities.
Next, we show how the graphical structure of MEN can be used to effectively
classify the pure states of three-qubit systems. We also demonstrate that, in
large systems, exploiting conditional independencies may dramatically reduce
the computational burden of various inference tasks. In principle, the
graph-theoretic representation of conditional independencies afforded by MEN
may not only facilitate the classical simulation of quantum systems, but also
provide a guide to the efficient design and complexity analysis of quantum
algorithms and circuits.


title: Krawtchouk polynomials and Krawtchouk matrices

abstract:
  Krawtchouk matrices have as entries values of the Krawtchouk polynomials for
nonnegative integer arguments. We show how they arise as condensed
Sylvester-Hadamard matrices via a binary shuffling function. The underlying
symmetric tensor algebra is presented. Our approach is used to solve Kac'
formulation of the Ehrenfest urn model. Connections with quantum and classical
random walks are shown as well as various extensions of the classical
polynomials.


title: QBC3: An Unconditionally Secure Quantum Bit Commitment Protocol

abstract:
  This article describes a quantum bit commitment protocol, QBC3, based on
entanglement destruction via forced measurements and proves its unconditional
security. Some comments on the current status of the field are also made.


title: Protecting an optical qubit against photon loss

abstract:
  We consider quantum error-correction codes for multimode bosonic systems,
such as optical fields, that are affected by amplitude damping. Such a process
is a generalization of an erasure channel. We demonstrate that the most
accessible method of transforming optical systems with the help of passive
linear networks has limited usefulness in preparing and manipulating such
codes. These limitations stem directly from the recoverability condition for
one-photon loss. We introduce a three-photon code protecting against the first
order of amplitude damping, i.e. a single photon loss, and discuss its
preparation using linear optics with single-photon sources and conditional
detection. Quantum state and process tomography in the code subspace can be
implemented using passive linear optics and photon counting. An experimental
proof-of-principle demonstration of elements of the proposed quantum error
correction scheme for a one-photon erasure lies well within present
technological capabilites.


title: Classification of two-particle quantum channels of information transfer

abstract:
  Classification of states of two-particle quantum channels of information
transfer is built on the basis of irreducible representations of qubit state
space group of symmetry and properties of density matrix spectrum. It is shown
that the reason of state disentanglement can be in degeneration of non-zero
density matrix eigenvalues. Among the states with non-degenerate density matrix
disentangled states form two-dimensional surface of special states.


title:
Unconditional privacy over channels which cannot convey quantum
  information

abstract:
  By sending systems in specially prepared quantum states, two parties can
communicate without an eavesdropper being able to listen. The technique, called
quantum cryptography, enables one to verify that the state of the quantum
system has not been tampered with, and thus one can obtain privacy regardless
of the power of the eavesdropper. All previous protocols relied on the ability
to faithfully send quantum states. In fact, until recently, they could all be
reduced to a single protocol where security is ensured though sharing maximally
entangled states. Here we show this need not be the case -- one can obtain
verifiable privacy even through some channels which cannot be used to reliably
send quantum states.


title:
Atomic Entanglement vs Photonic Visibility for Quantum Criticality of
  Hybrid System

abstract:
  To characterize the novel quantum phase transition for a hybrid system
consisting of an array of coupled cavities and two-level atoms doped in each
cavity, we study the atomic entanglement and photonic visibility in comparison
with the quantum fluctuation of total excitations. Analytical and numerical
simulation results show the happen of quantum critical phenomenon similar to
the Mott insulator to superfluid transition. Here, the contour lines
respectively representing the atomic entanglement, photonic visibility and
excitation variance in the phase diagram are consistent in the vicinity of the
non-analytic locus of atomic concurrences.


title: Quantum Non-Demolition Test of Bipartite Complementarity

abstract:
  We present a quantum circuit that implements a non-demolition measurement of
complementary single- and bi-partite properties of a two-qubit system:
entanglement and single-partite visibility and predictability. The system must
be in a pure state with real coefficients in the computational basis, which
allows a direct operational interpretation of those properties. The circuit can
be realized in many systems of interest to quantum information.


title: Composite Geometric Phase for Multipartite Entangled States

abstract:
  When an entangled state evolves under local unitaries, the entanglement in
the state remains fixed. Here we show the dynamical phase acquired by an
entangled state in such a scenario can always be understood as the sum of the
dynamical phases of its subsystems. In contrast, the equivalent statement for
the geometric phase is not generally true unless the state is separable. For an
entangled state an additional term is present, the mutual geometric phase, that
measures the change the additional correlations present in the entangled state
make to the geometry of the state space. For $N$ qubit states we find this
change can be explained solely by classical correlations for states with a
Schmidt decomposition and solely by quantum correlations for W states.


title:
Minimal set of local measurements and classical communication for
  two-mode Gaussian state entanglement quantification

abstract:
  We develop the minimal requirements for the complete entanglement
quantification of an arbitrary two-mode bipartite Gaussian state via local
measurements and a classical communication channel. The minimal set of
measurements is presented as a reconstruction protocol of local covariance
matrices and no previous knowledge of the state is required but its Gaussian
character. The protocol becomes very simple mostly when dealing with Gaussian
states transformed to its standard form, since photocounting/intensity
measurements define the whole set of entangled states. In addition, conditioned
on some prior information, the protocol is also useful for a complete global
state reconstruction.


title: Efficient quantum state transfer in spin chains via adiabatic passage

abstract:
  We propose a method for quantum state transfer in spin chains using an
adiabatic passage technique. Modifying even and odd nearest-neighbour couplings
in time allows to achieve transfer fidelities arbitrarily close to one, without
the need for a precise control of coupling strengths and timing. We study in
detail transfer by adiabatic passage in a spin-1 chain governed by a
generalized Heisenberg Hamiltonian. We consider optimization of the transfer
process applying optimal control techniques. We discuss a realistic
experimental implementation using cold atomic gases confined in deep optical
lattices.


title: Quantum gate entangler for general multipartite systems

abstract:
  We construct quantum gate entangler for general multipartite states based on
topological unitary operators. We show that these operators can entangle
quantum states if they satisfy the separability condition that is given by the
complex multi-projective Segre variety. We also in detail discuss the
construction of quantum gate entangler for higher dimensional bipartite and
three-partite quantum systems.


title: Secure Quantum Telephones

abstract:
  We propose in this paper a novel deterministic protocol using particular
maximally entangled states of polarized photons for a genuine bidirectional
secure communication setup. We further propose a plausible experimental setup
for such a protocol using currently available optical technology which
liberates two communicating party from sharing identical apparatus. We note
that security of the protocol is promised by the monogamous nature of maximally
entangled states. We discuss the security of our protocol in the light of some
simple eavesdropping scenarios.


title: Coherent manipulation of atomic qubits in optical micropotentials

abstract:
  We experimentally demonstrate the coherent manipulation of atomic states in
far-detuned dipole traps and registers of dipole traps based on two-dimensional
arrays of microlenses. By applying Rabi, Ramsey, and spin-echo techniques, we
systematically investigate the dephasing mechanisms and determine the coherence
time. Simultaneous Ramsey measurements in up to 16 dipole traps are performed
and proves the scalability of our approach. This represents an important step
in the application of scalable registers of atomic qubits for quantum
information processing. In addition, this system can serve as the basis for
novel atomic clocks making use of the parallel operation of a large number of
individual clocks each remaining separately addressable.


title:
Quantum key distribution based on phase encoding and polarization
  measurement

abstract:
  A one-way quantum key distribution scheme based on intrinsically stable
Faraday-mirror type Michelson interferometers with four-port polarizing
beampslitters has been demonstrated which can compensate for birefringence
effects automatically. The encoding is performed with phase modulators, but
decoding is accomplished through measurement of the polarization state of Bob's
photons. An extinction ratio of about 30dB was maintained for several hours
over 50km of fiber at 1310nm without any adjustment to the setup, which shows
its good potential for practical systems


title: Light force fluctuations in a strongly coupled atom-cavity system

abstract:
  Between mirrors, the density of electromagnetic modes differs from the one in
free space. This changes the radiation properties of an atom as well as the
light forces acting on an atom. It has profound consequences in the
strong-coupling regime of cavity quantum electrodynamics. For a single atom
trapped inside the cavity, we investigate the atom-cavity system by scanning
the frequency of a probe laser for various atom-cavity detunings. The avoided
crossing between atom and cavity resonance is visible in the transmission of
the cavity. It is also visible in the loss rate of the atom from the
intracavity dipole trap. On the normal-mode resonances, the dominant
contribution to the loss rate originates from dipole-force fluctuations which
are dramatically enhanced in the cavity. This conclusion is supported by
Monte-Carlo simulations.


title: The Impossibility of Quantum State Mirroring on Square Lattices

abstract:
  We discuss the possibility of engineering a Hamiltonian that can perfectly
mirror a state of many excitations stored on a square lattice. In comparison to
the well-studied case of a chain, there is potential for a speed-up of
information transfer. However, we prove that in a large class of cases, perfect
state mirroring on a square lattice is impossible.


title:
Reply to ``Comment on ``Lateral Casimir Force beyond the Proximity Force
  Approximation'' ''

abstract:
  We reply to the comment arXiv:quant-ph/0702060 on our letter
arXiv:quant-ph/0603120 [Phys. Rev. Lett. 96, 100402 (2006)]


title:
Entanglement generation via phase-matched processes: different Bell
  states within the linewidth

abstract:
  It is shown, theoretically and experimentally, that at any type-II
spontaneous parametric down-conversion (SPDC) phase matching, the
decoherence-free singlet Bell state is always present within the natural
bandwidth and can be filtered out by a proper spectral selection. Instead of
the frequency selection, one can perform time selection of the two-photon time
amplitude at the output of a dispersive fibre. Applications to quantum
communication are outlined.


title: Linear-optics manipulations of photon-loss codes

abstract:
  We discuss codes for protecting logical qubits carried by optical fields from
the effects of amplitude damping, i.e. linear photon loss. We demonstrate that
the correctability condition for one-photon loss imposes limitations on the
range of manipulations than can be implemented with passive linear-optics
networks.


title: The Topological Properties of Fault-Tolerant Circuits

abstract:
  The design of time-independent local Hamiltonians that realise quantum
algorithms is derived from the study of perfect state transfer. The novel
features of this evolution are the perfect realisation of the computation, and
the ability to implement operations in parallel rather than sequentially. This
is applied to a quantum circuit for concatenated error correcting codes, and
the properties of the eigenstates are compared to those of topological
memories. An erroneous implementation of the algorithm (one where a single
error could lead to a fault in the output) is found not to be topological,
whereas a true fault-tolerant algorithm possesses self-correcting properties,
suggesting the existence of a unifying structure for fault-tolerant memories.


title: On the Security of the Y-00 (AlphaEta) Direct Encryption Protocol

abstract:
  We review the current status of the AlphaEta direct encryption protocol.
After describing AlphaEta, we summarize the main security claims made on it. We
then describe recent attacks developed against it in the literature, and
suggest security enhancements and future research directions based on our
results.


title: Generalising Landauer's Principle

abstract:
  In a recent paper [Mar05] it is argued that to properly understand the
thermodynamics of Landauer's Principle it is necessary extend the concept of
logical operations to include indeterministic operations. Here we examine the
thermodynamics of such operations in more detail, extending the work of
Landuaer[Lan61] to include indeterministic operations and to include logical
states with variable entropies, temperatures and mean energies. We derive the
most general statement of Landauer's Principle and prove it's universality,
extending considerably the validity of previous proofs. This confirms
conjectures made in [Mar05b], in particular that all logical operations may, in
principle, be performed in a thermodynamically reversible fashion. We
demonstrate a physical process that can perform any computation without work
requirements or heat exchange with the environment. Many widespread statements
of Landauer's Principle are shown to be only special cases of our generalised
principle.


title: Macroscopic quantum jumps and entangled state preparation

abstract:
  Recently we predicted a random blinking, i.e. macroscopic quantum jumps, in
the fluorescence of a laser-driven atom-cavity system [Metz et al., Phys. Rev.
Lett. 97, 040503 (2006)]. Here we analyse the dynamics underlying this effect
in detail and show its robustness against parameter fluctuations. Whenever the
fluorescence of the system stops, a macroscopic dark period occurs and the
atoms are shelved in a maximally entangled ground state. The described setup
can therefore be used for the controlled generation of entanglement. Finite
photon detector efficiencies do not affect the success rate of the state
preparation, which is triggered upon the observation of a macroscopic
fluorescence signal. High fidelities can be achieved even in the vicinity of
the bad cavity limit due to the inherent role of dissipation in the jump
process.


title:
The method of partial wave functions and the structure of time interval
  between the subsequent quantum transitions

abstract:
  We present the formulation of non relativistic quantum mechanics in the
extended space (u,x,t) where x and t are coordinates of particles and time, and
u - an additional real parameter that corresponds to generalized virial - an
integral over path on potential energy of the particle. If the u value is
defined, the state of a particle is described by the partial wave function
F(u,x,t) (PWF). The wave function is obtained from F(u,x,t) by special integral
transform. The "drift" wave equation (DWE) for F(u,x,t) is introduced. The
integral invariants of F(u,x,t) evolution are obtained. The sets of orthonormal
solutions for stationary DWE are obtained; the moments of distribution of are
calculated. The process of "aging" of PWF is described. Effective time interval
necessary for the creation of the state is calculated within the limits of PWF
formalism. The structure of the time interval between the processes of
consequent quantum transition is investigated. The theoretical basis for the
describing counterfactual situations in quantum mechanics is examined.


title:
Strong Super-additivity of the entanglement of formation for pure
  stabilizer states

abstract:
  We prove the strong super-additivity of the entanglement of formation for
stabilizer pure states, and the set of mixed states which minimize their
average entropy of entanglement as a mixture of stabilizer pure states sharing
the same stabilizer group up to phases. The implications of the result on the
additivity of the Holevo capacity of a quantum channel transmitting stabilizer
states with Pauli noise is discussed.


title: Additivity of Entangled Channel Capacity for Quantum Input States

abstract:
  An elementary introduction into algebraic approach to unified quantum
information theory and operational approach to quantum entanglement as
generalized encoding is given. After introducing compound quantum state and two
types of informational divergences, namely, Araki-Umegaki (a-type) and of
Belavkin-Staszewski (b-type) quantum relative entropic information, this paper
treats two types of quantum mutual information via entanglement and defines two
types of corresponding quantum channel capacities as the supremum via the
generalized encodings. It proves the additivity property of quantum channel
capacities via entanglement, which extends the earlier results of V. P.
Belavkin to products of arbitrary quantum channels for quantum relative entropy
of any type.


title:
On The Significance of Which-Way Expositions: Propounding a New
  Possibility

abstract:
  In this article, we survey some controversial problems concerning the idea of
erasing Which Way information proposed in recent years. A statistical
examination of these proposals suggests that whenever the Bayesian rule is
taken into account for two relevant events in two successive times, the
probabilistic description of them is unavoidably time-symmetric. Consequently,
it seems that they cannot fulfill the implications of a so-called
delayed-choice experiment. As a possible alternative, however, we suggest a new
experimental arrangement in which one can change the whole state of a given
system at a proper time (without measurement) to accomplish an actual
delayed-choice experiment with a time-asymmetric attribute. The peculiar
features of this experiment are then discussed.


title:
Uncertainty functions of the open quantum harmonic oscillator in the
  Lindblad theory

abstract:
  In the framework of the Lindblad theory for open quantum systems, we derive
closed analytical expressions of the Heisenberg and Schr\"odinger generalized
uncertainty functions for a particle moving in a harmonic oscillator potential.
The particle is initially in an arbitrary correlated coherent state, and
interacts with an environment at finite temperature. We describe how the
quantum and thermal fluctuations contribute to the uncertainties in the
canonical variables of the system and analyze the relative importance of these
fluctuations in the evolution of the system. We show that upon contact with the
bath the system evolves from a quantum-dominated to a thermal-dominated state
in a time that is of the same order as the decoherence time calculated in other
models in the context of transitions from quantum to classical physics.


title: Negativity as Entanglement Degree of the Jaynes-Cummings Model

abstract:
  In this paper, by using the notion of negativity, we study the degree of
entanglement of a two-level atom interacting with a quantized radiation field,
described by the Jaynes-Cummings model (JCM). We suppose that initially the
field is in a pure state and the atom is in a general mixed state. In this case
the negativity fully captures the entanglement of the JCM. We investigate the
case for that the initial state of the field is a coherent state. The
influences of the detuning on the degree of entanglement is also examined.


title: A statistical mechanics view on Kitaev's proposal for quantum memories

abstract:
  We compute rigorously the ground and equilibrium states for Kitaev's model in
2D, both the finite and infinite version, using an analogy with the 1D Ising
ferromagnet. Next, we investigate the structure of the reduced dynamics in the
presence of thermal baths in the Markovian regime. Special attention is paid to
the dynamics of the topological freedoms which have been proposed for storing
quantum information.


title:
Matrix realignment and partial transpose approach to entangling power of
  quantum evolutions

abstract:
  Based on the matrix realignment and partial transpose, we develop an approach
to entangling power and operator entanglement of quantum unitary operators. We
demonstrate efficiency of the approach by studying several unitary operators on
qudits, and indicate that these two matrix rearrangements are not only powerful
for studying separability problem of quantum states, but also useful in
studying entangling capabilities of quantum operators.


title: Scalable quantum computer using superconducting charge qubits

abstract:
  We present a scalable scheme for superconducting charge qubits with the
assistance of one-dimensional superconducting transmission line resonator
(STLR) playing the role of data bus. The coupling between qubit and data bus
may be turned on and off by just controlling the gate voltage and externally
applied flux of superconducting charge qubit. In our proposal, the entanglement
between arbitrary two qubits and $W$ states of three qubits can be generated
quickly and easily.


title: Ponderomotive tunneling in electron-laser interactions

abstract:
  It is known that the ponderomotive potential from the laser electron
interaction behaves like a static potential that scatters off electrons. We
have investigated the process of the electron tunneling the ponderomotive
potential by using the nonperturbative quantum electrodynamic approach with a
modified Gaussian quantized laser field. The results show that the
ponderomotive tunneling is significantly larger than the tunneling of a static
potential of the same profile. The tunneled electron is discrete in energy
spectrum and spatial diffraction as the result of multiphoton processes. A
resonant tunneling occurs when the ponderomotive energy equals the multiple
integer of the laser photon energy.


title:
Frequencies and energy levels of the weakly relativistic harmonic
  oscillator from the action variable

abstract:
  The frequency of a classical periodic system and the energy levels of the
corresponding quantum system can both be obtained using action variables. We
demonstrate the construction of two forms of the action variable for a one
dimensional harmonic oscillator in classical, relativistic and quantum regimes.
The relativistic effects are considered as perturbative, within the context of
a non-relativistic quantum formalism. The transition of the relativistic
quantum system to both classical relativistic and classical non-relativistic
regimes is illustrated in a unified framework. Formulas for the frequency of a
classical relativistic oscillator and the energy eigenvalues of the
corresponding quantum oscillator for the weak relativistic case are derived.
Also studied are the non-relativistic and classical limits of these formulas
which provide valuable insights on the parallels between relativistic and
non-relativistic systems on the one hand and between classical and quantum
systems on the other.


title: The Quantum Mellin transform

abstract:
  We uncover a new type of unitary operation for quantum mechanics on the
half-line which yields a transformation to ``Hyperbolic phase space''. We show
that this new unitary change of basis from the position x on the half line to
the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin
transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform
to find quantum wavefunctions whose Hyperbolic momentum representation
approximate a class of higher transcendental functions, and in particular,
approximate the Riemann Zeta function. We finally give possible physical
realisations to perform an indirect measurement of the Hyperbolic momentum of a
quantum system on the half-line.


title: Output radiation from a degenerate parametric oscillator

abstract:
  We study the squeezing as well as the statistical properties of the output
radiation from a degenerate parametric oscillator coupled to a squeezed vacuum
reservoir employing the stochastic differential equations associated with the
normal ordering. It is found that the degree of squeezing of the output
radiation is less than the corresponding cavity radiation. However, for output
radiation the correlation of the quadrature operators evaluated at different
times also exhibits squeezing, which is the reason for quenching of the overall
noise in one of the quadrature components of the squeezing spectrum even when
the oscillator is coupled to a vacuum reservoir. Moreover, coupling the
oscillator to the squeezed vacuum reservoir enhances the squeezing
exponentially and it also increases the mean photon number.


title:
Vector Cooper Pairs and Coherent-Population-Trapping-like States in
  Ensemble of Interacting Fermions

abstract:
  Using the standard Hamiltonian of the BCS theory, we show that in an ensemble
of interacting fermions with the spin 1/2 there exist coherent states $|NC>$,
which nullify the Hamiltonian of the interparticle interaction (scattering).
These states have an analogy with the well-known in quantum optics the coherent
population trapping (CPT) effect. The structure of these CPT-like states
corresponds to Cooper pairs with the total spin $S$=1. The found states have a
huge degree of degeneracy and carry a macroscopic magnetic moment, that allows
us to construct a new model of the magnetism connected with the delocalized
electrons in metals (conductors). A principal possibility to apply the obtained
results to the superfluid $^3$He is also demonstrated.

categories: quant-ph cond-mat.str-el cond-mat.supr-con physics.atom-ph


title: The Canonical Function Method and its applications in Quantum Physics

abstract:
  The Canonical Function Method (CFM) is a powerful method that solves the
radial Schr\"{o}dinger equation for the eigenvalues directly without having to
evaluate the eigenfunctions. It is applied to various quantum mechanical
problems in Atomic and Molecular physics with presence of regular or singular
potentials. It has also been developed to handle single and multiple channel
scattering problems where the phaseshift is required for the evaluation of the
scattering cross-section. Its controllable accuracy makes it a valuable tool
for the evaluation of vibrational levels of cold molecules, a sensitive test of
Bohr correspondance principle and a powerful method to tackle local and
non-local spin dependent problems.


title: A selfadjoint variant of the time operator

abstract:
  We study the selfadjoint time operator recently constructed by one of the
authors. We will show that this time operator must be interpreted as a
``selfadjoint variant'' of the time operator.


title: Are elementary particles point-like objects?

abstract:
  Simple arguments based on uncertainty principle and Dirac's equation are
examined which show that electron behaves either as a point-like charge or as
an extended distribution according as high- or low-energy experiments are
considered.


title:
Quadrature and polarization squeezing in a dispersive optical
  bistability model

abstract:
  We theoretically study quadrature and polarization squeezing in dispersive
optical bistability through a vectorial Kerr cavity model describing a
nonlinear cavity filled with an isotropic chi(3) medium in which self-phase and
cross-phase modulation, as well as four--wave mixing, occur. We derive
expressions for the quantum fluctuations of the output field quadratures as a
function of which we express the spectrum of fluctuations of the output field
Stokes parameters. We pay particular attention to study how the bifurcations
affecting the non-null linearly polarized output mode squeezes the orthogonally
polarized vacuum mode, and show how this produces polarization squeezing.


title:
Nature as the observer: A simplified approach to the measurement problem
  and related issues

abstract:
  Several theories have been advanced recently which appear to offer a
resolution to that portion of the measurement problem which previously dealt
with a possible reduction of the state vector in a subjective fashion by the
brain, mind or consciousness. It now appears, based on both biological and
mathematical analysis, that collapse of the wave function always takes place in
an objective fashion in the retinal rod-rhodopsin molecule, and that only
measured information is ever presented to the brain, mind or consciousness for
possible subjective analysis. The remaining portion of the measurement problem
has to do with the use and legitimacy of such terms as boundary (Heisenberg or
von Neumann cut), information, irreversible, measurement, microscopic,
macroscopic, observer (apparatus or measuring system), observed (measured
system) and wave function collapse. This portion of the measurement problem may
be resolved in two ways. First, by adopting Dirac's theory that it is nature
that makes the choice of measuremental result. Second, by the insertion of a
mesoscopic bridge between the microscopic and macroscopic worlds, in the
existing form of the rhodopsin molecule with its retinal and opsin components.


title: Coherent control of single photon states

abstract:
  We define a class of multi-mode single photon states suitable for quantum
information applications. We show how standard amplitude modulation techniques
may be used to control the pulse shape of single photon states.


title: Fundamentals of universality in one-way quantum computation

abstract:
  We build a framework allowing for a systematic investigation of the issue:
"Which quantum states are universal resources for one-way quantum computation?"
We start by re-examining what is exactly meant by "universality" in quantum
computation, and what the implications are for universal one-way quantum
computation. Given the framework of a measurement-based quantum computer, where
quantum information is processed by local operations only, the most general
universal one-way quantum computer is one which is capable of accepting
arbitrary classical inputs and producing arbitrary quantum outputs--we refer to
this property as CQ-universality. We then show that a systematic study of
CQ-universality in one-way quantum computation is possible by identifying
entanglement features that must be present in every universal resource. These
insights are used to identify several states as being not universal, such as 1D
cluster states, W states, and ground states of non-critical 1D spin systems.
Our criteria are strengthened by considering the efficiency of a quantum
computation, and we find that entanglement measures must obey a certain scaling
law with the system size for all efficient universal resources. This again
leads to examples of non-universal resources, such as, e.g., ground states of
critical 1D spin systems. We also provide several examples of efficient
universal resources, namely graph states corresponding to hexagonal, triangular
and Kagome lattices. Finally, we consider the more general notion of encoded
CQ-universality, where quantum outputs are allowed to be produced in an encoded
form. Again we provide entanglement-based criteria for encoded universality.
Moreover, we present a general procedure to construct encoded universal
resources.


title: Van der Waals Interactions in a Magneto-Dielectric Medium

abstract:
  The van der Waals interaction between two ground-state atoms is calculated
for two electrically or magnetically polarizable particles embedded in a
dispersive magneto-dielectric medium. Unlike previous calculations which infer
the atom-atom interaction from the dilute-medium limit of the macroscopic,
many-body van der Waals interaction, the interaction is calculated directly for
the system of two atoms in a magneto-dielectric medium. Two approaches are
presented, the first based on the quantized electromagnetic field in a
dispersive medium without absorption and the second on Green functions that
allow for absorption. We show that the correct van der Waals interactions are
obtained regardless of whether absorption in the host medium is taken into
account.


title: Six-qubit permutation-based decoherence-free orthogonal basis

abstract:
  There is a natural orthogonal basis of the 6-qubit decoherence-free (DF)
space robust against collective noise. Interestingly, most of the basis states
can be obtained from one another just permuting qubits. This property: (a) is
useful for encoding qubits in DF subspaces, (b) allows the implementation of
the Bennett-Brassard 1984 (BB84) protocol in DF subspaces just permuting
qubits, which completes a the method for quantum key distribution using DF
states proposed by Boileau et al. [Phys. Rev. Lett. 92, 017901 (2004)], and (c)
points out that there is only one 6-qubit DF state which is essentially new
(not obtained by permutations) and therefore constitutes an interesting
experimental challenge.


title:
On spin evolution in a time-dependent magnetic field: post-adiabatic
  corrections and geometric phases

abstract:
  We examine both quantum and classical versions of the problem of spin
evolution in a slowly varying magnetic field. Main attention is given to the
first- and second-order adiabatic corrections in the case of in-plane
variations of the magnetic field. While the first-order correction relates to
the adiabatic Berry phase and Coriolis-type lateral deflection of the spin, the
second-order correction is shown to be responsible for the next-order geometric
phase and in-plain deflection. A comparison between different approaches,
including the exact (non-adiabatic) geometric phase, is presented.


title:
Sideband cooling while preserving coherences in the nuclear spin state
  in group-II-like atoms

abstract:
  We propose a method for laser cooling group-II-like atoms without changing
the quantum state of their nuclear spins, thus preserving coherences that are
usually destroyed by optical pumping. As group-II-like atoms have a $^1S_0$
closed-shell ground state, nuclear spin and electronic degrees of freedom are
decoupled, allowing for independent manipulation. The hyperfine interaction
that couples these degrees of freedom in excited states can be suppressed
through the application of external magnetic fields. Our protocol employs
resolved-sideband cooling on the forbidden clock transition, $^1S_0 \to
{}^3P_0$, with quenching via coupling to the rapidly decaying $^1P_1$ state,
deep in the Paschen-Back regime. This makes it possible to laser cool neutral
atomic qubits without destroying the quantum information stored in their
nuclear spins, as shown in two examples, $^{171}$Yb and $^{87}$Sr.


title: Certainty and Uncertainty in Quantum Information Processing

abstract:
  This survey, aimed at information processing researchers, highlights
intriguing but lesser known results, corrects misconceptions, and suggests
research areas. Themes include: certainty in quantum algorithms; the "fewer
worlds" theory of quantum mechanics; quantum learning; probability theory
versus quantum mechanics.


title: Chirping a two-photon transition in a multi-state ladder

abstract:
  We consider a two-photon transition in a specific ladder system driven by a
chirped laser pulse. In the weak field limit, we find that the excited state
probability amplitude arises due to interference of multiple quantum paths
which are weighted by quadratic phase factors. The excited state population has
the form of a Gauss sum which plays a prominent role in number theory.


title: Subspace Confinement: How good is your qubit?

abstract:
  The basic operating element of standard quantum computation is the qubit, an
isolated two-level system that can be accurately controlled, initialized and
measured. However, the majority of proposed physical architectures for quantum
computation are built from systems that contain much more complicated Hilbert
space structures. Hence, defining a qubit requires the identification of an
appropriate controllable two-dimensional sub-system. This prompts the obvious
question of how well a qubit, thus defined, is confined to this subspace, and
whether we can experimentally quantify the potential leakage into to states
outside the qubit subspace. In this paper we demonstrate that subspace leakage
can be quantitatively characterized using minimal theoretical assumptions by
examining the Fourier spectrum of the Rabi oscillation experiment.


title:
An Information-Theoretic Approach to Quantum Theory, I: The Abstract
  Quantum Formalism

abstract:
  In this paper and a companion paper, we attempt to systematically investigate
the possibility that the concept of information may enable a derivation of the
quantum formalism from a set of physically comprehensible postulates. To do so,
we formulate an abstract experimental set-up and a set of assumptions based on
generalizations of experimental facts that can be reasonably taken to be
representative of quantum phenomena, and on theoretical ideas and principles,
and show that it is possible to deduce the quantum formalism. In particular, we
show that it is possible to derive the abstract quantum formalism for
finite-dimensional quantum systems and the formal relations, such as the
canonical commutation relationships and Dirac's Poisson Bracket rule, that are
needed to apply the abstract formalism to particular systems of interest. The
concept of information, via an information-theoretic invariance principle,
plays a key role in the derivation, and gives rise to some of the central
structural features of the quantum formalism.


title:
Probing quantum phases of ultracold atoms in optical lattices by
  transmission spectra in cavity QED

abstract:
  Studies of ultracold atoms in optical lattices link various disciplines,
providing a playground where fundamental quantum many-body concepts, formulated
in condensed-matter physics, can be tested in much better controllable atomic
systems, e.g., strongly correlated phases, quantum information processing.
Standard methods to measure quantum properties of Bose-Einstein condensates
(BECs) are based on matter-wave interference between atoms released from traps
which destroys the system. Here we propose a nondestructive method based on
optical measurements, and prove that atomic statistics can be mapped on
transmission spectra of a high-Q cavity. This can be extremely useful for
studying phase transitions between Mott insulator and superfluid states, since
various phases show qualitatively distinct light scattering. Joining the
paradigms of cavity quantum electrodynamics (QED) and ultracold gases will
enable conceptually new investigations of both light and matter at ultimate
quantum levels, which only recently became experimentally possible. Here we
predict effects accessible in such novel setups.


title: Conditional generation of an arbitrary superposition of coherent states

abstract:
  We present a scheme to conditionally generate an arbitrary superposition of a
pair of coherent states from a squeezed vacuum by means of the modified photon
subtraction where a coherent state ancilla and two on/off type detectors are
used. We show that, even including realistic imperfections of the detectors,
our scheme can generate a target state with a high fidelity. The amplitude of
the generated states can be amplified by conditional homodyne detections.


title: Monogamy Inequality in terms of Negativity for Three-Qubit States

abstract:
  We propose a new entanglement measure to quantify three qubits entanglement
in terms of negativity. A monogamy inequality analogous to
Coffman-Kundu-Wootters (CKW) inequality is established. This consequently leads
to a definition of residual entanglement, which is referred to as three-$\pi$
in order to distinguish from three-tangle. The three-$\pi$ is proved to be a
natural entanglement measure. By contrast to the three-tangle, it is shown that
the three-$\pi$ always gives greater than zero values for $W$ and GHZ classes,
implying there always exists three-way entanglement for them, and three-tangle
generally underestimates three-way entanglement of a given system. This
investigation will offer an alternative tool to understand genuine multipartite
entanglement.


title:
Structure of the photon and magnetic field induced birefringence and
  dichroism

abstract:
  In this letter we show that the dichroism and ellipticity induced on a linear
polarized light beam by the presence of a magnetic field in vacuum can be
explained in the framework of the de Broglie's fusion model of a photon. In
this model it is assumed that the usual photon is the spin 1 state of a
particle-antiparticle bound state of two spin 1/2 fermions. The other S=0 state
is referred to as the \emph{second} photon. On the other hand, since no charged
particle neither particles having an electric dipole are considered, no effect
is predicted in the presence of electric fields and this model is not in
contradiction with star cooling data or solar axion search.


title: Quantum expanders and the quantum entropy difference problem

abstract:
  We define quantum expanders in a natural way. We show that under certain
conditions classical expander constructions generalize to the quantum setting,
and in particular so does the Lubotzky, Philips and Sarnak construction of
Ramanujan expanders from Cayley graphs of the group PGL. We show that this
definition is exactly what is needed for characterizing the complexity of
estimating quantum entropies.


title: Detection loophole in asymmetric Bell experiments

abstract:
  The problem of closing the detection loophole with asymmetric systems, such
as entangled atom-photon pairs, is addressed. We show that, for the Bell
inequality I_3322, a minimal detection efficiency of 43% can be tolerated for
one of the particles, if the other one is always detected. We also study the
influence of noise and discuss the prospects of experimental implementation.


title: Quantum Process Tomography: Resource Analysis of Different Strategies

abstract:
  Characterization of quantum dynamics is a fundamental problem in quantum
physics and quantum information science. Several methods are known which
achieve this goal, namely Standard Quantum Process Tomography (SQPT),
Ancilla-Assisted Process Tomography (AAPT), and the recently proposed scheme of
Direct Characterization of Quantum Dynamics (DCQD). Here, we review these
schemes and analyze them with respect to some of the physical resources they
require. Although a reliable figure-of-merit for process characterization is
not yet available, our analysis can provide a benchmark which is necessary for
choosing the scheme that is the most appropriate in a given situation, with
given resources. As a result, we conclude that for quantum systems where
two-body interactions are not naturally available, SQPT is the most efficient
scheme. However, for quantum systems with controllable two-body interactions,
the DCQD scheme is more efficient than other known QPT schemes in terms of the
total number of required elementary quantum operations.


title: Calibration of a single atom detector for atomic micro chips

abstract:
  We experimentally investigate a scheme for detecting single atoms
magnetically trapped on an atom chip. The detector is based on the
photoionization of atoms and the subsequent detection of the generated ions. We
describe the characterization of the ion detector with emphasis on its
calibration via the correlation of ions with simultaneously generated
electrons. A detection efficiency of 47.8% (+-2.6%) is measured, which is
useful for single atom detection, and close to the limit allowing atom counting
with sub-Poissonian uncertainty.


title: Cluster state quantum computation in coupled cavity arrays

abstract:
  Measurement-based quantum computation has revolutionized quantum information
processing, and the physical systems with which it can be implemented. One
simply needs the ability to prepare a particular state, known as the cluster
state, and subsequently to perform single-qubit measurements on it.
Nevertheless, a scalable implementation is yet to be realized. Here we propose
a hybrid light-matter system comprised of coupled cavities interacting with two
level systems. Utilising the stable, individually addressable, qubits resulting
from the localised long-lived atom-photon excitations, we demonstrate how to
use the natural system dynamics to `weave' these qubits into a cluster state
and propose the implementation of quantum algorithms employing just two rows of
qubits. Finally, we briefly discuss the prospects for experimental
implementation using atoms, quantum dots or Cooper pair boxes.


title: Qubit-Qubit and Qubit-Qutrit Separability Functions and Probabilities

abstract:
  We list in increasing order -- 1/3, 3/8, 2/5, 135 pi/1024, 16/(3 pi^2), 3
pi/16, 5/8, 105 pi/512, 2 - 435 pi/1024, 11/16, 1 -- a number of exact
two-qubit Hilbert-Schmidt (HS) separability probabilities, we are able to
compute. Each probability corresponds to a specific scenario -- a class of 4 x
4 density matrices (rho) with an m-subset (m<6) of its six off-diagonal pairs
of symmetrically located entries set to zero. Initially, we consider only
scenarios in which the (6-m) non-nullified pairs are real, but then permit them
to be complex (as well as quaternionic) in nature also. The general analytical
strategy we implement is based on the Bloore density matrix parameterization
(J. Phys. A, 9, 2059 [1976]), allowing us to conveniently reduce the
dimensionalities of required integrations. For each scenario, we identify a
certain univariate ``separability function'' S_{scenario}(nu), where nu =
rho_{11} rho_{44}/(rho_{22} rho_{33}). The integral over nu in [0,infty] of the
product of this function with a scenario-specific (marginal) jacobian function
J_{scenario}(nu) yields the HS {separable} volume (V^{HS}_{sep}). The ratio of
V^{HS}_{sep} to the HS total (entangled and non-entangled) volume, gives us the
HS scenario-specific separability probability. Among the possible forms that we
have so far determined for S_{scenario}(nu) are piecewise combinations of c, c
sqrt{nu} and c nu for nu in [0,1] and (in a dual manner) c, c/sqrt{nu} and c/nu
for nu in [1,infty]. We also obtain bivariate separability functions
S_{scenario)^{6 x 6}(nu_{1},nu_{2}} in the qubit-qutrit case, involving 6 x 6
density matrices, with ratio variables, nu_{1}= rho_{11} rho_{55}/(rho_{22}
rho_{44}), and nu_{2}= rho_{22} rho_{66}/(rho_{33} rho_{55}). Additionally, we
investigate parallel two-qutrit and three-qubit problems.


title: The Quantum Measurement Process: Lessons from an Exactly Solvable Model

abstract:
  The measurement of a spin-$\half$ is modeled by coupling it to an apparatus,
that consists of an Ising magnetic dot coupled to a phonon bath. Features of
quantum measurements are derived from the dynamical solution of the
measurement, regarded as a process of quantum statistical mechanics.
Schr\"odinger cat terms involving both the system and the apparatus, die out
very quickly, while the registration is a process taking the apparatus from its
initially metastable state to one of its stable final states. The occurrence of
Born probabilities can be inferred at the macroscopic level, by looking at the
pointer alone. Apparent non-unitary behavior of the measurement process is
explained by the arisal of small many particle correlations, that characterize
relaxation.


title:
Remarks on the equivalence of full additivity and monotonicity for the
  entanglement cost

abstract:
  We analyse the relationship between the full additivity of the entanglement
cost and its full monotonicity under local operations and classical
communication. We show that the two properties are equivalent for the
entanglement cost. The proof works for the regularization of any convex,
subadditive, and asymptotically continuous entanglement monotone, and hence
also applies to the asymptotic relative entropy of entanglement.


title:
Nonclassicality of quantum excitation of classical coherent fields in
  thermal environments

abstract:
  The nonclassicality of photon-added coherent fields in the thermal channel is
investigated by exploring the volume of the negative part of the Wigner
function which reduces with the dissipative time. The Wigner functions become
positive when the decay time exceeds a threshold value. For the case of the
single photon-added coherent state, we derive the exact threshold values of
decay time in the thermal channel. For arbitrary partial negative Wigner
distribution function, a generic analytical relation between the mean photon
number of heat bath and the threshold value of decay time is presented.
Finally, the possible application of SPACSs in quantum computation has been
briefly discussed.
  OCIS codes: 270.0270, 270.2500, 000.5490


title:
Quantum non-demolition measurement of photon-arrival using an
  atom-cavity system

abstract:
  A simple and efficient quantum non-demolition measurement (QND) scheme is
proposed in which the arrival of a signal photon is detected without affecting
the qubit state. The proposed QND scheme functions even if the ancillary photon
is replaced with weak light composed of vacuum and one-photon states. Although
the detection scheme is designed for entanglement sharing applications, it is
also suitable for general purification of a single photon state.


title:
Observation of -9 dB quadrature squeezing with improvement of phase
  stability in homodyne measurement

abstract:
  We observe -9.01$\pm$0.14 dB of squeezing and +15.12$\pm$0.14 dB of
antisqueezing with a local oscillator phase locked in homodyne measurement. In
reference [1], two main factors are pointed out which degrade the observed
squeezing level: phase fluctuation in homodyne measurement and intracavity
losses of an optical parametric oscillator for squeezing. We have improved the
phase stability of homodyne measurement and have reduced the intracavity
losses. We measure pump power dependences of the squeezing and antisqueezing
levels, which show good agreement with theoretical calculations taking account
of the phase fluctuation.


title: Slowing the Decay of an Excited Atom by the Presence of a Detector

abstract:
  The decay of an excited is shown to slow down in the presence of a photo
detector. This is similar to the behavior of an atom in a mistuned cavity, and
under the conditions of the quantum Zeno effect. No external perturbing field
is applied to measure the survival probability of the unstable state.


title:
Exact solutions of the radial Schrodinger equation for some physical
  potentials

abstract:
  By using an ansatz for the eigenfunction, we have obtained the exact
analytical solutions of the radial Schrodinger equation for the pseudoharmonic
and Kratzer potentials in two dimensions. The energy levels of all the bound
states are easily calculated from this eigenfunction ansatz. The normalized
wavefunctions are also obtained.


title:
Strong-field spatial intensity-intensity correlations of light scattered
  from regular structures of atoms

abstract:
  Photon correlations and cross-correlations of light scattered by a regular
structure of strongly driven atoms are investigated. At strong driving, the
scattered light separates into distinct spectral bands, such that each band can
be treated as independent, thus extending the set of observables. We focus on
second-order intensity-intensity correlation functions in two- and multi-atom
systems. We demonstrate that for a single two-photon detector as, e.g., in
lithography, increasing the driving field intensity leads to an increased
spatial resolution of the second-order two-atom interference pattern. We show
that the cross-correlations between photons emitted in the spectral sidebands
violate Cauchy-Schwartz inequalities, and that their emission ordering cannot
be predicted. Finally, the results are generalized for multi-particle
structures, where we find results different from those in a Dicke-type sample.


title:
On the Threshold for the Pair Production and Localization of Spinless
  Particles

abstract:
  The one-dimensional Klein-Gordon equation is investigated with the most
general Lorentz structure for the external potentials. The analysis of the
scattering of particles in a step potential with an arbitrary mixing of vector
and scalar couplings reveals that the scalar coupling contributes for
increasing the threshold energy for the particle-antiparticle pair production.
Furthermore, it is shown that the pair production is only feasible whether the
vector coupling exceeds the scalar one. An apparent paradox concerning the
localization of a particle in an arbitrarily small region of space, due to the
presence of the scalar coupling, is solved by introducing the concept of
effective Compton wavelength.


title: A Quantum Algorithm for the Hamiltonian NAND Tree

abstract:
  We give a quantum algorithm for the binary NAND tree problem in the
Hamiltonian oracle model. The algorithm uses a continuous time quantum walk
with a run time proportional to sqrt N. We also show a lower bound of sqrt N
for the NAND tree problem in the Hamiltonian oracle model.


title: On the consistency in the adiabatic theorem and quantum geometric phase

abstract:
  The recent discovery of inconsistency (MS inconsistency) in the adiabatic
approximation is discussed. In particular, the so-called, inconsistency in
Berry phase is analyzed. On the contrary to some authors, we found that the MS
inconsistency persisted and the so-called inconsistency in Berry phase does not
exist.


title: A Quantum Scattering Interferometer

abstract:
  The collision of two ultra-cold atoms results in a quantum-mechanical
superposition of two outcomes: each atom continues without scattering and each
atom scatters as a spherically outgoing wave with an s-wave phase shift. The
magnitude of the s-wave phase shift depends very sensitively on the interaction
between the atoms. Quantum scattering and the underlying phase shifts are
vitally important in many areas of contemporary atomic physics, including
Bose-Einstein condensates, degenerate Fermi gases, frequency shifts in atomic
clocks, and magnetically-tuned Feshbach resonances. Precise measurements of
quantum scattering phase shifts have not been possible until now because, in
scattering experiments, the number of scattered atoms depends on the s-wave
phase shifts as well as the atomic density, which cannot be measured precisely.
Here we demonstrate a fundamentally new type of scattering experiment that
interferometrically detects the quantum scattering phase shifts of individual
atoms. By performing an atomic clock measurement using only the scattered part
of each atom, we directly and precisely measure the difference of the s-wave
phase shifts for the two clock states in a density independent manner. Our
method will give the most direct and precise measurements of ultracold
atom-atom interactions and will place stringent limits on the time variations
of fundamental constants.


title:
Optimal control of quantum gates and suppression of decoherence in a
  system of interacting two-level particles

abstract:
  Methods of optimal control are applied to a model system of interacting
two-level particles (e.g., spin-half atomic nuclei or electrons or two-level
atoms) to produce high-fidelity quantum gates while simultaneously negating the
detrimental effect of decoherence. One set of particles functions as the
quantum information processor, whose evolution is controlled by a
time-dependent external field. The other particles are not directly controlled
and serve as an effective environment, coupling to which is the source of
decoherence. The control objective is to generate target one- and two-qubit
unitary gates in the presence of strong environmentally-induced decoherence and
under physically motivated restrictions on the control field. The quantum-gate
fidelity, expressed in terms of a novel state-independent distance measure, is
maximized with respect to the control field using combined genetic and gradient
algorithms. The resulting high-fidelity gates demonstrate the feasibility of
precisely guiding the quantum evolution via optimal control, even when the
system complexity is exacerbated by environmental coupling. It is found that
the gate duration has an important effect on the control mechanism and
resulting fidelity. An analysis of the sensitivity of the gate performance to
random variations in the system parameters reveals a significant degree of
robustness attained by the optimal control solutions.


title: Quantum Mechanics with Complex Time : A Comment to the Paper by Rajeev

abstract:
  In (quant-ph/0701141) Rajeev studied quantization of the damped simple
harmonic oscillator and introduced a complex-valued Hamiltonian (which is
normal). In this note we point out that the quantization is interpreted as a
quantum mechanics with {\bf complex time}. We also present a problem on
quantization of classical control systems.


title:
An Information-Theoretic Approach to Quantum Theory, II: The Formal
  Rules of Quantum Theory

abstract:
  In a companion paper (hereafter referred to as Paper I), we have presented an
attempt to derive the finite-dimensional abstract quantum formalism from a set
of physically comprehensible assumptions. In this paper, we formulate a
correspondence principle, the Average-Value Correspondence Principle, that
allows relations between measurement outcomes which are known to hold in a
classical model of a system to be systematically taken over into the quantum
model of the system. Using this principle, we derive the explicit form of the
temporal evolution operator (thereby completing the derivation of the abstract
quantum formalism begun in Paper I), and derive many of the formal rules (such
as operator rules, commutation relations, and Dirac's Poisson bracket rule)
that are needed to apply the abstract quantum formalism to model particular
physical systems.


title:
The Bell bases decomposition of a general N-qubit state Teleportation
  through a non-maximally entangled quantum channel

abstract:
  We propose a method of the Bell bases decomposition to teleport an arbitrary
unknown N-qubit state through a nonmaximally entangled quantum channel, and
give the universal decomposition matrix of N-qubit. Using the decomposition
matrix, we can easily obtain the collapsed state at the receiver site. The
inverse matrix that the decomposition matrix is just the transformation matrix
that the receiver can manipulate. The decomposition matrix is a function of the
parameters of the quantum channel. After defining the sub-matrix of the quantum
channel, we find that the decomposition matrix is a tensor product of the
sub-matrixes.


title: A search on Dirac equation

abstract:
  The solutions, in terms of orthogonal polynomials, of Dirac equation with
analytically solvable potentials are investigated within a novel formalism by
transforming the relativistic equation into a Schrodinger like one. Earlier
results are discussed in a unified framework and certain solutions of a large
class of potentials are given.


title:
Device-independent security of quantum cryptography against collective
  attacks

abstract:
  We present the optimal collective attack on a Quantum Key Distribution (QKD)
protocol in the "device-independent" security scenario, where no assumptions
are made about the way the QKD devices work or on what quantum system they
operate. Our main result is a tight bound on the Holevo information between one
of the authorized parties and the eavesdropper, as a function of the amount of
violation of a Bell-type inequality.


title: Catalytic majorization and $\ell_p$ norms

abstract:
  An important problem in quantum information theory is the mathematical
characterization of the phenomenon of quantum catalysis: when can the
surrounding entanglement be used to perform transformations of a jointly held
quantum state under LOCC (local operations and classical communication) ?
Mathematically, the question amounts to describe, for a fixed vector $y$, the
set $T(y)$ of vectors $x$ such that we have $x \otimes z \prec y \otimes z$ for
some $z$, where $\prec$ denotes the standard majorization relation. Our main
result is that the closure of $T(y)$ in the $\ell_1$ norm can be fully
described by inequalities on the $\ell_p$ norms: $\|x\|_p \leq \|y\|_p$ for all
$p \geq 1$. This is a first step towards a complete description of $T(y)$
itself. It can also be seen as a $\ell_p$-norm analogue of Ky Fan dominance
theorem about unitarily invariant norms. The proofs exploits links with another
quantum phenomenon: the possibiliy of multiple-copy transformations
($x^{\otimes n} \prec y^{\otimes n}$ for given $n$). The main new tool is a
variant of Cram\'er$ theorem on large deviations for sums of i.i.d. random
variables.


title: Asymptotics of random density matrices

abstract:
  We investigate random density matrices obtained by partial tracing larger
random pure states. We show that there is a strong connection between these
random density matrices and the Wishart ensemble of random matrix theory. We
provide asymptotic results on the behavior of the eigenvalues of random density
matrices, including convergence of the empirical spectral measure. We also
study the largest eigenvalue (almost sure convergence and fluctuations).


title: Entanglement purification with two-way classical communication

abstract:
  We present an improved protocol for entanglement purification of bipartite
mixed states. The protocol requires two-way classical communication and hence
implies an improved lower bound on the quantum capacity with two-way classical
communication of the quantum depolarizing channel.


title:
Adaptive Entanglement Purification Protocols with Two-way Classical
  Communication

abstract:
  We present a family of entanglement purification protocols that generalize
four previous methods, namely the recurrence method, the modified recurrence
method, and the two methods proposed by Maneva-Smolin and Leung-Shor. We will
show that this family of protocols have improved yields over a wide range of
initial fidelities F, and hence imply new lower bounds on the quantum capacity
assisted by two-way classical communication of the quantum depolarizing
channel. In particular, the yields of these protocols are higher than the yield
of universal hashing for F less than 0.993 and as F goes to 1.


title: Quantum Mechanical Heat Transport in Disordered Harmonic Chains

abstract:
  We investigate the mechanism of heat conduction in ordered and disordered
harmonic onedimensional chains within the quantum mechanical Langevin method.
In the case of the disordered chains we find indications for normal heat
conduction which means that there is a finite temperature gradient but we
cannot clearly decide whether the heat resistance increases linearly with the
chain length. Furthermore we observe characteristic quantum mechanical features
like Bose-Einstein statistics of the occupation numbers of the normal modes,
freezing of the heat conductivity and the influence of the entanglement within
the chain on the current. For the ordered chain we recover some classical
results like a vanishing temperature gradient and a heat flux independent of
the length of the chain.


title: Quantum entropy dynamics for chaotic systems beyond the classical limit

abstract:
  The entropy production rate for an open quantum system with a classically
chaotic limit has been previously argued to be independent of $\hbar$ and $D$,
the parameter denoting coupling to the environment, and to be equal to the sum
of generalized Lyapunov exponents, with these results applying in the
near-classical regime. We present results for a specific system going well
beyond earlier work, considering how these dynamics are altered for the Duffing
problem by changing $\hbar,D$ and show that the entropy dynamics have a
transition from classical to quantum behavior that scales, at least for a
finite time, as a function of $\hbar^2/D$.


title: Photoionization and Photoelectric Loading of Barium Ion Traps

abstract:
  Simple and effective techniques for loading barium ions into linear Paul
traps are demonstrated. Two-step photoionization of neutral barium is achieved
using a weak intercombination line (6s2 1S0 <-> 6s6p 3P1, 791 nm) followed by
excitation above the ionization threshold using a nitrogen gas laser (337 nm).
Isotopic selectivity is achieved by using a near Doppler-free geometry for
excitation of the triplet 6s6p 3P1 state. Additionally, we report a
particularly simple and efficient trap loading technique that employs an
in-expensive UV epoxy curing lamp to generate photoelectrons.


title: Discrete-query quantum algorithm for NAND trees

abstract:
  Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for
evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian
query model. In this note, we point out that their algorithm can be converted
into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional
quantum query model, for any fixed epsilon > 0.


title: Decoherence of two qubit systems: A random matrix description

abstract:
  We study decoherence of two non-interacting qubits. The environment and its
interaction with the qubits are modelled by random matrices. Decoherence,
measured in terms of purity, is calculated in linear response approximation.
Monte Carlo simulations illustrate the validity of this approximation and of
its extension by exponentiation. The results up to this point are also used to
study one qubit decoherence. Purity decay of entangled and product states are
qualitatively similar though for the latter case it is slower. Numerical
studies for a Bell pair as initial state reveal a one to one correspondence
between its decoherence and its internal entanglement decay. For strong and
intermediate coupling to the environment this correspondence agrees with the
one for Werner states. In the limit of a large environment the evolution
induces a unital channel in the two qubits, providing a partial explanation for
the relation above.


title: Trapping and observing single atoms in the dark

abstract:
  A single atom strongly coupled to a cavity mode is stored by
three-dimensional confinement in blue-detuned cavity modes of different
longitudinal and transverse order. The vanishing light intensity at the trap
center reduces the light shift of all atomic energy levels. This is exploited
to detect a single atom by means of a dispersive measurement with 95%
confidence in 0.010 ms, limited by the photon-detection efficiency. As the atom
switches resonant cavity transmission into cavity reflection, the atom can be
detected while scattering about one photon.


title:
Selective Rotational Excitation of Molecular Isotopes and Nuclear Spin
  Isomers

abstract:
  Following excitation by a strong ultra-short laser pulse, molecules develop
coordinated rotational motion, exhibiting transient alignment along the
direction of the laser electric field, followed by periodic full and fractional
revivals that depend on the molecular rotational constants. In mixtures, the
different species undergo similar rotational dynamics, all starting together
but evolving differently with each demonstrating its own periodic revival
cycles. For a bimolecular mixture of linear molecules, at predetermined times,
one species may attain a maximally aligned state while the other is
anti-aligned (i.e. molecular axes are confined in a plane perpendicular to the
laser electric field direction). By a properly timed second laser pulse, the
rotational excitation of the undesired species may be almost completely removed
leaving only the desired species to rotate and periodically realign, thus
facilitating further selective manipulations by polarized light. In this paper,
such double excitation schemes are demonstrated for mixtures of molecular
isotopes (isotopologues) and for nuclear spin isomers.


title: Non-universal level statistics in a chaotic quantum spin chain

abstract:
  We study the level statistics of an interacting multi-qubit system, namely
the kicked Ising spin chain, in the regime of quantum chaos. Long range
quasi-energy level statistics show effects analogous to the ones observed in
semi-classical systems due to the presence of classical periodic orbits, while
short range level statistics display perfect statistical agreement with random
matrix theory. Even though our system possesses no classical limit, our result
suggest existence of an important non-universal system specific behavior at
short time scale, which clearly goes beyond finite size effects in random
matrix theory.


title:
Violation of Bell's inequality using classical measurements and
  non-linear local operations

abstract:
  We find that Bell's inequality can be significantly violated (up to
Tsirelson's bound) with two-mode entangled coherent states using only homodyne
measurements. This requires Kerr nonlinear interactions for local operations on
the entangled coherent states. Our example is a demonstration of
Bell-inequality violations using classical measurements. We conclude that
entangled coherent states with coherent amplitudes as small as 0.842 are
sufficient to produce such violations.


title: Global information balance in quantum measurements

abstract:
  We perform an information-theoretical analysis of quantum measurement
processes and obtain the global information balance in quantum measurements, in
the form of a closed chain equation for quantum mutual entropies. Our balance
provides a tight and general entropic information-disturbance trade-off, and
explains the physical mechanism underlying it. Finally, the single-outcome
case, that is, the case of measurements with post-selection, is briefly
discussed.


title: Quantum Game Theory Based on the Schmidt Decomposition

abstract:
  We present a novel formulation of quantum game theory based on the Schmidt
decomposition, which has the merit that the entanglement of quantum strategies
is manifestly quantified. We apply this formulation to 2-player, 2-strategy
symmetric games and obtain a complete set of quantum Nash equilibria. Apart
from those available with the maximal entanglement, these quantum Nash
equilibria are extensions of the Nash equilibria in classical game theory. The
phase structure of the equilibria is determined for all values of entanglement,
and thereby the possibility of resolving the dilemmas by entanglement in the
game of Chicken, the Battle of the Sexes, the Prisoners' Dilemma, and the Stag
Hunt, is examined. We find that entanglement transforms these dilemmas with
each other but cannot resolve them, except in the Stag Hunt game where the
dilemma can be alleviated to a certain degree.


title: Enhanced Spontaneous Emission Into The Mode Of A Cavity QED System

abstract:
  We study the light generated by spontaneous emission into a mode of a cavity
QED system under weak excitation of the orthogonally polarized mode. Operating
in the intermediate regime of cavity QED with comparable coherent and
decoherent coupling constants, we find an enhancement of the emission into the
undriven cavity mode by more than a factor of 18.5 over that expected by the
solid angle subtended by the mode. A model that incorporates three atomic
levels and two polarization modes quantitatively explains the observations.


title: Quantum wavefunction annealing of spin glasses

abstract:
  A technique inspired on quantum annealing is proposed in order to obtain the
classical ground state of a spin-glass by tracking the full wavefunction of a
given system within the subspace of matrix product states (MPS), using the
density matrix renormalization group (DMRG). The technique is exemplified
within the problem of obtention of the classical ground state of an Ising spin
glass on ladder geometries. Its performance is evaluated and related to the
entanglement entropy.


title: Quantum states for Heisenberg-limited interferometry

abstract:
  The phase resolution of interferometers is limited by the so-called
Heisenberg limit, which states that the optimum phase sensitivity is inversely
proportional to the number of interfering particles N, a 1/sqrt{N} improvement
over the standard quantum limit. We have used simulated annealing, a global
optimization strategy, to systematically search for quantum interferometer
input states that approach the Heisenberg limited uncertainty in estimates of
the interferometer phase shift. We compare the performance of these states to
that of other non-classical states already known to yield Heisenberg limited
uncertainty.


title: Why quantum dynamics is linear

abstract:
  Quantum dynamics is linear. How do we know? From theory or experiment? The
history of this question is reviewed. Nonlinear generalizations of quantum
mechanics have been proposed. They predict small but clear nonlinear effects,
which very accurate experiments have not seen. Is there a reason in principle
why nonlinearity is not found? Is it impossible? Does quantum dynamics have to
be linear? Attempts to prove this have not been decisive, because either their
assumptions are not compelling or their arguments are not conclusive. The
question has been left unsettled. There is a simple answer, based on a simple
assumption. It was found in two steps separated by 44 years. They are steps
back to simpler and more compelling assumptions. A proof of the assumptions of
the Wigner-Bargmann proof has been known since 1962. It assumes that the maps
of density matrices in time are linear. For this step, it is also assumed that
density matrices are mapped one-to-one onto density matrices. An alternative is
to assume that pure states are mapped one-to-one onto pure states and that
entropy does not decrease. In a step taken in 2006, it is proved that the maps
of density matrices in time are linear. It is assumed, as in the earlier step,
that at each time the physical quantities and states are described by the usual
linear structures of quantum mechanics, so the question is only about how
things change in time. Beyond that, the proof assumes only that the dynamics
does not depend on anything outside the system, but must allow the system to be
described as part of a larger system.


title:
Quantum Entanglement dependence on bifurcations and scars in non
  autonomous systems. The case of Quantum Kicked Top

abstract:
  Properties related to entanglement in quantum systems, are known to be
associated with distinct properties of the corresponding classical systems, as
for example stability, integrability and chaos. This means that the detailed
topology, both local and global, of the classical phase space may reveal, or
influence, the entangling power of the quantum system. As it has been shown in
the literature, the bifurcation points, in autonomous dynamical systems, play a
crucial role for the onset of entanglement. Similarly, the existence of scars
among the quantum states seems to be a factor in the dynamics of entanglement.
Here we study these issues for a non-autonomous system, the Quantum Kicked Top,
as a collective model of a multi-qubit system. Using the bifurcation diagram of
the corresponding classical limit (the Classical Kicked Top), we analyzed the
pair-wise and the bi-partite entanglement of the qubits and their relation to
scars, as a function of the critical parameter of the system. We found that the
pair-wise entanglement and pair-wise negativity show a strong maximum precisely
at the bifurcation points, while the bi-partite entanglement changes slope at
these points. We have also investigated the connection between entanglement and
the fixed points on the branch of the bifurcation diagram between the two first
bifurcation points and we found that the entanglement measures take their
extreme values precisely on these points. We conjecture that our results on
this behaviour of entanglement is generic for many quantum systems with a
non-linear classical analogue.


title: Krawtchouk matrices from classical and quantum random walks

abstract:
  Krawtchouk's polynomials occur classically as orthogonal polynomials with
respect to the binomial distribution. They may be also expressed in the form of
matrices, that emerge as arrays of the values that the polynomials take. The
algebraic properties of these matrices provide a very interesting and
accessible example in the approach to probability theory known as quantum
probability. First it is noted how the Krawtchouk matrices are connected to the
classical symmetric Bernoulli random walk. And we show how to derive Krawtchouk
matrices in the quantum probability context via tensor powers of the elementary
Hadamard matrix. Then connections with the classical situation are shown by
calculating expectation values in the quantum case.


title:
Non-monotonicity in the quantum-classical transition: Chaos induced by
  quantum effects

abstract:
  The transition from classical to quantum behavior for chaotic systems is
understood to be accompanied by the suppression of chaotic effects as the
relative size of $\hbar$ is increased. We show evidence to the contrary in the
behavior of the quantum trajectory dynamics of a dissipative quantum chaotic
system, the double-well Duffing oscillator. The classical limit in the case
considered has regular behavior, but as the effective $\hbar$ is increased we
see chaotic behavior. This chaos then disappears deeper into the quantum
regime, which means that the quantum-classical transition in this case is
non-monotonic in $\hbar$.


title:
On the Transport of Atomic Ions in Linear and Multidimensional Ion Trap
  Arrays

abstract:
  Trapped atomic ions have become one of the most promising architectures for a
quantum computer, and current effort is now devoted to the transport of trapped
ions through complex segmented ion trap structures in order to scale up to much
larger numbers of trapped ion qubits. This paper covers several important
issues relevant to ion transport in any type of complex multidimensional rf
(Paul) ion trap array. We develop a general theoretical framework for the
application of time-dependent electric fields to shuttle laser-cooled ions
along any desired trajectory, and describe a method for determining the effect
of arbitrary shuttling schedules on the quantum state of trapped ion motion. In
addition to the general case of linear shuttling over short distances, we
introduce issues particular to the shuttling through multidimensional
junctions, which are required for the arbitrary control of the positions of
large arrays of trapped ions. This includes the transport of ions around a
corner, through a cross or T junction, and the swapping of positions of
multiple ions in a laser-cooled crystal. Where possible, we make connections to
recent experimental results in a multidimensional T junction trap, where
arbitrary 2-dimensional transport was realized.


title: Quantum theory of degenerate $\chi^{(3)}$ two-photon state

abstract:
  We developed a quantum theory for degenerate $\chi^{(3)}$ two-photon state
generated from optical fiber, and compared the theory predictions with an
experimental result which exhibits a Hong-Ou-Mandel dip visibility of around
94%. Excellent agreement between theory and experiment has been achieved, and
we attribute the missing 6% visibility mainly to spatial mode mismatch between
signal and idler photons at the beamsplitter.