title: Optimum Quantum Error Recovery using Semidefinite Programming

abstract:
  Quantum error correction (QEC) is an essential element of physical quantum
information processing systems. Most QEC efforts focus on extending classical
error correction schemes to the quantum regime. The input to a noisy system is
embedded in a coded subspace, and error recovery is performed via an operation
designed to perfectly correct for a set of errors, presumably a large subset of
the physical noise process. In this paper, we examine the choice of recovery
operation. Rather than seeking perfect correction on a subset of errors, we
seek a recovery operation to maximize the entanglement fidelity for a given
input state and noise model. In this way, the recovery operation is optimum for
the given encoding and noise process. This optimization is shown to be
calculable via a semidefinite program (SDP), a well-established form of convex
optimization with efficient algorithms for its solution. The error recovery
operation may also be interpreted as a combining operation following a quantum
spreading channel, thus providing a quantum analogy to the classical diversity
combining operation.


title:
Geometric phases in open systems: an exact model to study how they are
  corrected by decoherence

abstract:
  We calculate the geometric phase for an open system (spin-boson model) which
interacts with an environment (ohmic or nonohmic) at arbitrary temperature.
However there have been many assumptions about the time scale at which the
geometric phase can be measured, there has been no reported observation yet for
mixed states under nonunitary evolution. We study not only how they are
corrected by the presence of the different type of environments but also
estimate the corresponding times at which decoherence becomes effective. These
estimations should be taken into account when planning experimental setups to
study the geometric phase in the nonunitary regime, particularly important for
the application of fault-tolerant quantum computation.


title: Spinor Dynamics-Driven Formation of a Dual-Beam Atom Laser

abstract:
  We demonstrate a novel dual-beam atom laser formed by outcoupling oppositely
polarized components of an F=1 spinor Bose-Einstein condensate whose Zeeman
sublevel populations have been coherently evolved through spin dynamics. The
condensate is formed through all-optical means using a single-beam running-wave
dipole trap. We create a condensate in the field-insensitive $m_F=0$ state, and
drive coherent spin-mixing evolution through adiabatic compression of the
initially weak trap. Such dual beams, number-correlated through the angular
momentum-conserving reaction $2m_0\leftrightharpoons m_{+1}+m_{-1}$, have been
proposed as tools to explore entanglement and squeezing in Bose-Einstein
condensates, and have potential use in precision phase measurements.


title:
Remarks on an attempted axiomatisation of Quantum Mechanics, due to
  Lucien Hardy, and Ten Theses on Hilbert's Sixth Problem and Quantum
  Measurement

abstract:
  From the standpoint of Hilbert's Sixth Problem, which is the axiomatisation
of Physics, the famous paper of Lucien Hardy's, Quantum Theory from Five
Reasonable Axioms, is not relevant. The present paper argues that Hardy does
not give a physical definition of `limit', and if we assume the usual
mathematical definition of limit of a sequence, he fails to define a sequence
in physical terms to which the usual definition is applicable. We argue that
one should not, in fact, try to define probability in terms of the usual notion
of limit of a sequence of results of a measurement because of seemingly
insurmountable difficulties in axiomatising the notion of function or sequence
in this context. Von Plato's and the authour's work (see
http:arxiv.org/abs/quant-ph/0502124 and
euclid.unh.edu/~jjohnson/axiomatics.html for larger context and further
references) on the definition of physical probability needs to be used in this
context. We conclude with ten theses on quantum measurement, from the
standpoint of the Hilbert problem.


title: Degree of entanglement for qubit-qutrit state

abstract:
  In this paper we consider a system consist of a qubit and a qutrit, and find
a formula to evaluate the concurrence for it. We show that entanglement of
formation for this system obeys the same relation as for two-qubits.


title:
On the additivity conjecture for the Weyl channels being covariant with
  respect to the maximum commutative group of unitaries

abstract:
  Some new examples of quantum channels for which the infimum of the output
entropy is additive under taking a tensor product of channels are given.


title:
Measuring the absolute photo detection efficiency using photon number
  correlations

abstract:
  We present two methods for determining the absolute detection efficiency of
photon-counting detectors directly from their singles rates under illumination
from a nonclassical light source. One method is based on a continuous variable
analogue to coincidence counting in discrete photon experiments, but does not
actually rely on high detector time resolutions. The second method is based on
difference detection which is a typical detection scheme in continuous variable
quantum optics experiments. Since no coincidence detection is required with
either method, they are useful for detection efficiency measurements of photo
detectors with detector time resolutions far too low to resolve coincidence
events.


title: Biased tomography schemes: an objective approach

abstract:
  We report on an intrinsic relationship between the maximum-likelihood
quantum-state estimation and the representation of the signal. A quantum
analogy of the transfer function determines the space where the reconstruction
should be done without the need for any ad hoc truncations of the Hilbert
space. An illustration of this method is provided by a simple yet practically
important tomography of an optical signal registered by realistic binary
detectors.


title: The Aladin2 experiment: sensitivity study

abstract:
  Aladin2 is an experiment devoted to the first measurement of variations of
Casimir energy in a rigid body. The main short-term scientific motivation
relies on the possibility of the first demonstration of a phase transition
influenced by vacuum fluctuations while, in the long term and in the mainframe
of the cosmological constant problem, it can be regarded as the first step
towards a measurement of the weight of vacuum energy. In this paper, after a
presentation of the guiding principle of the measurement, the experimental
apparatus and sensitivity studies on final cavities will be presented.


title: Electromagnetically induced coherent backscattering

abstract:
  We demonstrate a strong coherent backward wave oscillation using forward
propagating fields only. This is achieved by applying laser fields to an
ultra-dispersive medium with proper chosen detunings to excite a molecular
vibrational coherence that corresponds to a backward propagating wave. The
physics then has much in common with propagation of ultra-slow light.
Applications to coherent scattering and remote sensing are discussed.


title: Quantum Games Entropy

abstract:
  We propose the study of quantum games from the point of view of quantum
information theory and statistical mechanics. Every game can be described by a
density operator, the von Neumann entropy and the quantum replicator dynamics.
There exists a strong relationship between game theories, information theories
and statistical physics. The density operator and entropy are the bonds between
these theories. The analysis we propose is based on the properties of entropy,
the amount of information that a player can obtain about his opponent and a
maximum or minimum entropy criterion. The natural trend of a physical system is
to its maximum entropy state. The minimum entropy state is a characteristic of
a manipulated system i.e. externally controlled or imposed. There exist tacit
rules inside a system that do not need to be specified or clarified and search
the system equilibrium under the collective welfare principle. The other rules
are imposed over the system when one or many of its members violate this
principle and maximize its individual welfare at the expense of the group.


title:
On the reconstruction of diagonal elements of density matrix of quantum
  optical states by on/off detectors

abstract:
  We discuss a scheme for reconstructing experimentally the diagonal elements
of the density matrix of quantum optical states. Applications to PDC heralded
photons, multi-thermal and attenuated coherent states are illustrated and
discussed in some details.


title: Preparation of atomic velocities by bound-state to resonance conversion

abstract:
  A procedure is proposed to control the average and width of the velocity
distribution of ultra-cold atoms. The atoms are set initially in a bound state
of an optical trap formed by an inner red detuned laser and an outer blue
detuned laser. The bound state is later converted into a resonance by a
suitable change of the laser intensities. An optimal time dependence of the
switching process, between the sudden and adiabatic limits, adjusts the final
translational energies to the Lorentzian shape of the resonance state.


title:
Branching ratio measurement of a "Lambda" system in Tm3+:YAG under
  magnetic field

abstract:
  A three-level Lambda system in Tm3+ doped YAG crystal is experimentally
investigated in the prospect of quantum information processing. Zeeman effect
is used to lift the nuclear spin degeneracy of this ion. In a previous paper
[de Seze et al. Phys. Rev. B, 73, 85112 (2006) we measured the gyromagnetic
tensor components and concluded that adequate magnetic field orientation could
optimize the optical connection of both ground state sublevels to each one of
the excited state sublevels, thus generating Lambda systems. Here we report on
the direct measurement of the transition probability ratio along the two legs
of the Lambda. Measurement techniques combine frequency selective optical
pumping with optical nutation or photon echo processes.


title: Full security of quantum key distribution from no-signaling constraints

abstract:
  We analyze a cryptographic protocol for generating a distributed secret key
from correlations that violate a Bell inequality by a sufficient amount, and
prove its security against eavesdroppers, constrained only by the assumption
that any information accessible to them must be compatible with the
non-signaling principle. The claim holds with respect to the state-of-the-art
security definition used in cryptography, known as universally-composable
security. The non-signaling assumption only refers to the statistics of
measurement outcomes depending on the choices of measurements; hence security
is independent of the internal workings of the devices --- they do not even
need to follow the laws of quantum theory. This is relevant for practice as a
correct and complete modeling of realistic devices is generally impossible. The
techniques developed are general and can be applied to other Bell
inequality-based protocols. In particular, we provide a scheme for estimating
Bell-inequality violations when the samples are not independent and identically
distributed.


title: Connecting the discrete and continuous-time quantum walks

abstract:
  Recently, quantized versions of random walks have been explored as effective
elements for quantum algorithms. In the simplest case of one dimension, the
theory has remained divided into the discrete-time quantum walk and the
continuous-time quantum walk. Though the properties of these two walks have
shown similarities, it has remained an open problem to find the exact relation
between the two. The precise connection of these two processes, both quantally
and classically, is presented. Extension to higher dimensions is also
discussed.


title: Tightly Localized Stationary Pulses in Multi-Level Atomic System

abstract:
  We show the pulse matching phenomenon can be obtained in the general
multi-level system with electromagnetically induced transparency (EIT). For
this we find a novel way to create tightly localized stationary pulses by using
counter-propagating pump fields. The present process is a spatial compression
of excitation so that it allows us to shape and further intensify the localized
stationary pulses, without using standing waves of pump fields or spatially
modulated pump fields.


title: Multiple scattering and electron-uracil collisions at low energies

abstract:
  Links between two well known methods: methods of zero-range and
non-overlapped (muffin-tin) potentials are discussed. Some difficulties of the
method of zero-range potentials and its possible elimination are discussed. We
argue that such advanced method of ZRP potential can be applied to realistic
electron-molecular processes. The method reduces electron-molecule scattering
to generalized eigenvalue problem for hermitian matrices and admit fast
numerical scheme. A noteworthy feature of the method is direct possibility to
calculate the wave functions (partial waves). The theory is applied to
electron-uracil scattering. Partial phases and cross-sections at low energies
are evaluated and plotted.


title: Vanishing environment-induced decoherence

abstract:
  For a central system uniformly coupled to a XY spin-1/2 bath in a transverse
field, we explicitly calculate the Loschmidt echo(LE) to characterize
decoherence quantitatively. We find that the anisotropy parameter $\gamma $
affects decoherence of the central system sensitively when $\gamma \in [0,1]$%
, in particular, the LE becomes unit without varying with time when $\gamma =0
$, implying that environment-induced decoherence vanishes . Some other cases in
which the LE is unit are discussed also.


title:
Formally exact quantization condition for nonrelativistic quantum
  systems

abstract:
  Based on the standard transfer matrix, a formally exact quantization
condition for arbitrary potentials, which outflanks and unifies the historical
approaches, is derived. It can be used to find the exact bound-state energy
eigenvalues of the quantum system without solving an equation of motion for the
system wave functions.


title:
Schmidt number of pure bi-partite entangled states and methods of its
  calculation

abstract:
  An entanglement measure for pure-state continuous-variable bi-partite
problem, the Schmidt number, is analytically calculated for one simple model of
atom-field scattering.


title:
Application of a renormalization algorithm in Hilbert space to the study
  of many-body quantum systems

abstract:
  We implement an algorithm which is aimed to reduce the number of basis states
spanning the Hilbert space of quantum many-body systems. We test the efficiency
of the procedure by working out and analyzing the spectral properties of
strongly correlated and frustrated quantum spin systems. The role and
importance of symmetries are investigated


title:
Analysis and identification of quantum dynamics using Lie algebra
  homomorphisms and Cartan decompositions

abstract:
  In this paper, we consider the problem of model equivalence for quantum
systems. Two models are said to be (input-output) equivalent if they give the
same output for every admissible input. In the case of quantum systems, the
output is the expectation value of a given observable or, more in general, a
probability distribution for the result of a quantum measurement. We link the
input-output equivalence of two models to the existence of a homomorphism of
the underlying Lie algebra. In several cases, a Cartan decomposition of the Lie
algebra su(n) is useful to find such a homomorphism and to determine the
classes of equivalent models. We consider in detail the important cases of two
level systems with a Cartan structure and of spin networks. In the latter case,
complete results are given generalizing previous results to the case of
networks of spin particles with any value of the spin. In treating this
problem, we prove some instrumental results on the subalgebras of su(n) which
are of independent interest.


title: Limit to manipulation of qubits due to spontaneous symmetry breaking

abstract:
  We consider a two-spin qubit that is subject to the orderparameter field of a
symmetry broken manipulation device. It is shown that the thin spectrum of the
manipulation device limits the coherence of the qubit.


title:
Comment on "Optimum Quantum Error Recovery using Semidefinite
  Programming"

abstract:
  In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery
operation in an error correction scheme can be considered as a semidefinite
program. As a possible future improvement it is noted that still better error
correction might be obtained by optimizing the encoding as well. In this note
we present the result of such an improvement, specifically for the four-bit
correction of an amplitude damping channel considered in [1]. We get a strict
improvement for almost all values of the damping parameter. The method (and the
computer code) is taken from our earlier study of such correction schemes
(quant-ph/0307138).


title: Emergent Quantum Jumps in a Nano-Electro-Mechanical System

abstract:
  We describe a nano-electromechnical system that exhibits the "retroactive"
quantum jumps discovered by Mabuchi and Wiseman [Phys. Rev. Lett. 81, 4620
(1998)]. This system consists of a Cooper-pair box coupled to a nano-mechanical
resonator, in which the latter is continuously monitored by a single-electron
transistor or quantum point-contact. Further, we show that these kinds of
jumps, and the jumps that emerge in a continuous quantum non-demolition
measurement are one and the same phenomena. We also consider manipulating the
jumps by applying feedback control to the Cooper-pair box.


title: Simplifying Quantum Circuits via Circuit Invariants and Dressed CNOTs

abstract:
  Quantum Compiling Algorithms decompose (exactly, without approximations) an
arbitrary $2^\nb$ unitary matrix acting on $\nb$ qubits, into a sequence of
elementary operations (SEO). There are many possible ways of decomposing a
unitary matrix into a SEO, and some of these decompositions have shorter length
(are more efficient) than others. Finding an optimum (shortest) decomposition
is a very hard task, and is not our intention here. A less ambitious, more
doable task is to find methods for optimizing small segments of a SEO. Call
these methods piecewise optimizations. Piecewise optimizations involve
replacing a small quantum circuit by an equivalent one with fewer CNOTs. Two
circuits are said to be equivalent if one of them multiplied by some external
local operations equals the other. This equivalence relation between circuits
has its own class functions, which we call circuit invariants. Dressed CNOTs
are a simple yet very useful generalization of standard CNOTs. After discussing
circuit invariants and dressed CNOTs, we give some methods for simplifying
2-qubit and 3-qubit circuits. We include with this paper software (written in
Octave/Matlab) that checks many of the algorithms proposed in the paper.


title: Probing the quantum state of a guided atom laser pulse

abstract:
  We describe bichromatic superradiant pump-probe spectroscopy as a tomographic
probe of the Wigner function of a dispersing particle beam. We employed this
technique to characterize the quantum state of an ultracold atomic beam,
derived from a Rb-87 Bose-Einstein condensate, as it propagated in a 2.5 mm
diameter circular waveguide. Our measurements place an upper bound on the
longitudinal phase-space area occupied by the 300,000 atom beam of 9(1) $\hbar$
and a lower bound on the coherence length (L > 13 microns). These results are
consistent with full quantum degeneracy after multiple orbits around the
waveguide.


title: The Collapse of Bell Determinism

abstract:
  The Bell-Kochen-Specker conditions (BKS) for a deterministic noncontextual
hidden-variable model are wonderfully simple to state, deal with just
one-dimensional projectors on a Hilbert space H and make no reference to a
probabilistic phase space or quantum system. They only ask for an assignment of
zero or one to every projector such that the assignment respects orthogonal
resolutions of the identity. Various no-go results in the literature show that
the pair of statements {BKS is valid; dim H greater than or equal to 3} are
inconsistent. Here we show, more radically, that the pair actually contradicts
the dimensionality of the space itself, by implying that there can exist at
most a single one-dimensional projector acting on H. Our derivation involves
only elementary inner product spaces. It is non-probabilistic, inequality-free,
state independent, does not use entanglement, and is simultaneously valid in
all dimensions three or greater.


title:
On the distance between unitary propagators of quantum systems of
  differing dimensions

abstract:
  A distance measure is presented between two unitary propagators of quantum
systems of differing dimensions along with a corresponding method of
computation. A typical application is to compare the propagator of the actual
(real) process with the propagator of the desired (ideal) process; the former
being of a higher dimension then the latter. The proposed measure has the
advantage of dealing with possibly correlated inputs, but at the expense of
working on the whole space and not just the information bearing part as is
usually the case, i.e., no partial trace operation is explicitly involved. It
is also shown that the distance measure and an average measure of channel
fidelity both depend on the size of the same matrix: as the matrix size
increases, distance decreases and fidelity increases.


title: Perfect quantum state transfer with spinor bosons on weighted graphs

abstract:
  A duality between the properties of many spinor bosons on a regular lattice
and those of a single particle on a weighted graph reveals that a quantum
particle can traverse an infinite hierarchy of networks with perfect
probability in polynomial time, even as the number of nodes increases
exponentially. The one-dimensional `quantum wire' and the hypercube are special
cases in this construction, where the number of spin degrees of freedom is
equal to one and the number of particles, respectively. An implementation of
near-perfect quantum state transfer across a weighted parallelepiped with
ultracold atoms in optical lattices is discussed.


title: Exponential Separation of Quantum and Classical Online Space Complexity

abstract:
  Although quantum algorithms realizing an exponential time speed-up over the
best known classical algorithms exist, no quantum algorithm is known performing
computation using less space resources than classical algorithms. In this
paper, we study, for the first time explicitly, space-bounded quantum
algorithms for computational problems where the input is given not as a whole,
but bit by bit. We show that there exist such problems that a quantum computer
can solve using exponentially less work space than a classical computer. More
precisely, we introduce a very natural and simple model of a space-bounded
quantum online machine and prove an exponential separation of classical and
quantum online space complexity, in the bounded-error setting and for a total
language. The language we consider is inspired by a communication problem (the
set intersection function) that Buhrman, Cleve and Wigderson used to show an
almost quadratic separation of quantum and classical bounded-error
communication complexity. We prove that, in the framework of online space
complexity, the separation becomes exponential.


title: The Three-Box Paradox Revisited

abstract:
  The classical three-box paradox of Kirkpatrick [J. Phys. A 36 4891 (2003)] is
compared to the original quantum Three-Box paradox of Aharonov and Vaidman [J.
Phys. A 24 2315 (1991)]. It is argued that the quantum Three-Box experiment is
a "quantum paradox" in the sense that it is an example of a classical task
which cannot be accomplished using classical means, but can be accomplished
using quantum devices. It is shown that Kirkpatrick's card game is analogous to
a different game with a particle in three boxes which does not contain
paradoxical features.


title:
Phase information revealed by interferences in the ionization of
  rotational wave packets

abstract:
  Time-resolved photoelectron spectra are proposed for the measurement of
classical information recorded in the quantum phases of a molecular rotational
wave packet. Taking Li2 as a prototypical system, we show that an interference
arises from the electron-nuclei entanglement induced by the molecular
anisotropy. This phenomenon is used to transfer the information that was stored
initially in the nuclear rotational degree of freedom into the electronic
degree of freedom.


title: Dynamical entanglement and chaos: the case of Rydberg molecules

abstract:
  A Rydberg molecule is composed of an outer electron that collides on the
residual ionic core. Typical states of Rydberg molecules display entanglement
between the outer electron and the core. In this work we quantify the average
entanglement of molecular eigenstates and further investigate the time
evolution of entanglement production from initially unentangled states. The
results are contrasted with the underlying classical dynamics, obtained from
the semiclassical limit of the core-electron collision. Our findings indicate
that entanglement is not simply correlated with the degree of classical chaos,
but rather depends on the specific phase-space features that give rise to
inelastic scattering. Hence mixed phase-space or even regular classical
dynamics can be associated with high entanglement generation.


title:
On some meaningful inner product for real Klein-Gordon fields with
  positive semi-definite norm

abstract:
  A simple derivation of a meaningful, manifestly covariant inner product for
real Klein-Gordon (KG) fields with positive semi-definite norm is provided
which turns out - assuming a symmetric bilinear form - to be the real-KG-field
limit of the inner product for complex KG fields reviewed by A. Mostafazadeh
and F. Zamani in December, 2003, and February, 2006 (quant-ph/0312078,
quant-ph/0602151, quant-ph/0602161). It is explicitly shown that the positive
semi-definite norm associated with the derived inner product for real KG fields
measures the number of active positive and negative energy Fourier modes of the
real KG field on the relativistic mass shell. The very existence of an inner
product with positive semi-definite norm for the considered real, i.e. neutral,
KG fields shows that the metric operator entering the inner product does not
contain the charge-conjugation operator. This observation sheds some additional
light on the meaning of the C operator in the CPT inner product of PT-symmetric
Quantum Mechanics defined by C.M. Bender, D.C. Brody and H.F. Jones.


title: Entangled three-qubit states without concurrence and three-tangle

abstract:
  We provide a complete analysis of mixed three-qubit states composed of a GHZ
state and a W state orthogonal to the former. We present optimal decompositions
and convex roofs for the three-tangle. Further, we provide an analytical method
to decide whether or not an arbitrary rank-2 state of three qubits has
vanishing three-tangle. These results highlight intriguing differences compared
to the properties of two-qubit mixed states, and may serve as a quantitative
reference for future studies of entanglement in multipartite mixed states. By
studying the Coffman-Kundu-Wootters inequality we find that, while the amounts
of inequivalent entanglement types strictly add up for pure states, this
``monogamy'' can be lifted for mixed states by virtue of vanishing tangle
measures.


title: Free-space quantum key distribution with entangled photons

abstract:
  We report on a complete experimental implementation of a quantum key
distribution protocol through a free space link using polarization-entangled
photon pairs from a compact parametric down-conversion source. Over 10 hours of
uninterrupted communication between sites 1.5 km apart, we observe average key
generation rates of 630 per second after error correction and privacy
amplification. Our scheme requires no specific hardware channel for
synchronization apart from a classical wireless link, and no explicit random
number generator.


title: Ramsey interferometry with oppositely detuned fields

abstract:
  We report a narrowing of the interference pattern obtained in an atomic
Ramsey interferometer if the two separated fields have different frequency and
their phase difference is controlled. The width of the Ramsey fringes depends
inversely on the free flight time of ground state atoms before entering the
first field region in addition to the time between the fields. The effect is
stable also for atomic wavepackets with initial position and momentum
distributions and for realistic mode functions.


title: Conservative chaotic map as a model of quantum many-body environment

abstract:
  We study the dynamics of the entanglement between two qubits coupled to a
common chaotic environment, described by the quantum kicked rotator model. We
show that the kicked rotator, which is a single-particle deterministic
dynamical system, can reproduce the effects of a pure dephasing many-body bath.
Indeed, in the semiclassical limit the interaction with the kicked rotator can
be described as a random phase-kick, so that decoherence is induced in the
two-qubit system. We also show that our model can efficiently simulate
non-Markovian environments.


title: Best separable approximation with semi-definite programming method

abstract:
  The present methods for obtaining the optimal Lewenestein- Sanpera
decomposition of a mixed state are difficult to handle analytically. We provide
a simple analytical expression for the optimal Lewenstein-Sanpera decomposition
by using semidefinite programming. Specially, we obtain the optimal
Lewenstein-Sanpera decomposition for some examples such as: Bell decomposable
state, Iso-concurrence state, generic two qubit state in Wootters's basis,
$2\otimes 3$ Bell decomposable state, $d\otimes d$ Werner and isotropic states,
a one parameter $3\otimes 3$ state and finally multi partite isotropic state.


title: Polarization squeezing by optical Faraday rotation

abstract:
  We show that it is possible to generate continuous-wave fields and pulses of
polarization squeezed light by sending classical, linearly polarized laser
light twice through an atomic sample which causes an optical Faraday rotation
of the field polarization. We characterize the performance of the process, and
we show that an appreciable degree of squeezing can be obtained under realistic
physical assumptions.


title: On an implementation of the Solovay-Kitaev algorithm

abstract:
  In quantum computation we are given a finite set of gates and we have to
perform a desired operation as a product of them. The corresponding
computational problem is approximating an arbitrary unitary as a product in a
topological generating set of $SU(d)$. The problem is known to be solvable in
time $polylog(1/\epsilon)$ with product length $polylog(1/\epsilon)$, where the
implicit constants depend on the given generators. The existing algorithms
solve the problem but they need a very slow and space consuming preparatory
stage. This stage runs in time exponential in $d^2$ and requires memory of size
exponential in $d^2$. In this paper we present methods which make the
implementation of the existing algorithms easier. We present heuristic methods
which make a time-length trade-off in the preparatory step. We decrease the
running time and the used memory to polynomial in $d$ but the length of the
products approximating the desired operations will increase (by a factor which
depends on $d$). We also present a simple method which can be used for
decomposing a unitary into a product of group commutators for $2<d<256$, which
is an important part of the existing algorithm.


title: Quantum Error Correction via Convex Optimization

abstract:
  We show that the problem of designing a quantum information error correcting
procedure can be cast as a bi-convex optimization problem, iterating between
encoding and recovery, each being a semidefinite program. For a given encoding
operator the problem is convex in the recovery operator. For a given method of
recovery, the problem is convex in the encoding scheme. This allows us to
derive new codes that are locally optimal. We present examples of such codes
that can handle errors which are too strong for codes derived by analogy to
classical error correction techniques.


title: Cavity QED with Multiple Hyperfine Levels

abstract:
  We calculate the weak-driving transmission of a linearly polarized cavity
mode strongly coupled to the D2 transition of a single Cesium atom. Results are
relevant to future experiments with microtoroid cavities, where the
single-photon Rabi frequency g exceeds the excited-state hyperfine splittings,
and photonic bandgap resonators, where g is greater than both the excited- and
ground-state splitting.


title: Body-assisted van der Waals interaction between two atoms

abstract:
  Using fourth-order perturbation theory, a general formula for the van der
Waals potential of two neutral, unpolarized, ground-state atoms in the presence
of an arbitrary arrangement of dispersing and absorbing magnetodielectric
bodies is derived. The theory is applied to two atoms in bulk material and in
front of a planar multilayer system, with special emphasis on the cases of a
perfectly reflecting plate and a semi-infinite half space. It is demonstrated
that the enhancement and reduction of the two-atom interaction due to the
presence of a perfectly reflecting plate can be understood, at least in the
nonretarded limit, by using the method of image charges. For the semi-infinite
half space, both analytical and numerical results are presented.


title: Mass Detection with Nonlinear Nanomechanical Resonator

abstract:
  Nanomechanical resonators having small mass, high resonance frequency and low
damping rate are widely employed as mass detectors. We study the performances
of such a detector when the resonator is driven into a region of nonlinear
oscillations. We predict theoretically that in this region the system acts as a
phase-sensitive mechanical amplifier. This behavior can be exploited to achieve
noise squeezing in the output signal when homodyne detection is employed for
readout. We show that mass sensitivity of the device in this region may exceed
the upper bound imposed by thermomechanical noise upon the sensitivity when
operating in the linear region. On the other hand, we show that the high mass
sensitivity is accompanied by a slowing down of the response of the system to a
change in the mass.


title:
Microwave potentials and optimal control for robust quantum gates on an
  atom chip

abstract:
  We propose a two-qubit collisional phase gate that can be implemented with
available atom chip technology, and present a detailed theoretical analysis of
its performance. The gate is based on earlier phase gate schemes, but uses a
qubit state pair with an experimentally demonstrated, very long coherence
lifetime. Microwave near-fields play a key role in our implementation as a
means to realize the state-dependent potentials required for conditional
dynamics. Quantum control algorithms are used to optimize gate performance. We
employ circuit configurations that can be built with current fabrication
processes, and extensively discuss the impact of technical noise and
imperfections that characterize an actual atom chip. We find an overall
infidelity compatible with requirements for fault-tolerant quantum computation.


title: The state space for two qutrits has a phase space structure in its core

abstract:
  We investigate the state space of bipartite qutrits. For states which are
locally maximally mixed we obtain an analog of the ``magic'' tetrahedron for
bipartite qubits--a magic simplex W. This is obtained via the Weyl group which
is a kind of ``quantization'' of classical phase space. We analyze how this
simplex W is embedded in the whole state space of two qutrits and discuss
symmetries and equivalences inside the simplex W. Because we are explicitly
able to construct optimal entanglement witnesses we obtain the border between
separable and entangled states. With our method we find also the total area of
bound entangled states of the parameter subspace under intervestigation. Our
considerations can also be applied to higher dimensions.


title: Counter-Factual Meaningfulness and the Bell and CHSH Inequalities

abstract:
  We discuss the role of counter-factual meaningfulness (a weaker cousin of
"counter-factual definiteness") as a premise in the derivation of the Bell and
CHSH inequalities. The basic question motivating the discussion is this: can
the CHSH inequality, unlike the original Bell inequality, be derived without
making a hidden-variables (or equivalent counter-factual definiteness)
assumption? We answer, somewhat tentatively, in the negative, and suggest that
an appropriately-modified version of the EPR argument is needed to rigorously
establish that the empirical violation of Bell-type inequalities can only be
blamed on the failure, in nature, of local causality.


title:
Generation of Squeezing in Higher Order Hermite-Gaussian Modes with an
  Optical Parametric Amplifier

abstract:
  We demonstrate quantum correlations in the transverse plane of continuous
wave light beams by producing -4.0 dB, -2.6 dB and -1.5 dB of squeezing in the
TEM00, TEM10 and TEM20 Hermite- Gauss modes with an optical parametric
amplifier, respectively. This has potential applications in quantum information
networking, enabling parallel quantum information processing. We describe the
setup for the generation of squeezing and analyze the effects of various
experimental issues such as mode overlap between pump and seed and nonlinear
losses.


title: Measurement-driven quantum evolution from a known state

abstract:
  We study the problem of driving a known initial quantum state onto a known
pure state without using a unitary evolution. This task can be achieved by
means of von Neumann measurement processes, introducing N observables which are
consecutively measured in order to approach the state of the system to the
target state. We proved that the probability of projecting onto the target
state can be increased meaningfully by adding suitable observables to the
process, that is, it converges to 1 when N increases. We also discuss a
physical implementation of this scheme.


title: Single atom quantum walk with 1D optical superlattices

abstract:
  A proposal for the implementation of quantum walks using cold atom technology
is presented. It consists of one atom trapped in time varying optical
superlattices. The required elements are presented in detail including the
preparation procedure, the manipulation required for the quantum walk evolution
and the final measurement. These procedures can be, in principle, implemented
with present technology.


title:
Conclusive quantum-state transfer with a single randomly coupled spin
  chain

abstract:
  We studied the quantum state transfer in randomly coupled spin chains. By
using local memories storing the information and dividing the task into
transfer portion and decoding portion, conclusive transfer was ingeniously
achieved with just one single spin chain. In our scheme, the probability of
successful transfer can be made arbitrary close to unity. Especially, our
scheme is a good protocol to decode information from memories without adding
another spin chain. Compared with Time-reversed protocol, the average decoding
time is much less in our scheme.


title: Flying Spin Qubits

abstract:
  We present a method for encoding and transporting qubits within a dimerized
Heisenberg spin-1/2 chain. Logical qubits are localized at the domain walls
that separate the two possible dimerized states. The domain walls can be moved
to produce "flying spin qubits". The topological nature of these states makes
them stable against a wide class of perturbations. Pairs of domain walls can be
used to generate Einstein-Podolsky-Rosen pairs of entangled qubits. We discuss
speed limitations within an exactly solvable three-spin model and describe a
possible physical realization using quantum dot arrays.


title: Entanglement purification protocols for all graph states

abstract:
  We present multiparty entanglement purification protocols that are capable of
purifying arbitrary graph states directly. We develop recurrence and breeding
protocols and compare our methods with strategies based on bipartite
entanglement purification in static and communication scenarios. We find that
direct multiparty purification is of advantage with respect to achievable
yields and minimal required fidelity in static scenarios, and with respect to
obtainable fidelity in the case of noisy operations in both scenarios.


title: Inverse kinetic theory for quantum hydrodynamic equations

abstract:
  We propose a solution for the inverse kinetic theory for quantum hydrodynamic
equations associated to the non-relativistic Schr\"{o}dinger equation. It is
shown that an inverse kinetic equation of the form of the Vlasov equation can
be non-uniquely determined under suitable mathematical prescriptions.


title: The limits of counterfactual computation

abstract:
  We show that the protocol recently proposed by Hosten et al. does not allow
all possible results of a computation to be obtained counterfactually, as was
claimed. It only gives a counterfactual outcome for one of the computer
outputs. However, we confirm the observation that the protocol gives some
protection against decoherence. In some situations, though, it may be more
effective simply to run the computer several times.


title: Unifying Decoherence and the Heisenberg Principle

abstract:
  We exhibit three inequalities involving quantum measurement, all of which are
sharp and state independent. The first inequality bounds the performance of
joint measurement. The second quantifies the trade-off between the measurement
quality and the disturbance caused on the measured system. Finally, the third
inequality provides a sharp lower bound on the amount of decoherence in terms
of the measurement quality. This gives a unified discription of both the
Heisenberg principle and the collapse of the wave function.


title: Quantum walks with infinite hitting times

abstract:
  Hitting times are the average time it takes a walk to reach a given final
vertex from a given starting vertex. The hitting time for a classical random
walk on a connected graph will always be finite. We show that, by contrast,
quantum walks can have infinite hitting times for some initial states. We seek
criteria to determine if a given walk on a graph will have infinite hitting
times, and find a sufficient condition, which for discrete time quantum walks
is that the degeneracy of the evolution operator be greater than the degree of
the graph. The set of initial states which give an infinite hitting time form a
subspace. The phenomenon of infinite hitting times is in general a consequence
of the symmetry of the graph and its automorphism group. Using the irreducible
representations of the automorphism group, we derive conditions such that
quantum walks defined on this graph must have infinite hitting times for some
initial states. In the case of the discrete walk, if this condition is
satisfied the walk will have infinite hitting times for any choice of a coin
operator, and we give a class of graphs with infinite hitting times for any
choice of coin. Hitting times are not very well-defined for continuous time
quantum walks, but we show that the idea of infinite hitting-time walks
naturally extends to the continuous time case as well.


title: Entangled spin clusters: some special features

abstract:
  In this paper, we study three specific aspects of entanglement in small spin
clusters. We first study the effect of inhomogeneous exchange coupling strength
on the entanglement properties of the S=1/2 antiferromagnetic linear chain
tetramer compound NaCuAsO_{4}. The entanglement gap temperature, T_{E}, is
found to have a non-monotonic dependence on the value of $\alpha$, the exchange
coupling inhomogeneity parameter. We next determine the variation of T_{E} as a
function of S for a spin dimer, a trimer and a tetrahedron. The temperature
T_{E} is found to increase as a function of S, but the scaled entanglement gap
temperature t_{E} goes to zero as S becomes large. Lastly, we study a spin-1
dimer compound to illustrate the quantum complementarity relation. We show that
in the experimentally realizable parameter region, magnetization and
entanglement plateaus appear simultaneously at low temperatures as a function
of the magnetic field. Also, the sharp increase in one quantity as a function
of the magnetic field is accompanied by a sharp decrease in the other so that
the quantum complementarity relation is not violated.


title: Photon States from Propagating Complex Electromagnetic Fields

abstract:
  A wavefunction for single- and many-photon states is defined by associating
photons with different momenta to different spectral and polarization
components of the classical, generally complex, electromagnetic field that
propagates in a definite direction. By scaling each spectral component of the
classical field to the square root of the photon energy, the appropriately
normalized photon wavefunction acquires the desired interpretation of
probability density amplitude, in contradistinction to the Riemann-Silbertsein
wavefunction that can be considered as the amplitude of the photon probability
energy density.


title: Strongly Interacting Polaritons in Coupled Arrays of Cavities

abstract:
  The experimental observation of quantum phenomena in strongly correlated many
particle systems is difficult because of the short length- and timescales
involved. Obtaining at the same time detailed control of individual
constituents appears even more challenging and thus to date inhibits employing
such systems as quantum computing devices. Substantial progress to overcome
these problems has been achieved with cold atoms in optical lattices, where a
detailed control of collective properties is feasible but it is very difficult
to address and hence control or measure individual sites. Here we show, that
polaritons, combined atom and photon excitations, in an array of cavities such
as a photonic crystal or coupled toroidal micro-cavities, can form a strongly
interacting many body system, where individual particles can be controlled and
measured. All individual building blocks of the proposed setting have already
been experimentally realised, thus demonstrating the potential of this device
as a quantum simulator. With the possibility to create attractive on-site
potentials the scheme allows for the creation of highly entangled states and a
phase with particles much more delocalised than in superfluids.


title: A scheme for unconventional geometric quantum computation in cavity QED

abstract:
  We present a scheme for implementing the unconventional geometric two-qubit
phase gate with nonzero dynamical phase by using the two-channel Raman
interaction of two atoms in a cavity. We show that the dynamical phase acquired
in a cyclic evolution is proportional to the geometric phase acquired in the
same cyclic evolution, hence the the total phase possesses the same geometric
features as the geometric phase. In our scheme the atomic excited state is
adiabatically eliminated and the operation of the proposed logic gate involves
only in the metastable states of the atom and hence is not affected by
spontaneous emission.


title:
Prospects of employing superconducting stripline resonators for studying
  the dynamical Casimir effect experimentally

abstract:
  We discuss the prospects of employing an NbN superconducting microwave
stripline resonator for studying the dynamical Casimir effect experimentally.
Preliminary experimental results, in which optical illumination is employed for
modulating the resonance frequencies of the resonator, show that such a system
is highly promising for this purpose. Moreover, we discuss the undesirable
effect of heating which results from the optical illumination, and show that
degradation in noise properties can be minimized by employing an appropriate
design.


title: Semi-spectral Chebyshev method in Quantum Mechanics

abstract:
  Traditionally, finite differences and finite element methods have been by
many regarded as the basic tools for obtaining numerical solutions in a variety
of quantum mechanical problems emerging in atomic, nuclear and particle
physics, astrophysics, quantum chemistry, etc. In recent years, however, an
alternative technique based on the semi-spectral methods has focused
considerable attention. The purpose of this work is first to provide the
necessary tools and subsequently examine the efficiency of this method in
quantum mechanical applications. Restricting our interest to time independent
two-body problems, we obtained the continuous and discrete spectrum solutions
of the underlying Schroedinger or Lippmann-Schwinger equations in both, the
coordinate and momentum space. In all of the numerically studied examples we
had no difficulty in achieving the machine accuracy and the semi-spectral
method showed exponential convergence combined with excellent numerical
stability.


title:
Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ +
  $ip_y$ Superfluid of Fermionic Cold Atoms

abstract:
  We propose to use the recently predicted two-dimensional `weak-pairing' $p_x
+ ip_y$ superfluid state of fermionic cold atoms as a platform for topological
quantum computation. In the core of a vortex, this state supports a zero-energy
Majorana mode, which moves to finite energy in the corresponding topologically
trivial `strong-pairing' state. By braiding vortices in the `weak-pairing'
state, unitary quantum gates can be applied to the Hilbert space of Majorana
zero-modes. For read-out of the topological qubits, we propose realistic
schemes suitable for atomic superfluids.


title: Hypersensitivity and chaos signatures in the quantum baker's maps

abstract:
  Classical chaotic systems are distinguished by their sensitive dependence on
initial conditions. The absence of this property in quantum systems has lead to
a number of proposals for perturbation-based characterizations of quantum
chaos, including linear growth of entropy, exponential decay of fidelity, and
hypersensitivity to perturbation. All of these accurately predict chaos in the
classical limit, but it is not clear that they behave the same far from the
classical realm. We investigate the dynamics of a family of quantizations of
the baker's map, which range from a highly entangling unitary transformation to
an essentially trivial shift map. Linear entropy growth and fidelity decay are
exhibited by this entire family of maps, but hypersensitivity distinguishes
between the simple dynamics of the trivial shift map and the more complicated
dynamics of the other quantizations. This conclusion is supported by an
analytical argument for short times and numerical evidence at later times.


title: Survival of entanglement in thermal states

abstract:
  We present a general sufficiency condition for the presence of multipartite
entanglement in thermal states stemming from the ground state entanglement. The
condition is written in terms of the ground state entanglement and the
partition function and it gives transition temperatures below which
entanglement is guaranteed to survive. It is flexible and can be easily adapted
to consider entanglement for different splittings, as well as be weakened to
allow easier calculations by approximations. Examples where the condition is
calculated are given. These examples allow us to characterize a minimum gapping
behavior for the survival of entanglement in the thermodynamic limit. Further,
the same technique can be used to find noise thresholds in the generation of
useful resource states for one-way quantum computing.


title:
Cooling to the Ground State of Axial Motion for One Atom Strongly
  Coupled to an Optical Cavity

abstract:
  Localization to the ground state of axial motion is demonstrated for a
single, trapped atom strongly coupled to the field of a high finesse optical
resonator. The axial atomic motion is cooled by way of coherent Raman
transitions on the red vibrational sideband. An efficient state detection
scheme enabled by strong coupling in cavity QED is used to record the Raman
spectrum, from which the state of atomic motion is inferred. We find that the
lowest vibrational level of the axial potential with zero-point energy 13uK is
occupied with probability P0~0.95.


title:
Suboptimal quantum-error-correcting procedure based on semidefinite
  programming

abstract:
  In this paper, we consider a simplified error-correcting problem: for a fixed
encoding process, to find a cascade connected quantum channel such that the
worst fidelity between the input and the output becomes maximum. With the use
of the one-to-one parametrization of quantum channels, a procedure finding a
suboptimal error-correcting channel based on a semidefinite programming is
proposed. The effectiveness of our method is verified by an example of the
bit-flip channel decoding.


title: Computational approach to quantum encoder design for purity optimization

abstract:
  In this paper, we address the problem of designing a quantum encoder that
maximizes the minimum output purity of a given decohering channel, where the
minimum is taken over all possible pure inputs. This problem is cast as a
max-min optimization problem with a rank constraint on an appropriately defined
matrix variable. The problem is computationally very hard because it is
non-convex with respect to both the objective function (output purity) and the
rank constraint. Despite this difficulty, we provide a tractable computational
algorithm that produces the exact optimal solution for codespace of dimension
two. Moreover, this algorithm is easily extended to cover the general class of
codespaces, in which case the solution is suboptimal in the sense that the
suboptimized output purity serves as a lower bound of the exact optimal purity.
The algorithm consists of a sequence of semidefinite programmings and can be
performed easily. Two typical quantum error channels are investigated to
illustrate the effectiveness of our method.


title: Asymmetric quantum error correcting codes

abstract:
  The noise in physical qubits is fundamentally asymmetric: in most devices,
phase errors are much more probable than bit flips. We propose a quantum error
correcting code which takes advantage of this asymmetry and shows good
performance at a relatively small cost in redundancy, requiring less than a
doubling of the number of physical qubits for error correction.


title: Stable polarization-encoded quantum key distribution in fiber

abstract:
  Polarizations of single-photon pulses have been controlled with long-term
stability of more than 10 hours by using an active feedback technique for
auto-compensation of unpredictable polarization scrambling in long-distance
fiber. Experimental tests of long-term operations in 50, 75 and 100 km fibers
demonstrated that such a single-photon polarization control supported stable
polarization encoding in long-distance fibers to facilitate stable one-way
fiber system for polarization-encoded quantum key distribution, providing
quantum bit error rates below the absolute security threshold.


title:
GHZ-type and W-type entangled coherent states: generation and Bell-type
  inequality tests without photon counting

abstract:
  We study GHZ-type and W-type three-mode entangled coherent states. Both the
types of entangled coherent states violate Mermin's version of the Bell
inequality with threshold photon detection (i.e., without photon counting).
Such an experiment can be performed using linear optics elements and threshold
detectors with significant Bell violations for GHZ-type entangled coherent
states. However, to demonstrate Bell-type inequality violations for W-type
entangled coherent states, additional nonlinear interactions are needed. We
also propose an optical scheme to generate W-type entangled coherent states in
free-traveling optical fields. The required resources for the generation are a
single-photon source, a coherent state source, beam splitters, phase shifters,
photodetectors, and Kerr nonlinearities. Our scheme does not necessarily
require strong Kerr nonlinear interactions, i.e., weak nonlinearities can be
used for the generation of the W-type entangled coherent states. Furthermore,
it is also robust against inefficiencies of the single-photon source and the
photon detectors.


title:
Entanglement between atomic condensates in an optical lattice: effects
  of interaction range

abstract:
  We study the area-dependent entropy and two-site entanglement for two state
Bose-Einstein condensates in a 2D optical lattice. We consider the case where
the array of two component condensates behave like an ensemble of spin-half
particles with the interaction to its nearest neighbors and next nearest
neighbors. We show how the Hamiltonian of their Bose-Einstein condensate
lattice with nearest-neighbor and next-nearest-neighbor interactions can be
mapped into a harmonic lattice. We use this to determine the entropy and
entanglement content of the lattice.


title:
Quality of a Quantum Error Correcting Scheme and Memory Error Threshold
  Estimation

abstract:
  The error correcting capabilities of the Calderbank-Shor-Steane [[7,1,3]]
quantum code, together with a fault-tolerant syndrome extraction by means of
several ancilla states, have been numerically studied. A simple probability
expression to characterize the code ability for correcting an encoded qubit has
been considered. This probability, as a correction quality criterion, permits
the error correction capabilities among different recovery schemes to be
compared. The memory error threshold is calculated by means of the best method
of those considered.


title: Optimal partial estimation of quantum states from several copies

abstract:
  We derive analytical formula for the optimal trade-off between the mean
estimation fidelity and the mean fidelity of the qubit state after a partial
measurement on N identically prepared qubits. We also conjecture analytical
expression for the optimal fidelity trade-off in case of a partial measurement
on N identical copies of a d-level system.


title: Inserting two atoms into a single optical micropotential

abstract:
  We recently demonstrated that strings of trapped atoms inside a standing wave
optical dipole trap can be rearranged using optical tweezers [Y. Miroshnychenko
et al., Nature, in press (2006)]. This technique allows us to actively set the
interatomic separations on the scale of the individual trapping potential
wells. Here, we use such a distance-control operation to insert two atoms into
the same potential well. The detected success rate of this manipulation is
16(+4/-3) %, in agreement with the predictions of a theoretical model based on
our independently determined experimental parameters.


title:
$q$ - Deformed Spin Networks, Knot Polynomials and Anyonic Topological
  Quantum Computation

abstract:
  We review the q-deformed spin network approach to Topological Quantum Field
Theory and apply these methods to produce unitary representations of the braid
groups that are dense in the unitary groups. Our methods are rooted in the
bracket state sum model for the Jones polynomial. We give our results for a
large class of representations based on values for the bracket polynomial that
are roots of unity. We make a separate and self-contained study of the quantum
universal Fibonacci model in this framework. We apply our results to give
quantum algorithms for the computation of the colored Jones polynomials for
knots and links, and the Witten-Reshetikhin-Turaev invariant of three
manifolds.


title:
Efficient Quantum State Estimation by Continuous Weak Measurement and
  Dynamical Control

abstract:
  We demonstrate a fast, robust and non-destructive protocol for quantum state
estimation based on continuous weak measurement in the presence of a controlled
dynamical evolution. Our experiment uses optically probed atomic spins as a
testbed, and successfully reconstructs a range of trial states with fidelities
of ~90%. The procedure holds promise as a practical diagnostic tool for the
study of complex quantum dynamics, the testing of quantum hardware, and as a
starting point for new types of quantum feedback control.


title:
On Lower Bound of Worst Case Error Probability for Quantum
  Fingerprinting with Shared Entanglement

abstract:
  This paper discusses properties of quantum fingerprinting with shared
entanglement. Under certain restriction of final measurement, a relation is
given between unitary operations of two parties. Then, by reducing to spherical
coding problem, this paper gives a lower bound of worst case error probability
for quantum fingerprinting with shared entanglement, showing a relation between
worst case error probability and the amount of entanglement(measured by Schmidt
number).


title: Charge Detection in a Closed-Loop Aharonov-Bohm Interferometer

abstract:
  We report on a study of complementarity in a two-terminal "closed-loop"
Aharonov-Bohm interferometer. In this interferometer, the simple picture of
two-path interference cannot be applied. We introduce a nearby quantum point
contact to detect the electron in a quantum dot inserted in the interferometer.
We found that charge detection reduces but does not completely suppress the
interference even in the limit of perfect detection. We attribute this
phenomenon to the unique nature of the closed-loop interferometer. That is, the
closed-loop interferometer cannot be simply regarded as a two-path
interferometer because of multiple reflections of electrons. As a result, there
exist indistinguishable paths of the electron in the interferometer and the
interference survives even in the limit of perfect charge detection. This
implies that charge detection is not equivalent to path detection in a
closed-loop interferometer. We also discuss the phase rigidity of the
transmission probability for a two-terminal conductor in the presence of a
detector.


title:
Demonstration of Controllable Temporal Distinguishability in a
  Three-Photon State

abstract:
  Multi-photon interference is at the heart of the recently proposed linear
optical quantum computing scheme and plays an essential role in many protocols
in quantum information. Indistinguishability is what leads to the effect of
quantum interference. Optical interferometers such as Michaelson interferometer
provide a measure for second-order coherence at one-photon level and
Hong-Ou-Mandel interferometer was widely employed to describe two-photon
entanglement and indistinguishability. However, there is not an effective way
for a system of more than two photons. Recently, a new interferometric scheme
was proposed to quantify the degree of multi-photon distinguishability. Here we
report an experiment to implement the scheme for three-photon case. We are able
to generate three photons with different degrees of temporal distinguishability
and demonstrate how to characterize them by the visibility of three-photon
interference. This method of quantitative description of multi-photon
indistinguishability will have practical implications in the implementation of
quantum information protocols.


title: Quantification of entanglement via uncertainties

abstract:
  We show that entanglement of pure multi-party states can be quantified by
means of quantum uncertainties of certain basic observables through the use of
measure that has been initially proposed in [10] for bipartite systems.


title:
Economical realization of phase covariant devices in arbitrary
  dimensions

abstract:
  We describe a unified framework of phase covariant multi user quantum
transformations for d-dimensional quantum systems. We derive the optimal phase
covariant cloning and transposition tranformations for multi phase states. We
show that for some particular relations between the input and output number of
copies they correspond to economical tranformations, which can be achieved
without the need of auxiliary systems. We prove a relation between the optimal
phase covariant cloning and transposition maps, and optimal estimation of
multiple phases for equatorial states.


title: On connection between classical and quantum mechanics

abstract:
  We discuss an alternative version of non- relativistic Newtonian mechanics in
terms of a real Hilbert space mathematical framework. It is demonstrated that
the physics of this scheme correspondent with the standard formulation.
Heisenberg-Schrodinger non-relativistic quantum mechanics is considered
adequate and complete. Since the suggested theory is dispersion free, linear
superposition principle is not violated but cannot affect results of
measurements due to spectral decomposition theorem for self-adjoint operators
(the collapse of wave function).


title: Is the Fair Sampling Assumption supported by EPR Experiments?

abstract:
  We analyze optical EPR experimental data performed by Weihs et al in
Innsbruck 1997-1998. We show that for some linear combinations of the raw
coincidence rates, the experimental results display some anomalous behavior
that a more general source state (like non-maximally entangled state) cannot
straightforwardly account for. We attempt to explain these anomalies by taking
account of the relative efficiencies of the four channels. For this purpose, we
use the fair sampling assumption, and assume explicitly that the detection
efficiencies for the pairs of entangled photons can be written as a product of
the two corresponding detection efficiencies for the single photons. We show
that this explicit use of fair sampling cannot be maintained to be a reasonable
assumption as it leads to an apparent violation of the no-signalling principle.


title: The hidden geometric character of relativistic quantum mechanics

abstract:
  The presentation makes use of geometric algebra, also known as Clifford
algebra, in 5-dimensional spacetime. The choice of this space is given the
character of first principle, justified solely by the consequences that can be
derived from such choice and their consistency with experimental results. Given
a metric space of any dimension, one can define monogenic functions, the
natural extension of analytic functions to higher dimensions; such functions
have null vector derivative and have previously been shown by other authors to
play a decisive role in lower dimensional spaces. All monogenic functions have
null Laplacian by consequence; in an hyperbolic space this fact leads
inevitably to a wave equation with plane-like solutions. This is also true for
5-dimensional spacetime and we will explore those solutions, establishing a
parallel with the solutions of the Dirac equation. For this purpose we will
invoke the isomorphism between the complex algebra of 4x4 matrices, also known
as Dirac's matrices. There is one problem with this isomorphism, because the
solutions to Dirac's equation are usually known as spinors (column matrices)
that don't belong to the 4x4 matrix algebra and as such are excluded from the
isomorphism. We will show that a solution in terms of Dirac spinors is
equivalent to a plane wave solution. Just as one finds in the standard
formulation, monogenic functions can be naturally split into positive/negative
energy together with left/right ones. This split is provided by geometric
projectors and we will show that there is a second set of projectors providing
an alternate 4-fold split. The possible implications of this alternate split
are not yet fully understood and are presently the subject of profound
research.


title: Current behavior of a quantum Hamiltonian ratchet in resonance

abstract:
  We investigate the ratchet current that appears in a kicked Hamiltonian
system when the period of the kicks corresponds to the regime of quantum
resonance. In the classical analogue, a spatial-temporal symmetry should be
broken to obtain a net directed current. It was recently discovered that in
quantum resonance the temporal symmetry can be kept, and we prove that breaking
the spatial symmetry is a necessary condition to find this effect.
  Moreover, we show numerically and analytically how the direction of the
motion is dramatically influenced by the strength of the kicking potential and
the value of the period. By increasing the strength of the interaction this
direction changes periodically, providing us with a non-expected source of
current reversals in this quantum model. These reversals depend on the kicking
period also, though this behavior is theoretically more difficult to analyze.
Finally, we generalize the discussion to the case of a non-uniform initial
condition.


title: Entanglement Purification of Any Stabilizer State

abstract:
  We present a method for multipartite entanglement purification of any
stabilizer state shared by several parties. In our protocol each party measures
the stabilizer operators of a quantum error-correcting code on his or her
qubits. The parties exchange their measurement results, detect or correct
errors, and decode the desired purified state. We give sufficient conditions on
the stabilizer codes that may be used in this procedure and find that Steane's
seven-qubit code is the smallest error-correcting code sufficient to purify any
stabilizer state. An error-detecting code that encodes two qubits in six can
also be used to purify any stabilizer state. We further specify which classes
of stabilizer codes can purify which classes of stabilizer states.


title: Optimal and Efficient Decoding of Concatenated Quantum Block Codes

abstract:
  We consider the problem of optimally decoding a quantum error correction code
-- that is to find the optimal recovery procedure given the outcomes of partial
"check" measurements on the system. In general, this problem is NP-hard.
However, we demonstrate that for concatenated block codes, the optimal decoding
can be efficiently computed using a message passing algorithm. We compare the
performance of the message passing algorithm to that of the widespread
blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit
and Steane's code on a depolarizing channel demonstrate significant advantages
of the message passing algorithms in two respects. 1) Optimal decoding
increases by as much as 94% the error threshold below which the error
correction procedure can be used to reliably send information over a noisy
channel. 2) For noise levels below these thresholds, the probability of error
after optimal decoding is suppressed at a significantly higher rate, leading to
a substantial reduction of the error correction overhead.


title: A Panoply of Quantum Algorithms

abstract:
  We create a variety of new quantum algorithms that use Grover's algorithm and
similar techniques to give polynomial speedups over their classical
counterparts. We begin by introducing a set of tools that carefully minimize
the impact of errors on running time; those tools provide us with speedups to
already-published quantum algorithms, such as improving Durr, Heiligman, Hoyer
and Mhalla's algorithm for single-source shortest paths [quant-ph/0401091] by a
factor of lg N. The algorithms we construct from scratch have a range of
speedups, from O(E)->O(sqrt(VE lg V)) speedups in graph theory to an
O(N^3)->O(N^2) speedup in dynamic programming.


title: How to observe a coherent superposition of an atom and a molecule

abstract:
  We demonstrate that it is possible, in principle, to perform a Ramsey-type
interference experiment to exhibit a coherent superposition of a single atom
and a diatomic molecule. This gedanken experiment, based on the techniques of
Aharonov and Susskind [Phys. Rev. 155, 1428 (1967)], explicitly violates the
commonly-accepted superselection rule that forbids coherent superpositions of
eigenstates of differing atom number. This interference experiment makes use of
a Bose-Einstein condensate as a reference frame with which to perform the
coherent operations analogous to Ramsey pulses. We also investigate an
analogous gedanken experiment to exhibit a coherent superposition of a single
boson and a fermion, violating the commonly-accepted superselection rule
forbidding coherent superpositions of states of differing particle statistics;
in this case, the reference frame is realized by a multi-mode state of many
fermions. This latter case reproduces all of the relevant features of Ramsey
interferometry, including Ramsey fringes over many repetitions of the
experiment. However, the apparent inability of this proposed experiment to
produce well-defined relative phases between two distinct systems each
described by a coherent superposition of a boson and a fermion demonstrates
that there are additional, outstanding requirements to fully ``lift'' the
univalence superselection rule.


title: Scattering in PT-symmetric quantum mechanics

abstract:
  A general formalism is worked out for the description of one-dimensional
scattering in non-hermitian quantum mechanics and constraints on transmission
and reflection coefficients are derived in the cases of P, T, or PT invariance
of the Hamiltonian. Applications to some solvable PT-symmetric potentials are
shown in detail. Our main original results concern the association of
reflectionless potentials with asymptotic exact PT symmetry and the
peculiarities of separable kernels of non-local potentials in connection with
hermiticity, T invariance and PT invariance.


title:
Ground state fidelity and quantum phase transitions in free Fermi
  systems

abstract:
  We compute the fidelity between the ground states of general quadratic
fermionic hamiltonians and analyze its connections with quantum phase
transitions. Each of these systems is characterized by a $L\times L$ real
matrix whose polar decomposition, into a non-negative $\Lambda$ and a unitary
$T$, contains all the relevant ground state (GS) information. The boundaries
between different regions in the GS phase diagram are given by the points of,
possibly asymptotic, singularity of $\Lambda$. This latter in turn implies a
critical drop of the fidelity function. We present general results as well as
their exemplification by a model of fermions on a totally connected graph.


title: How many copies are needed for state discrimination?

abstract:
  Given a collection of states (rho_1, ..., rho_N) with pairwise fidelities
F(rho_i, rho_j) <= F < 1, we show the existence of a POVM that, given
rho_i^{otimes n}, will identify i with probability >= 1-epsilon, as long as
n>=2(log N/eps)/log (1/F). This improves on previous results which were either
dimension-dependent or required that i be drawn from a known distribution.


title: Quantum Capacities of Bosonic Channels

abstract:
  We investigate the capacity of bosonic quantum channels for the transmission
of quantum information. Achievable rates are determined from measurable moments
of the channel by showing that every channel can asymptotically simulate a
Gaussian channel which is characterized by second moments of the initial
channel. We calculate the quantum capacity for a class of Gaussian channels,
including channels describing optical fibers with photon losses, by proving
that Gaussian encodings are optimal. Along the way we provide a complete
characterization of degradable Gaussian channels and those arising from
teleportation protocols.


title:
Local entanglement and quantum phase transition in 1D transverse field
  Ising model

abstract:
  In this paper, we study the entanglement between two-neighboring sites and
the rest of the system in a simple quantum phase transition of 1D transverse
field Ising model. We find that the entanglement shows interesting scaling and
singular behavior around the critical point, and then can be use as a
convenient marker for the transition point.


title: Purity and decoherence in the theory of a damped harmonic oscillator

abstract:
  For the generalized master equations derived by Karrlein and Grabert for the
microscopic model of a damped harmonic oscillator, the conditions for purity of
states are written, in particular for different initial conditions and
different types of damping, including Ohmic, Drude and weak coupling cases,
Agarwal and Weidlich-Haake models. It is shown that the states which remain
pure are the squeezed states with constant in time variances. For pure states,
the generalized nonlinear Schr\" odinger-type equations corresponding to these
master equations are also obtained. Then the condition for purity of states of
a damped harmonic oscillator is considered in the framework of Lindblad theory
for open quantum systems. For a special choice of the environment coefficients,
the correlated coherent states with constant variances and covariance are shown
to be the only states which remain pure all the time during the evolution of
the considered system. In Karrlein-Grabert and Lindblad models, as well as in
the considered particular models, the expressions of the rate of entropy
production is written and it is shown that the states which preserve their
purity in time are also the states which minimize the entropy production and,
therefore, they are the most stable ones under evolution in the presence of the
environment and play an important role in the description of decoherence
phenomenon.


title:
Casimir-Polder interaction between an excited atom and a gas dielectric
  medium

abstract:
  The Casimir-Polder potential for interaction between an excited atom and a
ground-state one in the retarded case obtained with the help of perturbation
technique drops as R^-2 with the distance between the atoms [E.A. Power,
T.Thirunamachandran, Phys. Rev. A, 47, 2539 (1993)]. It results in diverdent
integrals for interaction between an excited atom and a dilute gas medium. We
investigate interaction between two atoms embedded in a dielectric medium with
the help of non-perturbative approach. We take into account absorption of
photons in the medium. This approach solves the problem of divergence. We
consider interaction between an excited atom and a planar dielectric gas medium
of ground-state atoms. We show that the retarded interaction between an excited
atom and a gas of ground-state atoms is not oscillating but follows a simple
power law. We show that to obtain coventional non-retarded expression for the
van der Waals force between an excited atom and a dilute gas the distance
between the atom and the interface should be much smaller than the free mean
pass of a photon in the medium. Interaction between an excited atom and a
hemisphere of ground-state atoms is considered.


title: Threshold quantum cryptograph based on Grover's algorithm

abstract:
  Grover's operator in the two-qubit case can transform a basis into its
conjugated basis. A permutation operator can transform a state in the two
conjugated bases into its orthogonal state. These properties are included in a
threshold quantum protocol. The proposed threshold quantum protocol is secure
based the proof that the legitimate participators can only eavesdrop 2 bits of
3 bits operation information on one two-qubit with error probability 3/8. We
propose a scheme to detect the Trojan horse attack without destroying the legal
qubit.


title: Quantum Knitting

abstract:
  We analyze the connections between the mathematical theory of knots and
quantum physics by addressing a number of algorithmic questions related to both
knots and braid groups.
  Knots can be distinguished by means of `knot invariants', among which the
Jones polynomial plays a prominent role, since it can be associated with
observables in topological quantum field theory.
  Although the problem of computing the Jones polynomial is intractable in the
framework of classical complexity theory, it has been recently recognized that
a quantum computer is capable of approximating it in an efficient way. The
quantum algorithms discussed here represent a breakthrough for quantum
computation, since approximating the Jones polynomial is actually a `universal
problem', namely the hardest problem that a quantum computer can efficiently
handle.


title:
Grothendieck's constant and local models for noisy entangled quantum
  states

abstract:
  We relate the nonlocal properties of noisy entangled states to Grothendieck's
constant, a mathematical constant appearing in Banach space theory. For
two-qubit Werner states $\rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}$, we show
that there is a local model for projective measurements if and only if $p \le
1/K_G(3)$, where $K_G(3)$ is Grothendieck's constant of order 3. Known bounds
on $K_G(3)$ prove the existence of this model at least for $p \lesssim 0.66$,
quite close to the current region of Bell violation, $p \sim 0.71$. We
generalize this result to arbitrary quantum states.


title: A Finite de Finetti Theorem for Infinite-Dimensional Systems

abstract:
  We formulate and prove a de Finetti representation theorem for finitely
exchangeable states of a quantum system consisting of k infinite-dimensional
subsystems. The theorem is valid for states that can be written as the partial
trace of a pure state chosen from a family of subsets C_n of the full symmetric
subspace for $n$ subsystems. We show that such states become arbitrarily close
to mixtures of pure power states as n increases. We give a second equivalent
characterization of the family C_n.


title: The Complexity of Stoquastic Local Hamiltonian Problems

abstract:
  We study the complexity of the Local Hamiltonian Problem (denoted as LH-MIN)
in the special case when a Hamiltonian obeys conditions of the Perron-Frobenius
theorem: all off-diagonal matrix elements in the standard basis are real and
non-positive. We will call such Hamiltonians, which are common in the natural
world, stoquastic. An equivalent characterization of stoquastic Hamiltonians is
that they have an entry-wise non-negative Gibbs density matrix for any
temperature. We prove that LH-MIN for stoquastic Hamiltonians belongs to the
complexity class AM -- a probabilistic version of NP with two rounds of
communication between the prover and the verifier. We also show that 2-local
stoquastic LH-MIN is hard for the class MA. With the additional promise of
having a polynomial spectral gap, we show that stoquastic LH-MIN belongs to the
class POSTBPP=BPPpath -- a generalization of BPP in which a post-selective
readout is allowed. This last result also shows that any problem solved by
adiabatic quantum computation using stoquastic Hamiltonians lies in PostBPP.


title: An axiomatic approach to Einstein's boxes

abstract:
  The fallacies inherent in the Einstein's Boxes thought experiment are made
evident by taking an axiomatic approach to quantum mechanics while ignoring
notions not supported by the postulates or by experimental observation. We
emphasize that the postulates contain everything needed to completely describe
a quantum experiment. We discuss the non-classical nature of both the state
vector and the experiment that it represents. Einstein's Boxes is then
described by the formalism alone. We see that it is no different from any other
experiment in which a two-state observable is measured.


title:
Mode Coupling and Cavity-Quantum-Dot Interactions in a Fiber-Coupled
  Microdisk Cavity

abstract:
  A quantum master equation model for the interaction between a two-level
system and whispering-gallery modes (WGMs) of a microdisk cavity is presented,
with specific attention paid to current experiments involving a semiconductor
quantum dot (QD) embedded in a fiber-coupled, AlGaAs microdisk cavity. In
standard single mode cavity QED, three important rates characterize the system:
the QD-cavity coupling rate g, the cavity decay rate kappa, and the QD
dephasing rate gamma_perpendicular. A more accurate model of the microdisk
cavity includes two additional features. The first is a second cavity mode that
can couple to the QD, which for an ideal microdisk corresponds to a traveling
wave WGM propagating counter to the first WGM. The second feature is a coupling
between these two traveling wave WGMs, at a rate beta, due to backscattering
caused by surface roughness that is present in fabricated devices. We consider
the transmitted and reflected signals from the cavity for different parameter
regimes of {g,beta,kappa,gamma_perpendicular}. A result of this analysis is
that even in the presence of negligible roughness induced backscattering, a
strongly coupled QD mediates coupling between the traveling wave WGMs,
resulting in an enhanced effective coherent coupling rate g = sqrt(2)*g0
corresponding to that of a standing wave WGM with an electric field maximum at
the position of the QD. In addition, analysis of the second-order correlation
function of the reflected signal from the cavity indicates that regions of
strong photon antibunching or bunching may be present depending upon the
strength of coupling of the QD to each of the cavity modes. Such intensity
correlation information will likely be valuable in interpreting experimental
measurements of a strongly-coupled QD to a bi-modal WGM cavity.


title: Bohr-Heisenberg Reality and System-Free Quantum Mechanics

abstract:
  Motivated by Heisenberg's assertion that electron trajectories do not exist
until they are observed, we present a new approach to quantum mechanics in
which the concept of observer independent system under observation is
eliminated. Instead, the focus is only on observers and apparatus, the former
describing the latter in terms of labstates. These are quantum states over
time-dependent Heisenberg nets, which are quantum registers of qubits
representing information gateways accessible to the observers. We discuss the
motivation for this approach and lay down the basic principles and mathematical
notation.


title: A Novel Quasi-Exactly Solvable Model with Total Transmission Modes

abstract:
  In this paper we present a novel quasi-exactly solvable model with symmetric
inverted potentials which are unbounded from below. The quasi-exactly solvable
states are shown to be total transmission (or reflectionless) modes. From these
modes even and odd wavefunctions can be constructed which are normalizable and
flux-zero. Under the procedure of self-adjoint extension, a discrete spectrum
of bound states can be obtained for these inverted potentials and the solvable
part of the spectrum is the quasi-exactly solvable states we have discovered.


title:
Atom Lithography with Near-Resonant Light Masks: Quantum Optimization
  Analysis

abstract:
  We study the optimal focusing of two-level atoms with a near resonant
standing wave light, using both classical and quantum treatments of the
problem. Operation of the focusing setup is considered as a nonlinear spatial
squeezing of atoms in the thin- and thick-lens regimes. It is found that the
near-resonant standing wave focuses the atoms with a reduced background in
comparison with far-detuned light fields. For some parameters, the quantum
atomic distribution shows even better localization than the classical one.
Spontaneous emission effects are included via the technique of quantum Monte
Carlo wave function simulations. We investigate the extent to which
non-adiabatic and spontaneous emission effects limit the achievable minimal
size of the deposited structures.


title:
Entanglement enhancement and postselection for two atoms interacting
  with thermal light

abstract:
  The evolution of entanglement for two identical two-level atoms coupled to a
resonant thermal field is studied for two different families of input states.
Entanglement enhancement is predicted for a well defined region of the
parameter space of one of these families. The most intriguing result is the
possibility of probabilistic production of maximally entangled atomic states
even if the input atomic state is factorized and the corresponding output state
is separable.


title:
Theory for a Hanbury Brown Twiss experiment with a ballistically
  expanding cloud of cold atoms

abstract:
  We have studied one-body and two-body correlation functions in a
ballistically expanding, non-interacting atomic cloud in the presence of
gravity. We find that the correlation functions are equivalent to those at
thermal equilibrium in the trap with an appropriate rescaling of the
coordinates. We derive simple expressions for the correlation lengths and give
some physical interpretations. Finally a simple model to take into account
finite detector resolution is discussed.


title: Invariants for a Class of Nongeneric Three-qubit States

abstract:
  We investigate the equivalence of quantum states under local unitary
transformations. A complete set of invariants under local unitary
transformations is presented for a class of non-generic three-qubit mixed
states. It is shown that two such states in this class are locally equivalent
if and only if all these invariants have equal values for them.


title: Entanglement in single particle systems

abstract:
  We address some of the most commonly raised questions about entanglement,
especially with regard to so-called occupation number entanglement. To answer
unambiguously whether entanglement can exist in a one-atom delocalized state,
we propose an experiment capable of showing violations of Bell's inequality
using only this state and local operations. As a byproduct, this experiment
suggests a means of creating an entangled state of two different chemical
species. By comparison with a massless system, we argue that there should be no
fundamental objection to such a superposition and its creation may be within
reach of present technology.


title: Noisy Teleportation

abstract:
  Entanglement is a key resource in many quantum information applications. One
of these applications is quantum teleportation.The purpose of teleportation is
sending qubits across quantum channels. In general these quantum channels are
noisy and therefore limit the fidelity of transmission.In this paper we
consider the effect of noise on teleportation and finally find the fidelity of
teleportation in presence of noise.


title: Strong-field spatial interference in a tailored electromagnetic bath

abstract:
  Light scattered by a regular structure of atoms can exhibit interference
signatures, similar to the classical double-slit. These first-order
interferences, however, vanish for strong light intensities, restricting
potential applications. Here, we show how to overcome these limitations to
quantum interference in strong fields. First, we recover the first-order
interference in strong fields via a tailored electromagnetic bath with a
suitable frequency dependence. At strong driving, the optical properties for
different spectral bands are distinct, thus extending the set of observables.
We further show that for a two-photon detector as, e.g., in lithography,
increasing the field intensity leads to twice the spatial resolution of the
second-order interference pattern compared to the weak-field case.


title:
Multiatom and resonant interaction scheme for quantum state transfer and
  logical gates between two remote cavities via an optical fiber

abstract:
  A system consisting of two single-mode cavities spatially separated and
connected by an optical fiber and multiple two-level atoms trapped in the
cavities is considered. If the atoms resonantly and collectively interact with
the local cavity fields but there is no direct interaction between the atoms,
we show that an ideal quantum state transfer and highly reliable quantum swap,
entangling, and controlled-Z gates can be deterministically realized between
the distant cavities. We find that the operation of state transfer and swap,
entangling, and controlled-Z gates can be greatly speeded up as number of the
atoms in the cavities increases. We also notice that the effects of spontaneous
emission of atoms and photon leakage out of cavity on the quantum processes can
also be greatly diminished in the multiatom case.


title:
Conditional quantum-state engineering using ancillary squeezed-vacuum
  states

abstract:
  We investigate an optical scheme to conditionally engineer quantum states
using a beam splitter, homodyne detection and a squeezed vacuum as an ancillar
state. This scheme is efficient in producing non-Gaussian quantum states such
as squeezed single photons and superpositions of coherent states (SCSs). We
show that a SCS with well defined parity and high fidelity can be generated
from a Fock state of $n\leq4$, and conjecture that this can be generalized for
an arbitrary $n$ Fock state. We describe our experimental demonstration of this
scheme using coherent input states and measuring experimental fidelities that
are only achievable using quantum resources.


title: Entanglement conditions for two-mode states: Applications

abstract:
  We examine the implications of several recently derived conditions [Hillery
and Zubairy, Phys. Rev. Lett. 96, 050503 (2006)] for determining when a
two-mode state is entangled. We first find examples of non-Gaussian states that
satisfy these conditions. We then apply the entanglement conditions to the
study of several linear devices, the beam splitter, the parametric amplifier,
and the linear phase-insensitive amplifier. For the first two, we find
conditions on the input states that guarantee that the output states are
entangled. For the linear amplifier, we determine in the limit of high and no
gain, when an entangled input leads to an entangled output. Finally, we show
how application of two two-mode entanglement conditions to a three-mode state
can serve as a test of genuine three-mode entanglement.


title:
Coherent control of collective spontaneous emission in an extended
  atomic ensemble and quantum storage

abstract:
  Coherent control of collective spontaneous emission in an extended atomic
ensemble resonantly interacting with single-photon wave packets is analyzed. A
scheme for coherent manipulation of collective atomic states is developed such
that superradiant states of the atomic system can be converted into subradiant
ones and vice versa. Possible applications of such a scheme for optical quantum
state storage and single-photon wave packet shaping are discussed. It is shown
that also in the absence of inhomogeneous broadening of the resonant line,
single-photon wave packets with arbitrary pulse shape may be recorded as a
subradiant state and reconstructed even although the duration of the wave
packets is larger than the superradiant life-time. Specifically the
applicability for storing time-bin qubits, which are used in quantum
cryptography is analyzed.


title: Optimal probabilistic estimation of quantum states

abstract:
  We extend the concept of probabilistic unambiguous discrimination of quantum
states to quantum state estimation. We consider a scenario where the
measurement device can output either an estimate of the unknown input state or
an inconclusive result. We present a general method how to evaluate the maximum
fidelity achievable by the probabilistic estimation strategy. We illustrate our
method on two explicit examples: estimation of a qudit from a pair of conjugate
qudits and phase covariant estimation of a qubit from N copies. We show that by
allowing for inconclusive results it is possible to reach estimation fidelity
higher than that achievable by the best deterministic estimation strategy.


title: A Scalable Architecture for Coherence-Preserving Qubits

abstract:
  We propose scalable architectures for the coherence-preserving qubits
introduced by Bacon, Brown, and Whaley [Phys. Rev. Lett. {\bf 87}, 247902
(2001)]. These architectures employ extra qubits providing additional degrees
of freedom to the system. We show that these extra degrees of freedom can be
used to counter errors in coupling strength within the coherence-preserving
qubit and to combat interactions with environmental qubits. The presented
architectures incorporate experimentally viable methods for inter-logical-qubit
coupling and can implement a controlled phase gate via three simultaneous
Heisenberg exchange operations. The extra qubits also provide flexibility in
the arrangement of the physical qubits. Specifically, all physical qubits of a
coherent-preserving qubit lattice can be placed in two spatial dimensions. Such
an arrangement allows for universal cluster state computation.


title: Correcting low-frequency noise with continuous measurement

abstract:
  Low-frequency noise presents a serious source of decoherence in solid-state
qubits. When combined with a continuous weak measurement of the eigenstates,
the low-frequency noise induces a second-order relaxation between the qubit
states. Here we show that the relaxation provides a unique approach to
calibrate the low-frequency noise in the time-domain. By encoding one qubit
with two physical qubits that are alternatively calibrated, quantum logic gates
with high fidelity can be performed.


title:
Photon blockade induced Mott transitions and XY spin models in coupled
  cavity arrays

abstract:
  As photons do not interact with each other, it is interesting to ask whether
photonic systems can be modified to exhibit the phases characteristic of
strongly coupled many-body systems. We demonstrate how a Mott insulator type of
phase of excitations can arise in an array of coupled electromagnetic cavities,
each of which is coupled resonantly to a {\em single} two level system
(atom/quantum dot/Cooper pair) and can be individually addressed from outside.
In the Mott phase each atom-cavity system has the same integral number of net
polaritonic (atomic plus photonic) excitations with photon blockade providing
the required repulsion between the excitations in each site. Detuning the
atomic and photonic frequencies suppresses this effect and induces a transition
to a photonic superfluid. We also show that for zero detuning, the system can
simulate the dynamics of many body spin systems.


title:
Cooperating or Fighting with Decoherence in the Optimal Control of
  Quantum Dynamics

abstract:
  This paper explores the use of laboratory closed-loop learning control to
either fight or cooperate with decoherence in the optimal manipulation of
quantum dynamics. Simulations of the processes are performed in a Lindblad
formulation on multilevel quantum systems strongly interacting with the
environment without spontaneous emission. When seeking a high control yield it
is possible to find fields that successfully fight with decoherence while
attaining a good quality yield. When seeking modest control yields, fields can
be found which are optimally shaped to cooperate with decoherence and thereby
drive the dynamics more efficiently. In the latter regime when the control
field and the decoherence strength are both weak, a theoretical foundation is
established to describe how they cooperate with each other. In general, the
results indicate that the population transfer objectives can be effectively met
by appropriately either fighting or cooperating with decoherence.