title: Measurement-based quantum computation with superconducting charge qubits

abstract:
  We present a robust method, based only on measurements, to produce
superconducting cluster states. The measurement of the current of a few
parallel Josephson-junction qubits realizes a novel type of quantum-state
selector. Using this selector, one can produce various quantum entangled states
and also realize a controlled-NOT gate without requiring an exact control of
the interqubit interactions. In particular, cluster states for quantum
computation could be produced with only single-qubit measurements.


title: Computation in Finitary Stochastic and Quantum Processes

abstract:
  We introduce stochastic and quantum finite-state transducers as
computation-theoretic models of classical stochastic and quantum finitary
processes. Formal process languages, representing the distribution over a
process's behaviors, are recognized and generated by suitable specializations.
We characterize and compare deterministic and nondeterministic versions,
summarizing their relative computational power in a hierarchy of finitary
process languages. Quantum finite-state transducers and generators are a first
step toward a computation-theoretic analysis of individual, repeatedly measured
quantum dynamical systems. They are explored via several physical systems,
including an iterated beam splitter, an atom in a magnetic field, and atoms in
an ion trap--a special case of which implements the Deutsch quantum algorithm.
We show that these systems' behaviors, and so their information processing
capacity, depends sensitively on the measurement protocol.


title: Critical Property of Geometric Phase in the Dicke Model

abstract:
  We obtain the ground-state energy level and associated geometric phase in the
Dicke model analytically by means of the Holstein-Primakoff transformation and
the boson expansion approach in the thermodynamic limit. The non-adiabatic
geometric phase induced by the photon field is derived with the time-dependent
unitary transformation. It is shown that the quantum phase transition
characterized by the non-analyticity of the geometric phase is remarkably of
the first-order. We also investigate the scaling behavior of the geometric
phase at the critical point, which can be measured in a practical experiment to
detect the quantum phase transition.


title:
Generation of three-qubit entangled states using coupled multi-quantum
  dots

abstract:
  We discuss a mechanism for generating a maximum entangled state (GHZ) in a
coupled quantum dots system, based on analytical techniques. The reliable
generation of such states is crucial for implementing solid-state based quantum
information schemes. The signature originates from a remarkably weak field
pulse or a far off-resonance effects which could be implemented using
technology that is currently being developed. The results are illustrated with
an application to a specific wide-gap semiconductor quantum dots system, like
Zinc Selenide (ZnSe) based quantum dots.


title:
Quantum Entanglement of Electromagnetic Fields in Non-inertial Reference
  Frames

abstract:
  Recently relativistic quantum information has received considerable attention
due to its theoretical importance and practical application. Especially,
quantum entanglement in non-inertial reference frames has been studied for
scalar and Dirac fields. As a further step along this line, we here shall
investigate quantum entanglement of electromagnetic fields in non-inertial
reference frames. In particular, the entanglement of photon helicity entangled
state is extensively analyzed. Interestingly, the resultant logarithmic
negativity and mutual information remain the same as those for inertial
reference frames, which is completely different from that previously obtained
for the particle number entangled state.


title: Multi-dark-state resonances in cold multi-Zeeman-sublevel atoms

abstract:
  We present our experimental and theoretical studies of multi-dark-state
resonances (MDSRs) generated in a unique cold rubidium atomic system with only
one coupling laser beam. Such MDSRs are caused by different transition
strengths of the strong coupling beam connecting different Zeeman sublevels.
Controlling the transparency windows in such electromagnetically induced
transparency system can have potential applications in multi-wavelength optical
communication and quantum information processing.


title:
On the exactness of the Semi-Classical Approximation for
  Non-Relativistic One Dimensional Propagators

abstract:
  For one dimensional non-relativistic quantum mechanical problems, we
investigate the conditions for all the position dependence of the propagator to
be in its phase, that is, the semi-classical approximation to be exact. For
velocity independent potentials we find that:
  (i) the potential must be quadratic in space, but can have arbitrary time
dependence.
  (ii) the phase may be made proportional to the classical action, and the
magnitude (``fluctuation factor'') can also be found from the classical
solution.
  (iii) for the driven harmonic oscillator the fluctuation factor is
independent of the driving term.


title: Decoherence in a scalable adiabatic quantum computer

abstract:
  We consider the effects of decoherence on Landau-Zener crossings encountered
in a large-scale adiabatic-quantum-computing setup. We analyze the dependence
of the success probability, i.e. the probability for the system to end up in
its new ground state, on the noise amplitude and correlation time. We determine
the optimal sweep rate that is required to maximize the success probability. We
then discuss the scaling of decoherence effects with increasing system size. We
find that those effects can be important for large systems, even if they are
small for each of the small building blocks.


title: Low Cost and Compact Quantum Cryptography

abstract:
  We present the design of a novel free-space quantum cryptography system,
complete with purpose-built software, that can operate in daylight conditions.
The transmitter and receiver modules are built using inexpensive off-the-shelf
components. Both modules are compact allowing the generation of renewed shared
secrets on demand over a short range of a few metres. An analysis of the
software is shown as well as results of error rates and therefore shared secret
yields at varying background light levels. As the system is designed to
eventually work in short-range consumer applications, we also present a use
scenario where the consumer can regularly 'top up' a store of secrets for use
in a variety of one-time-pad and authentication protocols.


title:
Quantum sensitivity limit of a Sagnac hybrid interferometer based on
  slow-light propagation in ultra-cold gases

abstract:
  The light--matter-wave Sagnac interferometer based on ultra-slow light
proposed recently in (Phys. Rev. Lett. 92, 253201 (2004)) is analyzed in
detail. In particular the effect of confining potentials is examined and it is
shown that the ultra-slow light attains a rotational phase shift equivalent to
that of a matter wave, if and only if the coherence transfer from light to
atoms associated with slow light is associated with a momentum transfer and if
an ultra-cold gas in a ring trap is used. The quantum sensitivity limit of the
Sagnac interferometer is determined and the minimum detectable rotation rate
calculated. It is shown that the slow-light interferometer allows for a
significantly higher signal-to-noise ratio as possible in current matter-wave
gyroscopes.


title: Experimental Proof of Quantum Nonlocality without Squeezing

abstract:
  It is shown that the ensemble $\{p (\alpha),|\alpha>|\alpha^*>\}$ where $p
(\alpha)$ is a Gaussian distribution of finite variance and $| \alpha>$ is a
coherent state can be better discriminated with an entangled measurement than
with any local strategy supplemented by classical communication. Although this
ensemble consists of products of quasi-classical states, it exhibits some
quantum nonlocality. This remarkable effect is demonstrated experimentally by
implementing the optimal local strategy together with a joint nonlocal strategy
that yields a higher fidelity.


title: On two-dimensional Bessel functions

abstract:
  The general properties of two-dimensional generalized Bessel functions are
discussed. Various asymptotic approximations are derived and applied to analyze
the basic structure of the two-dimensional Bessel functions as well as their
nodal lines.


title:
Quantum transport and localization in biased periodic structures under
  bi- and polychromatic driving

abstract:
  We consider the dynamics of a quantum particle in a one-dimensional periodic
potential (lattice) under the action of a static and time-periodic field. The
analysis is based on a nearest-neighbor tight-binding model which allows a
convenient closed form description of the transport properties in terms of
generalized Bessel functions. The case of bichromatic driving is analyzed in
detail and the intricate transport and localization phenomena depending on the
communicability of the two excitation frequencies and the Bloch frequency are
discussed. The case of polychromatic driving is also discussed, in particular
for flipped static fields, i.e. rectangular pulses, which can support an almost
dispersionless transport with a velocity independent of the field amplitude.


title: Strength of interaction for information distribution

abstract:
  Let us consider two quantum systems: system A and system B. Suppose that a
classical information is encoded to quantum states of the system A and we
distribute this information to both systems by making them interact with each
other. We show that it is impossible to achieve this goal perfectly if the
strength of interaction between the quantum systems is smaller than a quantity
that is determined by noncommutativity between a Hamiltonian of the system A
and the states (density operators) used for the information encoding. It is a
consequence of a generalized Winger-Araki-Yanase theorem which enables us to
treat conserved quantities other than additive ones.


title:
Theoretical Study of Fast Light with Short sech Pulses in Coherent Gain
  Media

abstract:
  We investigate theoretically the phenomenon of so-called fast light in an
unconventional regime, using pulses sufficiently short that relaxation effects
in a gain medium can be ignored completely. We show that previously recognized
gain instabilities, including superfluorescence, can be tolerated in achieving
a pulse peak advance of one full peak width.


title: Quantum channels in random spin chains

abstract:
  We study the entanglement between pairs of qubits in a random
antiferromagnetic spin-1/2 chain at zero temperature. We show that some very
distant pairs of qubits are highly entangled, being almost pure Bell states.
Furthermore, the probability to obtain such spin pairs is proportional to the
chain disorder strenght and inversely proportional to the square of their
separation.


title: Dirac Hamiltonian with superstrong Coulomb field

abstract:
  We consider the quantum-mechanical problem of a relativistic Dirac particle
moving in the Coulomb field of a point charge $Ze$. In the literature, it is
often declared that a quantum-mechanical description of such a system does not
exist for charge values exceeding the so-called critical charge with $%
Z=\alpha ^{-1}=137$ based on the fact that the standard expression for the
lower bound state energy yields complex values at overcritical charges. We show
that from the mathematical standpoint, there is no problem in defining a
self-adjoint Hamiltonian for any value of charge. What is more, the transition
through the critical charge does not lead to any qualitative changes in the
mathematical description of the system. A specific feature of overcritical
charges is a non uniqueness of the self-adjoint Hamiltonian, but this non
uniqueness is also characteristic for charge values less than the critical one
(and larger than the subcritical charge with $Z=(\sqrt{3}% /2)\alpha
^{-1}=118$). We present the spectra and (generalized) eigenfunctions for all
self-adjoint Hamiltonians. The methods used are the methods of the theory of
self-adjoint extensions of symmetric operators and the Krein method of guiding
functionals. The relation of the constructed one-particle quantum mechanics to
the real physics of electrons in superstrong Coulomb fields where multiparticle
effects may be of crucial importance is an open question.


title:
Quantum dynamics of bosons in a double-well potential: Josephson
  oscillations, self-trapping and ultralong tunneling times

abstract:
  The dynamics of the population imbalance of bosons in a double-well potential
is investigated from the point of view of many-body quantum mechanics in the
framework of the two-mode model. For small initial population imbalances,
coherent superpositions of almost equally spaced energy eigenstates lead to
Josephson oscillations. The suppression of tunneling at population imbalance
beyond a critical value is related to a high concentration of initial state
population in the region of the energy spectrum with quasi-degenerate doublets
resulting in imbalance oscillations with a very small amplitude. For
unaccessible long times, however, the system recovers the regime of Josephson
oscillations.


title: Quantum network communication -- the butterfly and beyond

abstract:
  We study the k-pair communication problem for quantum information in networks
of quantum channels. We consider the asymptotic rates of high fidelity quantum
communication between specific sender-receiver pairs. Four scenarios of
classical communication assistance (none, forward, backward, and two-way) are
considered. (i) We obtain outer and inner bounds of the achievable rate regions
in the most general directed networks. (ii) For two particular networks
(including the butterfly network) routing is proved optimal, and the free
assisting classical communication can at best be used to modify the directions
of quantum channels in the network. Consequently, the achievable rate regions
are given by counting edge avoiding paths, and precise achievable rate regions
in all four assisting scenarios can be obtained. (iii) Optimality of routing
can also be proved in classes of networks. The first class consists of directed
unassisted networks in which (1) the receivers are information sinks, (2) the
maximum distance from senders to receivers is small, and (3) a certain type of
4-cycles are absent, but without further constraints (such as on the number of
communicating and intermediate parties). The second class consists of arbitrary
backward-assisted networks with 2 sender-receiver pairs. (iv) Beyond the k-pair
communication problem, observations are made on quantum multicasting and a
static version of network communication related to the entanglement of
assistance.


title: Concurrence for multipartite states

abstract:
  We construct a generalized concurrence for general multipartite states based
on local W-class and GHZ-class operators. We explicitly construct the
corresponding concurrence for three-partite states. The construction of the
concurrence is interesting since it is based on local operators.


title:
Exact calculation of robustness of entanglement via convex semi-definite
  programming

abstract:
  In general the calculation of robustness of entanglement for the mixed
entangled quantum states is rather difficult to handle analytically. Using the
the convex semi-definite programming method, the robustness of entanglement of
some mixed entangled quantum states such as: $2\otimes 2$ Bell decomposable
(BD) states, a generic two qubit state in Wootters basis, iso-concurrence
decomposable states, $2\otimes 3$ Bell decomposable states, $d\otimes d$ Werner
and isotropic states, a one parameter $3\otimes 3$ state and finally multi
partite isotropic state, is calculated exactly, where thus obtained results are
in agreement with those of :$2\otimes 2$ density matrices, already calculated
by one of the authors in \cite{Bell1,Rob3}. Also an analytic expression is
given for separable states that wipe out all entanglement and it is further
shown that they are on the boundary of separable states as pointed out in
\cite{du}.
  {\bf Keywords: Robustness of entanglement, Semi-definite programming, Bell
decomposable states, Werner and isotropic states.}


title:
Evaluation of relative entropy of entanglement and derivation of optimal
  Lewenstein-Sanpera decomposition of Bell decomposable states via convex
  optimization

abstract:
  We provide an analytical expression for optimal Lewenstein-Sanpera
decomposition of Bell decomposable states by using semi-definite programming.
Also using the Karush-Kuhn-Tucker optimization method, the minimum relative
entropy of entanglement of Bell decomposable states has been evaluated and it
is shown that the same separable Bell decomposable state lying at the boundary
of convex set of separable Bell decomposable states, optimizes both
Lewenstein-Sanpera decomposition and relative entropy of entanglement.
  {\bf Keywords: Minimum relative entropy of entanglement, Semi-definite
programming, Convex optimization, Lewenstein-Sanpera decomposition, Bell
decomposable states.}
  {\bf PACs Index: 03.65.Ud}


title: Complementary reductions for two qubits

abstract:
  In connection with optimal state determination for two qubits, the question
was raised about the maximum number of pairwise complementary reductions. The
main result of the paper tells that the maximum number is 4, that is, if A1,
A2,... Ak are pairwise complementary (or quasi-orthogonal) subalgebras of the
algebra of all 4x4$ matrices and they are isomorphic to the algebra of all 2x2
matrices, then k is at most 4. In the way to this result, contributions are
made to the understanding of the structure of complementary reductions.


title: Radio-frequency dressed state potentials for neutral atoms

abstract:
  Potentials for atoms can be created by external fields acting on properties
like magnetic moment, charge, polarizability, or by oscillating fields which
couple internal states. The most prominent realization of the latter is the
optical dipole potential formed by coupling ground and electronically excited
states of an atom with light. Here we present an experimental investigation of
the remarkable properties of potentials derived from radio-frequency (RF)
coupling between electronic ground states. The coupling is magnetic and the
vector character allows to design state dependent potential landscapes. On atom
chips this enables robust coherent atom manipulation on much smaller spatial
scales than possible with static fields alone. We find no additional heating or
collisional loss up to densities approaching $10^{15}$ atoms / cm$^3$ compared
to static magnetic traps. We demonstrate the creation of Bose-Einstein
condensates in RF potentials and investigate the difference in the interference
between two independently created and two coherently split condensates in
identical traps. All together this makes RF dressing a powerful new tool for
micro manipulation of atomic and molecular systems.


title: Remote preparation of an atomic quantum memory

abstract:
  Storage and distribution of quantum information are key elements of quantum
information processing and quantum communication. Here, using atom-photon
entanglement as the main physical resource, we experimentally demonstrate the
preparation of a distant atomic quantum memory. Applying a quantum
teleportation protocol on a locally prepared state of a photonic qubit, we
realized this so-called remote state preparation on a single, optically trapped
87Rb atom. We evaluated the performance of this scheme by the full tomography
of the prepared atomic state, reaching an average fidelity of 82%.


title:
Increasing entanglement between Gaussian states by coherent photon
  subtraction

abstract:
  We experimentally demonstrate that the entanglement between Gaussian
entangled states can be increased by non-Gaussian operations. Coherent
subtraction of single photons from Gaussian quadrature-entangled light pulses,
created by a non-degenerate parametric amplifier, produces delocalized states
with negative Wigner functions and complex structures, more entangled than the
initial states in terms of negativity. The experimental results are in very
good agreement with the theoretical predictions.


title:
Path Integral Approach for Quantum Motion on Spaces of Non-constant
  Curvature According to Koenigs

abstract:
  In this contribution I discuss a path integral approach for the quantum
motion on two-dimensional spaces according to Koenigs, for short
``Koenigs-Spaces''. Their construction is simple: One takes a Hamiltonian from
two-dimensional flat space and divides it by a two-dimensional superintegrable
potential. These superintegrable potentials are the isotropic singular
oscillator, the Holt-potential, and the Coulomb potential. In all cases a
non-trivial space of non-constant curvature is generated. We can study free
motion and the motion with an additional superintegrable potential. For
possible bound-state solutions we find in all three cases an equation of eighth
order in the energy E. The special cases of the Darboux spaces are easily
recovered by choosing the parameters accordingly.


title: Contract Signature Using Quantum Information

abstract:
  This paper describes how to perform contract signature in a fair way using
quantum information. The protocol proposed permits two partners, users of a
communication network, to perform a contract signature based on the RSA
security. The authentication of the signers is based on the use of a non-local
XOR function of two classical bits.


title:
Room-temperature manipulation and decoherence of a single spin in
  diamond

abstract:
  We report on room-temperature coherent manipulation of the spin of a single
nitrogen-vacancy center in diamond and a study of its coherence as a function
of magnetic field. We use magnetic resonance to induce Rabi nutations, and
apply a Hahn spin echo to remove the effect of low-frequency dephasing. A sharp
rise in the decoherence rate is observed at magnetic fields where the
nitrogen-vacancy center spin couples resonantly to substitutional nitrogen
spins via the magnetic dipolar coupling. Finally, we find evidence that away
from these energy resonances spin flips of nitrogen electrons are the main
source of decoherence.


title:
Controlled polarization rotation of an optical field in
  multi-Zeeman-sublevel atoms

abstract:
  We investigate, both theoretically and experimentally, the phenomenon of
polarization rotation of a weak, linearly-polarized optical (probe) field in an
atomic system with multiple three-level electromagnetically induced
transparency (EIT) sub-systems. The polarization rotation angle can be
controlled by a circularly-polarized coupling beam, which breaks the symmetry
in number of EIT subsystems seen by the left- and right-circularly-polarized
components of the weak probe beam. A large polarization rotation angle (up to
45 degrees) has been achieved with a coupling beam power of only 15 mW.
Detailed theoretical analyses including different transition probabilities in
different transitions and Doppler-broadening are presented and the results are
in good agreements with the experimentally measured results.


title:
Realization of positive-operator-valued measures by projective
  measurements without introducing ancillary dimensions

abstract:
  We propose a scheme that can realize a class of positive-operator-valued
measures (POVMs) by performing a sequence of projective measurements on the
original system, in the sense that for an arbitrary input state the probability
distribution of the measurement outcomes is faithfully reproduced. A necessary
and sufficient condition for a POVM to be realizable in this way is also
derived. In contrast to the canonical approach provided by Neumark's theorem,
our method has the advantage of requiring no auxiliary system. Moreover, an
arbitrary POVM can be realized by utilizing our protocol on an extended space
which is formed by adding only a single extra dimension.


title: Robustness of multiparty nonlocality to local decoherence

abstract:
  We investigate the robustness of multiparty nonlocality under local
decoherence, acting independently and equally on each subsystems. To be
specific, we consider an N-qubit GHZ state under depolarization, dephasing, or
dissipation channel, and tested the nonlocality by violation of Mermin-Klyshko
inequality, which is one of Bell's inequalities for multi-qubit systems. The
results show that the robustness of nonlocality increases with the number of
qubits, and that the nonlocality of an N-qubit GHZ state with even N is
extremely persistent against dephasing.


title: On geometric phases for quantum trajectories

abstract:
  A sequence of completely positive maps can be decomposed into quantum
trajectories. The geometric phase or holonomy of such a trajectory is
delineated. For nonpure initial states, it is shown that well-defined
holonomies can be assigned by using Uhlmann's concept of parallel transport
along the individual trajectories. We put forward an experimental realization
of the geometric phase for a quantum trajectory in interferometry. We argue
that the average over the phase factors for all quantum trajectories that build
up a given open system evolution, fails to reflect the geometry of the open
system evolution itself.


title: Extensible router for multi-user quantum key distribution network

abstract:
  A feasible quantum key distribution (QKD) network scheme has been proposed
with the wavelength routing. An apparatus called "quantum router", which is
made up of many wavelength division multiplexers, can route the quantum signals
without destroying their quantum states. Combining with existing point-to-point
QKD technology, we can setup a perfectly QKD star-network. A simple
characteristic and feasibility of this scheme has also been obtained.


title: Massive Parallel Quantum Computer Simulator

abstract:
  We describe portable software to simulate universal quantum computers on
massive parallel computers. We illustrate the use of the simulation software by
running various quantum algorithms on different computer architectures, such as
a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI
Altix 3700 and clusters of PCs running Windows XP. We study the performance of
the software by simulating quantum computers containing up to 36 qubits, using
up to 4096 processors and up to 1 TB of memory. Our results demonstrate that
the simulator exhibits nearly ideal scaling as a function of the number of
processors and suggest that the simulation software described in this paper may
also serve as benchmark for testing high-end parallel computers.


title: A multi-party correlation measure based on cumulant

abstract:
  We propose a genuine multi-party correlation measure for a multi-party
quantum system as the trace norm of the cumulant of the state. The legitimacy
of our multi-party correlation measure is explicitly demonstrated by proving it
satisfies the five basic conditions required for a correlation measure. As an
application we construct an efficient algorithm for the calculation of our
measures for all stabilizer states.


title: Quantum Computing with Global One-and Two-Qubit Gates

abstract:
  We present generalized and improved constructions for simulating quantum
computers with a polynomial slowdown on lattices composed of qubits on which
certain global versions of one- and two-qubit operations can be performed.


title:
Creation of macroscopic superposition states from arrays of
  Bose-Einstein condensates

abstract:
  We consider how macroscopic quantum superpositions may be created from arrays
of Bose-Einstein condensates. We study a system of three condensates in Fock
states, all with the same number of atoms and show that this has the form of a
highly entangled superposition of different quasi-momenta. We then show how, by
partially releasing these condensates and detecting an interference pattern
where they overlap, it is possible to create a macroscopic superposition of
different relative phases for the remaining portions of the condensates. We
discuss methods for confirming these superpositions.


title:
Relational physics with real rods and clocks and the measurement problem
  of quantum mechanics

abstract:
  The use of real clocks and measuring rods in quantum mechanics implies a
natural loss of unitarity in the description of the theory. We briefly review
this point and then discuss the implications it has for the measurement problem
in quantum mechanics. The intrinsic loss of coherence allows to circumvent some
of the usual objections to the measurement process as due to environmental
decoherence.


title: Higher-Rank Numerical Ranges of Unitary and Normal Matrices

abstract:
  We verify a conjecture on the structure of higher-rank numerical ranges for a
wide class of unitary and normal matrices. Using analytic and geometric
techniques, we show precisely how the higher-rank numerical ranges for a
generic unitary matrix are given by complex polygons determined by the spectral
structure of the matrix. We discuss applications of the results to quantum
error correction, specifically to the problem of identification and
construction of codes for binary unitary noise models.


title:
Fubctional integral approach to quantum gauge theories on a
  noncommutative space-time

abstract:
  We propose a construction of actions of a quantum gauge field theory on a
noncommutative space-time, based on a Fourier transform on the
Doplicher-Fredenhagen-Roberts group. This approach leads to a functional
integral representation of the action, which in turn leads to considering the
space of probability measures on the classical space-time as a noncommutative
version of the space-time. This approach allows a very natural treatment of
gauge fields terms in the action.


title: Efficient error characterization in Quantum Information Processing

abstract:
  We describe how to use the fidelity decay as a tool to characterize the
errors affecting a quantum information processor through a noise generator
$G_{\tau}$. For weak noise, the initial decay rate of the fidelity proves to be
a simple way to measure the magnitude of the different terms in $G_{\tau}$.
When the generator has only terms associated with few-body couplings, our
proposal is scalable. We present the explicit protocol for estimating the
magnitude of the noise generators when the noise consists of only one and
two-body terms, and describe a method for measuring the parameters of more
general noise models. The protocol focuses on obtaining the magnitude with
which these terms affect the system during a time step of length $\tau$;
measurement of this information has critical implications for assesing the
scalability of fault-tolerant quantum computation in any physical setup.


title: Quantum many-body simulations using Gaussian phase-space representations

abstract:
  Phase-space representations are of increasing importance as a viable and
successful means to study exponentially complex quantum many-body systems from
first principles. This review traces the background of these methods, starting
from the early work of Wigner, Glauber and Sudarshan. We focus on modern
phase-space approaches using non-classical phase-space representations. These
lead to the Gaussian representation, which unifies bosonic and fermionic
phase-space. Examples treated include quantum solitons in optical fibers,
colliding Bose-Einstein condensates, and strongly correlated fermions on
lattices.


title:
Particle decay processes, the quantum Zeno effect and the continuity of
  time

abstract:
  Signal-state quantum mechanics is used to discuss quantum mechanical particle
decay probabilities and the quantum Zeno effect. This approach avoids the
assumption of continuous time, conserves total probability and requires neither
non-Hermitian Hamiltonians nor the ad-hoc introduction of complex energies. The
formalism is applied to single channel decays, the ammonium molecule, and
neutral Kaon decay processes.


title: Entanglement and the Lower Bounds on the Speed of Quantum Evolution

abstract:
  The concept of quantum speed limit-time (QSL) was initially introduced as a
lower bound to the time interval that a given initial state $\psi_I$ may need
so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S.
Lloyd, and L. Maccone, Phys. Rev. A {\bf 67}, 052109 (2003)] this bound has
been generalized to the case where $\psi_I$ does not necessarily evolve into an
orthogonal state, but into any other $\psi_F$. It was pointed out that, for
certain classes of states, quantum entanglement enhances the evolution "speed"
of composite quantum systems. In this work we provide an exhaustive and
systematic QSL study for pure and mixed states belonging to the whole
15-dimensional space of two qubits, with $\psi_F$ a not necessarily orthogonal
state to $\psi_I$. We display convincing evidence for a clear correlation
between concurrence, on the one hand, and the speed of quantum evolution
determined by the action of a rather general local Hamiltonian, on the other
one.


title: NPPT Bound Entanglement Exists

abstract:
  Every dXd bipartite system is shown to have a large family of undistillable
states with nonpositive partial transpose (NPPT). This family subsumes the
family of conjectured NPPT bound entangled Werner states. In particular, all
one-copy undistillable NPPT Werner states are shown to be bound entangled.


title:
Probability Representation of Quantum Mechanics: Comments and
  Bibliography

abstract:
  The probability representation of states in standard quantum mechanics where
the quantum states are associated with fair probability distributions (instead
of wave function or density matrix) is shortly commented and bibliography
related to the probability representation is given.


title: Shor's algorithm on a nearest-neighbor machine

abstract:
  We give a new ``nested adds'' circuit for implementing Shor's algorithm in
linear width and quadratic depth on a nearest-neighbor machine. Our circuit
combines Draper's transform adder with approximation ideas of Zalka. The
transform adder requires small controlled rotations. We also give another
version, with slightly larger depth, using only reversible classical gates. We
do not know which version will ultimately be cheaper to implement.


title:
A simple nearest-neighbor two-body Hamiltonian system for which the
  ground state is a universal resource for quantum computation

abstract:
  We present a simple quantum many-body system - a two-dimensional lattice of
qubits with a Hamiltonian composed of nearest-neighbor two-body interactions -
such that the ground state is a universal resource for quantum computation
using single-qubit measurements. This ground state approximates a cluster state
that is encoded into a larger number of physical qubits. The Hamiltonian we use
is motivated by the projected entangled pair states, which provide a
transparent mechanism to produce such approximate encoded cluster states on
square or other lattice structures (as well as a variety of other quantum
states) as the ground state. We show that the error in this approximation takes
the form of independent errors on bonds occurring with a fixed probability. The
energy gap of such a system, which in part determines its usefulness for
quantum computation, is shown to be independent of the size of the lattice. In
addition, we show that the scaling of this energy gap in terms of the coupling
constants of the Hamiltonian is directly determined by the lattice geometry. As
a result, the approximate encoded cluster state obtained on a hexagonal lattice
(a resource that is also universal for quantum computation) can be shown to
have a larger energy gap than one on a square lattice with an equivalent
Hamiltonian.


title: Influence of classical resonances on chaotic tunnelling

abstract:
  Dynamical tunnelling between symmetry-related stable modes is studied in the
periodically driven pendulum. We present strong evidence that the tunnelling
process is governed by nonlinear resonances that manifest within the regular
phase-space islands on which the stable modes are localized. By means of a
quantitative numerical study of the corresponding Floquet problem, we identify
the trace of such resonances not only in the level splittings between
near-degenerate quantum states, where they lead to prominent plateau
structures, but also in overlap matrix elements of the Floquet eigenstates,
which reveal characteristic sequences of avoided crossings in the Floquet
spectrum. The semiclassical theory of resonance-assisted tunnelling yields good
overall agreement with the quantum-tunnelling rates, and indicates that partial
barriers within the chaos might play a prominent role.


title:
Spectral structure and decompositions of optical states, and their
  applications

abstract:
  We discuss the spectral structure and decomposition of multi-photon states.
Ordinarily `multi-photon states' and `Fock states' are regarded as synonymous.
However, when the spectral degrees of freedom are included this is not the
case, and the class of `multi-photon' states is much broader than the class of
`Fock' states. We discuss the criteria for a state to be considered a Fock
state. We then address the decomposition of general multi-photon states into
bases of orthogonal eigenmodes, building on existing multi-mode theory, and
introduce an occupation number representation that provides an elegant
description of such states that in many situations simplifies calculations.
Finally we apply this technique to several example situations, which are highly
relevant for state of the art experiments. These include Hong-Ou-Mandel
interference, spectral filtering, finite bandwidth photo-detection, homodyne
detection and the conditional preparation of Schr\"odinger Kitten and Fock
states. Our techniques allow for very simple descriptions of each of these
examples.


title:
Quantum state tomography of single photons in the spectral degree of
  freedom

abstract:
  Quantum State Tomography (QST) of optical states is typically performed in
the photon number degree of freedom, a procedure which is well understood and
has been experimentally demonstrated. However, optical states have other
degrees of freedom than just photon number, such as the spatial and
temporal/spectral ones. Full characterization of photonic states requires state
reconstruction in these additional degrees of freedom. In this paper we present
a technique for performing QST of single photon states in the spectral degree
of freedom. This is of importance, for example, in quantum information
processing applications, which typically impose strict requirements on the
purity and distinguishability of independently produced single photons. The
described technique allows for full reconstruction of the spectral density
matrix, allowing the purity and distinguishability of different sources to be
readily calculated.


title: Two-Qubit Separability Probabilities and Beta Functions

abstract:
  Due to recent important work of Zyczkowski and Sommers (quant-ph/0302197 and
quant-ph/0304041), exact formulas are available (both in terms of the
Hilbert-Schmidt and Bures metrics) for the (n^2-1)-dimensional and
(n(n-1)/2-1)-dimensional volumes of the complex and real n x n density
matrices. However, no comparable formulas are available for the volumes (and,
hence, probabilities) of various separable subsets of them. We seek to clarify
this situation for the Hilbert-Schmidt metric for the simplest possible case of
n=4, that is, the two-qubit systems. Making use of the density matrix (rho)
parameterization of Bloore (J. Phys. A 9, 2059 [1976]), we are able to reduce
each of the real and complex volume problems to the calculation of a
one-dimensional integral, the single relevant variable being a certain ratio of
diagonal entries, nu = (rho_{11} rho_{44})/{rho_{22} rho_{33})$. The associated
integrand in each case is the product of a known (highly oscillatory near nu=1)
jacobian and a certain unknown univariate function, which our extensive
numerical (quasi-Monte Carlo) computations indicate is very closely
proportional to an (incomplete) beta function B_{nu}(a,b), with a=1/2,
b=sqrt{3}in the real case, and a=2 sqrt{6}/5, b =3/sqrt{2} in the complex case.
Assuming the full applicability of these specific incomplete beta functions, we
undertake separable volume calculations.


title: Measuring the size of a Schroedinger cat state

abstract:
  We propose a measure for the "size" of a Schroedinger cat state, i.e. a
quantum superposition of two many-body states with (supposedly) macroscopically
distinct properties, by counting how many single-particle operations are needed
to map one state onto the other. This definition gives sensible results for
simple, analytically tractable cases and is consistent with a previous
definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our
measure to the experimentally relevant, nontrivial example of a superconducting
three-junction flux qubit put into a superposition of left- and
right-circulating supercurrent states and find this Schroedinger cat to be
surprisingly small.


title:
Precise Control of Molecular Dynamics with a Femtosecond Frequency Comb
  - A Weak Field Route to Strong Field Coherent Control

abstract:
  We present a general and highly efficient scheme for performing narrow-band
Raman transitions between molecular vibrational levels using a coherent train
of weak pump-dump pairs of shaped ultrashort pulses. The use of weak pulses
permits an analytic description within the framework of coherent control in the
perturbative regime, while coherent accumulation of many pulse pairs enables
near unity transfer efficiency with a high spectral selectivity, thus forming a
powerful combination of pump-dump control schemes and the precision of the
frequency comb. The concept is presented analytically and its feasibility and
robustness are verified by simulations of dynamics in Rb$_2$. We consider
application of this concept to the formation of stable, deeply bound, ultracold
molecules.

categories: quant-ph physics.atm-clus physics.atom-ph physics.optics


title: Extended Coherence Time with Atom-Number Squeezed Sources

abstract:
  Coherence properties of Bose-Einstein condensates offer the potential for
improved interferometric phase contrast. However, decoherence effects due to
the mean-field interaction shorten the coherence time, thus limiting potential
sensitivity. In this work, we demonstrate increased coherence times with number
squeezed states in an optical lattice using the decay of Bloch oscillations to
probe the coherence time. We extend coherence times by a factor of 2 over those
expected with coherent state BEC interferometry. We observe quantitative
agreement with theory both for the degree of initial number squeezing as well
as for prolonged coherence times.


title:
Evolution Of Entanglement In Groverian Search Algorithm: Two-Qutrit
  System

abstract:
  Entanglement plays a crucial role in quantum processes particularly those
pertaining to quantum information and computation. An analytical expression for
entanglement measure defined in terms of success rate of Grover's search
algorithm has been obtained for a two-qutrit system and the calculated results
agree well with the conventional entropy based measure. Qutrit system are of
special interest because the Hilbert space dimensionality (for a given number
of qudits-d-dimensional system)is optimal for d=3 and this may be of
significance in the enhancement of computing power.


title:
Decay of discrete state resonantly coupled to a continuum of finite
  width

abstract:
  A simple quantum mechanical model consisting of a discrete level resonantly
coupled to a continuum of finite width, where the coupling can be varied from
perturbative to strong (Fano-Anderson model), is considered. The particle is
initially localized at the discrete level, and the time dependence of the
amplitude to find the particle at the discrete level is calculated without
resorting to perturbation theory. The deviations from the exponential decay
law, predicted by the Fermi's Golden Rule, are discussed. We also study
analytic structure of the Green's function (GF) for the model. We analyze the
GF poles, branch points and Riemann surface, and show how the Fermi's Golden
Rule, valid in perturbative regime for not to large time, appears in this
context. The knowledge of analytic structure of the GF in frequency
representation opens opportunities for obtaining easy for numerical
calculations formulas for the GF in time representation, alternative to those
using the spectral density.


title: Two-way and three-way negativities of three qubit entangled states

abstract:
  We propose to quantify three qubit entanglement using global negativity along
with K-way negativities, where K=2 and 3. K-way partial transpose with respect
to a subsystem is defined so as to shift the focus to K-way coherences of the
composite system instead of K subsystems of the composite system. While genuine
tripartite entanglement of three qubit composite system is generated by 3-way
coherences, tripartite entanglement can be present due to 2-way coherences as
well.


title:
One-mode Bosonic Gaussian channels: a full weak-degradability
  classification

abstract:
  A complete degradability analysis of one-mode Gaussian Bosonic channels is
presented. We show that apart from the class of channels which are unitarily
equivalent to the channels with additive classical noise, these maps can be
characterized in terms of weak- and/or anti-degradability. Furthermore a new
set of channels which have null quantum capacity is identified. This is done by
exploiting the composition rules of one-mode Gaussian maps and the fact that
anti-degradable channels can not be used to transfer quantum information.


title: The CNOT Quantum Logic Gate Using q-Deformed Oscillators

abstract:
  It is shown that the two qubit CNOT (controlled NOT) gate can also be
realised using q-deformed angular momentum states via the Jordan-Schwinger
mechanism.Thus all the three gates necessary for universality i.e. Hadamard,
Phase Shift and the two qubit CNOT gate are realisable with q-deformed
oscillators.


title:
Nature of the Angular Momentum of Light: Rotational Energy and Geometric
  Phase

abstract:
  The nature of intrinsic/extrinsic character of angular momentum is defined in
terms of the kind of the associated rotational energy of the light. The salient
features of the spin energy of light and photon are highlighted. Spin angular
momentum is intrinsic while orbital angular momentum possesses
quasi-intrinsicness only if the vortex-like singularities are present. The
claimed spin to orbital angular momentum conversion is interpreted in terms of
spin redirection geometric phase. It is pointed out that this interpretation
validates our angular momentum holonomy conjecture.


title: Semiclassical Tunneling of Wavepackets with Real Trajectories

abstract:
  Semiclassical approximations for tunneling processes usually involve complex
trajectories or complex times. In this paper we use a previously derived
approximation involving only real trajectories propagating in real time to
describe the scattering of a Gaussian wavepacket by a finite square potential
barrier. We show that the approximation describes both tunneling and
interferences very accurately in the limit of small Plank's constant. We use
these results to estimate the tunneling time of the wavepacket and find that,
for high energies, the barrier slows down the wavepacket but that it speeds it
up at energies comparable to the barrier height.


title: Fractional supersymmetry and hierarchy of shape invariant potentials

abstract:
  Fractional supersymmetric quantum mechanics is developed from a generalized
Weyl-Heisenberg algebra. The Hamiltonian and the supercharges of fractional
supersymmetric dynamical systems are built in terms of the generators of this
algebra. The Hamiltonian gives rise to a hierarchy of isospectral Hamiltonians.
Special cases of the algebra lead to dynamical systems for which the
isospectral supersymmetric partner Hamiltonians are connected by a
(translational or cyclic) shape invariance condition.


title: Quantum Gaussian Channels with Additive Correlated Classical Noise

abstract:
  We provide a model to study memory effects in quantum Gaussian channels with
additive classical noise over an arbitrary number of uses. The correlation
among different uses is introduced by contiguous two-mode interactions.
Numerical results for few modes are presented. They confirm the possibility to
enhance the classical information rate with the aid of entangled inputs, and
show a likely asymptotic behavior that should lead to the full capacity of the
channel.


title: Producing and Detecting Correlated atoms

abstract:
  We discuss experiments to produce and detect atom correlations in a
degenerate or nearly degenerate gas of neutral atoms. First we treat the atomic
analog of the celebrated Hanbury Brown Twiss experiment, in which atom
correlations result simply from interference effects without any atom
interactions.We have performed this experiment for both bosons and fermions.
Next we show how atom interactions produce correlated atoms using the atomic
analog of spontaneous four-wavemixing. Finally, we briefly mention experiments
on a one dimensional gas on an atom chip in which correlation effects due to
both interference and interactions have been observed.


title: The Quantum Cocktail Party

abstract:
  We consider the problem of decorrelating states of coupled quantum systems.
The decorrelation can be seen as separation of quantum signals, in analogy to
the classical problem of signal-separation rising in the so-called
cocktail-party context. The separation of signals cannot be achieved perfectly,
and we analyse the optimal decorrelation map in terms of added noise in the
local separated states. Analytical results can be obtained both in the case of
two-level quantum systems and for Gaussian states of harmonic oscillators.


title: Quantum probabilities for time-extended measurements

abstract:
  We study the probability assignment for the outcomes of time-extended
measurements. We construct the class-operator that incorporates the information
about a generic time-smeared quantity. These class-operators are employed for
the construction of Positive-Operator-Valued-Measures for the time-averaged
quantities. The scheme highlights the distinction between velocity and momentum
in quantum theory. Propositions about velocity and momentum are represented by
different class-operators, hence they define different probability measures. We
provide some examples, we study the classical limit and we construct
probabilities for generalized time-extended phase space variables.


title: Information transfer rates in spin quantum channels

abstract:
  We analyze the communication efficiency of quantum information transfer along
unmodulated spin chains by computing the communication rates of various
protocols. The effects of temporal correlations are discussed, showing that
they can be exploited to boost the transmission efficiency.


title: Path integrals and boundary conditions

abstract:
  The path integral approach to quantum mechanics provides a method of
quantization of dynamical systems directly from the Lagrange formalism. In
field theory the method presents some advantages over Hamiltonian quantization.
The Lagrange formalism preserves relativistic covariance which makes the
Feynman method very convenient to achieve the renormalization of field theories
both in perturbative and non-perturbative approaches. However, when the systems
are confined in bounded domains we shall show that the path integral approach
does not describe the most general type of boundary conditions. Highly
non-local boundary conditions cannot be described by Feynman's approach. We
analyse in this note the origin of this problem in quantum mechanics and its
implications for field theory.


title: Concurrence via entanglement witnesses

abstract:
  We derive an experimentally observable lower bound on concurrence of mixed
quantum states in terms of an entanglement witness, relating measurements on
single states with those on two copies.


title:
Observation of twin beam correlations and quadrature entanglement by
  frequency doubling in a two-port resonator

abstract:
  We demonstrate production of quantum correlated and entangled beams by second
harmonic generation in a nonlinear resonator with two output ports. The output
beams at wavelength 428.5 nm exhibit 0.9 dB of nonclassical intensity
correlations and 0.3 dB of entanglement.


title: Fidelity, entanglement, and information complementarity relation

abstract:
  We investigate the dynamics of information in isolated multi-qubit systems.
It is shown that information is in not only local form but also nonlocal form.
We apply a measure of local information based on fidelity, and demonstrate that
nonlocal information can be directly related to some appropriate well defined
entanglement measures. Under general unitary transformations, local and
nonlocal information will exhibit unambiguous complementary behavior with the
total information conserved.


title: Information-Theoretic Measure of Genuine Multi-Qubit Entanglement

abstract:
  We consider pure quantum states of N qubits and study the genuine N-qubit
entanglement that is shared among all the N qubits. We introduce an
information-theoretic measure of genuine N-qubit entanglement based on
bipartite partitions. When N is an even number, this measure is presented in a
simple formula, which depends only on the purities of the partially reduced
density matrices. It can be easily computed theoretically and measured
experimentally. When N is an odd number, the measure can also be obtained in
principle.


title: Secure Controlled Teleportation

abstract:
  Several protocols for controlled teleportation were suggested by Yang, Chu,
and Han [PRA 70, 022329 (2004)]. In these protocols, Alice teleports qubits (in
an unknown state) to Bob iff a controller allows it. We view this problem in
the perspective of secure multi-party quantum computation. We show that the
suggested entanglement-efficient protocols for $m$-qubit controlled
teleportation are open to cheating; Alice and Bob may teleport $(m-1)$-qubits
of quantum information, out of the controllers' control. We conjecture that the
straightforward protocol for controlled teleportation, which requires each
controller to hold $m$ entangled qubits, is optimal. We prove this conjecture
for a limited, but interesting, subset of protocols.


title: Anzatz of quantum correlation and disentanglement problem

abstract:
  Pedagogical introduction into the problem of the mathematical description of
the quantum correlation (entanglement) of composite quantum systems is
represented. The notion is substantiated about the fact that the conventional
algorithm of the reduction of von Neumann in the description of the dynamics of
the observed subsyatem is not universal and corresponds only to the case of
maximum macroscopicity of the unobservable subsystem. Is clearly shown the
sense of the algorithm of the correlated reduction proposed, which minimally
changes the entropy of composite system.


title: Quantum Communication with Quantum Dot Spins

abstract:
  Single electron spins in quantum dots are attractive for quantum
communication because of their expected long coherence times. We propose a
method to create entanglement between two remote spins based on the coincident
detection of two photons emitted by the dots. Local nodes of several qubits can
be realized using the dipole-dipole interaction between trions in neighboring
dots and spectral addressing, allowing the realization of quantum repeater
protocols. We have performed a detailed feasibility study of our proposal based
on tight-binding calculations of quantum dot properties.


title: Transient localization in the kicked Rydberg atom

abstract:
  We investigate the long-time limit of quantum localization of the kicked
Rydberg atom. The kicked Rydberg atom is shown to possess in addition to the
quantum localization time $\tau_L$ a second cross-over time $t_D$ where quantum
dynamics diverges from classical dynamics towards increased instability. The
quantum localization is shown to vanish as either the strength of the kicks at
fixed principal quantum number or the quantum number at fixed kick strength
increases. The survival probability as a function of frequency in the transient
localization regime $\tau_L<t<t_D$ is characterized by highly irregular,
fractal-like fluctuations.


title: Faster than Hermitian Quantum Mechanics

abstract:
  Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a
Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into
|psi_F>. Consider the following quantum brachistochrone problem: Subject to the
constraint that the difference between the largest and smallest eigenvalues of
H is held fixed, which H achieves this transformation in the least time tau?
For Hermitian Hamiltonians tau has a nonzero lower bound. However, among
non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint,
tau can be made arbitrarily small without violating the time-energy uncertainty
principle. This is because for such Hamiltonians the path from |psi_I> to
|psi_F> can be made short. The mechanism described here is similar to that in
general relativity in which the distance between two space-time points can be
made small if they are connected by a wormhole. This result may have
applications in quantum computing.


title:
Measuring photon anti-bunching from continuous variable sideband
  squeezing

abstract:
  We present a technique for measuring the second-order coherence function
$g^{(2)}(\tau)$ of light using a Hanbury-Brown Twiss intensity interferometer
modified for homodyne detection. The experiment was performed entirely in the
continuous variable regime at the sideband frequency of a bright carrier field.
We used the setup to characterize $g^{(2)}(\tau)$ for thermal and coherent
states, and investigated its immunity to optical loss. We measured
$g^{(2)}(\tau)$ of a displaced squeezed state, and found a best anti-bunching
statistic of $g^{(2)}(0) = 0.11 \pm 0.18$.


title: An Entanglement-Based Protocol For Strong Coin Tossing With Bias 1/4

abstract:
  In the literature, strong coin tossing protocols based on bit commitment have
been proposed. Here we examine a protocol that instead tries to achieve the
task by sharing entanglement securely. The protocol uses only qubits, and has
bias 1/4. This is equal to the best known bias for bit commitment based
schemes.


title: A random walk approach to quantum algorithms

abstract:
  The development of quantum algorithms based on quantum versions of random
walks is placed in the context of the emerging field of quantum computing.
Constructing a suitable quantum version of a random walk is not trivial: pure
quantum dynamics is deterministic, so randomness only enters during the
measurement phase, i.e., when converting the quantum information into classical
information. The outcome of a quantum random walk is very different from the
corresponding classical random walk, due to interference between the different
possible paths. The upshot is that quantum walkers find themselves further from
their starting point on average than a classical walker, and this forms the
basis of a quantum speed up that can be exploited to solve problems faster.
Surprisingly, the effect of making the walk slightly less than perfectly
quantum can optimize the properties of the quantum walk for algorithmic
applications. Looking to the future, with even a small quantum computer
available, development of quantum walk algorithms might proceed more rapidly
than it has, especially for solving real problems.


title: Generic Quantum Ratchet Accelerator with Full Classical Chaos

abstract:
  A simple model of quantum ratchet transport that can generate unbounded
linear acceleration of the quantum ratchet current is proposed, with the
underlying classical dynamics fully chaotic. The results demonstrate that
generic acceleration of quantum ratchet transport can occur with any type of
classical phase space structure. The quantum ratchet transport with full
classical chaos is also shown to be very robust to noise due to the large
linear acceleration afforded by the quantum dynamics. One possible experiment
allowing observation of these predictions is suggested.


title: Optimal Control for Generating Quantum Gates in Open Dissipative Systems

abstract:
  Optimal control methods for implementing quantum modules with least amount of
relaxative loss are devised to give best approximations to unitary gates under
relaxation. The potential gain by optimal control using relaxation parameters
against time-optimal control is explored and exemplified in numerical and in
algebraic terms: it is the method of choice to govern quantum systems within
subspaces of weak relaxation whenever the drift Hamiltonian would otherwise
drive the system through fast decaying modes. In a standard model system
generalising decoherence-free subspaces to more realistic scenarios,
openGRAPE-derived controls realise a CNOT with fidelities beyond 95% instead of
at most 15% for a standard Trotter expansion. As additional benefit it requires
control fields orders of magnitude lower than the bang-bang decouplings in the
latter.


title:
Quantum Optical Systems for the Implementation of Quantum Information
  Processing

abstract:
  We review the field of Quantum Optical Information from elementary
considerations through to quantum computation schemes. We illustrate our
discussion with descriptions of experimental demonstrations of key
communication and processing tasks from the last decade and also look forward
to the key results likely in the next decade. We examine both discrete (single
photon) type processing as well as those which employ continuous variable
manipulations. The mathematical formalism is kept to the minimum needed to
understand the key theoretical and experimental results.


title: Coherent Spin Dynamics into Space Quantization

abstract:
  We propose a mechanism to describe how a physical quantity, which initially
can take continuous values, is restricted within some discrete values after a
measurement. As an example of the present theory, in which interplay between
coherence of motion and fluctuation from disturbance plays an important role,
we investigate motion of a spin state in a magnetic field. First, we point out
that discrete eigenstates are formed from continuous states as a result of
coherence of precession motion of a spin. Next, by assuming disturbance from
environmental electromagnetic fields, we investigate temporal change of
direction of a spin state by applying the first order perturbation theory and
the Monte Carlo technique. Results of simulations show that the spins, whose
directions are randomly distributed at the initial time, are reoriented toward
only two directions due to fluctuation guided by coherence.


title:
Quantum White Noise and the Master Equation for Gaussian Reference
  States

abstract:
  We modify the Araki-Woods double Fock space construction in order to describe
general squeezed Gaussian states and use this to represent squeezed quantum
stochastic noise processes. Associated master equations are derived.


title: Star products, duality and double Lie algebras

abstract:
  Quantization of classical systems using the star-product of symbols of
observables is discussed. In the star-product scheme an analysis of dual
structures is performed and a physical interpretation is proposed. At the Lie
algebra level duality is shown to be connected to double Lie algebras. The
analysis is specified to quantum tomography. The classical tomographic Poisson
bracket is found.


title: Wave Algorithms: Optimal Database Search and Catalysis

abstract:
  Grover's database search algorithm, although discovered in the context of
quantum computation, can be implemented using any physical system that allows
superposition of states. A physical realization of this algorithm is described
using coupled simple harmonic oscillators, which can be exactly solved in both
classical and quantum domains. Classical wave algorithms are far more stable
against decoherence compared to their quantum counterparts. In addition to
providing convenient demonstration models, they may have a role in practical
situations, such as catalysis.


title:
Quantum random number generator based on photonic emission in
  semiconductors

abstract:
  We report upon a novel principle for realization of a fast nondeterministic
random number generator whose randomness relies on intrinsic randomness of the
quantum physical processes of photonic emission in semiconductors and
subsequent detection by the photoelectric effect. Timing information of
detected photons is used to generate binary random digits-bits. The bit
extraction method based on restartable clock theoretically eliminates both bias
and autocorrelation while reaching efficiency of almost 0.5 bits per random
event. A prototype has been built and statistically tested.


title: Entanglement of Collectively Interacting Harmonic Chains

abstract:
  We study the ground-state entanglement of one-dimensional harmonic chains
that are coupled to each other by a collective interaction as realized e.g. in
an anisotropic ion crystal. Due to the collective type of coupling, where each
chain interacts with every other one in the same way,the total system shows
critical behavior in the direction orthogonal to the chains while the isolated
harmonic chains can be gapped and non-critical. We derive lower and most
importantly upper bounds for the entanglement,quantified by the von Neumann
entropy, between a compact block of oscillators and its environment. For
sufficiently large size of the subsystems the bounds coincide and show that the
area law for entanglement is violated by a logarithmic correction.


title: On Entangled Multiparticle Systems in Bohmian Theory

abstract:
  Arguments are presented to show that the Bohmianian programme cannot be
implemented for entangled multiparticle systems in general, analogous to the
case of many-particle systems in classical mechanics. We give two examples.


title: Superbroadcasting of harmonic oscillators mixed states

abstract:
  We consider the problem of broadcasting quantum information encoded in the
displacement parameter for an harmonic oscillator, from N to M>N copies of a
thermal state. We show the Weyl-Heisenberg covariant broadcasting map that
optimally reduces the thermal photon number, and we prove that it minimizes the
noise in conjugate quadratures at the output for general input states. We find
that from two input copies broadcasting is feasible, with the possibility of
simultaneous purification (superbroadcasting).


title: Robust quantum searching with spontaneously decaying qubits

abstract:
  We present a modification of the standard single-item quantum search
procedure that acquires robustness from spontaneous decay of the qubits. This
damps the usual oscillation of populations, driving the system to a steady
state with a strongly enhanced population of the solution. Numerical evaluation
of the steady state was performed for up to 36 qubits. The huge size of the
state space in our analysis is dealt with by exploiting a symmetry in the
master equation that reduces the scaling of computer resources from exponential
to polynomial. Based on these results we estimate that an error-free solution
can be retrieved from the steady state after O(log log N) repetitions, with
near-unit probability. This brings the overall scaling to O(sqrt{N} log log N),
only slightly worse than for the ideal quantum case.


title:
Complementarity and Uncertainty in Mach-Zehnder Interferometry and
  beyond

abstract:
  A coherent account of the connections and contrasts between the principles of
com- plementarity and uncertainty is developed starting from a survey of the
various formalizations of these principles. The conceptual analysis is
illustrated by means of a set of experimental schemes based on Mach-Zehnder
interferometry. In particu- lar, path detection via entanglement with a probe
system and (quantitative) quan- tum erasure are exhibited to constitute
instances of joint unsharp measurements of complementary pairs of physical
quantities, path and interference observables. The analysis uses the
representation of observables as positive-operator-valued measures (POVMs). The
reconciliation of complementary experimental options in the sense of
simultaneous unsharp preparations and measurements is expressed in terms of
uncertainty relations of different kinds. The feature of complementarity,
manifest in the present examples in the mutual exclusivity of path detection
and interference observation, is recovered as a limit case from the appropriate
uncertainty relation. It is noted that the complementarity and uncertainty
principles are neither completely logically independent nor logical
consequences of one another. Since entanglement is an instance of the
uncertainty of quantum properties (of compound systems), it is moot to play out
uncertainty and entanglement against each other as possible mechanisms
enforcing complementarity.


title:
On the numerical characterization of atmospheric effects on an
  Earth-Space quantum communication channel

abstract:
  Earth-Space quantum communication is the next challenge of
telecommunications. As long as we want to know the outcome of a quantum
communication by means of single photons, we have to face the interaction
between a single photon and the atmosphere. In this brief article, we want to
report some preliminary simulation results for realistic and generic
atmospheric conditions.


title: NPT Bound Entanglement- The Problem Revisited

abstract:
  Recently [quant-ph/0608250] again created a lot of interest to prove the
existence of bound entangled states with negative partial transpose (NPT) in
any $d \times d (d \geq 3)$ Hilbert space. However the proof in
quant-ph/0608250 is not complete but it shows some interesting properties of
the Schmidt rank two states. In this work we are trying to probe the problem in
a different angle considering the work by D\"{u}r et.al [Phys. Rev. A, 61,
062313(2000)]. We have assumed that the Schmidt rank two states should satisfy
some bounds. Under some assumptions with these bounds one could prove the
existence of NPT bound entangled states. We particularly discuss the case of
two copy undistillability of the conjectured family of NPT states. Obviously
the class of NPT bound entangled states belong to the class of conjectured to
be bound entangled states by Divincenzo et.al [Phys. Rev. A, 61, 062312(2000)]
and by D\"{u}r et.al [Phys. Rev. A, 61, 062313(2000)]. However the problem of
existence of NPT bound entangled states still remain open.


title:
Computational Difficulty of Global Variations in the Density Matrix
  Renormalization Group

abstract:
  The density matrix renormalization group (DMRG) approach is arguably the most
successful method to numerically find ground states of quantum spin chains. It
amounts to iteratively locally optimizing matrix-product states, aiming at
better and better approximating the true ground state. To date, both a proof of
convergence to the globally best approximation and an assessment of its
complexity are lacking. Here we establish a result on the computational
complexity of an approximation with matrix-product states: The surprising
result is that when one globally optimizes over several sites of local
Hamiltonians, avoiding local optima, one encounters in the worst case a
computationally difficult NP-hard problem (hard even in approximation). The
proof exploits a novel way of relating it to binary quadratic programming. We
discuss intriguing ramifications on the difficulty of describing quantum
many-body systems.

categories: quant-ph cond-mat.stat-mech math-ph math.MP


title:
Efficient algorithm for multi-qudit twirling for ensemble quantum
  computation

abstract:
  We present an efficient algorithm for twirling a multi-qudit quantum state.
The algorithm can be used for approximating the twirling operation in an
ensemble of physical systems in which the systems cannot be individually
accessed. It can also be used for computing the twirled density matrix on a
classical computer. The method is based on a simple non-unitary operation
involving a random unitary. When applying this basic building block
iteratively, the mean squared error of the approximation decays exponentially.
In contrast, when averaging over random unitary matrices the error decreases
only algebraically. We present evidence that the unitaries in our algorithm can
come from a very imperfect random source or can even be chosen
deterministically from a set of cyclically alternating matrices. Based on these
ideas we present a quantum circuit realizing twirling efficiently.


title: Generation and transfer of single photons on a photonic crystal chip

abstract:
  We present a basic building block of a quantum network consisting of a
quantum dot coupled to a source cavity, which in turn is coupled to a target
cavity via a waveguide. The single photon emission from the high-Q/V source
cavity is characterized by a twelve-fold spontaneous emission (SE) rate
enhancement that results in a SE coupling efficiency near 0.98 into the source
cavity mode. Single photons are efficiently transferred into the target cavity
through the waveguide, with a source/target field intensity ratio of 0.12 (up
to 0.49 observed in other structures without coupled quantum dots). This system
shows great promise as a building block of future on-chip quantum information
processing systems.


title: How to Measure the Quantum State of Collective Atomic Spin Excitation

abstract:
  The spin state of an atomic ensemble can be viewed as two bosonic modes,
i.e., a quantum signal mode and a $c$-numbered ``local oscillator'' mode when
large numbers of spin-1/2 atoms are spin-polarized along a certain axis and
collectively manipulated within the vicinity of the axis. We present a concrete
procedure which determines the spin-excitation-number distribution, i.e., the
diagonal elements of the density matrix in the Dicke basis for the collective
spin state. By seeing the collective spin state as a statistical mixture of the
inherently-entangled Dicke states, the physical picture of its multi-particle
entanglement is made clear.


title:
Characterizing multiparticle entanglement in symmetric N-qubit states
  via negativity of covariance matrices

abstract:
  We show that higher order inter-group covariances involving even number of
qubits are necessarily positive semidefinite for N qubit separable states,
which are completely symmetric under permutations of the qubits. This
identification leads to a family of sufficient conditions of inseparability
based on the negativity of 2kth order inter-group covariance matrices of
symmetric N-qubit systems. These conditions have a simple structure and detect
entanglement in all even partitions of the symmetric multiqubit system. The
observables involved are feasible experimental quantities and do not demand
full state determination through quantum state tomography.


title:
Fuzzy Space-Time and Phase Space Structure as approach to
  Nonrelativistic Quantization

abstract:
  Quantum Space-Time and Phase Space with fuzzy geometric structure are studied
as possible formalism for quantization of massive particles and fields. In this
approach the state of nonrelativistic particle m described by the fuzzy point
of fuzzy (weakly) ordered Manifold X. Due to m partial ordering in X m
coordinate x principal uncertainty is generic in this ansatz. It's shown that
in 1+1 dimension such Fuzzy Mechanics (FM) is equivalent to Path Integral
formalism of Quantum Mechanics (QM).


title:
Investigation of a quantum mechanical detector model for moving,
  spread-out particles

abstract:
  We investigate a fully quantum mechanical spin model for the detection of a
moving particle. This model, developed in earlier work, is based on a
collection of spins at fixed locations and in a metastable state, with the
particle locally enhancing the coupling of the spins to an environment of
bosons. Appearance of bosons from particular spins signals the presence of the
particle at the spin location, and the first boson indicates its arrival. The
original model used discrete boson modes. Here we treat the continuum limit,
under the assumption of the Markov property, and calculate the arrival-time
distribution for a particle to reach a specific region.


title:
Path Integral Approach for Superintegrable Potentials on Spaces of
  Non-constant Curvature: II. Darboux Spaces DIII and DIV

abstract:
  This is the second paper on the path integral approach of superintegrable
systems on Darboux spaces, spaces of non-constant curvature. We analyze in the
spaces $\DIII$ and $\DIV$ five respectively four superintegrable potentials,
which were first given by Kalnins et al. We are able to evaluate the path
integral in most of the separating coordinate systems, leading to expressions
for the Green functions, the discrete and continuous wave-functions, and the
discrete energy-spectra. In some cases, however, the discrete spectrum cannot
be stated explicitly, because it is determined by a higher order polynomial
equation.
  We show that also the free motion in Darboux space of type III can contain
bound states, provided the boundary conditions are appropriate. We state the
energy spectrum and the wave-functions, respectively.


title:
Shannon entropies of atomic structure factors, off-diagonal order and
  electron correlation

abstract:
  Shannon entropies of one- and two-electron atomic structure factors in the
position and momentum representations are used to examine the behavior of the
off-diagonal elements of density matrices with respect to the uncertainty
principle and to analyze the effects of electron correlation on off-diagonal
order. We show that electron correlation induces off-diagonal order in position
space which is characterized by larger entropic values. Electron correlation in
momentum space is characterized by smaller entropic values as information is
forced into regions closer to the diagonal. Related off-diagonal correlation
functions are also discussed.


title: On infinite matrices, Schur products, and operator measures

abstract:
  Measures with values in the set of sesquilinear forms on a subspace of a
Hilbert space are of interest in quantum mechanics, since they can be
interpreted as observables with only a restricted set of possible measurement
preparations. In this paper, we consider the question under which conditions
such a measure extends to an operator valued measure, in the concrete setting
where the measure is defined on the Borel sets of the interval $[0,2\pi)$ and
is covariant with respect to shifts. In this case, the measure is characterized
with a single infinite matrix, and it turns out that a basic sufficient
condition for the extensibility is that the matrix be a Schur multiplier.
Accordingly, we also study the connection between the extensibility problem and
the theory of Schur multipliers. In particular, we define some new norms for
Schur multipliers.


title:
Hadamard NMR spectroscopy for two-dimensional quantum information
  processing and parallel search algorithms

abstract:
  Hadamard spectroscopy has earlier been used to speed-up multi-dimensional NMR
experiments. In this work we speed-up the two-dimensional quantum computing
scheme, by using Hadamard spectroscopy in the indirect dimension, resulting in
a scheme which is faster and requires the Fourier transformation only in the
direct dimension. Two and three qubit quantum gates are implemented with an
extra observer qubit. We also use one-dimensional Hadamard spectroscopy for
binary information storage by spatial encoding and implementation of a parallel
search algorithm.


title: Hidden variables or hidden theories?

abstract:
  We show that a modified Relativity Principle could explain in a "classical"
way the strange correlations of entangled photons. We propose a gedanken
experiment with balls and boxes that predicts the same distribution of
probability of the Quantum Mechanics in the case of the EPR experiment with a
pair of entangled photons meeting a pair of polarizers. In the light of this
gedanken experiment, we find an alternative description of the real EPR
experiment postulating the existence of two observers (one for each polarizer)
embedded in two locally anisotropic spacetimes. In our model there is no need
to invoke quantum non separability or instantaneous action at distance.


title:
Studies on Entanglement in Nuclear and Electron Spin Systems for Quantum
  Computing

abstract:
  In this work, we have been working on the concept of quantum entanglement. At
first, we studied the theory of entanglement in its characterization and
measurement, introducing a new scheme for detection of entanglement. The new
approach links molecular-spin entities involving nuclear spins to quantum
computing as more appropriate physical systems of interest. Then, we continued
with the realization of entanglement in experiments. NMR has been the first
choice due to its well approved advantages for quantum computing. NMR, however,
has not been an appropriate system for demonstrating entangled states. Through
a mathematical proof, NMR with low spin polarization has been invalidated for
true implementations of non-local quantum algorithms, particularly supserdense
coding. The point is that high spin polarization is inevitably required to
acquire entanglement while in the current NMR it has been a formidable task to
get highly polarized nuclear spins. In order to acquire high spin polarization,
introducing electron spins can be much effective because of its
three-order-of-magnitude larger gyromagnetic ratio compared to nuclear spins.
Electron Nuclear DOuble Resonance (ENDOR) is spin manipulation technology that
enables us to deal with both electron and nuclear spins. Thus, in this context,
it can be more appropriate device for quantum computing. We emphasize that
(pseudo)entanglement and interconversion between the entangled states have been
realized with ENDOR on extremely stable organic molecular-spin entities. The
required experimental conditions to obtain true quantum entanglement are also
discussed. The appropriate entanglement witness for the corresponding ensemble
quantum computing is introduced and examined.


title:
Groverian entanglement measure and evolution of entanglement in search
  algorithm for n(=3 and 5)-qubit systems with real coefficients

abstract:
  Evolution of entanglement with the proceeding of quantum algorithms affects
the outcome of the algorithm. Particularly, the performance of Grover's search
algorithm gets worsened if the initial state of the algorithm is an entangled
one. The success probability of search can be seen as an operational measure of
entanglement. This paper demonstrates an entanglement measure based on the
performance of Grover's search algorithm for three and five qubit systems. We
also show that although the overall pattern shows growth of entanglement, its
rise to a maximum and then consequent decay, the presence of local fluctuation
within each iterative step is likely.


title: Hybrid Parallel Quantum Key Distribution Protocol

abstract:
  The practical realizations of BB84 quantum key distribution protocol using
single-photon or weak coherent states have normally presented low efficiency,
in the meaning that most bits sent by Alice are not useful for the final key.
In this work, we show an optical setup to improve the transmission rate of
useful bits putting together two ideas, parallel quantum key distribution and
physical encryption using mesoscopic coherent states. The final result is a
four time faster quantum key distribution setup.


title:
Renormalization of expansions for Regge trajectories of the
  Schr\"odinger equation

abstract:
  A recursion technique for the renormalization of semiclassical expansions for
the Regge trajectories of bound states of the Schr\"odinger equation is
developed. As an application of the proposed technique, the two-parameter
renormalization scheme of the Regge trajectories for the bound states in the
Martin potential is considered.


title:
Simple proof of equivalence between adiabatic quantum computation and
  the circuit model

abstract:
  We prove the equivalence between adiabatic quantum computation and quantum
computation in the circuit model. An explicit adiabatic computation procedure
is given that generates a ground state from which the answer can be extracted.
The amount of time needed is evaluated by computing the gap. We show that the
procedure is computationally efficient.


title: Generalized Coherent States as Preferred States of Open Quantum Systems

abstract:
  We investigate the connection between quasi-classical (pointer) states and
generalized coherent states (GCSs) within an algebraic approach to Markovian
quantum systems (including bosons, spins, and fermions). We establish
conditions for the GCS set to become most robust by relating the rate of purity
loss to an invariant measure of uncertainty derived from quantum Fisher
information. We find that, for damped bosonic modes, the stability of canonical
coherent states is confirmed in a variety of scenarios, while for systems
described by (compact) Lie algebras stringent symmetry constraints must be
obeyed for the GCS set to be preferred. The relationship between GCSs,
minimum-uncertainty states, and decoherence-free subspaces is also elucidated.


title:
New Model of One-dimensional Completed Scattering and the Problem of
  Quantum Nonlocality

abstract:
  The origin of nonlocality in quantum mechanics (QM) is analyzed from the
viewpoint of our new model of a one-dimensional (1D) completed scattering. Our
study of quantum nonlocality complements those carried out by Volovich and
Khrennikov. They pointed to an unphysical character of nonlocality in Bell's
theorem whose context does not contain the very structure of the space-time.
However, there is another reason leading to nonlocality in QM. The existing
model of a 1D completed scattering evidences that QM, as it stands, even with a
proper space-time context, contradicts special relativity. By our model this
scattering process represents an entanglement of two coherently evolved
alternative sub-processes, transmission and reflection; whose characteristics
are measured well after the scattering event. Quantum nonlocality appears in
this problem due to the inconsistency of the superposition principle with the
corpuscular properties of a particle. It can take part only in one of the
sub-processes. However the superposition principle allows introducing
observables common for them. In the fresh wording, this principle must forbid
introducing observables for entangled states.


title: Qudit surface codes and gauge theory with finite cyclic groups

abstract:
  Surface codes describe quantum memory stored as a global property of
interacting spins on a surface. The state space is fixed by a complete set of
quasi-local stabilizer operators and the code dimension depends on the first
homology group of the surface complex. These code states can be actively
stabilized by measurements or, alternatively, can be prepared by cooling to the
ground subspace of a quasi-local spin Hamiltonian. In the case of spin-1/2
(qubit) lattices, such ground states have been proposed as topologically
protected memory for qubits. We extend these constructions to lattices or more
generally cell complexes with qudits, either of prime level or of level
$d^\ell$ for $d$ prime and $\ell \geq 0$, and therefore under tensor
decomposition, to arbitrary finite levels. The Hamiltonian describes an exact
$\mathbb{Z}_d\cong\mathbb{Z}/d\mathbb{Z}$ gauge theory whose excitations
correspond to abelian anyons. We provide protocols for qudit storage and
retrieval and propose an interferometric verification of topological order by
measuring quasi-particle statistics.


title:
Optical state engineering, quantum communication, and robustness of
  entanglement promiscuity in three-mode Gaussian states

abstract:
  We present a novel, detailed study on the usefulness of three-mode Gaussian
states states for realistic processing of continuous-variable quantum
information, with a particular emphasis on the possibilities opened up by their
genuine tripartite entanglement. We describe practical schemes to engineer
several classes of pure and mixed three-mode states that stand out for their
informational and/or entanglement properties. In particular, we introduce a
simple procedure -- based on passive optical elements -- to produce pure
three-mode Gaussian states with {\em arbitrary} entanglement structure (upon
availability of an initial two-mode squeezed state). We analyze in depth the
properties of distributed entanglement and the origin of its sharing structure,
showing that the promiscuity of entanglement sharing is a feature peculiar to
symmetric Gaussian states that survives even in the presence of significant
degrees of mixedness and decoherence. Next, we discuss the suitability of the
considered tripartite entangled states to the implementation of quantum
information and communication protocols with continuous variables. This will
lead to a feasible experimental proposal to test the promiscuous sharing of
continuous-variable tripartite entanglement, in terms of the optimal fidelity
of teleportation networks with Gaussian resources. We finally focus on the
application of three-mode states to symmetric and asymmetric telecloning, and
single out the structural properties of the optimal Gaussian resources for the
latter protocol in different settings. Our analysis aims to lay the basis for a
practical quantum communication with continuous variables beyond the bipartite
scenario.

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


title: Deformed Geometric Algebra and Supersymmetric Quantum Mechanics

abstract:
  Deforming the algebraic structure of geometric algebra on the phase space
with a Moyal product leads naturally to supersymmetric quantum mechanics in the
star product formalism.


title:
On bipartite pure-state entanglement structure in terms of
  disentanglement

abstract:
  Schroedinger's disentanglement [E. Schroedinger, Proc. Cambridge Phil. Soc.
31, 555 (1935)], i. e., remote state decomposition, as a physical way to study
entanglement, is carried one step further with respect to previous work in
investigating the qualitative side of entanglement in any bipartite state
vector. Remote measurement (or, equivalently, remote orthogonal state
decomposition) from previous work is generalized to remote linearly-independent
complete state decomposition both in the non-selective and the selective
versions. The results are displayed in terms of commutative square diagrams,
which show the power and beauty of the physical meaning of the (antiunitary)
correlation operator inherent in the given bipartite state vector. This
operator, together with the subsystem states (reduced density operators),
constitutes the so-called correlated subsystem picture. It is the central part
of the antilinear representation of a bipartite state vector, and it is a kind
of core of its entanglement structure. The generalization of previously
elaborated disentanglement expounded in this article is a synthesis of the
antilinear representation of bipartite state vectors, which is reviewed, and
the relevant results of Cassinelli et al. [J. Math. Analys. and Appl., 210, 472
(1997)] in mathematical analysis, which are summed up. Linearly-independent
bases (finite or infinite) are shown to be almost as useful in some quantum
mechanical studies as orthonormal ones. Finally, it is shown that
linearly-independent remote pure-state preparation carries the highest
probability of occurrence. This singles out linearly-independent remote
influence from all possible ones.


title: The Generation and Exchange of Entanglement via Zeeman Effect

abstract:
  In this paper we show a new way to generate entanglement via two identical
three-level atoms splitting in the magnetic field interacting with the cavity
field. By the system we investigate, We can acquire the EPR state,
multi-dimensional entangled states etc. which are more stable than usual
realization by high-energy-level Rydberg atoms and we can realize the local
exchange operator too. We also achieve the goal of maintaining long- time
entanglement between atoms. At last, by using the procedure of local exchange,
we put forward an experimental scheme for quantum feedback.


title:
Quantum dynamics of electronic excitations in biomolecular chromophores:
  role of the protein environment and solvent

abstract:
  We consider continuum dielectric models as minimal models to understand the
effect of a surrounding globular protein and solvent on the quantum dynamics of
electronic excitations in a biological chromophore. We derive expressions for
the frequency dependent spectral density which describes the coupling of the
electronic levels in the chromophore to its environment. The magnitude and
frequency dependence of the spectral density determines whether or not the
quantum dynamics is coherent or incoherent, and thus whether on not one can
observe quantum interference effects such as Rabi oscillations. We find the
contributions to the spectral density from each component of the chromophore
environment: the bulk solvent, protein, and water bound to the protein. The
relative importance of each component to the quantum dynamics of the
chromophore is determined by the dynamics' time scale. Our results provide a
natural explanation and model for the different time scales observed in the
spectral density extracted from the solvation dynamics probed by ultra-fast
laser spectroscopy techniques such as the dynamic Stokes shift and three pulse
photon echo spectroscopy. Our results are used to define under what conditions
the dynamics of the excited chromophore is dominated by the surrounding protein
and when it is dominated by dielectric fluctuations in the solvent. We show
that even when the chromophore is shielded from the solvent by the protein
ultra-fast solvation can be dominated by the solvent. We suggest that the
ultra-fast solvation recently seen in some biological chromophores should not
necessarily be assigned to ultra-fast protein dynamics. Spectral densities
estimated from our continuum models and extracted from experiment suggest that
most quantum dynamics of electronic excitations is incoherent.


title: Maximum observable correlation for a bipartite quantum system

abstract:
  The maximum observable correlation between the two components of a bipartite
quantum system is a property of the joint density operator, and is achieved by
making particular measurements on the respective components. For pure states it
corresponds to making measurements diagonal in a corresponding Schmidt basis.
More generally, it is shown that the maximum correlation may be characterised
in terms of a `correlation basis' for the joint density operator, which defines
the corresponding (nondegenerate) optimal measurements. The maximum coincidence
rate for spin measurements on two-qubit systems is determined to be (1+s)/2,
where s is the spectral norm of the spin correlation matrix, and upper bounds
are obtained for n-valued measurements on general bipartite systems. It is
shown that the maximum coincidence rate is never greater than the computable
cross norm measure of entanglement, and a much tighter upper bound is
conjectured. Connections with optimal state discrimination and entanglement
bounds are briefly discussed.


title: An investigation into why macroscopic systems behave classically

abstract:
  We study why it is quite so hard to make a superposition of superfluid flows
in a Bose-Einstein condensate. To do this we initially investigate the quantum
states of $N$ atoms trapped in a 1D ring with a barrier at one position and a
phase applied around it. We show how macroscopic superpositions can in
principle be produced and investigate factors which affect the superposition.
We then use the Bose-Hubbard model to study an array of Bose-Einstein
condensates trapped in optical potentials and coupled to one another to form a
ring. We derive analytic expressions for the quality of the superposition for
this system, which agrees well with direct diagonalisation of the Hamiltonian
for relatively small numbers of atoms. We show that for macroscopic
superpositions to be realised there are essentially three straightforward
requirements, other than an absence of decoherence, which become harder to
achieve as the system size increases. Firstly, the energies of the two distinct
superfluid states must be sufficiently close. Secondly, coupling between the
two states must be sufficiently strong, and thirdly, other states must be well
separated from those participating in the superposition.


title: Configuration-Space Location of the Entanglement between Two Subsystems

abstract:
  In this paper we address the question: where in configuration space is the
entanglement between two particles located? We present a thought-experiment,
equally applicable to discrete or continuous-variable systems, in which one or
both parties makes a preliminary measurement of the state with only enough
resolution to determine whether or not the particle resides in a chosen region,
before attempting to make use of the entanglement. We argue that this provides
an operational answer to the question of how much entanglement was originally
located within the chosen region. We illustrate the approach in a spin system,
and also in a pair of coupled harmonic oscillators. Our approach is
particularly simple to implement for pure states, since in this case the
sub-ensemble in which the system is definitely located in the restricted region
after the measurement is also pure, and hence its entanglement can be simply
characterised by the entropy of the reduced density operators. For our spin
example we present results showing how the entanglement varies as a function of
the parameters of the initial state; for the continuous case, we find also how
it depends on the location and size of the chosen regions. Hence we show that
the distribution of entanglement is very different from the distribution of the
classical correlations.