title: Rotational Control and Selective Isotope Alignment by Ultrashort Pulses

abstract:
  Strong ultrashort laser pulses give rise to prompt molecular alignment
followed by full, half and quarter quantum revivals of the rotational wave
packets. In Four Wave Mixing (FWM) experiments, we make use of the long
succession of repetitive alignment revivals to demonstrate isotope-selective
alignment and time-resolved discrimination between different isotopic species.
For two isotopes with a commensurate ratio of their moments of inertia, we
observe constructive and destructive interferences of the FWM signals
originating from different isotopes. Such destructive interference serves as an
indication for distinct transient angular distributions of different isotopic
species, paving the way to novel time-resolved analytic techniques, as well as
to robust methods for isotope separation. When two pulses are used, enhancement
or reduction of the degree of rotational excitation and of the corresponding
molecular alignment is observed, depending on the delay between pulses. We
implement the double pulse excitation scheme in a binary isotopic mixture,
enhancing the rotational excitation of one isotopic component while almost
totally reducing the rotational excitation of the other.


title: Inversion of exciton level splitting in quantum dots

abstract:
  The demonstration of degeneracy of the exciton spin states is an important
step towards the production of entangled photons pairs from the biexciton
cascade. We measure the fine structure of exciton and biexciton states for a
large number of single InAs quantum dots in a GaAs matrix; the energetic
splitting of the horizontally and vertically polarised components of the
exciton doublet is shown to decrease as the exciton confinement decreases,
crucially passing through zero and changing sign. Thermal annealing is shown to
reduce the exciton confinement, thereby increasing the number of dots with
splitting close to zero.


title:
Magnetic-field-induced reduction of the exciton polarization splitting
  in InAs quantum dots

abstract:
  By the application of an in-plane magnetic field, we demonstrate control of
the fine structure polarisation splitting of the exciton emission lines in
individual InAs quantum dots. The selection of quantum dots with certain
barrier composition and confinement energies is found to determine the magnetic
field dependent increase or decrease of the separation of the bright exciton
emission lines, and has enabled the splitting to be tuned to zero within the
resolution of our experiments. Observed behaviour allows us to determine
g-factors and exchange splittings for different types of dots.


title: A comment on "A semiconductor source of entangled photons"

abstract:
  When basic tools of quantum information are applied to the quantum tomography
data presented in Nature 439, 179 (2006), none of their devices appears to be a
source of entangled photons.


title: Separable balls around the maximally mixed state for a 3-qubit system

abstract:
  We obtain a new lower bound on the radius of the largest ball of separable
unnormalized states around the identity matrix for a 3-qubit system. This also
enables us to improve the corresponding lower bounds for multi-qubit systems.
These bounds are approximately 5% better than the previously known ones. As a
by-product, we compute the radius of the largest ball that fits into the triple
projective tensor product of the unit ball in R^3.


title: Probing BEC phase fluctuations with atomic quantum dots

abstract:
  We consider the dephasing of two internal states |0> and |1> of a trapped
impurity atom, a so-called atomic quantum dot (AQD), where only state |1>
couples to a Bose-Einstein condensate (BEC). A direct relation between the
dephasing of the internal states of the AQD and the temporal phase fluctuations
of the BEC is established. Based on this relation we suggest a scheme to probe
BEC phase fluctuations nondestructively via dephasing measurements of the AQD.
In particular, the scheme allows to trace the dependence of the phase
fluctuations on the trapping geometry of the BEC.


title:
Linear optical scheme for error-free entanglement distribution and a
  quantum repeater

abstract:
  We present a linear optical scheme for error-free distribution of two-photon
polarization entangled Bell states over noisy channels. The scheme can be
applied to an elementary quantum repeater protocol with potentially significant
improvements in efficiency and system complexity. The scheme is based on the
use of polarization and time-bin encoding of photons and can perform
single-pair, single-step purification with currently available technology.


title: Cooperative spin decoherence and population transfer

abstract:
  An ensemble of multilevel atoms is a good candidate for a quantum information
storage device. The information is encrypted in the collective ground state
atomic coherence, which, in the absence of external excitation, is decoupled
from the vacuum and therefore decoherence free. However, in the process of
manipulation of atoms with light pulses (writing, reading), one inadvertently
introduces a coupling to the environment, i.e. a source of decoherence. The
dissipation process is often treated as an independent process for each atom in
the ensemble, an approach which fails at large atomic optical depths where
cooperative effects must be taken into account. In this paper, the cooperative
behavior of spin decoherence and population transfer for a system of two,
driven multilevel-atoms is studied. Not surprisingly, an enhancement in the
decoherence rate is found, when the atoms are separated by a distance that is
small compared to an optical wavelength; however, it is found that this rate
increases even further for somewhat larger separations for atoms aligned along
the direction of the driving field's propagation vector. A treatment of the
cooperative modification of optical pumping rates and an effect of polarization
swapping between atoms is also discussed, lending additional insight into the
origin of the collective decay.


title: Bell Locality and the Nonlocal Character of Nature

abstract:
  It is demonstrated that hidden variables of a certain type follow logically
from a certain local causality requirement (``Bell Locality'') and the
empirically well-supported predictions of quantum theory for the standard
EPR-Bell setup. The demonstrated hidden variables are precisely those needed
for the derivation of the Bell Inequalities. We thus refute the widespread view
that empirical violations of Bell Inequalities leave open a choice of whether
to reject (i) locality or (ii) hidden variables. Both principles are indeed
assumed in the derivation of the inequalities, but since, as we demonstrate
here, (ii) actually follows from (i), there is no choice but to blame the
violation of Bell's Inequality on (i). Our main conclusion is thus that no Bell
Local theory can be consistent with what is known from experiment about the
correlations exhibited by separated particles. Aside from our conclusion being
based on a different sense of locality this conclusion resembles one that has
been advocated recently by H.P. Stapp. We therefore also carefully contrast the
argument presented here to that proposed by Stapp.


title: Insecurity of Quantum Bit Commitment with Secret Parameters

abstract:
  The impossibility proof of unconditionally secure quantum bit commitment is
crucially dependent on the assertion that Bob is not allowed to generate
probability distributions unknown to Alice. This assertion is actually not
meaningful, because Bob can always cheat without being detected. In this paper
we prove that, for any concealing protocol involving secret probability
distributions, there exists a cheating unitary transformation that is known to
Alice. Our result closes a gap in the original impossibility proof.


title: Quantum Cryptography

abstract: Elementary review article on quantum cryptography.


title: Steady State Entanglement in Cavity QED

abstract:
  We investigate steady state entanglement in an open quantum system,
specifically a single atom in a driven optical cavity with cavity loss and
spontaneous emission. The system reaches a steady pure state when driven very
weakly. Under these conditions, there is an optimal value for atom-field
coupling to maximize entanglement, as larger coupling favors a loss port due to
the cavity enhanced spontaneous emission. We address ways to implement
measurements of entanglement witnesses and find that normalized
cross-correlation functions are indicators of the entanglement in the system.
The magnitude of the equal time intensity-field cross correlation between the
transmitted field of the cavity and the fluorescence intensity is proportional
to the concurrence for weak driving fields.


title: Quantization as a dimensional reduction phenomenon

abstract:
  Classical mechanics, in the operatorial formulation of Koopman and von
Neumann, can be written also in a functional form. In this form two Grassmann
partners of time make their natural appearance extending in this manner time to
a three dimensional supermanifold. Quantization is then achieved by a process
of dimensional reduction of this supermanifold. We prove that this procedure is
equivalent to the well-known method of geometric quantization.


title: An anomaly of non-locality

abstract:
  Ever since the work of Bell, it has been known that entangled quantum states
can rise non-local correlations. However, for almost forty years, it has been
assumed that the most non-local states would be the maximally entangled ones.
Surprisingly it is not the case: non-maximally entangled states are generally
more non-local than maximally entangled states for all the measures of
non-locality proposed to date: Bell inequalities, the Kullback-Leibler
distance, entanglement simulation with communication or with non-local boxes,
the detection loophole and efficiency of cryptography. In fact, one can even
find simple examples in low dimensions, confirming that it is not an artefact
of a specifically constructed Hilbert space or topology. This anomaly shows
that entanglement and non-locality are not only different concepts, but also
truly different resources. We review the present knowledge on this anomaly,
point out that Hardy's theorem has the same feature, and discuss the
perspectives opened by these discoveries.


title:
Spin-1/2 square-root operator equation with Coulomb potential - a
  perturbation analysis

abstract:
  Seeking for a relativistic generalisation of the non-relativistic
Schroedinger equation, one very soon arrives at equations with a square-root
operator by having applied the quantum mechanical correspondence principle to
the formula of relativistic energy. The problems of these equations are at
least two fold: when coupled to an electromagnetic field, their relativistic
invariance is not evident or even doubtful and due to their non-local
character, it seems to be that they cannot be maintained mathematically in an
easy way. For spin-1/2 particles, these difficulties can be overcome by the
Dirac equation, which leads e.g. to the prediction of binding energies of an
electron in a hydrogen atom that are compatible with experimental results up to
the forth order of the fine structure constant, inclusively. Ignoring the
problem with relativistic invariance, one may ask, if there exists a
square-root equation, for which one can achieve the same good agreement with
experiments for the latter physical system. It is going to be shown, that the
answer to this question is affirmative and does not exceed the skills obtained
in a course about non-relativistic quantum mechanics and physics of atoms,
respectively.


title:
Thermodynamics analogue for self-trapped spinning-stationary Madelung
  fluid

abstract:
  We discuss two-dimensional Madelung fluid dynamics whose irrotational case
reduces into the Schr\"odinger equation for a free single particle. We show
that the self-trapped spinning-stationary Madelung fluid reported in the
previous paper can be analogically identified as an equilibrium thermodynamics
system. This is done by making correspondence between Shannon entropy over
Madelung density and internal energy to be defined in the main text,
respectively with thermal-entropy and thermal-internal energy of equilibrium
thermodynamics system. This leads us to identify a Madelung fluid analog of
thermal-temperature at the vanishing value of which the stationary Madelung
fluid will be no more spinning and is equal to the quantum mechanical ground
state of a particle trapped inside a cylindrical tube external potential.


title:
Improvement by laser quenching of an "atom diode": a one-way barrier for
  ultra-cold atoms

abstract:
  Different laser devices working as ``atom diodes'' or ``one-way barriers''
for ultra-cold atoms have been proposed recently. They transmit ground state
level atoms coming from one side, say from the left, but reflect them when they
come from the other side. We combine a previous model, consisting of the
stimulated Raman adiabatic passage (STIRAP) from the ground to an excited state
and a state-selective mirror potential, with a localized quenching laser which
produces spontaneous decay back to the ground state. This avoids backwards
motion, provides more control of the decay process and therefore a more compact
and useful device.


title: Hudson's Theorem for finite-dimensional quantum systems

abstract:
  We show that, on a Hilbert space of odd dimension, the only pure states to
possess a non-negative Wigner function are stabilizer states. The Clifford
group is identified as the set of unitary operations which preserve positivity.
The result can be seen as a discrete version of Hudson's Theorem. Hudson
established that for continuous variable systems, the Wigner function of a pure
state has no negative values if and only if the state is Gaussian. Turning to
mixed states, it might be surmised that only convex combinations of stabilizer
states give rise to non-negative Wigner distributions. We refute this
conjecture by means of a counter-example. Further, we give an axiomatic
characterization which completely fixes the definition of the Wigner function
and compare two approaches to stabilizer states for Hilbert spaces of
prime-power dimensions. In the course of the discussion, we derive explicit
formulas for the number of stabilizer codes defined on such systems.


title: Operator Gauge Symmetry in QED

abstract:
  In this paper, operator gauge transformation, first introduced by Kobe, is
applied to Maxwell's equations and continuity equation in QED. The gauge
invariance is satisfied after quantization of electromagnetic fields. Inherent
nonlinearity in Maxwell's equations is obtained as a direct result due to the
nonlinearity of the operator gauge transformations. The operator gauge
invariant Maxwell's equations and corresponding charge conservation are
obtained by defining the generalized derivatives of the first and second kinds.
Conservation laws for the real and virtual charges are obtained too. The
additional terms in the field strength tensor are interpreted as electric and
magnetic polarization of the vacuum.


title: Scaling and Suppression of Anomalous Quantum Decoherence in Ion Traps

abstract:
  We measure and characterize anomalous motional decoherence of an atomic ion
confined in the lowest quantum levels of a novel rf ion trap that features
moveable electrodes. The scaling of decoherence rate with electrode proximity
is measured, and when the electrodes are cooled from 300 K to 150 K, the
decoherence rate is suppressed by an order of magnitude. This provides direct
evidence that anomalous motional decoherence of trapped ions stems from
microscopic noisy potentials on the electrodes. These observations are relevant
to quantum information processing schemes using trapped ions or other
charge-based systems.


title: Error models for mode-mismatch in linear optics quantum computing

abstract:
  One of the most significant challenges facing the development of linear
optics quantum computing (LOQC) is mode-mismatch, whereby photon
distinguishability is introduced within circuits, undermining quantum
interference effects. We examine the effects of mode-mismatch on the parity (or
fusion) gate, the fundamental building block in several recent LOQC schemes. We
derive simple error models for the effects of mode-mismatch on its operation,
and relate these error models to current fault tolerant threshold estimates.


title: Quantum correlations in successive spin measurements

abstract:
  In this paper we present a new approach for testing QM against the realism
aspect of hidden variable theory (HVT). We consider successive measurements of
non-commuting operators on a input spin $s$ state. The key point is that,
although these operators are non-commuting, they act on different states so
that the joint probabilities for the outputs of successive measurements are
well defined. We show that, in this scenario HVT leads to Bell type
inequalities for the correlation between the outputs of successive
measurements. We account for the maximum violation of these inequalities by
quantum correlations by varying spin value and the number of successive
measurements. Our approach can be used to obtain a measure of the deviation of
QM from realism say in terms of the amount of information needed to be
transferred between successive measurements in order to classically simulate
the quantum correlations.


title: A cavity-QED scheme for Heisenberg-limited interferometry

abstract:
  We propose a Ramsey interferometry experiment using an entangled state of N
atoms to reach the Heisenberg limit for the estimation of an atomic phase shift
if the atom number parity is perfectly determined. In a more realistic
situation, due to statistical fluctuations of the atom source and the finite
detection efficiency, the parity is unknown. We then achieve about half the
Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms
which dispersively interact successively with two initially empty microwave
cavities. The scheme does not require very high-Q cavities. An experimental
realization with about ten entangled Rydberg atoms is achievable with state of
art apparatuses.


title: Value statistics of chaotic Wigner function

abstract:
  We study Wigner function value statistics of classically chaotic quantum maps
on compact 2D phase space. We show that the Wigner function statistics of a
random state is a Gaussian, with the mean value becoming negligible compared to
the width in the semi-classical limit. Using numerical example of quantized
sawtooth map we demonstrate that the relaxation of time-dependent Wigner
function statistics, starting from a coherent initial state, takes place on a
logarithmically short log (hbar) time scale.


title:
Error tolerance of two-basis quantum key-distribution protocols using
  qudits and two-way classical communication

abstract:
  We investigate the error tolerance of quantum cryptographic protocols using
$d$-level systems. In particular, we focus on prepare-and-measure schemes that
use two mutually unbiased bases and a key-distillation procedure with two-way
classical communication. For arbitrary quantum channels, we obtain a sufficient
condition for secret-key distillation which, in the case of isotropic quantum
channels, yields an analytic expression for the maximally tolerable error rate
of the cryptographic protocols under consideration. The difference between the
tolerable error rate and its theoretical upper bound tends slowly to zero for
sufficiently large dimensions of the information carriers.


title:
A Quantum Gate as a Physical Model of an Universal Arithmetical
  Algorithm without Church's Undecidability and Godel's Incompleteness

abstract:
  In this work we define an universal arithmetical algorithm, by means of the
standard quantum mechanical formalism, called universal qm-arithmetical
algorithm. By universal qm-arithmetical algorithm any decidable arithmetical
formula (operation) can be decided (realized, calculated. Arithmetic defined by
universal qm-arithmetical algorithm called qm-arithmetic one-to-one corresponds
to decidable part of the usual arithmetic. We prove that in the qm-arithmetic
the undecidable arithmetical formulas (operations) cannot exist (cannot be
consistently defined). Or, we prove that qm-arithmetic has no undecidable
parts. In this way we show that qm-arithmetic, that holds neither Church's
undecidability nor Godel's incompleteness, is decidable and complete. Finally,
we suggest that problems of the foundation of the arithmetic, can be solved by
qm-arithmetic.


title: Optimized production of large Bose Einstein Condensates

abstract:
  We suggest different simple schemes to efficiently load and evaporate a
''dimple'' crossed dipolar trap. The collisional processes between atoms which
are trapped in a reservoir load in a non adiabatic way the dimple. The
reservoir trap can be provided either by a dark SPOT Magneto Optical Trap, the
(aberrated) laser beam itself or by a quadrupolar or quadratic magnetic trap.
Optimal parameters for the dimple are derived from thermodynamical equations
and from loading time, including possible inelastic and Majorana losses. We
suggest to load at relatively high temperature a tight optical trap. Simple
evaporative cooling equations, taking into account gravity, the possible
occurrence of hydrodynamical regime, Feshbach resonance processes and three
body recombination events are given. To have an efficient evaporation the
elastic collisional rate (in s$^{-1}$) is found to be on the order of the
trapping frequency and lower than one hundred times the temperature in
micro-Kelvin. Bose Einstein condensates with more than $10^7$ atoms should be
obtained in much less than one second starting from an usual MOT setup.


title: Information-theoretic temporal Bell inequality and quantum computation

abstract:
  An information-theoretic temporal Bell inequality is formulated to contrast
classical and quantum computations. Any classical algorithm satisfies the
inequality, while quantum ones can violate it. Therefore, the violation of the
inequality is an immediate consequence of the quantumness in the computation.
Furthermore, this approach suggests a notion of temporal nonlocality in quantum
computation.


title: Nonlinear Quantum Gravity

abstract:
  Nonlinear quantum mechanics at the Planck scale can produce nonlocal effects
contributing to resolution of singularities, to cosmic acceleration, and
modified black-hole dynamics, while avoiding the usual causality issues.


title: Transversal laser excitation of atoms in a waveguide

abstract:
  We investigate the effect of a laser shining perpendicularly to a waveguide
channeling two-level atoms. For weak transversal coupling the excitation of
transverse atomic levels occurs at avoided crossings associated with "Rabi
resonances" in which the Rabi frequency coincides with the transition frequency
between the transverse levels.


title: Hamiltonian engineering for quantum systems

abstract:
  We describe different strategies for using a semi-classical controller to
engineer quantum Hamiltonians to solve control problems such as quantum state
or process engineering or optimization of observables.


title:
Demonstration of Temporal Distinguishability in a Four-Photon State and
  a Six-Photon State

abstract:
  An experiment is performed to demonstrate the temporal distinguishability of
a four-photon state and a six-photon state, both from parametric
down-conversion. The experiment is based on a multi-photon interference scheme
in a recent discovered NOON-state projection measurement. By measuring the
visibility of the interference dip, we can distinguish the various scenarios in
the temporal distribution of the pairs and thus quantitatively determine the
degree of temporal (in)distinguishability of a multi-photon state.


title: Inseparability of Quantum Parameters

abstract:
  In this work, we show that 'splitting of quantum information' [6] is an
impossible task from three different but consistent principles of unitarity of
Quantum Mechanics, no-signalling condition and non increase of entanglement
under Local Operation and Classical Communication.


title: Controlling Polar Molecules in Optical Lattices

abstract:
  We investigate theoretically the interaction of polar molecules with optical
lattices and microwave fields. We demonstrate the existence of frequency
windows in the optical domain where the complex internal structure of the
molecule does not influence the trapping potential of the lattice. In such
frequency windows the Franck-Condon factors are so small that near-resonant
interaction of vibrational levels of the molecule with the lattice fields have
a negligible contribution to the polarizability and light-induced decoherences
are kept to a minimum. In addition, we show that microwave fields can induce a
tunable dipole-dipole interaction between ground-state rotationally symmetric
(J=0) molecules. A combination of a carefully chosen lattice frequency and
microwave-controlled interaction between molecules will enable trapping of
polar molecules in a lattice and possibly realize molecular quantum logic
gates. Our results are based on ab initio relativistic electronic structure
calculations of the polar KRb and RbCs molecules combined with calculations of
their rovibrational motion.


title: A semiconductor source of triggered entangled photon pairs?

abstract:
  The realisation of a triggered entangled photon source will be of great
importance in quantum information, including for quantum key distribution and
quantum computation. We show here that: 1) the source reported in ``A
semiconductor source of triggered entangled photon pairs''[1. Stevenson et al.,
Nature 439, 179 (2006)]} is not entangled; 2) the entanglement indicators used
in Ref. 1 are inappropriate, relying on assumptions invalidated by their own
data; and 3) even after simulating subtraction of the significant quantity of
background noise, their source has insignificant entanglement.


title: Computational Complexity of Continuous Variable Quantum Key Distribution

abstract:
  The continuous variable quantum key distribution has been considered to have
the potential to provide high secret key rate. However, in present experimental
demonstrations, the secret key can be distilled only under very small loss
rates. Here, by calculating explicitly the computational complexity with the
channel transmission, we show that under high loss rate it is hard to distill
the secret key in present continuous variable scheme and one of its advantages,
the potential of providing high secret key rate, may therefore be limited.


title: Spherically confined isotropic harmonic oscillator

abstract:
  The generalized pseudospectral Legendre method is used to carry out accurate
calculations of eigenvalues of the spherically confined isotropic harmonic
oscillator with impenetrable boundaries. The energy of the confined state is
found to be equal to that of the unconfined state when the radius of
confinement is suitably chosen as the location of the radial nodes in the
unconfined state. This incidental degeneracy condition is numerically shown to
be valid in general. Further, the full set of pairs of confined states defined
by the quantum numbers [(n+1, \ell) ; (n, \ell+2)], n = 1,2,.., and with the
radius of confinement {(2 \ell +3)/2}^{1/2} a.u., which represents the single
node in the unconfined (1, \ell) state, is found to display a constant energy
level separation exactly given by twice the oscillator frequency. The results
of similar numerical studies on the confined Davidson oscillator with
impenetrable boundary as well as the confined isotropic harmonic oscillator
with finite potential barrier are also reported .The significance of the
numerical results are discussed.


title: A uniform description of electromagnetism and wave mechanics

abstract:
  The paper shows the relationship between the major wave equations in quantum
mechanics and electromagnetism, such as Schroedinger's equation, Dirac's
equation and the Maxwell equations. It is shown that they can be derived in a
striking simple way from a common root. This root is the relativistic
fourvector formulation of the momentum conservation law. This is shown to be a
more attractive starting-point than Einstein's energy relationship for moving
particles, which is commonly used for the purpose. The theory developed gives a
new interpretation for the origin of antiparticles.


title:
Single-qubit operations in the double-donor structure driven by strongly
  detuned optical pulses

abstract:
  We study theoretically the quantum dynamics of an electron in the
singly-ionized double-donor structure in the semiconductor host under the
influence of two strongly detuned laser pulses. This structure can be used as a
charge qubit where the logical states are defined by the lowest two energy
states of the remaining valence electron localized around one or another donor.
The quantum operations are performed via Raman-like transitions between the
localized (qubit) states and the manyfold of states delocalized over the
structure. The possibility of realization of arbitrary single-qubit rotations,
including the phase gate, the NOT gate, and the Hadamard gate, is demonstrated.
The advantages of the off-resonant driving scheme for charge qubit
manipulations are discussed in comparison with the resonant scheme proposed
earlier.


title: Ramsey interferometry with ultracold atoms

abstract:
  We examine the passage of ultracold two-level atoms through two separated
laser fields for the nonresonant case. We show that implications of the atomic
quantized motion change dramatically the behavior of the interference fringes
compared to the semiclassical description of this optical Ramsey
interferometer. Using two-channel recurrence relations we are able to express
the double-laser scattering amplitudes by means of the single-laser ones and to
give explicit analytical results. When considering slower and slower atoms, the
transmission probability of the system changes considerably from an
interference behavior to a regime where scattering resonances prevail. This may
be understood in terms of different families of trajectories that dominate the
overall transmission probability in the weak field or in the strong field
limit.


title: Probability in relativistic quantum mechanics and foliation of spacetime

abstract:
  The conserved probability densities (attributed to the conserved currents
derived from relativistic wave equations) should be non-negative and the
integral of them over an entire hypersurface should be equal to one. To satisfy
these requirements in a covariant manner, the foliation of spacetime must be
such that each integral curve of the current crosses each hypersurface of the
foliation once and only once. In some cases, it is necessary to use
hypersurfaces that are not spacelike everywhere. The generalization to the
many-particle case is also possible.


title: Macroscopic superpositions of superfluid flows

abstract:
  We present a scheme for creating macroscopic superpositions of the direction
of superfluid flow around a loop. Using the Bose-Hubbard model we study an
array of Bose-Einstein condensates trapped in optical potentials and coupled to
one another to form a ring. By rotating the ring so that each particle acquires
on average half a quantum of superfluid flow, it is possible to create a
multiparticle superposition of all the particles rotating and all the particles
stationary. Under certain conditions it is possible to scale up the number of
particles to form a macroscopic superposition. The simplicity of the model has
allowed us to study macroscopic superpositions at an atomic level for different
variables. Here we concentrate on the tunnelling strength between the
potentials. Further investigation remains important, because it could lead us
to making an ultra-precise quantum-limited gyroscope.


title: Local distinguishability with preservation of entanglement

abstract:
  I consider deterministic distinguishability of a set of orthogonal, bipartite
states when only a single copy is available and the parties are restricted to
local operations and classical communication, but with the additional
requirement that entanglement must be preserved in the process. Several general
theorems aimed at characterizing sets of states with which the parties can
succeed in such a task are proven. These include (1) a maximum for the number
of states when the Schmidt rank of every outcome must be at least a given
minimum; (2) an upper bound (equal to the dimension of Hilbert space if
entanglement need not be preserved) for the sum over Schmidt ranks of the
initial states when only one-way classical communication is allowed; and (3)
separately, a necessary and a sufficient condition on the states such that
their original Schmidt ranks can always be preserved. It is shown that our
bound on the sum of Schmidt ranks can be exceeded if two-way communication is
permitted, and this includes the case that entanglement need not be preserved,
so that this sum can exceed the dimension of Hilbert space. Such questions,
concerning how the various results are effected by the resources used by the
parties are addressed for each theorem. This subject is closely related to the
problem of locally purifying an entangled state from a mixed state, which is of
direct relevance to teleportation and dense coding using a mixed-state
resource. In an appendix, I give an extremely simple and transparent proof of
"non-locality without entanglement", a phenomenon originally discussed by
Bennett and co-workers several years ago.


title: Spin Decoherence from Hamiltonian dynamics in Quantum Dots

abstract:
  The dynamics of a spin-1/2 particle coupled to a nuclear spin bath through an
isotropic Heisenberg interaction is studied, as a model for the spin
decoherence in quantum dots. The time-dependent polarization of the central
spin is calculated as a function of the bath-spin distribution and the
polarizations of the initial bath state. For short times, the polarization of
the central spin shows a gaussian decay, and at later times it revives
displaying nonmonotonic time dependence. The decoherence time scale dep ends on
moments of the bath-spin distribuition, and also on the polarization strengths
in various bath-spin channels. The bath polarizations have a tendency to
increase the decoherence time scale. The effective dynamics of the central spin
polarization is shown to be describ ed by a master equation with non-markovian
features.


title:
Simplified approach to double jumps for fluorescing dipole-dipole
  interacting atoms

abstract:
  A simplified scheme for the investigation of cooperative effects in the
quantum jump statistics of small numbers of fluorescing atoms and ions in a
trap is presented. It allows the analytic treatment of three dipole-dipole
interacting four-level systems which model the relevant level scheme of Ba+
ions. For the latter, a huge rate of double and triple jumps was reported in a
former experiment and the huge rate was attributed to the dipole-dipole
interaction. Our theoretical results show that the effect of the dipole-dipole
interaction on these rates is at most 5% and that for the parameter values of
the experiment there is practically no effect. Consequently it seems that the
dipole-dipole interaction can be ruled out as a possible explanation for the
huge rates reported in the experiment.


title:
Large Cross-Phase Modulation between Slow Co-propagating Weak Pulses in
  Rb

abstract:
  We propose a scheme to generate double electromagnetically induced
transparency and optimal cross-phase modulation for two slow, copropagating
pulses with matched group velocities in a single species of atom, namely 87 Rb.
A single pump laser is employed and a homogeneous magnetic field is utilized to
avoid cancellation effects through the nonlinear Zeeman effect. We suggest a
feasible preparational procedure for the atomic initial state to achieve
matched group velocities for both signal fields.


title: Schemes for robust quantum computation with polar molecules

abstract:
  We propose to use a new platform - ultracold polar molecules - for quantum
computing with switchable interactions. The on/off switch is accomplished by
selective excitation of one of the "0" or "1" qubits - long-lived molecular
states - to an "excited" molecular state with a considerably different dipole
moment. We describe various schemes based on this switching of dipolar
interactions where the selective excitation between ground and excited states
is accomplished via optical, micro-wave, or electric fields. We also generalize
the schemes to take advantage of the dipole blockade mechanism when dipolar
interactions are very strong. These schemes can be realized in several recently
proposed architectures.


title:
Connecting the generalized robustness and the geometric measure of
  entanglement

abstract:
  The main goal of this paper is to provide a connection between the
generalized robustness of entanglement ($R_g$) and the geometric measure of
entanglement ($E_{GME}$). First, we show that the generalized robustness is
always higher than or equal to the geometric measure. Then we find a tighter
lower bound to $R_g(\rho)$ based only on the purity of $\rho$ and its maximal
overlap to a separable state. As we will see it is also possible to express
this lower bound in terms of $E_{GME}$.


title: Hamiltonian Oracles

abstract:
  Hamiltonian oracles are the continuum limit of the standard unitary quantum
oracles. In this limit, the problem of finding the optimal query algorithm can
be mapped into the problem of finding shortest paths on a manifold. The study
of these shortest paths leads to lower bounds of the original unitary oracle
problem. A number of example Hamiltonian oracles are studied in this paper,
including oracle interrogation and the problem of computing the XOR of the
hidden bits. Both of these problems are related to the study of geodesics on
spheres with non-round metrics. For the case of two hidden bits a complete
description of the geodesics is given. For n hidden bits a simple lower bound
is proven that shows the problems require a query time proportional to n, even
in the continuum limit. Finally, the problem of continuous Grover search is
reexamined leading to a modest improvement to the protocol of Farhi and
Gutmann.


title:
Continuous variable tripartite entanglement and Einstein-Podolsky-Rosen
  correlations from triple nonlinearities

abstract:
  We compare theoretically the tripartite entanglement available from the use
of three concurrent $\chi^{(2)}$ nonlinearities and three independent squeezed
states mixed on beamsplitters, using the van Loock-Furusawa inequalities. We
also define three-mode generalisations of the Einstein-Podolsky-Rosen paradox
which are an alternative for demonstrating the inseparability of the density
matrix.


title:
High-Purity Telecom-Band Entangled Photon-Pairs via Four-Wave Mixing in
  Dispersion-Shifted Fiber

abstract:
  We have studied the purity of entangled photon-pairs generated in a
dispersion-shifted fiber at various temperatures. Two-photon interference with
visibility > 98% is observed at 77K, without subtraction of the background
Raman photons.


title: Elementary quantum cloning machines

abstract:
  The task of reception of a copy of an arbitrary quantum state with use of a
minimum quantity of quantum operations is considered.


title: 7 dB quadrature squeezing at 860 nm with periodically-poled KTiOPO4

abstract:
  We observed -7.2 dB quadrature squeezing at 860 nm by using a sub-threshold
continuous-wave pumped optical parametric oscillator with a periodically-poled
KTiOPO4 crystal as a nonlinear optical medium. The squeezing level was measured
with the phase of homodyne detection locked at the quadrature. The blue light
induced infrared absorption was not observed in the experiment.


title: Superbroadcasting of conjugate quantum variables

abstract:
  We consider the problem of broadcasting arbitrary states of radiation modes
from N to M>N copies by a map that preserves the average value of the field and
optimally reduces the total noise in conjugate variables. For N>=2 the
broadcasting can be achieved perfectly, and for sufficiently noisy input states
one can even purify the state while broadcasting--the so-called
superbroadcasting. For purification (i.e. M<=N), the reduction of noise is
independent of M. Similar results are proved for broadcasting with
phase-conjugation. All the optimal maps can be implemented by linear optics and
linear amplification.


title: Multi-photon entanglement from distant single photon sources on demand

abstract:
  We describe a scheme that allows for the generation of any desired N-photon
state on demand. Under ideal conditions, this requires only N single photon
sources, laser pulses and linear optics elements. First, the sources should be
initialised with the help of single-qubit rotations and repeat-until-success
two-qubit quantum gates [Lim et al., Phys. Rev. Lett. 95, 030305 (2005)].
Afterwards, the state of the sources can be mapped onto the state of N newly
generated photons whenever needed.


title: A generalized quantum microcanonical ensemble

abstract:
  We discuss a generalized quantum microcanonical ensemble. It describes
isolated systems that are not necessarily in an eigenstate of the Hamilton
operator. Statistical averages are obtained by a combination of a time average
and a maximum entropy argument to resolve the lack of knowledge about initial
conditions. As a result, statistical averages of linear observables coincide
with values obtained in the canonical ensemble. Non-canonical averages can be
obtained by taking into account conserved quantities which are non-linear
functions of the microstate.


title: Beating quantum limits in optomechanical sensor by cavity detuning

abstract:
  We study the quantum limits in an optomechanical sensor based on a detuned
high-finesse cavity with a movable mirror. We show that the radiation pressure
exerted on the mirror by the light in the detuned cavity induces a modification
of the mirror dynamics and makes the mirror motion sensitive to the signal.
This leads to an amplification of the signal by the mirror dynamics, and to an
improvement of the sensor sensitivity beyond the standard quantum limit, up to
an ultimate quantum limit only related to the mechanical dissipation of the
mirror. This improvement is somewhat similar to the one predicted in detuned
signal-recycled gravitational-waves interferometers, and makes a high-finesse
cavity a model system to test these quantum effects


title: The Partition Function in the Wigner-Kirkwood expansion

abstract:
  We study the semiclassical Wigner-Kirkwood (WK) expansion of the partition
function $Z(t)$ for arbitrary even homogeneous potentials, starting from the
Bloch equation. As is well known, the phase-space kernel of $Z$ satisfies the
so-called Uhlenbeck-Beth equation, which depends on the gradients of the
potential. We perform a chain of transformations to obtain novel forms of this
equation that invite analogies with various physical phenomena and formalisms,
such as diffusion processes, the Fokker-Planck equation, and supersymmetric
quantum mechanics.


title:
The Electronic Ground State Energy Problem: a New Reduced Density Matrix
  Approach

abstract:
  We present here a formulation of the electronic ground-state energy in terms
of the second order reduced density matrix, using a duality argument. It is
shown that the computation of the ground-state energy reduces to the search of
the projection of some two-electron reduced Hamiltonian on the dual cone of
$N$-representability conditions. Some numerical results validate the approach,
both for equilibrium geometries and for the dissociation curve of N$_2$.


title:
Inequivalent representations of commutator or anticommutator rings of
  field operators and their applications

abstract:
  Hamiltonian of a system in quantum field theory can give rise to infinitely
many partition functions which correspond to infinitely many inequivalent
representations of the canonical commutator or anticommutator rings of field
operators. This implies that the system can theoretically exist in infinitely
many Gibbs states. The system resides in the Gibbs state which corresponds to
its minimal Helmholtz free energy at a given range of the thermodynamic
variables. Individual inequivalent representations are associated with
different thermodynamic phases of the system. The BCS Hamiltonian of
superconductivity is chosen to be an explicit example for the demonstration of
the important role of inequivalent representations in practical applications.
Its analysis from the inequivalent representations' point of view has led to a
recognition of a novel type of the superconducting phase transition.


title: Electrodynamically trapped Yb+ ions for quantum information processing

abstract:
  Highly efficient, nearly deterministic, and isotope selective generation of
Yb$^+$ ions by 1- and 2-color photoionization is demonstrated. State
preparation and state selective detection of hyperfine states in \ybodd is
investigated in order to optimize the purity of the prepared state and to
time-optimize the detection process. Linear laser cooled Yb$^+$ ion crystals
ions confined in a Paul trap are demonstrated. Advantageous features of
different previous ion trap experiments are combined while at the same time the
number of possible error sources is reduced by using a comparatively simple
experimental apparatus. This opens a new path towards quantum state
manipulation of individual trapped ions, and in particular, to scalable quantum
computing.


title: Entangling oscillators through environment noise

abstract:
  We consider two independent bosonic oscillators immersed in a common bath,
evolving in time with a completely positive, markovian, quasi-free (Gaussian)
reduced dynamics. We show that an initially separated Gaussian state can become
entangled as a result of a purely noisy mechanism. In certain cases, the
dissipative dynamics allows the persistence of these bath induced quantum
correlations even in the asymptotic equilibrium state.


title: Mutual information and electron correlation in momentum space

abstract:
  Mutual information and information entropies in momentum space are proposed
as measures of the non-local aspects of information. Singlet and triplet state
members of the helium isoelectronic series are employed to examine Coulomb and
Fermi correlation, and their manifestations, in both the position and momentum
space mutual information measures. The triplet state measures exemplify that
the magnitude of the spatial correlations relative to the momentum
correlations, depends on, and may be controlled by the strength of the
electronic correlation. Examination of one and two-electron Shannon entropies
in the triplet state series yields a crossover point, which is characterized by
a localized momentum density. The mutual information density in momentum space
illustrates that this localization is accompanied by strong correlation at
small values of $p$.


title:
Klein-Gordon and square-root operator equations for two-spinors and
  scalars: perturbation calculations for hydrogen-like systems

abstract:
  There exists a Klein-Gordon-like equation for a spin-1/2 particle in an
electromagnetic field with 2-spinors as wave functions that is a direct
consequence of the corresponding Dirac equation. Thus, it reproduces the same
binding energies for an electron in a hydrogen atom as the Dirac equation.
There is also a square-root equation for 2-spinors which can give the same
binding energies up to the forth order of the fine structure constant,
inclusively, what will be shown by means of a comparison of the
non-relativistic limit plus a first relativistic correction of both equations
for 2-spinors within the framework of a perturbation analysis. A parallel will
also be drawn to the spin-0 case.


title: Single-Site Entanglement of Fermions at a Quantum Phase Transition

abstract:
  We show that the single-site entanglement of a generic spin-1/2 fermionic
lattice system can be used as a reliable marker of a finite-order quantum phase
transition, given certain provisos. We discuss the information contained in the
single-site entanglement measure, and provide illustrations from the
Mott-Hubbard metal-insulator transitions of the one-dimensional Hubbard model,
and the Hubbard model with long-range hopping.


title:
Pinning and transport of cyclotron/Landau orbits by electromagnetic
  vortices

abstract:
  Electromagnetic waves with phase defects in the form of vortex lines combined
with a constant magnetic field are shown to pin down cyclotron orbits (Landau
orbits in the quantum mechanical setting) of charged particles at the location
of the vortex. This effect manifests itself in classical theory as a trapping
of trajectories and in quantum theory as a Gaussian shape of the localized wave
functions. Analytic solutions of the Lorentz equation in the classical case and
of the Schr\"odinger or Dirac equations in the quantum case are exhibited that
give precise criteria for the localization of the orbits. There is a range of
parameters where the localization is destroyed by the parametric resonance.
Pinning of orbits allows for their controlled positioning -- they can be
transported by the motion of the vortex lines.


title: A quantum violation of the second law?

abstract:
  An apparent violation of the second law of thermodynamics occurs when an atom
coupled to a zero-temperature bath, being necessarily in an excited state, is
used to extract work from the bath. Here the fallacy is that it takes work to
couple the atom to the bath and this work must exceed that obtained from the
atom. For the example of an oscillator coupled to a bath described by the
single relaxation time model, the mean oscillator energy and the minimum work
required to couple the oscillator to the bath are both calculated explicitly
and in closed form. It is shown that the minimum work always exceeds the mean
oscillator energy, so there is no violation of the second law.


title:
The Entanglement in Anisotropic Heisenberg XYZ Chain with inhomogeneous
  magnetic field

abstract:
  The thermal entanglement of a two-qubit anisotropic Heisenberg $XYZ$ chain
under an inhomogeneous magnetic field b is studied. It is shown that when
inhomogeneity is increased to certain value, the entanglement can exhibit a
larger revival than that of less values of b. The property is both true for
zero temperature and a finite temperature. The results also show that the
entanglement and critical temperature can be increased by increasing
inhomogeneous exteral magnetic field.


title: Decoherence and Matter Wave Interferometry

abstract:
  A two-slit interference of a massive particle in the presence of environment
induced decoherence is theoretically analyzed using a fully quantum mechanical
calculation. The Markovian Master equation, derived from coupling the particle
to a harmonic-oscillator heat bath, is used to obtain exact solutions which
show the existence of an interference. Interestingly, decoherence does not
affect the pattern, but only leads to a reduction in the fringe visibility.


title: Combinatorial approach to multipartite quantum systems:basic formulation

abstract:
  In this paper we give a method to associate a graph with an arbitrary density
matrix referred to a standard orthonormal basis in the Hilbert space of a
finite dimensional quantum system. We study the related issues like
classification of pure and mixed states, Von-Neumann entropy, separability of
multipartite quantum states and quantum operations in terms of the graphs
associated with quantum states. In order to address the separability and
entanglement questions using graphs, we introduce a modified tensor product of
weighted graphs, and establish its algebraic properties. In particular, we show
that Werner's definition [1] of a separable state can be written in terms of a
graphs, for the states in a real or complex Hilbert space. We generalize the
separability criterion (degree criterion) due to S.L. Braunstein, S. Ghosh, T.
Mansour, S. Severini, R.C. Wilson [2], to a class of weighted graphs with real
weights. We have given some criteria for the Laplacian associated with a
weighted graph to be positive semidefinite.


title:
Optimal Conditions for Atomic Homodyne Detection on Bose-Einstein
  Condensates

abstract:
  The dynamics of a two-mode Bose-Einstein condensate trapped in a double-well
potential results approximately in an effective Rabi oscillation regime of
exchange of population between both wells for sufficiently strong overlap
between the modes functions. Facing this system as a temporal atomic beam
splitter we show that this regime is optimal for a nondestructive atom-number
measurement allowing an atomic homodyne detection, thus yielding indirect
relative phase information about one of the two-mode condensates.


title: Exact solution and perturbation theory in a general quantum system

abstract:
  By splitting a Hamiltonian into two parts, using the solvability of
eigenvalue problem of one part of the Hamiltonian, proving a useful identity
and deducing an expansion formula of power of operator binomials, we obtain an
explicit and general form of time evolution operator in the representation of
solvable part of the Hamiltonian. Further we find out an exact solution of
Schr\"{o}dinger equation in a general time-independent quantum system, and
write down its concrete form when the solvable part of this Hamiltonian is
taken as the kinetic energy term. Comparing our exact solution with the usual
perturbation theory makes some features and significance of our solution clear.
Moreover, through deriving out the improved forms of the zeroth, first, second
and third order perturbed solutions including the partial contributions from
the higher order even all order approximations, we obtain the improved
transition probability. In special, we propose the revised Fermi's golden rule.
Then we apply our scheme to obtain the improved forms of perturbed energy and
perturbed state. In addition, we study an easy understanding example to
illustrate our scheme and show its advantage. All of this implies the physical
reasons and evidences why our exact solution and perturbative scheme are
formally explicit, actually calculable, operationally efficient, conclusively
more accurate. Therefore our exact solution and perturbative scheme can be
thought of theoretical developments of quantum dynamics. Further applications
of our results in quantum theory can be expected.


title: Entangled Markov Chains generated by Symmetric Channels

abstract:
  A notion of entangled Markov chain was introduced by Accardi and Fidaleo in
the context of quantum random walk. They proved that, in the finite dimensional
case, the corresponding states have vanishing entropy density, but they did not
prove that they are entangled.
  In the present note this entropy result is extended to the infinite
dimensional case under the assumption of finite speed of hopping. Then the
entanglement problem is discussed for spin 1/2, entangled Markov chains
generated by a binary symmetric channel with hopping probability $1-q$. The von
Neumann entropy of these states, restricted on a sublattice is explicitly
calculated and shown to be independent of the size of the sublattice. This is a
new, purely quantum, phenomenon.
  Finally the entanglement property between the sublattices ${\cal
A}(\{0,1,...,N\})$ and ${\cal A}(\{N+1\})$ is investigated using the PPT
criterium. It turns out that, for $q\neq 0,1,{1/2}$ the states are non
separable, thus truly entangled, while for $q=0,1,{1/2}$, they are separable.


title: Information-Disturbance Theorem for Mutually Unbiased Observables

abstract:
  We derive a novel version of information-disturbance theorems for mutually
unbiased observables. We show that the information gain by Eve inevitably makes
the outcomes by Bob in the conjugate basis not only erroneous but random.


title:
Many-body perturbation procedure for energy-dependent perturbation:
  Merging many-body perturbation theory with QED

abstract:
  A formalism for energy-dependent many-body perturbation theory (MBPT),
previously indicated in our recent review articles (Lindgren et al., Phys.Rep.
389,161(2004), Can.J.Phys. 83,183(2005)), is developed in more detail. The
formalism allows for a mixture of energy-dependent (retarded) and
energy-independent (instantaneous) interactions and hence for a merger of QED
and standard (relativistic) MBPT. This combination is particularly important
for light elements, such as light heliumlike ions, where electron correlation
is pronounced. It can also be quite significant in the medium-heavy mass range,
as recently discussed by Fritzsche et al. (J.Phys. B38,S707(2005)), with the
consequence that the effects might be significant also in analyzing the data of
experiments with highly charged ions. A numerical procedure for treating the
combined effect is described, and some preliminary numerical results are given
for heliumlike ions. This represent the first numerical evaluation of effects
beyond two-photon exchange involving a retarded interaction. It is found that
for heliumlike neon the effect of one retarded photon (with Coulomb
interactions of all orders) represents about 99% of the non-radiative effects
beyond energy-independent MBPT.


title: Dispersive forces on bodies and atoms: a unified approach

abstract:
  A unified approach to the calculation of dispersive forces on ground-state
bodies and atoms is given. It is based on the ground-state Lorentz force
density acting on the charge and current densities attributed to the
polarization and magnetization in linearly, locally, and causally responding
media. The theory is applied to dielectric macro- and micro-objects, including
single atoms. Existing formulas valid for weakly polarizable matter are
generalized to allow also for strongly polarizable matter. In particular when
micro-objects can be regarded as single atoms, well-known formulas for the
Casimir-Polder force on atoms and the van der Waals interaction between atoms
are recovered. It is shown that the force acting on medium atoms--in contrast
to isolated atoms--is in general screened by the other medium atoms.


title:
Relational interpretation of the wave function and a possible way around
  Bell's theorem

abstract:
  The famous ``spooky action at a distance'' in the EPR-szenario is shown to be
a local interaction, once entanglement is interpreted as a kind of ``nearest
neighbor'' relation among quantum systems. Furthermore, the wave function
itself is interpreted as encoding the ``nearest neighbor'' relations between a
quantum system and spatial points. This interpretation becomes natural, if we
view space and distance in terms of relations among spatial points. Therefore,
``position'' becomes a purely relational concept. This relational picture leads
to a new perspective onto the quantum mechanical formalism, where many of the
``weird'' aspects, like the particle-wave duality, the non-locality of
entanglement, or the ``mystery'' of the double-slit experiment, disappear.
Furthermore, this picture cirumvents the restrictions set by Bell's
inequalities, i.e., a possible (realistic) hidden variable theory based on
these concepts can be local and at the same time reproduce the results of
quantum mechanics.


title: Non-adiabatic Semiclassical Dressed States

abstract:
  We introduce non-adiabatic semiclassical dressed states for a quantum system
interacting with an electromagnetic field of variable amplitude and phase, and
presence of dumping. We also introduce a generalized adiabatic condition, which
allows finding of closed form solution for the dressed states. The influence of
the non-adiabatic factors on the dressed states due to the amplitude and phase
field variations and dumping has been found.


title:
Nonadiabatic Induced Dipole Moment by High Intensity Femtosecond Optical
  Pulses

abstract:
  Nonadiabtic dressed states and nonadiabatic induced dipole moment in the
leading order of nonadiabaticity is proposed. The nonadiabatic induced dipole
moment is studied in the femtosecond time domain.


title: Topological Quantum Error Correction with Optimal Encoding Rate

abstract:
  We prove the existence of topological quantum error correcting codes with
encoding rates $k/n$ asymptotically approaching the maximum possible value.
Explicit constructions of these topological codes are presented using surfaces
of arbitrary genus. We find a class of regular toric codes that are optimal.
For physical implementations, we present planar topological codes.

categories: quant-ph cond-mat.str-el cs.GR hep-th math-ph math.AT math.CO math.MP


title: Winning strategies for pseudo-telepathy games using single non-local box

abstract:
  Using a single NL-box, a winning strategy is given for the impossible
colouring pseudo-telepathy game for the set of vectors having Kochen-Specker
property in four dimension. A sufficient condition to have a winning strategy
for the impossible colouring pseudo-telepathy game for general $d$-dimension,
with single use of NL-box, is then described. It is also shown that the magic
square pseudo-telepathy game of any size can be won by using just two ebits of
entanglement -- for quantum strategy, and by a single NL-box -- for non-local
strategy.


title: Alternative representation of N \times N density matrix

abstract:
  We use polarization operators known from quantum theory of angular momentum
to expand the $N \times N$ dimensional density operators. Thereby, we construct
generalized Bloch vectors representing density matrices. We study their
properties and derive positivity conditions for any $N$. We also apply the
procedure to study Bloch vector space for a qubit and a qutrit.


title:
On the Proof by Reductio ad Absurdum of the Hohenberg-Kohn Theorem for
  Ensembles of Fractionally Occupied States of Coulomb Systems

abstract:
  It is demonstrated that the original reductio ad absurdum proof of the
generalization of the Hohenberg-Kohn theorem for ensembles of fractionally
occupied states for isolated many-electron Coulomb systems with Coulomb-type
external potentials by Gross et al. [Phys. Rev. A 37, 2809 (1988)] is
self-contradictory since the to-be-refuted assumption (negation) regarding the
ensemble one-electron densities and the assumption about the external
potentials are logically incompatible to each other due to the Kato
electron-nuclear cusp theorem. It is however proved that the Kato theorem
itself provides a satisfactory proof of this theorem.

categories: quant-ph cond-mat.other nucl-th physics.chem-ph


title: Entanglement in Gaussian matrix-product states

abstract:
  Gaussian matrix product states are obtained as the outputs of projection
operations from an ancillary space of M infinitely entangled bonds connecting
neighboring sites, applied at each of N sites of an harmonic chain. Replacing
the projections by associated Gaussian states, the 'building blocks', we show
that the entanglement range in translationally-invariant Gaussian matrix
product states depends on how entangled the building blocks are. In particular,
infinite entanglement in the building blocks produces fully symmetric Gaussian
states with maximum entanglement range. From their peculiar properties of
entanglement sharing, a basic difference with spin chains is revealed: Gaussian
matrix product states can possess unlimited, long-range entanglement even with
minimum number of ancillary bonds (M=1). Finally we discuss how these states
can be experimentally engineered from N copies of a three-mode building block
and N two-mode finitely squeezed states.

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


title: Detection of multipartite entanglement with two-body correlations

abstract:
  We show how to detect entanglement with criteria built from simple two-body
correlation terms. Since many natural Hamiltonians are sums of such correlation
terms, our ideas can be used to detect entanglement by energy measurement. Our
criteria can straightforwardly be applied for detecting different forms of
multipartite entanglement in familiar spin models in thermal equilibrium.


title: Degradation of a quantum reference frame

abstract:
  We investigate the degradation of reference frames, treated as dynamical
quantum systems, and quantify their longevity as a resource for performing
tasks in quantum information processing. We adopt an operational measure of a
reference frame's longevity, namely, the number of measurements that can be
made against it with a certain error tolerance. We investigate two distinct
types of reference frame: a reference direction, realized by a spin-j system,
and a phase reference, realized by an oscillator mode with bounded energy. For
both cases, we show that our measure of longevity increases quadratically with
the size of the reference system and is therefore non-additive. For instance,
the number of measurements that a directional reference frame consisting of N
parallel spins can be put to use scales as N^2. Our results quantify the extent
to which microscopic or mesoscopic reference frames may be used for repeated,
high-precision measurements, without needing to be reset - a question that is
important for some implementations of quantum computing. We illustrate our
results using the proposed single-spin measurement scheme of magnetic resonance
force microscopy.


title: Continuous-time quantum walks on ultrametric spaces

abstract:
  We introduce a continuous-time quantum walk on an ultrametric space
corresponding to the set of p-adic integers and compute its time-averaged
probability distribution. It is shown that localization occurs for any location
of the ultrametric space for the walk. This result presents a striking contrast
to the classical random walk case. Moreover we clarify a difference between the
ultrametric space and other graphs, such as cycle graph, line, hypercube and
complete graph, for the localization of the quantum case. Our quantum walk may
be useful for a quantum search algorithm on a tree-like hierarchical structure.


title: Non-classicality of photon added coherent and thermal radiations

abstract:
  Production and analysis of non-Gaussian radiation fields has evinced a lot of
attention recently. Simplest way of generating such non-Gaussians is through
adding (subtracting) photons to Gaussian fields. Interestingly, when photons
are added to classical Gaussian fields, the resulting states exhibit {\em
non-classicality}. Two important classical Gaussian radiation fields are
coherent and thermal states. Here, we study the non-classical features of such
states when photons are added to them. Non-classicality of these states shows
up in the negativity of the Wigner function. We also work out the {\em
entanglement potential}, a recently proposed measure of non-classicality for
these states. Our analysis reveals that photon added coherent states are
non-classical for all seed beam intensities; their non-classicality increases
with the addition of more number of photons. Thermal state exhibits
non-classicality at all temperatures, when a photon is added; lower the
temperature, higher is their non-classicality.


title: Generalized Bayesian predictive density operators

abstract:
  Recently the quantum Bayesian prediction problem was formulated by Tanaka and
Komaki (2005). It is shown that Bayesian predictive density operators are the
best predictive density operators when we evaluate them by using the averaged
quantum relative entropy based on a prior distribution. In the present paper,
we adopt the quantum alpha-divergence as a wider class of loss function. The
generalized Bayesian predictive density operator is defined and shown to be
best among all the estimates of the unknown density operator.


title: On channels with finite Holevo capacity

abstract:
  We consider a nontrivial class of infinite dimensional quantum channels
characterized by finiteness of the Holevo capacity. Some general properties of
channels of this class are described. In particular, a special sufficient
condition of existence of an optimal measure is obtained and examples of
channels with no optimal measure are constructed.
  It is shown that each channel with finite Holevo capacity has a natural
extension to the set of all positive normalized functionals on the algebra of
all bounded operators. General properties of such an extension are described.
  The class of infinite dimensional channels, for which the Holevo capacity can
be explicitly determined, is considered.


title: High order non-unitary split-step decomposition of unitary operators

abstract:
  We propose a high order numerical decomposition of exponentials of hermitean
operators in terms of a product of exponentials of simple terms, following an
idea which has been pioneered by M. Suzuki, however implementing it for complex
coefficients. We outline a convenient fourth order formula which can be written
compactly for arbitrary number of noncommuting terms in the Hamiltonian and
which is superiour to the optimal formula with real coefficients, both in
complexity and accuracy. We show asymptotic stability of our method for
sufficiently small time step and demonstrate its efficiency and accuracy in
different numerical models.


title: A reply to P W Shor

abstract:
  Two additional reasons are suggested for the seeming lack of progress in
producing quantum algorithms.


title: A new class of states with positive partial transposition

abstract:
  We construct a new class of PPT states for bipartite "d x d" systems. This
class is invariant under the maximal commutative subgroup of U(d) and contains
as special cases almost all known examples of PPT states. Theses states may be
used to test the atomic property of positive maps which are crucial in studying
quantum entanglement.


title: Experimental distillation of squeezing from non-Gaussian quantum states

abstract:
  We show theoretically and experimentally that single copy distillation of
squeezing from continuous variable non-Gaussian states is possible using linear
optics and conditional homodyne detection. A specific non-Gaussian noise
source, corresponding to a random linear displacement, is investigated.
Conditioning the signal on a tap measurement, we observe probabilistic recovery
of squeezing.


title:
Book Review of Stephen L. Adler's, "Quantum theory as an emergent
  phenomenon."

abstract:
  In Stephen Adler's book, "Quantum theory as an emergent phenomenon," the
author starts from a classical mechanics structure and "derives" the formalism
of quantum theory, together with wave function collapse dynamics, the latter
providing the interpretation of quantum theory. A detailed outline of the
author's argument is presented in this book review.


title: Quantum communication, reference frames and gauge theory

abstract:
  We consider quantum communication in the case that the communicating parties
not only do not share a reference frame but use imperfect quantum communication
channels, in that each channel applies some fixed but unknown unitary rotation
to each qubit. We discuss similarities and differences between reference frames
within that quantum communication model and gauge fields in gauge theory. We
generalize the concept of refbits and analyze various quantum communication
protocols within the communication model.


title: Nonlocality, Bell's Ansatz and Probability

abstract:
  Quantum Mechanics lacks an intuitive interpretation, which is the cause of a
generally formalistic approach to its use. This in turn has led to a certain
insensitivity to the actual meaning of many words used in its description and
interpretation. Herein, we analyze carefully the possible mathematical meanings
of those terms used in analysis of EPR's contention, that Quantum Mechanics is
incomplete, as well as Bell's work descendant therefrom. As a result, many
inconsistencies and errors in contemporary discussions of nonlocality, as well
as in Bell's Ansatz with respect to the laws of probability, are identified.
Evading these errors precludes serious conflicts between Quantum Mechanics and
both Special Relativity and Philosophy.


title: Short-time quantum correlations in the atom optics kicked rotor

abstract:
  We experimentally verify the analytical expressions that exist for the
diffusion rate in the quantum delta kicked rotor system for small numbers of
kicks. We show development of diffusion resonances from two to five kicks, and
of multiple resonances for high kick strengths. Furthermore, we show that, in
contrast to classical predictions, the results are purely periodic in the kick
period, and reproduce the predicted quantum- and diffusion resonances.


title: Quantum hypercomputation based on the dynamical algebra su(1,1)

abstract:
  An adaptation of Kieu's hypercomputational quantum algorithm (KHQA) is
presented. The method that was used was to replace the Weyl-Heisenberg algebra
by other dynamical algebra of low dimension that admits infinite-dimensional
irreducible representations with naturally defined generalized coherent states.
We have selected the Lie algebra $\mathfrak{su}(1,1)$, due to that this algebra
posses the necessary characteristics for to realize the hypercomputation and
also due to that such algebra has been identified as the dynamical algebra
associated to many relatively simple quantum systems. In addition to an
algebraic adaptation of KHQA over the algebra $\mathfrak{su}(1,1)$, we
presented an adaptations of KHQA over some concrete physical referents: the
infinite square well, the infinite cylindrical well, the perturbed infinite
cylindrical well, the P{\"o}sch-Teller potentials, the Holstein-Primakoff
system, and the Laguerre oscillator. We conclude that it is possible to have
many physical systems within condensed matter and quantum optics on which it is
possible to consider an implementation of KHQA.


title: Entangled-state cycles from conditional quantum evolution

abstract:
  A system of cascaded qubits interacting via the oneway exchange of photons is
studied. While for general operating conditions the system evolves to a
superposition of Bell states (a dark state) in the long-time limit, under a
particular resonance condition no steady state is reached within a finite time.
We analyze the conditional quantum evolution (quantum trajectories) to
characterize the asymptotic behavior under this resonance condition. A distinct
bimodality is observed: for perfect qubit coupling, the system either evolves
to a maximally entangled Bell state without emitting photons (the dark state),
or executes a sustained entangled-state cycle - random switching between a pair
of Bell states while emitting a continuous photon stream; for imperfect
coupling, two entangled-state cycles coexist, between which a random selection
is made from one quantum trajectory to another.


title: Optimality of programmable quantum measurements

abstract:
  We prove that for a programmable measurement device that approximates every
POVM with an error $\le \delta$, the dimension of the program space has to grow
at least polynomially with $\frac{1}{\delta}$. In the case of qubits we can
improve the general result by showing a linear growth. This proves the
optimality of the programmable measurement devices recently designed in [G. M.
D'Ariano and P. Perinotti, Phys. Rev. Lett. \textbf{94}, 090401 (2005)].


title: Strong coupling between single photons in semiconductor microcavities

abstract:
  We discuss the observability of strong coupling between single photons in
semiconductor microcavities coupled by a chi(2) nonlinearity. We present two
schemes and analyze the feasibility of their practical implementation in three
systems: photonic crystal defects, micropillars and microdisks, fabricated out
of GaAs. We show that if a weak coherent state is used to enhance the chi(2)
interaction, the strong coupling regime between two modes at different
frequencies occupied by a single photon is within reach of current technology.
The unstimulated strong coupling of a single photon and a photon pair is very
challenging and will require an improvement in mirocavity quality factors of
2-4 orders of magnitude to be observable.


title:
Optimal Trade-Off: Information Gain vs Distortion Loss In
  Finite-Dimensional Quantum Systems

abstract:
  In this thesis, I reflect on quantum instruments that measure the state of
pure finite dimensional quantum systems. As the Heisenberg principle dictates,
there exists a joint restriction to the information gain and distortion by
measurement of a quantum system. I minimize the distortion of measurement and
maximize the quality of the outcome by finding the optimal (covariant)
instrument. In order to optimize this joint restriction, the family of
covariant instruments is classified. This is an important side result.


title: A quantum secret ballot

abstract:
  The paper concerns the protection of the secrecy of ballots, so that the
identity of the voters cannot be matched with their vote. To achieve this we
use an entangled quantum state to represent the ballots. Each ballot includes
the identity of the voter, explicitly marked on the "envelope" containing it.
Measuring the content of the envelope yields a random number which reveals no
information about the vote. However, the outcome of the elections can be
unambiguously decided after adding the random numbers from all envelopes. We
consider a few versions of the protocol and their complexity of implementation.


title:
Quantum Hardcore Functions by Complexity-Theoretical Quantum List
  Decoding

abstract:
  Hardcore functions have been used as a technical tool to construct secure
cryptographic systems; however, little is known on their quantum counterpart,
called quantum hardcore functions. With a new insight into fundamental
properties of quantum hardcores, we present three new quantum hardcore
functions for any (strong) quantum one-way function. We also give a "quantum"
solution to Damgard's question (CRYPTO'88) on a classical hardcore property of
his pseudorandom generator, by proving its quantum hardcore property. Our major
technical tool is the new notion of quantum list-decoding of "classical"
error-correcting codes (rather than "quantum" error-correcting codes), which is
defined on the platform of computational complexity theory and computational
cryptography (rather than information theory). In particular, we give a simple
but powerful criterion that makes a polynomial-time computable classical block
code (seen as a function) a quantum hardcore for all quantum one-way functions.
On their own interest, we construct efficient quantum list-decoding algorithms
for classical block codes whose associated quantum states (called codeword
states) form a nearly phase-orthogonal basis.


title:
Relation between concurrence and Berry phase of an entangled state of
  two spin 1/2 particles

abstract:
  We have studied here the influence of the Berry phase generated due to a
cyclic evolution of an entangled state of two spin 1/2 particles. It is shown
that the measure of formation of entanglement is related to the cyclic
geometric phase of the individual spins. \\


title:
Generation of bipartite spin entanglement via spin-independent
  scattering

abstract:
  We consider the bipartite spin entanglement between two identical fermions
generated in spin-independent scattering. We show how the spatial degrees of
freedom act as ancillas for the creation of entanglement to a degree that
depends on the scattering angle, $\theta$. The number of Slater determinants
generated in the process is greater than 1, corresponding to genuine quantum
correlations between the identical fermions. The maximal entanglement
attainable of 1 ebit is reached at $\theta=\pi/2$. We also analyze a simple
$\theta$ dependent Bell's inequality, which is violated for
$\pi/4<\theta\leq\pi/2$. This phenomenon is unrelated to the symmetrization
postulate but does not appear for unequal particles.


title: Berry Phases and Quantum Phase Transitions

abstract:
  We study the connection between Berry phases and quantum phase transitions of
generic quantum many-body systems. Consider sequences of Berry phases
associated to sequences of loops in the parameter space whose limit is a point.
If the sequence of Berry phases does not converge to zero, then the limit point
is a quantum critical point. Quantum critical points are associated to failures
of adiabaticity. We discuss the remarkable example of the anisotropic XY spin
chain in a transverse magnetic field and detect the XX region of criticality.


title:
Electron Spin Dynamics in a Quantum Dot due to Hyperfine Coupling with
  Nuclei in the Dot - An Exact Analysis

abstract:
  The time-dependent Schrodinger equation of a many particle spin system
consisting of an electron in a quantum dot interacting with the spins of the
nuclei (N) in the dot due to hyperfine interaction is solved exactly for a
given arbitrary initial state. The electron spin dynamics is then expressed in
terms of the reduced density matrix of the composite system by computing the
marginal density matrix of the electron. This is accomplished by classifying
states of the system by the total spin of the coupled electron and nuclear
system that commutes with the system Hamiltonian. These states are used in
enumerating and finding the exact solution of the time-dependent Schrodinger
equation. In each sector of the total spin, the problem reduces to solving a
linear simultaneous set of equations that are solved by matrix inversion. Such
solutions enable one to make a reliable approximate scheme for purposes of
numerical estimation of the various physical quantities. A methematical and
physical discussion of this procedure with the density matrix approach to this
problem is given here. To elucidate the procedure and its advantages, special
cases of N=3,4 are given in some detail in an Appendix.


title:
Optimal unambiguous discrimination of two subspaces as a case in mixed
  state discrimination

abstract:
  We show how to optimally unambiguously discriminate between two subspaces of
a Hilbert space. In particular we suppose that we are given a quantum system in
either the state \psi_{1}, where \psi_{1} can be any state in the subspace
S_{1}, or \psi_{2}, where \psi_{2} can be any state in the subspace S_{2}, and
our task is to determine in which of the subspaces the state of our quantum
system lies. We do not want to make a mistake, which means that our procedure
will sometimes fail if the subspaces are not orthogonal. This is a special case
of the unambiguous discrimination of mixed states. We present the POVM that
solves this problem and several applications of this procedure, including the
discrimination of multipartite states without classical communication.


title:
Scaling Behavior of Entanglement in Two- and Three-Dimensional Free
  Fermions

abstract:
  Exactly solving a spinless fermionic system in two and three dimensions, we
investigate the scaling behavior of the block entropy in critical and
non-critical phases. The scaling of the block entropy crucially depends on the
nature of the excitation spectrum of the system and on the topology of the
Fermi surface. Noticeably, in the critical phases the scaling violates the area
law and acquires a logarithmic correction \emph{only} when a well defined Fermi
surface exists in the system. When the area law is violated, we accurately
verify a conjecture for the prefactor of the logarithmic correction, proposed
by D. Gioev and I. Klich [quant-ph/0504151].


title: Quantum capacity of channel with thermal noise

abstract:
  The quantum capacity of thermal noise channel is studied. The extremal input
state is obtained at the postulation that the coherent information is convex or
concave at its vicinity. When the input energy tends to infinitive, it is
verified by perturbation theory that the coherent information reaches its
maximum at the product of identical thermal state input. The quantum capacity
is obtained for lower noise channel and it is equal the one shot capacity.


title: Entanglement in Graph States and its Applications

abstract:
  Graph states form a rich class of entangled states that exhibit important
aspects of multi-partite entanglement. At the same time, they can be described
by a number of parameters that grows only moderately with the system size. They
have a variety of applications in quantum information theory, most prominently
as algorithmic resources in the context of the one-way quantum computer, but
also in other fields such as quantum error correction and multi-partite quantum
communication, as well as in the study of foundational issues such as
non-locality and decoherence. In this review, we give a tutorial introduction
into the theory of graph states. We introduce various equivalent ways how to
define graph states, and discuss the basic notions and properties of these
states. The focus of this review is on their entanglement properties. These
include aspects of non-locality, bi-partite and multi-partite entanglement and
its classification in terms of the Schmidt measure, the distillability
properties of mixed entangled states close to a pure graph state, as well as
the robustness of their entanglement under decoherence. We review some of the
known applications of graph states, as well as proposals for their experimental
implementation.


title:
Universal behavior of dispersion forces between two dielectric plates in
  the low-temperature limit

abstract:
  The universal analytic expressions in the limit of low temperatures (short
separations) are obtained for the free energy, entropy and pressure between the
two parallel plates made of any dielectric. The analytical proof of the Nernst
heat theorem in the case of dispersion forces acting between dielectrics is
provided. This permitted us to formulate the stringent thermodynamical
requirement that must be satisfied in all models used in the Casimir physics.


title: On quantum phase crossovers in finite systems

abstract:
  In this work we define a formal notion of a quantum phase crossover for
certain Bethe ansatz solvable models. The approach we adopt exploits an exact
mapping of the spectrum of a many-body integrable system, which admits an exact
Bethe ansatz solution, into the quasi-exactly solvable spectrum of a one-body
Schr\"odinger operator. Bifurcations of the minima for the potential of the
Schr\"odinger operator determine the crossover couplings. By considering the
behaviour of particular ground-state correlation functions, these may be
identified as quantum phase crossovers in the many-body integrable system with
finite particle number. In this approach the existence of the quantum phase
crossover is not dependent on the existence of a thermodynamic limit, rendering
applications to finite systems feasible. We study two examples of bosonic
Hamiltonians which admit second-order crossovers.


title: Quantum String Seal Is Insecure

abstract:
  A quantum string seal encodes the value of a (bit) string as a quantum state
in such a way that everyone can extract a non-negligible amount of available
information on the string by a suitable measurement. Moreover, such measurement
must disturb the quantum state and is likely to be detected by an authorized
verifier. In this way, the intactness of the encoded quantum state plays the
role of a wax seal in the digital world. Here I analyze the security of quantum
string seal by studying the information disturbance tradeoff of a measurement.
This information disturbance tradeoff analysis extends the earlier results of
Bechmann-Pasquinucci et al. and Chau by concluding that all quantum string
seals are insecure. Specifically, I find a way to obtain non-trivial available
information on the string that escapes the verifier's detection with at least
50% chance.


title: Energy translation and Proper-Time Eigenstates

abstract:
  The usual quantum mechanics describes the mass eigenstates. To describe the
proper-time eigenstates, a duality theory of the usual quantum mechanics was
developed. The time interval is treated as an operator on an equal footing with
the space interval, and the quantization of the space-time intervals between
events is obtained. As a result, one can show that there exists a zero-point
time interval.


title:
Irreducible second order SUSY transformations between real and complex
  potentials

abstract:
  Second order SUSY transformations between real and complex potentials for
three important from physical point of view Sturm-Liouville problems, namely,
problems with the Dirichlet boundary conditions for a finite interval, for a
half axis and for the whole real line are analyzed. For every problem
conditions on transformation functions are formulated when transformations are
irreducible, i.e. when either the intermediate Hamiltonian is not well defined
in the same Hilbert space as the initial and final Hamiltonians or its
eigenfunctions cannot be obtained by applying transformation operator either on
eigenfunctions of the initial Hamiltonian or on these of the final Hamiltonian.
Obtained results are illustrated by numerous simple examples.


title:
Theory of non-Markovian decay of a cascade atom in high-Q cavities and
  photonic band-gap materials

abstract:
  The dynamics of a three-level atom in a cascade configuration with both
transitions coupled to a single structured reservoir of quantized field modes
is treated using Laplace transform methods applied to the coupled amplitude
equations. Results are also obtained from master equations by two different
approaches, that is, involving either pseudomodes or quasimodes. Two different
types of reservoir are considered, namely a high-Q cavity and a photonic
band-gap system, in which the respective reservoir structure functions involve
Lorentzians. Non-resonant transitions are included in the model. In all cases
non-Markovian behaviour for the atomic system can be found, such as oscillatory
decay for the high-Q cavity case and population trapping for the photonic
band-gap case. In the master equation approaches, the atomic system is
augmented by a small number of pseudomodes or quasimodes, which in the
quasimode approach themselves undergo Markovian relaxation into a flat
reservoir of continuum quasimodes. Results from these methods are found to be
identical to those from the Laplace transform method including two-photon
excitation of the reservoir with both emitting sequences. This shows that
complicated non-Markovian decays of an atomic system into structured EM field
reservoirs can be described by Markovian models for the atomic system coupled
to a small number of pseudomodes or quasimodes.


title: Trapped Particles in $PT$ Symmetric Theories

abstract:
  $PT$ symmetric quantum mechanics for a particle trapped by the generalized
non-Hermitian harmonic oscillator potential is studied. It is shown that energy
and the expectation value of the position operator $x$ can not be real
simultaneously, if the particle is trapped. Non-vanishing boundary conditions
for the trapped particle in $PT$ symmetric theory are also discussed.


title: Comments on a bound state model for a two body system

abstract:
  We show that in classical mechanics, as well as in nonrelativistic quantum
mechanics the equation of the relative motion for a two-body bound system at
rest can be replaced by individual dynamical equations of the same kind as the
first one, but with different parameters. We assume that in relativistic
quantum mechanics the individual equations are Dirac equations with modified
parameters in agreement with the individual Schr\"odinger equations. We find
that products of solutions to the individual equations with correlated
arguments are the quantum analogues of the classical representation of a bound
system and represent suitable models for the bound state wave functions. As
validity test for the new representation of bound states we suggest to use some
observable differences between this one and the representation in terms of
relative coordinates.


title: Complex Periodic Potentials with a Finite Number of Band Gaps

abstract:
  We obtain several new results for the complex generalized associated Lame
potential V(x)= a(a+1)m sn^2(y,m)+ b(b+1)m sn^2(y+K(m),m) + f(f+1)m
sn^2(y+K(m)+iK'(m),m)+ g(g+1)m sn^2(y+iK'(m),m), where y = x-K(m)/2-iK'(m)/2,
sn(y,m) is a Jacobi elliptic function with modulus parameter m, and there are
four real parameters a,b,f,g. First, we derive two new duality relations which,
when coupled with a previously obtained duality relation, permit us to relate
the band edge eigenstates of the 24 potentials obtained by permutations of the
four parameters a,b,f,g. Second, we pose and answer the question: how many
independent potentials are there with a finite number "a" of band gaps when
a,b,f,g are integers? For these potentials, we clarify the nature of the band
edge eigenfunctions. We also obtain several analytic results when at least one
of the four parameters is a half-integer. As a by-product, we also obtain new
solutions of Heun's differential equation.


title:
Entanglement and dynamics of spin-chains in periodically-pulsed magnetic
  fields: accelerator modes

abstract:
  We study the dynamics of a single excitation in a Heisenberg spin-chain
subjected to a sequence of periodic pulses from an external, parabolic,
magnetic field. We show that, for experimentally reasonable parameters, a pair
of counter-propagating coherent states are ejected from the centre of the
chain. We find an illuminating correspondence with the quantum time evolution
of the well-known paradigm of quantum chaos, the Quantum Kicked Rotor (QKR).
  From this we can analyse the entanglement production and interpret the
ejected coherent states as a manifestation of so-called `accelerator modes' of
a classically chaotic system.


title: Localising Relational Degrees of Freedom in Quantum Mechanics

abstract:
  This thesis presents a wide-ranging study of localising relational degrees of
freedom. Three physical systems are studied in depth, each built upon a simple
measurement-based process. For each physical system - light from independent
sources leaking onto a beam splitter monitored by photodetectors, spatially
interfering Bose-Einstein condensates extracted from separate preparation
procedures, and delocalised massive particles or mirrors scattering light which
is detected in the far-field - the thesis investigates the key features of the
underlying process of localisation, and explores the properties of the induced
post-measurement states of the system. A range of analytical and numerical
methods are used. Many new results are presented - for example, cases of mixed
initial states are considered in addition to the more commonly considered pure
states. Up to now there has been little attempt to develop in detail the themes
common to studies concerned with specific physical examples. This thesis
addresses this, and sets out a "modus operandi" that can be applied widely. A
variety of specific applications are considered - both in the context of
controlled laboratory experiments, and with a view to understanding processes
occurring in nature. The thesis is introduced and summarised in Chapter 1.
Chapter 2 studies localising relative optical phase in the canonical
interference process. This discussion is extended and applied in Chapter 3.
Chapter 4 discusses localising relative atomic phase in interference
experiments with Bose-Einstein condensates. The emergence of relative positions
between particles scattering light is explored in Chapter 5. The thesis
concludes with an Outlook, Chapter 6.


title: Efficient algorithm for a quantum analogue of 2-SAT

abstract:
  Complexity of a quantum analogue of the satisfiability problem is studied.
Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state
such that its k-qubit reduced density matrices have support on prescribed
subspaces. We present a classical algorithm solving quantum 2-SAT in a
polynomial time. It generalizes the well-known algorithm for the classical
2-SAT. Besides, we show that for any k>=4 quantum k-SAT is complete in the
complexity class QMA with one-sided error.


title:
Analytic Fits to Separable Volumes and Probabilities for Qubit-Qubit and
  Qubit-Qutrit Systems

abstract:
  We investigate the possibility of deriving analytical formulas for the
15-dimensional separable volumes, in terms of any of a number of metrics of
interest (Hilbert-Schmidt [HS], Bures,...), of the two-qubit (four-level)
systems. This would appear to require 15-fold symbolic integrations over a
complicated convex body (defined by both separability and feasibility
constraints). The associated 15-dimensional integrands -- in terms of the
Tilma-Byrd-Sudarshan Euler-angle-based parameterization of the 4 x 4 density
matrices \rho (math-ph/0202002) -- would be the products of 12-dimensional Haar
measure \mu_{Haar} (common to each metric) and 3-dimensional measures
\mu_{metric} (specific to each metric) over the 3d-simplex formed by the four
eigenvalues of \rho. We attempt here to estimate/determine the 3-dimensional
integrands (the products of the various [known] \mu_{metric}'s and an unknown
symmetric weighting function W) remaining after the (putative) 12-fold
integration of \mu_{Haar} over the twelve Euler angles. We do this by fitting W
so that the conjectured HS separable volumes and hyperareas (quant-ph/0410238;
cf. quant-ph/0609006) are reproduced. We further evaluate a number of possible
choices of W by seeing how well they also yield the conjectured separable
volumes for the Bures, Kubo-Mori, Wigner-Yanase and (arithmetic) average
monotone metrics and the conjectured separable Bures hyperarea
(quant-ph/0308037,Table VI). We, in fact, find two such exact (rather similar)
choices that give these five conjectured (non-HS) values all within 5%. In
addition to the above-mentioned Euler angle parameterization of \rho, we make
extensive use of the Bloore parameterization (J. Phys. A 9 [1976], 2059) in a
companion set of two-qubit separability analyses.


title: Interferometric tunability of the absorption

abstract:
  We propose an interferometric setup that permits to tune the quantity of
radiation absorbed by an object illuminated by a fixed light source. The method
can be used to selectively irradiate portions of an object based on their
transmissivities or to accurately estimate the transmissivities from rough
absorption measurements.


title: The Role of Measurement in Quantum Games

abstract:
  The game of Prisoner Dilemma is analyzed to study the role of measurement
basis in quantum games. Four different types of payoffs for quantum games are
identified on the basis of different combinations of initial state and
measurement basis. A relation among these different payoffs is established.